Performance Engine and Tuning Parts Distributor

Engine Science and Theory ICE

Internal Combustion Engine (ICE)

- Power and Torque -

Torque is measured; Power is calculated

In order to discuss powerplants in any depth, it is essential to understand the concepts of POWER and TORQUE.

HOWEVER, in order to understand POWER, you must first understand ENERGY and WORK.

If you have not reviewed these concepts for a while, it would be helpful to do so before studying this article. CLICK HERE for a quick review of Energy and Work.

It often seems that people are confused about the relationship between POWER and TORQUE. For example, we have heard engine builders, camshaft consultants, and other technical experts ask customers:

'Do you want your engine to make HORSEPOWER or TORQUE?'

And the question is usually asked in a tone which strongly suggests that these experts believe power and torque are somehow mutually exclusive.

In fact, the opposite is true, and you should be clear on these facts:

  1. POWER (the rate of doing WORK) is dependent on TORQUE and RPM.
  2. TORQUE and RPM are the MEASURED quantities of engine output.
  3. POWER is CALCULATED from torque and RPM, by the following equation:
HP = Torque x RPM ÷ 5252

(At the bottom of this page, the derivation of that equation is shown, for anyone interested.)

An engine produces POWER by providing a ROTATING SHAFT which can exert a given amount of TORQUE on a load at a given RPM. The amount of TORQUE the engine can exert usually varies with RPM.


TORQUE is defined as a FORCE around a given point, applied at a RADIUS from that point. Note that the unit of TORQUE is one pound-foot (often misstated), while the unit of WORK is one foot-pound.

Figure 1

Referring to Figure 1, assume that the handle is attached to the crank-arm so that it is parallel to the supported shaft and is located at a radius of 12' from the center of the shaft. In this example, consider the shaft to be fixed to the wall. Let the arrow represent a 100 lb. force, applied in a direction perpendicular to both the handle and the crank-arm, as shown.

Because the shaft is fixed to the wall, the shaft does not turn, but there is a torque of 100 pounds-feet (100 pounds times 1 foot) applied to the shaft.

Note that if the crank-arm in the sketch was twice as long (i.e. the handle was located 24' from the center of the shaft), the same 100 pound force applied to the handle would produce 200 lb-ft of torque (100 pounds times 2 feet).


POWER is the measure of how much WORK can be done in a specified TIME. In the example on the Work and Energy page, the guy pushing the car did 16,500 foot-pounds of WORK. If he did that work in two minutes, he would have produced 8250 foot-pounds per minute of POWER (165 feet x 100 pounds ÷ 2 minutes). If you are unclear about WORK and ENERGY, it would be a benefit to review those concepts HERE.

In the same way that one ton is a large amount of weight (by definition, 2000 pounds), one horsepower is a large amount of power. The definition of one horsepower is 33,000 foot-pounds per minute. The power which the guy produced by pushing his car across the lot (8250 foot-pounds-per-minute) equals ¼ horsepower (8,250 ÷ 33,000).

OK, all that’s fine, but how does pushing a car across a parking lot relate to rotating machinery?

Consider the following change to the handle-and-crank-arm sketch above. The handle is still 12' from the center of the shaft, but now, instead of being fixed to the wall, the shaft now goes through the wall, supported by frictionless bearings, and is attached to a generator behind the wall.

Suppose, as illustrated in Figure 2, that a constant force of 100 lbs. is somehow applied to the handle so that the force is always perpendicular to both the handle and the crank-arm as the crank turns. In other words, the 'arrow' rotates with the handle and remains in the same position relative to the crank and handle, as shown in the sequence below. (That is called a 'tangential force')


Figure 2

If that constant 100 lb. tangential force applied to the 12' handle (100 lb-ft of torque) causes the shaft to rotate at 2000 RPM, then the power the shaft is transmitting to the generator behind the wall is 38 HP, calculated as follows:

100 lb-ft of torque (100 lb. x 1 foot) times 2000 RPM divided by 5252 is 38 HP.

The following examples illustrate several different values of TORQUE which produce 300 HP.

Example 1: How much TORQUE is required to produce 300 HP at 2700 RPM?

since HP = TORQUE x RPM ÷ 5252
then by rearranging the equation:
TORQUE = HP x 5252 ÷ RPM

Answer: TORQUE = 300 x 5252 ÷ 2700 = 584 lb-ft.

Example 2: How much TORQUE is required to produce 300 HP at 4600 RPM?

Answer: TORQUE = 300 x 5252 ÷ 4600 = 343 lb-ft.

Example 3: How much TORQUE is required to produce 300 HP at 8000 RPM?

Answer: TORQUE = 300 x 5252 ÷ 8000 = 197 lb-ft.

Example 4: How much TORQUE does the 41,000 RPM turbine section of a 300 HP gas turbine engine produce?

Answer: TORQUE = 300 x 5252 ÷ 41,000 = 38.4 lb-ft.

Example 5: The output shaft of the gearbox of the engine in Example 4 above turns at 1591 RPM. How much TORQUE is available on that shaft?

Answer: TORQUE = 300 x 5252 ÷ 1591 = 991 lb-ft.
(ignoring losses in the gearbox, of course).

The point to be taken from those numbers is that a given amount of horsepower can be made from an infinite number of combinations of torque and RPM.

Think of it another way: In cars of equal weight, a 2-liter twin-cam engine that makes 300 HP at 8000 RPM (197 lb-ft) and 400 HP at 10,000 RPM (210 lb-ft) will get you out of a corner just as well as a 5-liter engine that makes 300 HP at 4000 RPM (394 lb-ft) and 400 HP at 5000 RPM (420 lb-ft). In fact, in cars of equal weight, the smaller engine will probably race BETTER because it's much lighter, therefore puts less weight on the front end. AND, in reality, the car with the lighter 2-liter engine will likely weigh less than the big V8-powered car, so will be a better race car for several reasons.

Measuring Power

A dynamometer determines the POWER an engine produces by applying a load to the engine output shaft by means of a water brake, a generator, an eddy-current absorber, or any other controllable device capable of absorbing power. The dynamometer control system causes the absorber to exactly match the amount of TORQUE the engine is producing at that instant, then measures that TORQUE and the RPM of the engine shaft, and from those two measurements, it calculates observed power. Then it applies various factors (air temperature, barometric pressure, relative humidity) in order to correct the observed power to the value it would have been if it had been measured at standard atmospheric conditions, called corrected power.

Power to Drive a Pump

In the course of working with lots of different engine projects, we often hear the suggestion that engine power can be increased by the use of a 'better' oil pump. Implicit in that suggestion is the belief that a 'better' oil pump has higher pumping efficiency, and can, therefore, deliver the required flow at the required pressure while consuming less power from the crankshaft to do so. While that is technically true, the magnitude of the improvement number is surprisingly small.

How much power does it take to drive a pump delivering a known flow at a known pressure? We have already shown that power is work per unit time, and we will stick with good old American units for the time being (foot-pounds per minute and inch-pounds per minute). And we know that flow times pressure equals POWER, as shown by:

Flow (cubic inches / minute) multiplied by pressure (pounds / square inch) = POWER (inch-pounds / minute)

From there it is simply a matter of multiplying by the appropriate constants to produce an equation which calculates HP from pressure times flow. Since flow is more freqently given in gallons per minute, and since it is well known that there are 231 cubic inches in a gallon, then:

Flow (GPM) x 231(cubic inches / gal) = Flow (cubic inches per minute).

Since, as explained above, 1 HP is 33,000 foot-pounds of work per minute, multiplying that number by 12 produces the number of inch-pounds of work per minute in one HP (396,000). Dividing 396,000 by 231 gives the units-conversion factor of 1714.3. Therefore, the simple equation is:

Pump HP = flow (GPM) x pressure (PSI) / 1714.

That equation represents the power consumed by a pump having 100% efficiency. When the equation is modified to include pump efficiency, it becomes:

Pump HP = (flow {GPM} x pressure {PSI} / (1714 x efficiency)

Common gear-type pumps typically operate at between 75 and 80% efficiency. So suppose your all-aluminum V8 engine requires 10 GPM at 50 psi. The oil pump will have been sized to maintain some preferred level of oil pressure at idle when the engine and oil are hot, so the pump will have far more capacity than is required to maintain the 10 GPM at 50 psi at operating speed. (That's what the 'relief' valve does: bypasses the excess flow capacity back to the inlet of the pump, which, as an added benefit, also dramatically reduces the prospect cavitation in the pump inlet line.)

So suppose your 75%-efficient pump is maintaining 50 psi at operating speed, and is providing the 10 GPM needed by the engine. It is actually pumping roughly 50 GPM ( 10 of which goes through the engine, and the remaining 40 goes through the relief valve ) at 50 psi. The power to drive that pressure pump stage is:

HP = ( 50 gpm x 50 psi ) / ( 1714 x 0.75 efficiency ) = 1.95 HP

Suppose you succumb to the hype and shuck out some really big bucks for an allegedly 90% efficient pump. That pump (at the same flow and pressure) will consume:

HP = ( 50 gpm x 50 psi ) / ( 1714 x 0.90 efficiency ) = 1.62 HP.

WOW. A net gain of a full 1/3 of a HP. Can YOUR dyno even measure a 1-HP difference accurately and repeatably?

General Observations

In order to design an engine for a particular application, it is helpful to plot out the optimal power curve for that specific application, then from that design information, determine the torque curve which is required to produce the desired power curve. By evaluating the torque requirements against realistic BMEP values you can determine the reasonableness of the target power curve.

Typically, the torque peak will occur at a substantially lower RPM than the power peak. The reason is that, in general, the torque curve does not drop off (%-wise) as rapidly as the RPM is increasing (%-wise). For a race engine, it is often beneficial ( within the boundary conditions of the application ) to operate the engine well beyond the power peak, in order to produce the maximum average power within a required RPM band.

However, for an engine which operates in a relatively narrow RPM band, such as an aircraft engine, it is generally a requirement that the engine produce maximum power at the maximum RPM. That requires the torque peak to be fairly close to the maximum RPM. For an aircraft engine, you typically design the torque curve to peak at the normal cruise setting and stay flat up to maximum RPM. That positioning of the torque curve would allow the engine to produce significantly more power if it could operate at a higher RPM, but the goal is to optimize the performance within the operating range.

An example of that concept is shown Figure 3 below. The three dashed lines represent three different torque curves, each having exactly the same shape and torque values, but with the peak torque values located at different RPM values. The solid lines show the power produced by the torque curves of the same color.


Figure 3

Note that, with a torque peak of 587 lb-ft at 3000 RPM, the pink power line peaks at about 375 HP between 3500 and 3750 RPM. With the same torque curve moved to the right by 1500 RPM (black, 587 lb-ft torque peak at 4500 RPM), the peak power jumps to about 535 HP at 5000 RPM. Again, moving the same torque curve to the right another 1500 RPM (blue, 587 lb-ft torque peak at 6000 RPM) causes the power to peak at about 696 HP at 6500 RPM

Using the black curves as an example, note that the engine produces 500 HP at both 4500 and 5400 RPM, which means the engine can do the same amount of work per unit time (power) at 4500 as it can at 5400. HOWEVER, it will burn less fuel to produce 450 HP at 4500 RPM than at 5400 RPM, because the parasitic power losses (power consumed to turn the crankshaft, reciprocating components, valvetrain) increases as the square of the crankshaft speed.

The RPM band within which the engine produces its peak torque is limited. You can tailor an engine to have a high peak torque with a very narrow band, or a lower peak torque value over a wider band. Those characteristics are usually dictated by the parameters of the application for which the engine is intended.

An example of that is shown in Figure 4 below. It is the same as the graph in Figure 3 (above), EXCEPT, the blue torque curve has been altered (as shown by the green line) so that it doesn't drop off as quickly. Note how that causes the green power line to increase well beyond the torque peak. That sort of a change to the torque curve can be achieved by altering various key components, including (but not limited to) cam lobe profiles, cam lobe separation, intake and/or exhaust runner length, intake and/or exhaust runner cross section. Alterations intended to broaden the torque peak will inevitable reduce the peak torque value, but the desirability of a given change is determined by the application.


Figure 4

Derivation of the Power Equation
(for anyone interested)

This part might not be of interest to most readers, but several people have asked:

'OK, if HP = RPM x TORQUE ÷ 5252, then where does the 5252 come from?'

Here is the answer.

By definition, POWER = FORCE x DISTANCE ÷ TIME

Using the example in Figure 2 above, where a constant tangential force of 100 pounds was applied to the 12' handle rotating at 2000 RPM, we know the force involved, so to calculate power, we need the distance the handle travels per unit time, expressed as:

Power = 100 pounds x distance per minute

OK, how far does the crank handle move in one minute? First, determine the distance it moves in one revolution:

DISTANCE per revolution = 2 x p x radius

DISTANCE per revolution. = 2 x 3.1416 x 1 ft = 6.283 ft.

Now we know how far the crank moves in one revolution. How far does the crank move in one minute?

DISTANCE per min. = 6.283 ft .per rev. x 2000 rev. per min. = 12,566 feet per minute

Now we know enough to calculate the power, defined as:

Power = 100 lb x 12,566 ft. per minute = 1,256,600 ft-lb per minute

Swell, but how about HORSEPOWER? Remember that one HORSEPOWER is defined as 33000 foot-pounds of work per minute. Therefore HP = POWER (ft-lb per min) ÷ 33,000. We have already calculated that the power being applied to the crank-wheel above is 1,256,600 ft-lb per minute.

How many HP is that?

HP = (1,256,600 ÷ 33,000) = 38.1 HP.

Now we combine some stuff we already know to produce the magic 5252. We already know that:


If we divide both sides of that equation by RADIUS, we get:


Now, if DISTANCE per revolution = RADIUS x 2 x p, then

(b) DISTANCE per minute = RADIUS x 2 x p x RPM

We already know

(c) POWER = FORCE x DISTANCE per minute

So if we plug the equivalent for FORCE from equation (a) and distance per minute from equation (b) into equation (c), we get:


Dividing both sides by 33,000 to find HP,

HP = TORQUE ÷ RADIUS x RPM x RADIUS x 2 x p ÷ 33,000

By reducing, we get

HP = TORQUE x RPM x 6.28 ÷ 33,000


33,000 ÷ 6.2832 = 5252


HP = TORQUE x RPM ÷ 5252

Note that at 5252 RPM, torque and HP are equal. At any RPM below 5252, the value of torque is greater than the value of HP; Above 5252 RPM, the value of torque is less than the value of HP.

Converting Fuel into Horsepower

AND How Efficiently Does It Happen?

A 'combustion engine' is a device which converts the chemical energy stored in a fuel into heat energy, and then converts a portion of that heat energy into mechanical work. Any combustion engine can be effectively visualized using what is commonly known as the 'Black Box' model. (A 'Black Box' is a colloquial name for a conceptual entity which has known inputs and outputs, and which performs a defined function, but whose innards and functioning are unknown.)

The following is a sketch of the 'black box' which represents a combustion engine.

The sketch is fairly self-explanatory. Air and fuel go into the box. Something happens inside. Shaft power comes out, along with an eclectic mixture of waste gasses, which contain both heat and velocity. (Acoustic energy and other small losses have been ignored here for the sake of simplicity.)

That model applies equally well to piston and turbine engines. In the turbine case, there is relatively more velocity in the exhaust stream, and there might or might not be any external shaft power extracted (turboshaft vs. turbojet). In both turbine and piston engines, the output gasses include heated air (from heat exchangers and air not consumed by combustion) and very hot gasses which are the products of combustion.

The exit configuration will define the temperature, pressure and velocity of the exiting stream. In certain applications, the exiting stream is a mixture of both components (cooling and exhaust gasses) and can be used to generate thrust.

The energy source for an engine is the chemical energy stored in the fuel. That energy is released by the oxidization of the fuel (combustion) by an oxidizing medium, which in most cases is the oxygen which makes up about 19% of the air we breathe. Variations on that theme include the use of oxidizing additives (Nitrous Oxide, for example) and high-energy fuels which contain a substantial supply of oxidizer in their makeup (Nitromethane, for example).

For this explanation, assume we are discussing a piston engine operating on gasoline for fuel. (This analysis works for Gasoline, Methanol, Diesel fuel, Jet fuel, Whale Oil, Whatever. Each fuel has it's own weight and energy content.)

Gasoline, according to Pratt & Whitney Aircraft data sheets, has a specific gravity of 0.71, and therefore a weight of about 5.92 pounds per gallon, and releases approximately 19,000 BTU of energy per pound of fuel burned.

What is a BTU? A 'British Thermal Unit' is defined as the heat energy required to raise the temperature of one pound of pure water by one degree F, and is equivalent to 778 foot-pounds of work / energy. By arithmetic, it can be shown that one horsepower (33,000 ft-lbs per minute) is the equivalent of 42.4 BTU's per minute or 2545 BTU's per hour (33,000 ÷ 778 = 42.4165 ˜ 42.4; 42.4165 × 60 = 2544.98).

How is that useful? Here is an example. We have tested a reasonably good 4-stroke piston engine which converts approximately 24 gallons of gasoline per hour ( 142 pounds of fuel per hour ) into 300 measured horsepower.

So how much of the total fuel energy does this engine convert into horsepower? If you burn 24 gallons of gasoline (142 pounds) over the course of one hour, you release 2,699,520 BTU's of energy (19,000 x 142). If you divide the 2,699,520 BTU's by 2545 (the number of BTU's-per-hour in one HP), you discover, to your surprise, that it is 1061 HP. But the engine is only making 300 HP. Where is all the rest of that energy going?

It is a known fact that a piston engine does a rather inefficient job of converting fuel energy into power. The rule of thumb approximation is that nearly 1/3 of the fuel energy goes out the exhaust pipe as lost heat, approximately 1/3 of the fuel energy is lost to the cooling system (coolant, oil and surrounding airflow), leaving roughly 1/3 of the energy (best case) available for power output. Some of that power is lost to making the pistons go up and down, driving accessories (oil pump, coolant pump, alternator, vacuum pump, hydraulic pump, etc.), losses from pumping air through the engine, thrashing the oil in the crankcase, and friction in various forms.

The difference between the energy content of the fuel consumed and the useful power extracted from the engine is known as Thermal Efficiency (TE). So in our 300-HP engine example, the TE is 300 HP / 1061 HP = 28.3 % (which is fairly good by contemporary standards for 4-stroke production piston engines).

The calculation for Thermal Efficiency (TE) is:

HP = TE x FUEL FLOW (PPH) x 19,000 (BTU per #) / 2545 (BTU per HP per Hour)

which reduces to:

HP = TE x FUEL FLOW (PPH) x 7.466

solving for THERMAL EFFICIENCY: TE = 0.1339 x HP / FUEL FLOW (PPH)

solving for FUEL FLOW: FUEL FLOW (PPH) = 0.1339 x HP / TE

Equation 1

Going back to our 300 HP example, TE = 0.1339 x 300 HP / 142 PPH = 0.283 (28.3 %)

(Note that when using % in a calculation, you must divide the percentage number by 100. That is how 28.3 % becomes 0.283.)

If you prefer gallons per hour, the Thermal Efficiency calculation is:

HP = TE x FUEL FLOW (GPH) x 5.92 (# per gallon) x 19,000 / 2545 (BTU per HP per Hour)

which reduces to:

HP = TE x FUEL FLOW (GPH) x 44.2

solving for THERMAL EFFICIENCY: TE = 0.0226 x HP / FUEL FLOW (GPH)

solving for FUEL FLOW: FUEL FLOW (GPH) = 0.0226 x HP / TE

The value of this Thermal Efficiency relationship is that, by assuming a reasonable TE value (27% - 29%), you can estimate the amount of fuel required to produce a given amount of power. (That will lead to an even more valuable equation a bit later.)

Here is an example. Suppose you need to produce 300 HP. What will be the required fuel flow assuming 28.3% TE ?

Simple. FUEL FLOW = 0.1339 x 300 HP / 0.283 (28.3 %), or

FUEL FLOW = 142 PPH or 24 GPH.

Brake Specific Fuel Consumption (BSFC)

A more commonly used yardstick for expressing thermal efficiency is known as Brake Specific Fuel Consumption (BSFC). It is simply fuel flow (in pounds-per-hour) divided by measured HP, and is expressed in Pounds-per-Hour-per-HP.

BSFC = Fuel Flow (PPH) ÷ Horsepower

or BSFC = 5.92 x Fuel Flow (GPH) ÷ Horsepower

Equation 2

This tool is also an important yardstick for comparing the performance of one engine to another and for evaluating the reasonableness of performance claims.

An excellent BSFC for a well-developed, 4-stroke naturally-aspirated, high-performance liquid-cooled engine at 100% power is in the neighborhood of 0.44 – 0.45. Claims of gasoline engine BSFC values less than 0.42 at max power tend to be suspect. At reduced power settings (in the region of 70% and below) BSFC values of 0.38 have been achieved, and will become more commonplace as refinements of combustion technology evolve in the pursuit of energy conservation.

The operator manual for a 300 HP Lycoming IO-540-K, L, or M series engine shows a full power fuel flow of 24 GPH which is a BSFC of 0.474 ( 24 * 5.92 ÷ 300 ) and a TE of 28.3% (explained above). Those numbers aren't too bad for an air cooled engine which meets the FAR-required detonation margins. However, the turbocharged TIO-540-V2AD requires a MINIMUM of 39.2 GPH at 350 HP for a BSFC of 0.663 and a TE of 20.4%.

So if someone tells you that they have developed a 4-stroke piston engine which, at max power, makes 300 HP on 20 GPH of gasoline, you can quickly calculate a BSFC of 0.39 and a Thermal Efficiency of 34.4%. You should be highly suspicious of such a claim.

- Volumetric Efficiency and Engine Airflow -

(It's actually MASS AIRFLOW that counts)

In a four-stroke naturally aspirated engine, the theoretical maximum volume of air that each cylinder can ingest during the intake cycle is equal to the swept volume of that cylinder (0.7854 x bore x bore x stroke).

Since each cylinder has one intake stroke every two revolutions of the crankshaft, then the theoretical maximum volume of air it can ingest during each rotation of the crankshaft is equal to one-half its displacement. The actual amount of air the engine ingests compared to the theoretical maximum is called volumetric efficiency (VE). An engine operating at 100% VE is ingesting its total displacement every two crankshaft revolutions.

There are many factors which determine the torque an engine can produce and the RPM at which the maximum torque occurs, but the fundamental determinant is the mass of air the engine can ingest into the cylinders. The mass is directly proportional to (a) the air density and (b) the volumetric efficiency. There is a remarkably close relationship between an engine's VE curve and its torque curve.

For contemporary naturally-aspirated, two-valve-per-cylinder, pushrod-engine technology, a VE over 95% is excellent, and 100% is achievable, but quite difficult. Only the best of the best can reach 110%, and that is by means of extremely specialized development of the complex system comprised of the intake passages, combustion chambers, exhaust passages and valve system components. The practical limit for normally-aspirated engines, typically DOHC layout with four or more valves per cylinder, is about 115%, which can only be achieved under the most highly-developed conditions, with precise intake and exhaust passage tuning.

Generally, the RPM at peak VE coincides with the RPM at the torque peak. And generally, automotive engines rarely exceed 90% VE. There is a variety of good reasons for that performance, including the design requirements for automotive engines (good low-end torque, good throttle response, high mileage, low emissions, low noise, low production costs, restrictive form factors, etc.), as well as the economically-feasible tolerances for components in high-volume production.

For a known engine displacement and RPM, you can calculate the engine airflow at 100% VE, in sea-level-standard-day cubic feet per minute (scfm) as follows:

100% VE AIRFLOW (scfm) = DISPLACEMENT (ci) x RPM / 3456

(Equation 3)

Using that equation to evaluate a 540 cubic-inch engine operating 2700 RPM reveals that, at 100% VE, the engine will flow 422 SCFM.

We have already shown (Equations 1 and 2 in Thermal Efficiency) how to calculate the fuel flow required for a given amount of power produced. Once you know the required fuel flow, you can calculate the mass airflow required for that amount of fuel, then by using that calculated airflow along with the engine displacement, the targeted operating RPM, and the achievable VE values, you can quickly determine the reasonableness of your expectations. Here's how.

Once you know the required fuel flow, you can determine the required airflow. It is generally accepted (and demonstrable) that a given engine (of reasonable design) will achieve its best power on a mixture strength of approximately 12.5 parts of air to one part of fuel (gasoline) by weight. (Other fuels have different best-power-mixture values. Methanol, for example, is somewhere around 5.0 to 1.)

Using that best-power air-to-fuel ratio, you calculate required airflow:

MASS AIRFLOW (pph) = 12.5 (Pounds-per-Pound) x FUEL FLOW (pph)

(Equation 4)

But airflow is usually discussed in terms of volume flow (Standard Cubic Feet per Minute, SCFM). One cubic foot of air at standard atmospheric conditions (29.92 inches of HG absolute pressure, 59°F temperature) weighs 0.0765 pounds. So the volume airflow required is:

AIRFLOW (scfm) = 12.5 (ppp) x FUEL FLOW (pph) / (60 min-per-hour x 0.0765 pounds per cubic foot)

That equation reduces to:

REQUIRED AIRFLOW (scfm) = 2.723 x FUEL FLOW (pph)

(Equation 5)

OK, hang on. The really useful bit is next.

If I solve Equation 2 (explained back in Thermal Efficiency) for FUEL FLOW, I get:


Replacing 'FUEL FLOW' in Equation 5 with 'HP x BSFC' from Equation 2, produces this very useful relationship:

REQUIRED AIRFLOW (scfm) = 2.723 x HP x BSFC

(Equation 6)

Now, using Equation 6 you can estimate the airflow required for a given amount of horsepower, and using Equation 3, you can calculate the 100% VE airflow your engine can generate at a known RPM.

Combining those two equations yields one equation which enables you to evaluate the reasonableness of any engine program by knowing just a few values:

  1. Required HP,
  2. Operating RPM,
  3. Engine displacement (cubic inches),
  4. and
  5. An assumed reasonable BSFC.

Here it is:


(Equation 7)

Here is an example of how useful that relationship can be. Suppose you decide that a certain 2.2 liter engine would make a great aircraft powerplant. You decide that 300 HP is a nice number, and 5200 RPM produces an acceptable mean piston speed (explained HERE). How reasonable is your goal?

The required VE for that engine will be:

Required VE = (9411 x 300 x .45 ) / (134 x 5200 ) = 1.82 (182 %)

Clearly that's not going to happen with a normally aspirated engine. Supercharging will be required, and you can use the 1.82 figure to calculate the approximate Manifold Absolute Pressure (MAP) needed (1.82 x 29.92' = 54.5' MAP, or 24.6 inches of 'boost') for that power level.

Here's another example. Suppose you want 300 HP from a 540 cubic inch engine at 2700 RPM, and assume a BSFC of 0.45. Plugging the known values into equation 7 produces:

Required VE = (9411 x 300 x .45 ) / (540 x 2700) = 0.87 (87 %)

That is a very reasonable, real-world number. (If you recognized those figures as being for the 300-HP Lycoming IO-540 discussed above, well done.)

Manifold Absolute Pressure (MAP)

We mentioned this term (MAP) in the preceding discussion, and it is used regularly in discussing engine performance, but just in case it is unfamiliar, here is a clarification.

First, the term Absolute Pressure means the pressure above a zero reference (a perfect vacuum). Ambient atmospheric pressure at sea level on a 'standard day' is approximately 14.696 psi absolute (or 29.92 inches of mercury, 'HG, explained below).

Manifold Absolute Pressure, then, is just what it says: The absolute pressure which exists in the inlet manifold, usually measured in the plenum (if one exists). The MAP in an engine which is not running is equal to atmospheric pressure. If, on a 'standard day', an engine is idling at a measured manifold 'vacuum' of 14 inches,, the MAP is actually 15.92 'HG (29.92 - 14 = 15.92).

The term 'inches of mercury', as used to express a pressure, can be a bit confusing. One common unit of measurement for MAP, barometric pressures, and other precise pressure measurements is 'inches of mercury'. Mercury is a heavy metal that is in the liquid state under conditions of standard temperature and pressure. Mercury is commonly used in manometers and barometers (a special application of a manometer) because of its high density and its liquidity. Recalling from high school chemistry, 'HG' is the chemical symbol for the element Mercury, derived from the Greek word HYDRARGERIUM, literally silver water.

In a mercury-filled barometer, the vertical distance between the two manisci, at sea-level, standard conditions, is 29.92 inches, hence the term inches of mercury, 'HG, or for the lazy, just inches.

- Brake Mean Effective Pressure -

BMEP: An important performance yardstick

We have presented the topics of Thermal Efficiency and Volumetric Efficiency as methods for estimating the potential output of a given engine configuration.

Brake Mean Effective Pressure (BMEP) is another very effective yardstick for comparing the performance of one engine to another, and for evaluating the reasonableness of performance claims or requirements.

The definition of BMEP is: the average (mean) pressure which, if imposed on the pistons uniformly from the top to the bottom of each power stroke, would produce the measured (brake) power output.

Note that BMEP is purely theoretical and has nothing to do with actual cylinder pressures. It is simply an effective comparison tool.

If you work through the derivation arithmetic (presented at the bottom of this page), you find that BMEP is simply a multiple of the torque per cubic inch of displacement. In fact, many talented people in the engine design and developmeny business currently use torque-per-cubic inch instead of BMEP, thereby avoiding that tedious multiplication.

A torque output of 1.0 lb-ft per cubic inch of displacement in a 4-stroke engine equals a BMEP of 150.8 psi. In a 2-stroke engine, that same 1.0 lb-ft of torque per cubic inch is a BMEP of 75.4 psi.

(The discussion on the remainder of this page is with respect to four-stroke engines, but it applies equally to two stroke engines if you simply substitute 75.4 everywhere you see 150.8)

If you know the torque and displacement of an engine, a very practical way to calculate BMEP is:

BMEP (psi) = 150.8 x TORQUE (lb-ft) / DISPLACEMENT (ci)

(Equation 8-a, 4-Stroke Engine)

BMEP (psi) = 75.4 x TORQUE (lb-ft) / DISPLACEMENT (ci)

(Equation 8-b, 2-Stroke Engine)

(IF you prefer pressure readings in Bar rather than PSI, simply divide PSI by 14.5)

(IF you are interested in the derivation of those relationships, it is explained at the bottom of this page.)

This tool is extremely handy to evaluate the performance which is claimed for any particular engine. For example, the 200 HP IO-360 (360 CID) and 300 HP IO-540 (540 CID) Lycomings make their rated power at 2700 RPM. At that RPM, the rated power requires 389 lb-ft and 584 lb-ft of torque respectively. (If you don't understand that calculation, CLICK HERE)

From those torque values, it is easy to see (from Equation 8-a above) that both engines operate at a BMEP of about 163 PSI (12.25 bar, or 1.08 lb-ft of torque per cubic inch) at peak power. The BMEP at peak torque is slightly greater.

For a long-life, naturally-aspirated, gasoline-fueled, two-valve-per-cylinder, pushrod engine, a BMEP over 200 PSI (13.8 bar) is difficult to achieve and requires a serious development program and very specialized components.

For comparison purposes, let's look at what is commonly believed to be the very pinnacle of engine performance: Formula-1 (Grand Prix).

An F1 engine is purpose-built and essentially unrestricted. For 2006, the rules required a 90° V8 engine of 2.4 liters displacement (146.4 CID) with a maximum bore of 98mm (3.858) and a required bore spacing of 106.5 mm (4.193). The resulting stroke to achieve 2.4 liters is 39.75 mm (1.565) and is implemented with a 180° crankshaft. The typical rod length is approximately 4.016 (102 mm), for a Rod/Stroke ratio of about 2.57. These engines are typically a 4-valve-per cylinder layout with two overhead cams per bank, and pneumatic valvesprings. In addition to the few restrictions stated above, there are the following additional restrictions: (a) no beryllium compounds, (b) no MMC pistons, (c) no variable-length intake pipes, (d) one injector per cylinder, and (e) the requirement that one engine last for two race weekends.

At the end of the 2006 season, most of these F1 engines ran up to 20,000 RPM in a race, and made in the vicinity of 750 HP. One engine for which I have the figures made 755 BHP at an astonishing 19,250 RPM. At a peak power of 755 HP, the torque is 206 lb-ft and peak-power BMEP would be 212 psi. (14.63 bar). Peak torque of 214 lb-ft occurred at 17,000 RPM for a BMEP of 220 psi (15.18 bar). There can be no argument that 212 psi at 19,250 RPM is truly amazing.

However, let's look at some astounding domestic technology.

The NASCAR Cup race engine is a severely-restricted powerplant, allegedly being derived from 'production' components, although as of 2010, all 4 engines competing at that level (Chevy, Dodge, Ford, Totota) are purpose-built race engines designed specifically to NASCAR's rule book.

By regulation, they use a cast-iron 90° V8 block and 90° steel crankshaft, with a maximum displacement of 358 CID (5.87 liters). A typical configuration has a 4.185' bore with a 3.25' stroke and a 6.20' conrod (R/S = 1.91). Cylinder heads are similarly purpose-designed and highly-developed, but limited to two valves per cylinder, specific valve angles, specific port floor heights, etc.. The valves are operated by a single, engineblock-mounted, flat-tappet camshaft (that's right, still no rollers as of 2012) and a pushrod / rocker-arm / coil-spring valvetrain. It is further hobbled by the requirement for a single four-barrel carburetor (until 2011) and now (2012 on), by a 4-barrel-carburetor-like throttle body and individial runner EFI. Electronically-controlled ignition is allowed (as of 2012), and there are minimum weight requirements for the conrods and pistons.

How does it perform? In early 2010, the engines were producing in the neighborhood of 860 HP at 9000 RPM (and could produce more at 10,000 RPM, but engine RPM has been restricted by means of a rule limiting the final drive ratio at each venue).

Consider the fact that, to produce 860 HP at 9000 RPM, requires 501 lb-ft of torque, for a peak-power BMEP of nearly 211 PSI (14.55 bar). Peak torque (2010) was typically about 535 lb-ft at 7800 RPM, for a peak BMEP of over 225 psi (15.5 bar).

THAT is truly astonishing. Compare the F1 engine figures to the Cup engine figures for a better grip on just how clever these Cup engine guys are.

To appreciate the value of this tool, suppose someone offers to sell you a 2.8 liter (171 cubic inch) Ford V6 which allegedly makes 230 HP at 5000 RPM, and is equipped with the standard OEM iron heads and an aftermarket intake manifold and camshaft. You could evaluate the reasonableness of this claim by calculating (a) that 230 HP at 5000 RPM requires 242 lb-ft of torque (230 x 5252 ÷ 5000), and (b) that 242 lb-ft. of torque from 171 cubic inches requires a BMEP of 213 PSI (150.8 x 242 ÷ 171).

You would then dismiss the claim as preposterous because you know that if a guy could do the magic required to make that kind of performance with the stock heads and intake design, he would be renowned as one of the pre-eminent engine gurus in the world. (You would later discover that the engine rating of '230' is actually 'Blantonpower', not Horsepower.)

As a matter of fact, in order to get a BMEP value of 214 PSI from our aircraft V8, we had to use extremely well developed, high-flowing, high velocity heads, a specially-developed tuned intake and fuel injection system, very well developed roller-cam profiles and valve train components, and a host of very specialized components which we designed and manufactured.


The definition of BMEP (Brake Mean Effective Pressure), as previously stated at the top of this page, is: ' the mean (average) pressure which, if imposed on the pistons uniformly from the top to the bottom of each power stroke, would produce the measured (brake) power output'. AGAIN, NOTE that BMEP is purely theoretical and has nothing to do with actual cylinder pressures.

If we put the definition into mathematical form, we get:,

HP = BMEP x piston area x (stroke / 12) x RPM x power-pulses-per-revolution / 33000

Working through that equation in terms of a single cylinder engine, BMEP (in PSI) multiplied by piston area (square inches) gives the mean force applied to the piston during the power stroke. Multiplying that force by the stroke (inches divided by 12, which changes the units to feet) gives the net WORK (in foot-pounds) produced by the piston moving from TDC to BDC with the BMEP exerted on it throughout that motion. (Clearly this is not an attempt to represent the reality in the combustion chamber. As previously stated, BMEP is simply a convenient tool for comparing and evaluating engine performance.)

Next, power is defined as work-per-unit time. Therefore, multiplying the WORK (ft-lbs) by the RPM, then multiplying by power-pulses-per-revolution (PPR) gives the net (brake) power (foot-pounds per minute in this example) produced by one cylinder. (In a single-cylinder engine, PPR is either 1 for a 2-stroke engine or 1/2 for a 4-stroke engine.

Since one HORSEPOWER is defined as 33,000 foot-pounds-of-work-per-minute, dividing the WORK (ft-lbs) by 33,000 changes the units from foot-pounds-per-minute to HP.

Since it is clear that piston area x stroke is the displacement of one cylinder (in cubic inches), then the equation can be simplified to:

HP = BMEP x (displacement / 12) x RPM x power-pulses-per-revolution / 33000

Horsepower is also defined as:

HP = Torque x RPM / 5252

Substituting that equation into the preceding one gives:

Torque x RPM / 5252 = BMEP x displacement / 12 x RPM x PPR / 33000

Reducing that equation gives:

BMEP = (Torque x 12 x 33,000 / 5252) / (Displacement x PPR)

Evaluating the constants, 12 x 33,000 / 5252 = 75.39985, which can safely be approximated by 75.4. Simplifying the equation again gives:

BMEP = (Torque x 75.4) / (Displacement x PPR)

It is also clear that because the equation includes PPR, it applies to engines with any number of cylinders by using the total displacement, total brake torque, and correct PPR.

Suppose, for example, that you measured 14.45 lb-ft of torque from a 125 cc (7.625 CID) single-cylinder 2-stroke engine at 12,950 RPM, you would have 35.63 HP (285 HP per liter, quite impressive indeed). The BMEP would be:

BMEP = (14.45 x 75.4) / (7.625 x 1) = 142.9 psi (9.85 bar)

That BMEP (9.85 bar) is an impressive number for a piston-ported 2-stroke engine.

However, suppose someone claimed to be making that same torque from a single cylinder 4-stroke 125 cc engine at 12,950 RPM. The power would be the same (35.63 HP, or 285 HP per liter). The power density would not necessarily set off alarms, (the 2008 2.4 liter F1 V8 engines approached 315 HP per liter), but the BMEP would cause that claim to be declared highly questionable:

BMEP = (14.45 x 75.4) / (7.625 x 1/2) = 285.8 psi (19.7 bar)

That BMEP (19.7 bar) is clearly absurd for a normally-aspirated engine. Professor Gordon Blair stated that exceeding 15 bar of BMEP in a N/A engine is virtually impossible, but that was a few years ago. NASCAR Cup engines are now approaching 15.6 bar

Clearly, the difference between 2- and 4-stroke engines is simply a factor of 2, because of the fact that a 2-stroke cylinder fires once per revoultion whereas a 4-stroke engine fires only once per two revolutions. The equations can be simplified further by incorporating that PPR factor in the constant 75.4 and eliminating PPR from the equation, therefore making the constant for a 4-stroke engine 2 x 75.4 = 150.8. That produces the equations shown at the top of this article, which use the full engine displacement and measured torque.

BMEP = 150.8 x TORQUE (lb-ft) / DISPLACEMENT (ci)

(Equation 8-a, 4-Stroke Engine)

BMEP = 75.4 x TORQUE (lb-ft) / DISPLACEMENT (ci)

(Equation 8-b, 2-Stroke Engine)

- Additional Engine Comparison Tools -

A Summary of Performance Comparison Yardsticks

In previous sections, we have covered the fundamental yardsticks for doing insightful comparisons of engine performance. The Thermal Efficiency section discusses the basic relationships between fuel consumed and power produced, and provides a method for evaluating engine performance claims. The Volumetric Efficiency section discusses methods for realistic evaluations of power capacity and another useful tool for evaluating performance claims. The BMEP section explains one of the most fundamental tools for evaluating performance and comparing performance among dissimilar engines.

This section introduces another tool for comparing the performance of piston engines.

Engine Performance Coefficient

Stepping back to engine fundamentals, we know that the potential power any engine can produce is directly dependent on two factors:

  1. The mass of air it can ingest per second, and
  2. The BSFC it can coax from the fuel.

The BSFC parameter encompasses elements including the heat content of the fuel, best-power air-fuel ratio, thermal efficiency, mechanical efficiency, mixture homogeneity, mixture motion, chamber design, combustion quality, and others.

The mass airflow parameter encompasses elements including bottom-end design (RPM capability), runner, port, valve and chamber design, cam profile and valvetrain design, and others.

Mass airflow is dependent on:

  1. Air density and
  2. Volumetric efficiency (VE).

As described in the section on Volumetric Efficiency, at 100% VE, the volume of air a four-stroke engine can ingest is proportional to: RPM x Displacement ÷ 2. The following relationship expresses that potential airflow as a dimensionless number (Potential Airflow Number, PAN) as:

Potential Airflow Nunber = (rpm / 1000) x (displacement / 2)

It is a revealing insight into engine performance to examine the relationship between power produced and potential airflow. We will now define an empiricism which clearly expresses that relationship. Let's name it Engine Performance Coefficient (EPC) because it provides another basis (in addition to BMEP, BSFC, MPS and BHP/Cubic-Inch) for comparing one engine to another.

EPC = Peak Power / Potential Airflow Number

Combining terms and rearranging the equation produces:

EPC = (Peak Power x 2000) / (rpm x displacement)

The EPC factor encompasses all the engine design variables and provides a basis for comparing two totally different engines on the basis of how well they convert fuel into power. For example, at peak power, the 2006 version of the 2.4-liter Formula 1 V8 engine (pre-19,000 RPM rev limit) produces roughly 755 BHP at 19,250 RPM. The EPC for that operating point is:

EPC = 755 x 2000 / (19,250 x 146.46) = 0.536

Now let's look at the EPC for a NASCAR Sprint Cup engine from the same time period. That engine (pre-gear-rule) produced about 825 BHP at around 9000 RPM. The EPC for that operating point is:

EPC = 825 x 2000 / (9000 x 357.65) = 0.513

It is quite surprising to discover that the EPC figure for the Cup engine is only 4.3% less than the F1 engine, especially in view of the fact that the F1 engine is a purpose-designed DOHC, 4-valve race engine with few restrictions, while the Cup engine is a severely restricted, nominally production-based iron block V8, with two-valves per cylinder, pushrod / rocker arm valvetrain, 0.875 diameter flat tappets, single central carburetor, and more.

Considering the restrictions, the small 4.3% difference in EPC between Formula One and Cup gives a real insight into just how clever the Cup engine people really are.

- Piston Motion Basics -

Travel, Velocity, Acceleration, Vibration

The crankshaft, connecting rods, wristpins and pistons in an engine comprise the mechanism which captures a portion of the energy released by combustion and transforms that energy into useful rotary motion. This page describes the characteristics of the reciprocating motion which the crankshaft and connecting rod assembly imparts to the pistons.

A crankshaft contains two or more centrally-located coaxial cylindrical ('main') journals and one or more offset cylindrical crankpin ('rod') journals. The V8 crankshaft pictured in Figure 1 has five main journals and four rod journals.

Figure 1

The crankshaft main journals rotate in a set of supporting bearings ('main bearings'), causing the offset rod journals to rotate in a circular path around the main journal centers, the diameter of which is twice the offset of the rod journals. The diameter of that path is the engine 'stroke': the distance the piston moves up and down in its cylinder. The big ends of the connecting rods ('conrods') contain bearings ('rod bearings') which ride on the offset rod journals. ( For details on the operation of crankshaft bearings, Click Here; For details on crankshaft design and implementation, Click Here )

The small end of the conrod is attached to the piston by means of a floating cylindrical pin ('wristpin', or in British, 'gudgeon pin'). The rotation of the big end of the conrod on the rod journal causes the small end, which is constrained by the piston to be coincident with the cylinder axis, to move the piston up and down the cylinder axis.

Figure 2: TDC

The following description explains the not-so-obvious characteristics of the motion which the crankshaft / conrod mechanism imparts to the piston.

Figure 2 shows a sectional end-view of a crankshaft, connecting rod and piston (CCP) mechanism when the piston is at the furthest extent of its upward (away from the crankshaft) travel, which is known as the top dead center (TDC) position.

The furthest extent of the piston's downward (toward the crankshaft) travel is known as the bottom dead center (BDC) position.

In the CCP mechanism shown, the crankshaft has a 4.000 inch stroke and the center-to-center length of the conrod is 6.100 inches. The rod to stroke ratio (R / S) is the center-to-center length of the conrod divided by the stroke. In this example, the R/S ratio is 6.100 / 4.000 = 1.525.

This ratio is important because it has a large influence on piston motion asymmetry, and on the resulting vibration and balance characteristics, as well as certain performance characteristics, as explained below.

For purposes of this discussion, the extended centerline of the cylinder bore intersects the center of the crankshaft main bearing, and the wristpin is coincident with the cylinder centerline (defined as zero wristpin offset). Although the following descriptions apply strictly to configurations with zero wristpin offset, the general observations apply to nonzero offset configurations as well.

Figure 3: 90° After TDC

It is important to understand that the motion of the piston within 90° before and after TDC is not symmetric with the motion within 90° before and after BDC. The rotation of the crankshaft when the crankpin is within 90° of TDC moves the piston substantially more than half the stroke value. Conversely, the rotation of the crankshaft when the crankpin is within 90° of BDC moves the piston substantially less than half the stroke value. This asymmetry of motion is important because it is the source of several interesting properties relating to the operation, performance and longevity of a piston engine.

Figure 3 shows the subject CCP with the crankpin rotated 90° past TDC. Note that the piston has moved over 58% of its total stroke (2.337 inches). That is because in addition to the 2.000' (half-stroke) downward motion of the crankpin (motion projected onto the vertical plane), the crankpin has also moved horizontally outward by 2.000', putting the conrod at an angle with the vertical plane.

The cosine effect of that conrod angle functionally shortens the projected length of the conrod in the vertical plane by 0.337', from 6.100' to the 5.763' shown in the picture. This dynamic 'shortening' of the conrod has the effect of adding 0.337' to the 2.000' of downward motion imparted by the crankpin rotation, as illustrated by the two vertical blue lines in Figure 3.

Figure 4: 180° After TDC

Now, since the piston has already moved about 58% of the stroke during the first 90° of crank rotation, it stands to reason that during the next 90° of crank rotation (to BDC) the piston will only have to travel the remaining 42% of the stroke to reach BDC, as shown in Figure 4.

The reason is that as the crank rotates toward BDC, the crankpin also moves horizontally back toward the center of the cylinder and 'restores' the effective length of the rod. That cosine-effect 'lengthening' of the conrod opposes the downward movement of the piston, subtracting 0.337 from the half-stroke of vertical motion produced from 90° to BDC. That effect is illustrated by the lower two vertical blue lines in Figure 4.

Clearly then, when the crankshaft is in any position other than TDC or BDC, the axis of the connecting rod is no longer parallel to the centerline of the cylinder (the line along which the piston, wristpin and small end of the rod are constrained to move). Therefore, the 'effective length' of the conrod at any point other than TDC or BDC is the actual conrod center-to-center length multiplied by the cosine of the angle between the rod and the cylinder centerline. It is clear that the dynamic change in the conrod effective length adds to and subtracts from the purely sinusoidal motion caused by crankpin rotation.

Figure 5: Half-Stroke

Figure 5 shows that, with the R / S ratio in this CCP example (1.525), the half-stroke position of the piston occurs at about 81° crank rotation after TDC. The rapid change in volume of the combustion chamber after the TDC position has some interesting ramifications with respect to the P-V diagram and thermal efficiency (discussed on a different page).

(Note: If you still believe that installing longer connecting rods will increase an engine's stroke, there's no need for you to go any further on this page, or on this entire site, for that matter.)


It is obvious that as the piston moves from TDC to BDC and back, the velocity is constantly changing, and that it is zero at TDC and BDC. Velocity is, by definition, the first feriative of the motion curve, or simply a measurement of how rapidly the motion is changing with respect to the reference (usually time). The value and location of the maximum velocity (the maximum slope of the motion curve) varies directly with engine RPM and are strongly influenced by the R / S ratio.

Figure 6: Maximum Velocity

Figure 6 shows the location of the point of maximum piston velocity, in crankshaft degrees before and after TDC, for the subject CCP. At that position (73.9° before and after TDC), the piston has traveled only 43.9% (1.756') of the total stroke (4.000'). For the configuration used in this example (4-inch stroke, 6.100' rod length, R / S = 1.525), at 4000 RPM, the peak piston velocity is 4390 feet per minute.

Figure 7 shows graphs of piston position and of instantaneous velocity as a function of crankshaft rotation. The blue line ('position') shows piston travel (as a % of stroke) at any point during one rotation of the crankshaft. The blue line is oriented so as to show position in an intuitive sense (top, bottom), therefore the '-' signs shoud be ignored. The green velocity line shows the relative speed of the piston (as a % of maximum) at any point. Velocity with a 'plus' sign is motion TOWARD the crankshaft; velocity with a 'minus' sign is motion AWAY from the crankshaft.

Note again that at TDC and again at BDC, the piston velocity is zero, because the piston reverses direction at those points, and in order to change direction, the piston must be stopped at some point.

Note also that the position plot (blue) shows that, for this R / S ratio ( 1.525 ), the 50% stroke positions occur at approximately 81° before and after TDC (as illustrated in Figure 5 above). The velocity plot (green line) shows the maximum piston velocities occur at about 74° before and after TDC (as illustrated in Figure 6 above). The velocity line also shows that the piston velocity at any rotation point from TDC up to the maximum velocity is greater than at the same number of degrees before BDC. For example, compare the velocity at 30° after TDC (62%) with the velocity at 30° before BDC (34%).

Piston Travel and Velocity

Figure 7

The profile of the velocity curve, and therefore the location of the maximum velocity, are influenced by the R / S ratio. As the rod gets shorter with respect to stroke (a smaller R / S ratio), two interesting things happen which can have important effects on cylinder filling: (1) the point of maximum piston velocity moves closer to TDC, and (2) the piston moves away from TDC faster, creating a stronger intake pulse. The location of maximum piston velocity influences the design of camshaft lobe profiles (especially intake) in order to optimize the intake event in a particular speed range, and can have an influence on the intake characteristics with regard to the strength and shaping of the intake pulse for ram tuning.


There is another piston velocity which is used more as a 'rule-of-thumb' in engine evaluations. It is called 'mean piston speed', which is a calculated value showing the average velocity of a piston at a known RPM in an engine having a known stroke length.

Keeping in mind that every crankshaft revolution, the piston travels a distance equal to twice the stroke length, then Mean Piston Speed (MPS) is calculated by:

MPS (ft per minute) = RPM x 2 x stroke (inches) / 12 (inches per foot) = RPM x stroke / 6

The Mean Piston Speed at 4000 RPM for the example 4.000 inch stroke engine is:

MPS (ft per minute) = 4000 x 4 / 6 = 2667 feet per minute.

For purposes of rules of thumb, it is generally agreed that for an engine in aircraft service, 3000 fpm is a comfortable maximum MPS and experience has shown that engines having an MPS substantially exceeding that value have experienced reliability issues. Note that R / S has no influence on MPS, although it strongly affects peak piston speed (4390 fpm for the example engine {R / S = 1.525} at 4000 RPM).


The force it takes to accelerate an object is proportional to the weight of the object times the acceleration. From that it is clear that piston acceleration is important because many of the significant forces exerted on the pistons, wristpins, connecting rods, crankshaft, bearings, and block are directly related to piston acceleration. Piston acceleration is also the main source of external vibration produced by an engine. (Torsional vibration is discussed separately on another page.)

Acceleration is, by definition, the first derivative of the velocity curve, or in other words, the slope of the velocity curve at any given point along the reference. More simply, it is a measure of how rapidly velocity is changing, usually expressed with reference to time. If velocity does not change with respect to the reference, there is no acceleration. Conversely, if velocity changes very rapidly with respect to the reference, there is a large acceleration. (See Velocity and Acceleration for a more thorough explanation.)

It is clear from Figure 7 that the piston velocity is constantly changing with respect to a constant value of crankshaft rotation. Therefore, In order to move from the zero-velocity point (TDC) to the maximum velocity point, the piston must be subjected to a large acceleration function which varies with the angular rotation of the crankshaft.

Figure 8 shows the acceleration, velocity and position plots for the example CCP under discussion. (All numeric values presented are for the R / S in this example.)

Piston Travel, Velocity and Acceleration

Figure 8

The maximum positive value of acceleration (100%) occurs at TDC. Between TDC and maximum piston velocitty (74° in this case), acceleration is positive but decreasing toward zero (the piston velocity is still increasing but less rapidly). At maximum piston velocity (74° at this R / S ), the piston stops speeding up and begins to slow down. At that point, the acceleration changes direction (from a 'plus' number to a 'minus' number), and in so doing, momentarily passes through zero.

At this R / S, the maximum negative acceleration does not occur at BDC, but about 40° either side of BDC. The value of this maximum negative acceleration is only about 53% of the maximum positive acceleration seen at TDC. The acceleration at BDC is only 49% of the TDC maximum. The acceleration from max piston velocity (74°) to BDC is negative, and that acceleration is slowing the piston to zero velocity. Therefore, it might be (incorrectly) called deceleration. However, that same negative acceleration is applied to the piston after BDC and is causing its velocity to increase.

The zero acceleration point occurs (by definition) at the point of maximum piston velocity (74° B/A TDC), where velocity is reversing direction, but the rate of change of velocity (the slope of the curve) is zero.

The somewhat odd shape at the bottom of the total piston acceleration (magenta) curve is the result of the fact that the total piston acceleration is the sum of several orders of acceleration, the first two being the most significant. The two major orders which combine to produce this total acceleration profile are important because they can produce significant vibration challenges to the engine designer (covered in Crankshafts).

Figure 8 shows the same total piston acceleration curve (magenta line) shown in Figure 7, along with the two significant orders of piston accelerations which combine to produce that curve. The total piston acceleration curve (magenta) is the sum of the two separate accelerationorders: primary (blue) and secondary (green).

Piston Motion Graph 3

Figure 8

As explained in Piston Motion above, the piston motion in the first 90° of rotation consists of the sum of the effect of the half-stroke motion of the crankpin projected onto the vertical plane (2.000') and the effect of the apparent 0.337' 'shortening' of the rod length projected onto the vertical plane. The second 90° of rotation also produces a half-stroke motion in the vertical plane, but the cosine-effect lengthening of the conrod in the vertical plane produces 0.337' motion which subtracts from the half-stroke.

The primary acceleration (blue line) is the result of the piston motion produced by the component of crankpin movement projected onto the vertical plane. This curve is a sinusoid which repeats once per revolution of the crankshaft (first order) and comprises the majority of the acceleration. Note that the primary acceleration curve crosses zero at the 90° rotation points and peaks at TDC and BDC.

The secondary acceleration (green line) is the result of the additional piston motion caused by the cosine-effect dynamic length-change of the conrod. This motion adds to the piston movement between TDC and the max velocity point and subtracts from the piston motion between the max velocity point and BDC. This curve is also sinusoidal and repeats twice per crankshaft rotation (second order) and crosses zero at the 45°, 135°, 225° and 315° rotation points. The total piston acceleration at any point is the sum of the values of the primary and secondary acceleration curves.

Contemporary piston engines tend to have R / S ratios in an approximate range of 1.5 to 2.0. Note that a rod / stroke ratio less than 1.3 is, for practical applications, not possible due to physical constraints such as the need for piston rings and a wristpin, sufficient piston skirt length, and the inconvenience of having the piston contact the crankshaft counterweight, not to mention the excessive side load such a small ratio would produce.

Here are two practical examples comparing the effects of R / S on acceleration and velocity. In a Lycoming IO-360 (and IO-540) the rod length is 6.75' and the stroke is 4.375', for a ratio of 1.543, close to the low end of the spectrum in contemporary design. At the other end of that spectrum, the connecting rod on a typical (circa 2007) 2.4-liter Formula-1 V8 engine is about 4.010' long, what your average race-engine mechanic would call a 'very short rod'. The stroke in the F1 engine is in the vicinity of 1.566', which produces a very large R / S ratio of 2.56. The following graph (Figure 9) clearly shows the effect of large and small R / S ratios.

Comparative Accel and Velocity

Figure 9

It is clear that the engine with the very small R / S ratio of 1.543 (the 'long' 6.75 inch conrod, the blue velocity and acceleration curves) has a substantially higher peak acceleration (10%), a higher secondary acceleration, a higher peak velocity (3%), an earlier velocity peak (5 crank degrees) and the distinct acceleration reversal around BDC, confirming the substantial secondary vibration component.

Compare that to the large 2.56 R / S ratio (the 'short' 4.01 inch conrod) magenta curves, showing a substantially lower peak acceleration (10%), a lower secondary acceleration, a later and slightly lower (3%) peak velocity, and the total acceleration curve is closer to symmetric, confirming the substantially-reduced secondary vibration component. Figure 9 also clearly demonstrates the absurdity of discussing conrod length as an absolute.

Figure 10 is a chart listing the main effects of R / S ratios varying from 1.40 to 2.55, with the reference point for Vmax %, PPA max-pos %, and PPA max-neg % being based on an R / S ratio of 2.00, since that ratio is the first at which the maximum negative acceleration occurs at BDC. Notice that at ratios beyond 2.00, the acceleration curve becomes more symmetric, but the peak velocity does not change much at all.

Comparative Motion Parameters

Figure 10
The Effects of R / S Ratio

NOTE: All the calculations and explanations on this page and the next page assume zero piston pin offset. A non-zero offset will slightly alter the calculations, SLIGHTLY being the operative word.

- Contemporary Crankshaft Design -

Design, Materials, Manufacturing


This page describes the important aspects of crankshaft design and implementation. Having a good understanding of the Basics of Piston Motion wll assist in the full understanding of some of the concepts presented here.


A crankshaft contains two or more centrally-located coaxial cylindrical ('main') journals and one or more offset cylindrical crankpin ('rod') journals. The two-plane V8 crankshaft pictured in Figure 1 has five main journals and four rod journals, each spaced 90° from its neigbors.

Figure 1: Example (2-plane) Crankshaft

The crankshaft main journals rotate in a set of supporting bearings ('main bearings'), causing the offset rod journals to rotate in a circular path around the main journal centers, the diameter of which is twice the offset of the rod journals. The diameter of that path is the engine 'stroke': the distance the piston moves up and down in its cylinder. The big ends of the connecting rods ('conrods') contain bearings ('rod bearings') which ride on the offset rod journals. ( For details on the operation of crankshaft bearings, Click Here; For important details on the motion which the crankshaft imparts to the piston assembly, Click Here )


The obvious source of forces applied to a crankshaft is the product of combustion chamber pressure acting on the top of the piston. High-performance, normally-aspirated Spark-ignition (SI) engines can have combustion pressures in the 100-bar neighborhood (1450 psi), while contemporary high-performance Compression-Ignition (CI) engines can see combustion pressures in excess of 200 bar (2900 psi). A pressure of 100 bar acting on a 4.00 inch diameter piston wil produce a force of 18,221 pounds. A pressure of 200 bar acting on a 4.00 inch diameter piston produces a force of 36,442 pounds. That level of force exerted onto a crankshaft rod journal produces substantial bending and torsional moments and the resulting tensile, compressive and shear stresses.

However, there is another major source of forces imposed on a crankshaft, namely Piston Acceleration. The combined weight of the piston, ring package, wristpin, retainers, the conrod small end and a small amount of oil are being continuously accelerated from rest to very high velocity and back to rest twice each crankshaft revolution. Since the force it takes to accelerate an object is proportional to the weight of the object times the acceleration (as long as the mass of the object is constant), many of the significant forces exerted on those reciprocating components, as well as on the conrod beam and big-end, crankshaft, crankshaft, bearings, and engine block are directly related to piston acceleration. The methods for dealing with those vibratory loads are covered in a dedicated article.

Combustion forces and piston acceleration are also the main source of external vibration produced by an engine. The torsional excitation contained in the engine output waveform is discussed in a separate article.

These acceleration forces combine in complex ways to produce primary and secondary shaking forces as well as primary and secondary rocking moments. The combinations of forces and moments vary with the cylinder arrangement (inline, opposed, 60°V, 90°V, 120°V, etc.) and with the crankpin separation (60° / 90° / 120° / 180°, etc.). They must, to the maximum extent possible, be counteracted by the implementation of the crankshaft counterweights.

Many of the common engine arrangements allow for complete balancing of primary and secondary forces and moments. Examples are inline six cylinder engines with 120° crankpin spacing and 90° V8 engines with conventional 90° ('two-plane', as shown in Figure 1) crankpin spacing.

Certain other engine arrangements do not allow for the complete counteracting of all the forces and moments, so there are design compromises which must be optimised. For example, an inline-four has a secondary vertical shake as the result of the secondary piston acceleration forces (explained HERE). In road vehicles, the secondary vertical shake is often suppressed by unbalanced counterweight shafts rotating at twice crank speed.

The 90° V8 engine with a single-plane crank (180° crankpin spacing as shown in Figure 2) such as is used in Formula One, IRL and Le Mans-style V8 engines produces a substantial external horizontal shaking force at twice the crankshaft frequency ('second order'). Because the secondary piston acceleration forces are parallel with the cylinder axes, in this engine design the vertical components of those forces on a given crankpin cancel each other, but the horizontal components add together.

At 18,000 RPM (Formula One) the horizontal shake frequency is 600 Hz. (2 x 18000 / 60) while at 9000 RPM (IRL) the frequency is 300 Hz. The amplitude is proportional to the magnitude of the secondary piston acceleration. This shake can become a major concern for designers of the chassis (or airframe) and the bits that attach to the engine.

In addition to these reciprocating forces and the resulting moments, there is a rotating mass associated with each crankpin, which must be counteracted. The rotating mass consists of the weight of the conrod big end(s), conrod bearing(s), some amount of oil, and the mass of the crankshaft structure comprising the crankpin and cheeks. These rotating forces are counteracted by counterweight masses located in appropriate angular locations opposing the rod journals. Figure 2 shows a single-plane V8 crankshaft, in which the counterweights are directly opposite their associated rod journal. A fully-counterweighted inline-4 cylinder engine has a similar layout.

Figure 2
Single-Plane V8 Crankshaft (Courtesy of Bryant Racing)

However, the counterweights are not always directly opposite the rod journals. For example, the commonly-used production version of a two-plane 90° V8 crankshaft has no counterweights around the center main journal, as shown in Figure 1 above. In that case, the centroid of each counterweight, instead of being 180° from its respective journal, is offset (to approximately 135°) in order to place the net counterbalancing forces in the optimal location. Note also (in Figure 1) that the front and rear counterweights are larger (thicker) than the others in order to fully counterbalance the end-to-end moments.


Many high performance crankshafts are formed by the forging process, in which a billet of suitable size is heated to the appropriate forging temperature, typically in the range of 1950 - 2250°F, and then successively pounded or pressed into the desired shape by squeezing the billet between pairs of dies under very high pressure. These die sets have the concave negative form of the desired external shape. Complex shapes and / or extreme deformations often require more than one set of dies to accomplish the shaping.

Originally, two-plane V8 cranks were forged in a single plane, then the number two and four main journals were reheated and twisted 90° to move crankpins number two and three into a perpendicular plane. Later developments in forging technology allowed the forging of a 2-plane 'non-twist' crank directly (Figure 3).

Figure 3
Two-Plane V8 Crankshaft Raw Forging

Crankshafts at the upper end of the motorsport spectrum are manufactured from billet. Billet crankshafts are fully machined from a round bar ('billet') of the selected material (Figure 4). This method of manufacture provides extreme flexibility of design and allows rapid alterations to a design in search of optimal performance characteristics. In addition to the fully-machined surfaces, the billet process makes it much easier to locate the counterweights and journal webs exactly where the designer wants them to be. This process involves demanding machining operations, especially with regard to counterweight shaping and undercutting, rifle-drilling main and rod journals, and drilling lubrication passages. The availability of multi-axis, high-speed, high precision CNC machining equipment has made the carved-from-billet method quite cost-effective, and, together with exacting 3D-CAD and FEA design methodologies, has enabled the manufacture of extremely precise crankshafts which often require very little in the way of subsequent massaging for balance purposes.

Figure 4
Billet Crankshaft Machining (Courtesy of Bryant Racing)

There is an old argument that a forged crank is superior to a billet crank because of the allegedly uninterrupted grain flow that can be obtained in the forging process. That might be true of some components, but with respect to crankshafts, the argument fails because of the large dislocations in the material that are necessary to move the crankpin and counterweight material from the center of the forging blank to the outer extremes of the part. The resulting grain structure in the typical V8 crank forging exhibits similar fractured grain properties to that of a machined billet. More than one crankshaft manufacturer has told me that there is no way that a forging from the commonly used steel alloy SAE-4340 (AMS-6414) would survive in one of today's Cup engines.

Some years ago, there was an effort at Cosworth to build a Formula One crankshaft by welding together various sections, which comprised the journals, webs and counterweights. The purported intent was to be better able to create exactly the shape and section of the various components, thereby reducing MMOI while achieving the same or better stiffness. While no one was willing to divulge details about the effort, it is rumored to have been run once or twice then abandoned due to the high cost and complexity compared to the measurable benefits.

In certain cases, there are benefits to the use of a built-up crankshaft. Because of the ‘master-rod’ mechanism necessary for the implementation of the radial piston engines that powered most aircraft until well into the second half of the 20th century, a bolted-together crankshaft configuration was used almost exclusively. Figure 5 illustrates a typical two-row composite radial crankshaft and master-rod layout. The loose counterweights will be addressed later in this article.

Built-Up Radial CrankshaftEngine Materials page).


Regarding the steel alloys typically used in high-grade crankshafts, the desired ultimate (and hence yield and fatigue) strength of the material is produced by a series of processes, known in aggregate as ‘heat treatment’.

The typical heat-treating process for carbon-steel alloys is first to transform the structure of the rough-machined part into the face-centered-cubic austenite crystalline structure (‘austenitize’) by heating the part in an oven until the temperature throughout the part stabilizes in the neighbourhood of 1550°F to 1650°F (depending on the specific material). Next, the part is removed from the heating oven and rapidly cooled ('quenched') to extract heat from the part at a rate sufficient to transform a large percentage of the austenitic structure into fine-grained martensite. The desired martensitic post-quench crystalline structure of the steel is the high-strength, high-hardness, form of the iron-carbon solution. The rate of cooling required to achieve maximum transformation varies with the hardenability of the material, determined by the combination of alloying elements.

Distortion and induced residual stress are two of the biggest problems involved in heat-treating. Less severe quenching methods tend to reduce residual stresses and distortion. Some alloys (EN-30B and certain tool steels, for example) can reach full hardness by quenching in air. Other alloys having less hardenability can be quenched in a bath of 400°F molten salt. Still others require quenching in a polymer-based oil, and the least hardenable alloys need to be quenched in water. The shock of water-quenching is often severe enough to crack the part or induce severe residual stresses and distortions. As the hardenability of a material decreases, the hardness (thus strength) varies more drastically from the surface to the core of the material. High hardenability materials can reach much more homogeneous post-quench hardness.

Cryogenic treatment, if used, directly follows quenching. The body of belief-based and empirical evidence supporting cryo is now supported by scientific data from a recent NASA study confirming that a properly-done cryo process does transform most of the retained austenite to martensite, relaxes the crystalline distortions, and produces helpful ? ('eta') particles at the grain boundaries. The resulting material is almost fully martensitic, has reduced residual stress, more homogeneous structure and therefore greater fatigue strength.

After quenching (and cryo if used), the alloy steel material has reached a very high strength and hardness, but at that hardness level, it lacks sufficient ductility and impact resistance for most applications. In order to produce the combination of material properties deemed suitable for a given application, the part is placed in a ‘tempering’ oven and soaked for a specific amount of time at a specific temperature (for that alloy) in order to reduce the hardness to the desired level, hence producing the desired strength, ductility, impact resistance and other desired mechanical properties. In the case of certain alloys, a double-tempering process can further improve fatigue strength and notch toughness. The tempering temperature and time must be carefully determined for each specific steel alloy, because in mid-range temperature bands, martensitic steels exhibit a property known as temper embrittlement, in which the steel, while having high strength, loses a great deal of its toughness and impact resistance.

Typically, the post-temper hardness which results in the best ductility and impact properties is not sufficient for the wear surfaces of the crank journals. In addition, the fatigue strength of the material at that hardness is insufficient for suitable life. The currently-favoured process which provides both the hard journal surfaces and dramatic improvements in fatigue life is nitriding (not nitrating - nitrates are oxygen-bearing compounds of nitrogen).

Nitriding is the process of diffusing elemental nitrogen into the surface of a steel, producing iron nitrides (FeNx). The result is a hard, high strength case along with residual surface compressive stresses. The part gains a high-strength, high hardness surface with high wear resistance, and greatly improved fatigue performance due to both the high strength of the case and the residual compressive stress. These effects occur without the need for quenching from the nitriding temperature. The case thickness is usually quite thin (0.10 to 0.20 mm), although at least one crankshaft manufacturer has developed a way to achieve nitride layer thickness approaching 1.0 mm.

There are three common nitriding processes: gas nitriding (typically ammonia), molten salt-bath nitriding (cyanide salts) and the more precise plasma-ion nitriding. All three occur at approximately the same temperatures (925 - 1050°F) which, of course, becomes the ultimate tempering temperature of the part. The effectiveness of nitriding varies with the chemistry of the steel alloy. The best results occur when the alloy contains one of more of the nitride-forming elements, including chromium, molybdenum and vanadium.

Older crankshaft technology involved heat-treating to a higher core hardness and shotpeening the fillet radii for fatigue improvement. Figure 7 shows the relative fatigue strength of 4340 material from heat treating alone, heat-treating plus shotpeening, and heat treating plus nitriding.

Fatigue Test Results

Figure 9
8-Counterweight V8 Crank (Courtesy of Bryant Racing)

Traditionally, many two-plane V8 crankshafts had been produced without center counterweights because of economies and difficulties forging the blanks, because the six-counterweight crank typically has a slightly lower MMOI, and because the benefits of an eight-counterweight crank in a short-stroke application were not fully appreciated. However, the bending deflection across the center main at high loadings and high speeds causes measurable losses, so many areas of racing which use two-plane V8 cranks are moving (or have already moved) to eight-counterweight cranks. From an overall engine design perspective, the relocation of the thrust bearing from the rear main to the center main also helps reduce center-main bending deflection.

There are varying opinions about whether high stiffness or low MMOI is more important. Low MMOI is most important at high engine acceleration rates. Road-course racing typically involves greater vehicle speed variation per lap, which implies greater requirements for quick acceleration through several gear ratios. In certain classes, the low weight of the vehicle and the high power of the engine can yield very high engine acceleration rates. At the higher-speed Cup racing circuits, the engine acceleration rates at speed are often less than 100 RPM per second, while at some of the shorter tracks, they can exceed 500 RPM per second. Of course, there are restarts and pit stops to be dealt with at all tracks, so it is easy to see how there can be varying approaches to this issue.

Reducing MMOI involves removing material, especially from places which are a long distance from the main bearing axis. However, these are also some of the most highly loaded areas as well, so reducing cross sectional properties necessarily increases the cyclic stress levels. Pushing the cyclic stress levels up impinges on the fatigue life of the component, which is especially important in classes where an engine must, by regulation, survive more than one meeting. Determining acceptable levels of cyclic stresses vs. expected life is not an exact science. Endurance limit testing of materials produces a highly statistical array of results data (as illustrated in Figure 7).

There has been quite a bit of discussion about the use of bolt-on counterweights in an attempt to reduce MMOI values. An example of this technology is shown in Figure 10. These detachable counterweights are made from variants of the ‘heavy metal’ used to balance crankshafts. This heavy metal is a tungsten-based alloy with several different chemistries (W-Ni-Cu; W-Ni-Fe; W-Ni-C) depending on the required properties. These alloys have nearly 2.5 times the density of steel, and are extremely expensive.

Figure 10
Bolt-On Counterweights

Another benefit of bolt-on counterweights is that several of the machining operations are much simpler to accomplish without having to deal with the integral counterweights getting in the way. If journal coatings are used, the more complete access to the journals provided by the absence of integral counterweights could also be a benefit.

There were some initial problems with bolt-on counterweights, which resulted (as one Formula One designer told me) in 'several deep holes being dug in the surface of a few racetracks'. There are tensile and fatigue stress issues, as well as the inevitable fretting between contact surfaces and the requirement for highly developed fastener technology. Usage in Formula One suggests that those issues have been resolved. There is a variance of opinion as to whether bolt on counterweights are being investigated in Cup. One person told me they are explicitly illegal, while two others told me they know of a certain amount of investigation and development going on in that regard.

In the world of two-plane V8 cranks, the traditional calculation for the balance-bobweight value is 100% of the rotating weight (big end, inserts and oil) plus 50% of the reciprocating weight (small end, wristpin, retainers, piston, rings and oil). However, there are differing approaches to the question of overbalance or underbalance. . Some experts stick with the 100% + 50% distribution, while others opt for a 46-47% underbalance (100% + 47%). Others prefer a 52-53% overbalance, while others add an arbitrary 100 grams to the 50% reciprocating calculation. There was a general reluctance to discuss the expected or observed effects of these strategies.

There has been an interesting development regarding two-plane V8 crankshaft lubrication drillings. Traditionally, each rod bearing was fed oil by a single angled hole from the loaded-during-compression side of the rod journal to the less-loaded side of the adjacent main journal, sometimes called ‘straight-shot oiling’, shown in Figure 11. That strategy reduced the effect of centrifugal-force starvation at high RPM and assured the availability of sufficient oil to provide the dynamic film strength for the combustion loading.

Figure 11
'Straight-Shot' Oiling

The problem with this scheme is that the intersection of the angled hole with the rod journal produces a large elliptical interruption in the journal surface. Add the chamfering usually done around that hole, and what results is a significant interruption of the hydrodynamic surface area. Coupled with the reduced bearing widths, that divot creates a substantial leakage path for the oil to escape.

The new approach rearranges the drillings so the holes in the rod journal can be perpendicular to the surface. One method is to drill a perpendicular oil hole into the rod journal, and drill an intersecting parallel hole partially through the rod journal and plug the open end. Next, an angled drilling from an adjacent main journal is made to intersect the parallel drilling. Another method involves horizontal drillings through the main journal, through the CPO into the rod journal, with perpendicular feeds into both journals. This rearrangement enables the lubrication of both rods on the same crankpin from a single main journal. That can be an advantage in view of data showing that two-plane V8 main journals numbers two and four are the most highly loaded, so the rods can be oiled from one, three and five while the oil delivered to mains two and four can do a better job because of reduced leakage and no surface interruptions. Figures 9 and 10 show examples of this approach.

An interesting byproduct of this new drilling strategy is the creation of internal sharp corners and edges where the drillings intersect. These sharp corners introduce the flow-restricting effect of sharp-edged orifices into the lube system at a critical point. Further, sharp corners and machining marks introduce stress concentrations due to of the surface discontinuities.

One major crank manufacturer (Bryant Racing) has developed a proprietary extrude-honing system in which an abrasive slurry is pumped through these drillings at high pressure. This abrasive treatment removes the sharp edges and surface flaws which cause flow restrictions and stress concentrations, leaving the inside surfaces of the holes with a mirror finish and nicely rounded intersections, which adds substantially to the fatigue life of the part..

- The Basics of Valvetrain Technology -

Cams, Lifters, Pushrods, Rockers, Springs, Retainers, Valves


As we presented in a previous section, the flow capability of the cylinder heads, intake passages and exhaust passages in a 4-stroke ('Four-Cycle') engine is extremely important to engine performance. However, the motion of the valves relative to the position and velocity of the piston is perhaps even more important in determining the power a given configuration can produce.

The valve motion is generated by the shape of the cam lobes, pushing on a cam follower, and connected to the valve by one of several mechanisms, including a pushrod and rocker arm, and overhead cam configurations which operate the valves directly from the cam follower ('direct-acting') or by means of any of several different rocker arm implementations.

The configuration we will discuss here is the pushrod / rocker-arm mechanism, used in domestic automotive engines since the early part of the 20th century, and which began to dominate domestic production V8 engines beginning in 1949 (the Oldsmobile 'Rocket' 324 cubic inch V8). Because of its inherent cost effectiveness, the pushrod / rocker arm OHV V8 is still used in many current engines. The following picture (courtesy of Ford Motor Company ) shows the components in this mechanism.

Pushrod Engine Section

As the cam lobe rotates, it imparts linear motion to the cam follower (aka 'lifter', aka 'tappet'). That motion is transmitted to the pushrod, then through the rocker arm to the valve. It is clear from the picture that the cam lobe is only able to directly control the opening portion of the valve motion, by pushing the follower away from it. After the follower has reached maximum lift, it is the job of the spring, through the rocker arm and pushrod, to keep the lifter in contact with the cam lobe in order that the closing portion of the valve motion is what is programmed on the cam lobe.

Given the inherent limitations of that layout at high engine speeds, it is a huge tribute to the skills and knowledge of the NASCAR engine builders at the 'Cup' level that they have succeeded in making this type of engine (358 cubic inch, pushrod / rocker-arm, two-valve-per-cylinder, normally aspirated, single-carburetor V8) operate reliably at over 10,000 RPM and produce unheard-of power levels (over 830 HP). This section will explain some of the very challenging problems involved in designing a reliable, high-performance valvetrain. The principles discussed apply to the other configurations.

The reason we focus on this configuration is that, with respect to aircraft engines, we think this pushrod / rocker-arm system is the best solution to the compromises required to achieve a good aircraft engine: (a) maximum power per pound of engine weight, combined with (b) reasonable piston speeds and valvetrain stresses for maximum reliability.

There is little question that an engine with a double-overhead-cam (DOHC) configuration and four valves per cylinder will produce more power per cubic inch of displacement. However, the additional weight of the components of that configuration and the fact that the four-valve DOHC achieves its advantage at higher engine speeds would tend to favor the pushrod / rocker arm layout.


Basic camshaft events (valve opening, closing and max lift) are commonly referenced to crankshaft position, because the motion of the valves needs to be studied relative to the position (and velocity) of the piston. For example, a typical intake lobe might begin to open the valve at 20 degrees Before Top Center (BTC, before the piston reaches the exact top of its stroke) and to close the valve at 50 degrees after Bottom Dead Center (BDC). And yes, the piston HAS reversed direction at BDC and is on its way up when the intake valve actually closes. This, and other apparent anomalies, are related to the dynamics of air motion, and will be discussed later.


An excellent example of the influence which cam lobe profiles have on performance is the evolution of what are known as 'restricted' race engines. These engines are 'restricted' with respect to the modifications that can be done to them, in an effort to limit the power, hence the cost of the engines. The most common engine in this category is an iron-block 355-cubic inch small-block Chevy (SBC) V8, which is limited to stock (unported, unmodified) cast-iron cylinder heads and intake manifold. In certain classes these engines are limited to a single two-barrel carburetor which, in stock form, can't flow more than 500 CFM of air at a pressure differential of 3' of water. This configuration represents the very incarnation of a 'flow-limited' engine.

In the early development of these engines, the max power we could coax from these engines was in the 425 HP neighborhood (which, in itself, is impressive). Today (2004) we are nearing 500 HP from these engines, while using essentially the same heads and manifolds (as specified by the NASCAR rules for these engines).

The big change has been in cam lobe profiles which are optimized to this particular flow-limited configuration. Of course, as you might expect, these cam profiles are very hard on the valve train components. Here, we will attempt to explain why, and how different requirements can be met through the various compromises taken in cam lobe design.


Here is a graph showing the motion of the cam followers for one cylinder of a two-valve (intake and exhaust) pushrod-rocker arm engine as a function of lobe rotation. Note that the rotation axis is plotted in degrees of crankshaft rotation (which is twice the camshaft rotation, since the camshaft spins at half crankshaft speed in a 4-stroke engine). Notice also that the lobe lift is roughly 0.420 inches, which with a nominal rocker ratio of 1.6, will theoretically produce nearly 0.675 of valve lift. The red trace is the exhaust follower travel and the blue trace is the intake follower travel.

Lobe Lift Curves
Cam Follower Motion

The commonly-quoted specifications for cam lobes are lift, duration, overlap, and lobe separation. The 'Lift' spec is the maximum amount of travel the cam follower experiences as the cam lobe rotates under it. The 'zero lift point' can be defined as the lift when the lobe is rotated 180 degrees from its maximum lift point, when the cam follower is said to be 'on the base circle' of the lobe (the constant-radius portion of the lobe).

'Duration' is the number of crankshaft degrees of rotation during which the cam follower lift is greater than a specified value. Without knowing the lift value at which a duration is measured, the duration number is meaningless. Because the cam lobe contains slow-motion ramps at the beginning and end of the lift period to take up clearances and to get the parts into motion gradually, it has become an accepted industry practice (initiated by Harvey Crane back in the 1960's) to specify lobe duration as the number of degrees between the points at which the lifter is 0.050 off the base circle.

Overlap, referring to the graph above, is the number of degrees of crankshaft rotation during which both valves are off their seat, and measured as the number of degrees of crankshaft rotation during which both lifters are more than a specified distance from the zero-lift point (off base circle). Again, without this reference number, an overlap spec is essentially worthless. If we use the 0.050 reference, the overlap of the cam above is roughly 40 degrees. Overlap, as we will discuss later, is a very important influence on engine performance. Ed Iskenderian, one of the early developers of aftermarket camshafts, used to refer to overlap an 'the 5th Cycle'.


exhaust lobe has 0.420 of lift at 108 degrees before TDC and 262 degrees of duration. In this case, the cam follower is away from it's zero-motion position for 250 degrees of crankshaft rotation (125 degrees of camshaft rotation). That lobe is described as having a 'duration' of 250 degrees. In this case, the valve begins to open 20 degrees before Top Dead Center (BTC) and doesn't close until 50 degrees after Bottom Dead Center (ABC). The lobe 'centerline' (the point of max lobe lift) is located at 105 degrees after TDC. To find the centerline, assume the max lobe lift occurs at the half-duration point (which is not necessarily so, but close enough for the purposes of this presentation). Since the valve opens 20° BTC, then the max lift (half-duration point, 125 ° of crankshaft travel) occurs at 125-20 = 105° after TDC.

Now, as you might expect, it can be difficult to determine, with sufficient accuracy, the exact crankshaft position when a valve begins to open or close. And, the exact value of the crankshaft position can be dramatically changed by changes in clearance between the valve and the mechanism which moves it (rocker arm or cam follower).

That situation is not much improved if, instead of valve motion, you use lifter motion to determine these points. The reason is because a cam lobe does not start the lifter moving suddenly. Each cam lobe includes opening and closing 'ramps' which allow the cam to start and to end the lifter motion in a gradual fashion. Therefore, the contemporary method of specifying cam lobe events is to state the number of degrees before and after TDC / BDC at which the lifter has moved to a distance of 0.050' from it's zero-motion position. The 'zero motion position' is measured when the maximum lift portion of the cam lobe is opposite (180° away from) the lifter (known as the 'base circle' or 'heel' of the lobe).

The next curve shows the cam follower velocity (red curve) which corresponds to the cam follower lift curve (blue).

Lobe Lift with Velocity

The next curve shows the cam follower acceleration (black) and velocity (red) which corresponds to the cam follower lift curve (blue).

Lobe Lift, Vel, Acc

The following graph shows the lifter motion caused by two different cam lobes, both of which have the same opening and closing specifications (as measured by the 0.050' travel points of the lifter). These plots are known as 'lift curves'. The horizontal axis is crankshaft rotation, referenced to TDC and BDC.


As you can see, both lift curves look fairly smooth. However, there is a substantial difference between the amount of force and vibration each of these two lobes impose on the remainder of the valvetrain they operate. Those differences can only be seen by examining the curves which show the velocity and the acceleration these lobes generate.

Comparison Lift Accel

More to come:
greater explanations and depth about preceding curves
Cam Followers: flat-cylindrical, flat-mushroom, radius, roller, rocker-arm
Pushrods: cylindrical, tapered, euler-column, stiffness, mass
Rocker Arms: shaft, pedestal, flat-end, roller end, needle bearing, plain bearing, spherical pivot, mmoi
Springs: single, double, triple, rev-kit, round wire, ovate wire, rate, res freq, mass
Excitations: lift, acceleration, fourier content of curves
Forces and Deflections: acceleration, vibration , resonance points

- Hydrodynamic Bearings -

Insight into how those seemingly-magic
rod and main bearings work



Most bearings can be described as belonging to one of four classes: (1) rolling element bearings (examples: ball, cylindrical roller, spherical roller, tapered roller, and needle), (2) dry bearings (examples: plastic bushings, coated metal bushings), (3) semi-lubricated (example: oil-impregnated bronze bushings) and (4) fluid film bearings (example: crankshaft bearings).

Aside from an occasional tangent like the Porsche 1.5 litre flat four engine of the sixties and certain radial-configuration aircraft engines, almost all piston engines use fluid film bearings. This is true for the crankshaft and sometimes the camshaft, although often the latter runs directly in the engine structure. He we put the spotlight onto fluid film bearings.

The point of the whole discussion is (a) to explain how fluid film bearings work (which is sometimes counterintuitive) and (b) to demonstrate how engine designers are reducing friction losses through bearing technology.

Fluid film bearings operate by generating, as a by-product of the relative motion between the shaft and the bearing, a very thin film of lubricant at a sufficiently-high pressure to match the applied load, as long as that load is within the bearing capacity.

Fluid film bearings represent a form of scientific magic, by virtue of providing very large load carrying capabilities in a compact, lightweight implementation, and unlike the other classes, in most cases can be designed for infinite life.

Fluid film bearings operate in one of three modes: (a) fully-hydrodynamic, (b) boundary, and (c) mixed.


In fully hydrodynamic (or 'full-film') lubrication, the moving surface of the journal is completely separated from the bearing surface by a very thin film of lubricant (as little as 0.0001' with isotropic-superfinished {ISF} surfaces). The applied load causes the centreline of the journal to be displaced from the centreline of the bearing. This eccentricity creates a circular 'wedge' in the clearance space, as shown in Figure 1.

Hydrodynamic Wedge

Figure 1

The lubricant, by virtue of its viscosity, clings to the surface of the rotating journal, and is drawn into the wedge, creating a very high pressure (sometimes in excess of 6,000 psi), which acts to separate the journal from the bearing to support the applied load.

The bearing eccentricity is expressed as the centreline displacement divided by the radial clearance. For example, if a bearing which has 0.0012' radial clearance (0.0024' diametral) is operating with a film thickness of 0.0001', then the eccentricity is (.0012 - .0001)/.0012 = 0.917.

The bearing eccentricity increases with applied load and decreases with greater journal speed and viscosity.

Note that the hydrodynamic pressure has no relationship at all to the engine oil pressure, except that if there is insufficient engine oil pressure to deliver the required copious volume of oil into the bearing, the hydrodynamic pressure mechanism will fail and the bearing(s) and journal(s) will be quickly destroyed.

It is interesting to study the pressure distribution in the hydrodynamic region of a fluid film bearing. The hydrodynamic pressure described above increases from quite low in the large clearance zone to its maximum at the point of minimum film thickness as oil (essentially incompressible) is pulled into the converging 'wedge' zone of the bearing. Figure 2 shows a representative sketch of the radial pressure distribution in the load-supporting area of the bearing.

Hydrodynamic Pressure Profile - Radial

Figure 2

However, this radial profile does not exist homogeneously across the axial length of the bearing. Figure 3 shows a sketch of the axial pressure distribution profile for fully-developed hydrodynamic lubrication with a non-grooved bearing surface (insert). As the picture shows, the pressure drops off rapidly at the edge of the bearing, because oil is leaking out of the edges under the influence of the high hydrodynamic pressure. Moving inward from the edges, the pressure rises dramatically. If the bearing has sufficient width, the profile will have a nearly flat shape across the high-pressure region.

Axial Pressure Distribution - Non-Grooved Bearing

Figure 3

Long ago, it was standard practice to use fully-grooved main bearings, the thought being that the groove would provide a better supply of oil to the conrod bearings. A quick study of the axial profile of the hydrodynamic pressure distribution for a grooved surface (insert), shown in Figure 4, demonstrates how any interruption of the smooth surface of the bearing in the load-carrying region will severely degrade the capacity of the bearing.

Axial Pressure Distribution - Grooved Bearing

Figure 4


The second mode of bearing operation is boundary lubrication. In boundary lubrication, the 'peaks' of the sliding surfaces (journal and bearing) are touching each other, but there is also an extremely thin film of oil only a few molecules thick which is located in the surface 'valleys'. That thin film tends to reduce the friction from what it would be if the surfaces were completely dry.


The third mode, mixed, is a region of transition between boundary and full-film lubrication. The surface peaks on the journal and bearing surfaces partially penetrate the fluid film and some surface contact occurs, but hydrodynamic pressure is beginning to increase.


To further explain the three lubrication modes, let's examine the operation of a journal bearing from startup to steady state. Figure 5 shows a journal bearing at rest. The applied load causes the journal to contact the bearing surface (eccentricity ratio = 1.0).

Journal Bearing at Rest

Figure 5

When motion begins, the journal tries to climb the wall of the bearing, as illustrated in Figure 6, due to the metal-to-metal friction (boundary lubrication) between the two surfaces.

Journal Bearing - Initial Motion

Figure 6

If there is an adequate supply of lubricant, the motion of the journal begins to drag the lubricant into the wedge area and hydrodynamic lubrication begins to occur along with the boundary lubrication (mixed lubrication).

Assuming the load and viscosity remain relatively constant during this startup period, then as RPM increases, the hydrodynamic operation strengthens until it is fully-developed and it moves the journal into its steady-state orientation (Figure 7), defined by the eccentricity (e) and the orientation angle (a). Note that the direction of the eccentricity, and hence the minimum film thickness, do not occur in line with the load vector, but are angularly displaced from the load.

Journal Bearing - Fully Hydrodynamic

Figure 7

There are three parameters which determine the mode (boundary, mixed, hydrodynamic) in which a given bearing will operate: (1) the speed of the shaft, (2) the viscosity of the lubricant, and (3) the applied unit load.

These three parameters can be combined in the following way to form a value we can call 'Bearing Operating Condition' (BOC).

BOC = Viscosity x RPM x Diameter x K / Unit Load

(Equation 1)

The Viscosity parameter is in units of absolute viscosity. The 'K' value is a factor which converts RPM and Diameter into journal surface speed. The bearing unit load is the applied force divided by the projected area of the bearing (the insert width times the journal diameter).


The BOC value will predict the operating mode of a bearing and the expected friction coefficient for that operating condition. The transitions between these different operating modes, and the related friction properties are illustrated more fully in the Stribeck Plot shown in below in Figure 8. This plot (also known as a 'ZN/P Curve') shows the bearing coefficient of friction (on a logarithmic scale) plotted as a function Bearing Operating Condition (BOC). The values plotted on the X-axis are nondimensionalized, and are shown as a percentage of full scale.

ZN/P Graph

Figure 8

The two vertical lines in the plot area show the boundaries between the three operating modes. Area 1, from BOC = zero to about 15, is where boundary lubrication occurs. Area 2 (BOC = 15 to 35) is the region of mixed lubrication, in which, as BOC increases, the hydrodynamic pressure is developing and taking over from boundary lubrication. Area 3 is fully-developed hydrodynamic lubrication.

Note that the purpose of presenting this BOC (or ZN/P) curve is to demonstrate the interrelationship between friction coefficient and the BOC (ZN/P) parameters, not to instruct in bearing design.

In the definitive 2001 reference text 'Applied Tribology: Bearing Design and Lubrication' by Dr. Michael Khonsari and Dr. Richard Booser (ref-2:6:12), the Stribeck Plot is shown on Page 12 and is described as a 'dimensionless uN/p curve relating lubrication regime and friction coefficient to absolute viscosity'. That same DIMENSIONLESS curve ('ZN/P') is shown on page 2097 of 'Machinery's Handbook, 24th ed.' (ref-2:22:2097)

The 'BOC' entity (often known as ZN/P) does indeed have units, which depend completely on the units you choose for (a) surface speed converted to RPM and (b) unit load: psi, n/mm², mpa, etc. Various engineering texts use specific portions of the curve and use whatever ZN/P units they prefer. Others retain the dimensionless construct.

The friction coefficient values shown in Figure 8 were taken from both 'Machinery's Handbook, 24th ed.' and from 'Design of Machine Elements', by M.F. Spotts, Professor of Mechanical Engineering, Northwest University (ref-2:2:302). Both reference works agreed that the low-point is about 0.001, the fluid film range is from 0.001 to at least 0.005, the boundary region is greater than 0.1 to as high as 0.03, and the mixed region is between the other two, as shown on the plot.

This curve illustrates that when operating in the hydrodynamic region (Area 3), if the unit load remains constant and either rpm or viscosity increase, the hydrodynamic pressure increases, the eccentricity decreases and the friction coefficient rises, increasing by a factor of 10 as eccentricity approaches zero.

However, if rpm remains fixed and either viscosity decreases or unit load increases, then the BOC will decrease. Friction coefficient decreases logarithmically down to the low point at around BOC = 35. If the unit load continues to increase and/or viscosity continues to decrease, the BOC will move into the mixed lubrication region and the lubrication mode will change from fully hydrodynamic back to the mixed mode and friction will increase dramatically. If the load increases and/or viscosity decreases even further, BOC continues to decrease, and eventually the journal asperities break through the film and the system reverts back to the very-high-friction boundary lubrication mode.

Note the values for friction coefficient. In the area of boundary lubrication, the friction coefficient is similar to that of a dry bearing (0.25-0.35). At the BOC value of 35, the friction coefficient is in the remarkably low region of 0.001, which is 50% less than the friction coefficient of deep-groove ball bearings. As the BOC increases (any combination of smaller load, higher rpm, higher viscosity) the curve shows that friction coefficient rises exponentially, approaching a value of 0.01, ten times greater than the ideal minimum. That fact illustrates why there is so much attention paid to optimizing the bearings for the application, trying to maintain the BOC in the 35-50 range.

In issues past, we have seen that combustion loads can apply forces in excess of 12,000 pounds to a rod journal. If the bearing were operating at a friction coefficient of 0.002, (BOC roughly 50), an applied load of 12,000 pounds would generate a friction load on the surface of one bearing of 24 pounds.

If the diameter of the journal carrying the 12,000 lb. is 2.50', then the friction torque lost to that bearing will be 24 lbs x 1.25' = 30 lb-in or 2.5 lb-ft. If all 5 main journals carry the same load, then the friction torque lost to the main bearings alone is 5 x 2.5 = 12.5 lb-ft, which at 9000 rpm, absorbs 21.4 HP.

If that journal diameter were reduced to 2.00', one might think that a 20% reduction in main bearing friction torque could be realized. However, for the same bearing width, reducing the journal diameter 20% reduces the projected area by 20%, which increases the unit loading, resulting in a reduced BOC for the same load, rpm and viscosity. Further, reducing the journal diameter by 20% also reduces the surface speed by 20%, which for the same RPM and viscosity, lowers BOC even further. Add in the effect of the very low viscosity lubricants some teams use, and the net effect can be a dramatic reduction of BOC. As long as the BOC stays within the hydrodynamic region, the smaller BOC will yield an even lower friction coefficient, which further reduces the bearing friction losses.

Of course in practice, it's not that big a payoff, because the 12,000 lb. load is not applied for the whole 360° of rotation. But the illustration serves to point out an area that savvy engine designers have been successfully harvesting.


There is another form of fluid-film lubrication, which adds to the load capacity in applications with oscillating loads (such as a piston engine), known as squeeze-film lubrication. Squeeze-film action is based on the fact that a given amount of time is required to squeeze the lubricant out of a bearing axially, thereby adding to the hydrodynamic pressure, and therefore to the load capacity. Since there is little or no significant rotating action in the wrist-pin bores, squeeze-film hydrodynamic lubrication is the prevailing mechanism which separates wrist pins from their bores in the rods and pistons.


Crankshaft bearings are not round. The main bearing journals and crankpins that run within these (conventionally) plain bearings are perfectly round but the bearing surfaces that surround them are not. For a start, the crush that locates a plain bearing in its housing causes distortion of the housing, the nature of which will reflect the material and geometry of the part forming it. On top of this, these bearings are actually designed to be out of round.

If engine load and speed were constant and bearing geometry could always be maintained during operation a perfectly round bearing surface profile would work fine. Of course in the internal combustion engine load and speed do vary constantly and the varying loading imparted to the bearing housing constantly alters its geometry. In fact, the racing engine is an elastic device, to an extent that is not always fully appreciated. Enormous loads go both up and down the con rod, lengthening and shortening it and distorting the shape of its big and small end. In view of this contemporary steel backed plain bearings are designed to be semi-flexible rather than rigid structures.

In The Definitive V8 Engines, we showed that a naturally aspirated 2.4 litre, 750 bhp Formula One V8 running to 20,000 rpm (2006 regulations) is subject to a maximum crankpin load in the region of 13,300 lb while a naturally aspirated 5.86 litre, 850 bhp Cup V8 running to 9500 rpm is subject to about 12,500 lb. Such crankpin loads deform the crankshaft, which in turn transfers deformation to the crankcase through its main bearing journals. Thus in operation, both the rod bearing housing (conrod big end) and the main bearing housings deform.

In practice it has been established that the appropriate static profile for a crankshaft bearing is normally oval, having its minimum diameter in line with the direction of maximum load. Generally this is taken to be at 90 degrees to the parting line. Bearings are therefore typically manufactured with a wall thickness that is greatest at 90 degrees to the parting line, tapering off from that point to the parting line each side by a specified amount. This is known as bearing ovality (sometimes called 'eccentricity', but that usage can be confused with the eccentricity essential to hydrodynamic lubrication) and it is tailored to the characteristics of a specific engine. For example, a heavy piston assembly and high rate of piston acceleration will result in high inertia loading at the top of the exhaust stroke that will cause pronounced stretch of the con rod, this in turn significantly squeezing the big end - a high degree of ovality is required to stop the bearing then pinching the crankpin.


While bearings are a source of friction (including consequent shearing of the oil film) and thus heat, they are also a route for heat to escape from the reciprocating/rotating assembly to the stationary structure of the engine and, more importantly, into the circulating oil. In terms of the stress that the bearings see, it is notable that the magnitude, and sometimes even the direction of the loading varies throughout the course of each stroke. How much stress a given bearing experiences is a function of net loading and bearing projected area, which fluctuates accordingly.

Net loading varies dramatically with throttle and rpm, and throughout an engine cycle at any given throttle and rpm. For example, on the power stroke the compression / combustion loading on the con rod is compressive and this opposes the tensile inertia loading caused by piston acceleration. At low engine speed with wide open throttle there is less inertia loading balancing the piston combustion forces and, depending on the engine's torque characteristics this can impart greater net loading to the bearings than WOT operation at higher speeds. Conversely, at engine speeds above peak torque inertia forces come to dominate and the net effect on the bearings is increased loading compared to operation at peak torque rpm. However, the con rod loading that occurs in the vicinity of TDC overlap is extremely high tensile loading because there is very little cylinder pressure to oppose the piston acceleration. That load varies with the square of rpm, and can apply immense loads (and consequent deflections) to the cap-half insert.

Sustained high rpm operation is another threat to the bearings since it causes high temperature running, which in turn can cause excessive oil heating and with that a loss of viscosity. In this respect Cup oval running can be more taxing to the bearings than Formula One road racing.

An article in Race Engine Technology, Issue 20, showed an example of cavitation damage on a big end bearing from the Cosworth 2.4 litre V8 engine of 2006, which was designed to run to 20,000 rpm. As the piston approached top dead center the tendency was for the upper portion of the titanium rod's big end to arch away from the steel crankshaft journal and for the steel backed bearing to distort accordingly. There was thus a cavity formed between the bearing and the journal upon which it ran, creating a low-pressure zone in the oil film, encouraging the formation of vapour bubbles. As the piston reversed direction the combustion pressure took out the cavity, collapsing the bubbles, which added to the loading on the big end. In fact, shock waves were formed that stressed the surface of the bearing, to the extent that material could even be lost from it. Following a problem of this nature at the Malaysian Grand Prix the oil viscosity was increased. This avoided any cavitation damage until design changes could be implemented to address the problem. High shear viscosity at high temperature is critical for bearing duty as this extreme example attests. Oil development through 2006 led to a reduction in the variation of viscosity with temperature ('viscosity index').


Ideally a bearing material should offer low friction properties, but given that in fully-hydrodynamic operation, the bearing surface is separated from the surface of the journal by a thin film of oil, it is clearly the lubricant rather than the respective surface materials that dominates the friction generated under normal running conditions.

Therefore, if there is an adequate supply of lubrication and a suitable load / speed ratio, the material forming the bearing's working surface is not crucial in terms of frictional losses. Inevitably, however, metal-to-metal contact will occur, particularly on start up. The journal is invariably steel, and copper, for example (used as the sole material for some early bearings) running on steel has a kinetic coefficient of 0.36. However, any metal running on steel given proper lubrication has a kinetic coefficient of in the region of 0.06 (it will vary as shown in the Stribeck curve above).

In view of the unavoidable metal-to-metal contact, low friction coatings are sometimes applied to bearings. For example, one manufacturer has developed an ultra-slippery moly/graphite blend, which is suspended in an inert PTFE substrate, which provides the adhesion necessary to attach it to the top surface of the bearing. This coating, only one thou thick, which is compatible with contemporary lubricants and lubricant additives, is sacrificial - the bearing will outlive it but in the meantime it is claimed to reduce friction and wear. If there is any contact it will prevent scuffing and even absorb debris.


Typically the tri-metal plain bearing common to contemporary high-performance engines is formed as a laminated structure having a relatively thick steel backing layer in contact with the housing, a harder, thin middle layer (copper-lead, lead-bronze, aluminum-tin, etc.) and a very thin upper layer of soft material (lead, zinc, cadmium, lead-indium, and a host of others), the top layer forming the actual bearing surface. The maximum applied pressure a bearing can carry is determined by the streength and hardness properties of the upper surface. The maximum relative velocity between the journal and the bearing is governed by the bearing's abilkity to dissipate the heat generated by the shearing of the oil film.

Except for the rare instances of built-up crankshafts, the plain bearing is split into upper and lower halves, so that it can be fitted over the journal. One half fits into the main structure, the other into the cap. Each half is known as a shell hence this type of bearing can be referred to as plain or shell-type. Normally only one of the main bearings is designed as the thrust bearing necessary to minimise axial movement of the crankshaft.

The multiple layers have been developed to provide the properties required for the specific application. While the backing will invariably be steel, a steel bearing running against a steel journal with no coating on either surface would cause high friction and wear in the boundary and mixed lubrication modes, and would provide little or no ability to allow foreign particles to embed in the material, but would instead capture them and turn them into cutting tools. Therefore, the upper layer is a softer metal, designed for minimum friction with sufficient embeddability. The idea is to allow abrasive particles to embed below the working surface and thereby minimise wear. Moreover, the softer upper layers will help the bearing act as a cushion in the face of severe operating forces. In addition to high mechanical strength and high resistance to temperature the composite bearing needs good conformability and good surface properties - it needs 'compatibility' to prevent pick up or even seizure if the oil film momentarily breaks down.

Due to the mechanical properties of the soft bearing material, one might think it would be squeezed out of the bearing due to the forces acting upon it. However, the very thin nature of the soft layer, supported by the much stronger and thicker base layer, prevents the extrusion of the soft material.

The inability of the applied load to squeeze out the soft layer is known as the principle of plastic constraint. Consider a thick layer of clay sandwiched between two plates of steel. If pressure is applied to the steel plates, the clay will deform and squeeze out the edges of the sandwich. But as the thickness of the clay gets ever smaller, it takes an ever-increasing amount of force to squeeze out more clay. Eventually, a thin layer of clay remains that cannot be extruded out without the application of an infinite amount of pressure.

A bearing needs to conform to the shape of its housing; a shape that is constantly in a state of flux since the engine is an elastic device. In view of this the bearing is designed so that when the two halves of the housing are correctly bolted together its parting line surfaces adjoin and the bearing correctly conforms to the housing, leaving the required running clearance between its working surface and the journal. However, when a bearing shell is fitted into its respective housing its edges will stand slightly proud of the housing faces so that when the cap bolts bring the parting line surfaces together there will be a slight gap between the housing faces. When further tightening brings the faces into contact the gap will have gone and the resultant 'crush' means that the bearing is compressed like a spring and applies a radial load to its housing.

Although a plain bearing is thus an interference fit in its housing locating lugs can be fitted to assist positioning during assembly. More typically each bearing shell is retained by a pin projecting into it from the housing. These lugs or pins will help avoid any danger of movement relative to the housing in operation but that is not their primary purpose and the interference fit must be good enough in this respect to ensure reliable operation.

In the case of the big end the interface between the plain bearing and its respective journal normally receives a supply of pressurised lubricant from a drilling in the journal. The relative movement of journal and bearing and the forces involved cause the oil to spread out and form the necessary film throughout the radial interface, before spilling into the crankcase.


Crankshaft main journals are subject to extremes of torsional vibration, and that influences their diameter. However, journal overlap and crankshaft balancing techniques are further factors, which may permit the use of smaller diameter and narrower journals. It is notable that the Cosworth DFV 3.0 litre V8 of 1967 had a main bearing journal diameter of 60 mm with a big end journal diameter of 49 mm. By contrast, a third of a century later a 3.0 litre V10 typically had a main journal diameter in the range 40-45 mm, a big end journal in the range 35-40 mm. However, there is also a very large difference between the operating speeds of those two engines. Since main journal diameter is a major factor in crankshaft torsional stiffness, perhaps the reduction in crankshaft torsional stiffness caused both by the reduced diameter and the increased length served to provide a greater separation between the crankshaft torsional resonance point and the much higher excitation frequency of today's engines.

- Engine Metals -

Properties of Existing and New Metals for Engine Applications



This article presents details on some new materials for race engine components as well as some additional engineering information on some alloys currently in use. The terms used here to define material properties and processing are explained immediately below.


Stress is a normalized method for expressing the severity of loading applied to a material. It is expressed as the applied load divided by the area to which the load is applied. For example, if a 9,800 pound tension load was applied to a 1/2-inch diameter bar (0.196 square inch cross-sectional area = diameter x diameter x 0.7854) the tensile stress would be 50,000 pounds per square inch (psi) (stress = load / area = 9800 / 0.196).

Note that this is the simplest form of stress, to illustrate the point. It does not take into account bending, shear, torsion, or any other complexities. Stress values in this article are stated in ksi, meaning thousands of pounds per square inch (300 ksi = 300,000 psi).

The Yield Stress (YS) of a given material is the stress value required to permanently stretch a test specimen a specific amount (usually 2%).

The Ultimate Tensile Stress (UTS) of a given material is the stress value required to fracture the specimen (pull it apart into two pieces). The UTS and YS values are measured on a testing apparatus designed to gradually increase the load on a specimen until it fails, and measure the deflection as the load is applied. Figures 1 and 2 show such a test before and after fracture.

Tensile Test - Pre-fracture

Figure 1
Tensile Test, Pre-fracture

Tensile Test - Post-fracture

Figure 2
Tensile Test, Post-fracture

Creep is the phenomenon in which a metal, when exposed to a high stress level over an extended time period (typically hundreds or even thousands of hours) will exhibit a quasi-permanent strain (deformation), which occurs at different rates depending on the length of exposure. High temperatures generally increase the rate of creep.

Fatigue is the term used to describe the breakage of a metal part that occurs when the part is subjected to a load which varies over time, even though the varying load is well below the YS of the material. Fatigue is covered in detail on a dedicated page on this site.

There are different types of fatigue loading. One is zero-to-max-to-zero, where a part carrying no load is subjected to a specific load, then the load is removed. An example is a chain used to pull logs behind a tractor. Another type is a varying-load-superimposed-on-a-constant-load. The suspension wires in a bridge are an example of this type. The wires carry a constant static load from the weight of the bridge, plus an additional varying tensile load from the vehicles traveling across the bridge. The most severe case is the fully-reversing-load in which a specific tensile load is applied to the part then released, then a compressive load of the same value is applied and released. An example is the load applied to the roots of the teeth in an idler gear.

Fatigue tests use fully reversing loading to test the properties of materials, and the results are extremely statistical. The number of cycles a given material can survive a specific fully-reversing stress increases as the stress level decreases. Certain materials exhibit a property known as ‘infinite life’, which is defined as the fully-reversing stress level (the endurance limit, or EL) which a material can survive for 10 million applications (cycles).

Notch Toughness is a measurement of a material's resistance to breakage from impact loading. If you hit a diamond with a hammer, it will shatter; If you hit the head of another hammer with a hammer and the hammer in your hand will spring back; If you hit the fender of your car with a hammer, well you know how that turns out...…

Notch toughness is measured by several different tests, the Charpy V-Notch (CVN) being one of the most frequently used. In that test, a specific size ‘V’-shaped notch is cut into a specific size rectangular bar of the test material ('specimen'), then the specimen is mounted in a testing machine which has a pendulum-type hammer. The pendulum is raised to a specific height and released. It strikes the specimen right behind the notch and fractures it. The kinetic energy (ft-lbs) contained in the pendulum at the time it strikes the specimen is easily calculated. The energy remaining in the pendulum after it breaks the specimen can be calculated from the distance it travels post-fracture. The energy required to break the specimen is obviously the difference between the two values, which is the CVN value (ft-lbs) for the material at the tested hardness.

HRc - The hardness of a material as measured on the Rockwell 'C' scale. (There are several other hardness scales: Rockwell A and B, Brinell, Vickers, Knoop, Shore, etc., having different uses and ranges. HRc is the most frequently used scale for steels; HRb is a common measurement for softer metals.) Since the strength versus hardness relationship is known for each material, this test is a simple way to verify the strength of a known material.

Work-Hardening is an increase in the strength and hardness of a metal resulting from plastic deformation at a temperature below the crystal-restructuring range.

Vacuum Induction Melting (VIM) is a primary-melt process for producing very high purity steels by melting the materials by induction heating inside a high-vacuum chamber.

Electro-Slag Remelting (ESR) is an open-air remelting process through a reactive slag which produces a clean steel with good crystallography.

Pressurized ESR (PESR) is an ESR remelt but the furnace is pressurized with 1-15 bar of nitrogen to prevent the formation of oxides, producing a cleaner steel than ESR.

Vacuum Arc Remelting (VAR) is a refining process in which steels are remelted inside a vacuum chamber to reduce the amount of dissolved gasses in the metal. Heating is by means of an electric arc between a consumable electrode and the ingot, and typically takes twice as long as ESR or PESR.

It is well established that material cleanliness (absence of contaminants, oxides, bubbles, unwanted elements) is a major contributor to high fatigue life. After the primary melt, there are various remelt processes which produce an increasing level of purity in the metal. VIM-VAR is generally used to produce the cleanest (and most expensive), of double-melt steel, nickel and titanium alloys, and therefore, the best fatigue properties of double-melt methods. Triple-melt VIM-ESR-VAR produces extreme cleanliness in exchange for extreme cost.

Hot Isostatic Processing (HIP) is a method of essentially eliminating internal voids and microporosity in cast components and powder forgings. The components are put in an autoclave and heated to a temperature appropriate for the material and held for several hours while being subjected to a high pressure atmosphere of inert gas (as high as 200 bar).


The correct selection of a material for a particular application is a highly specialized field and usually requires consideration of a wide spectrum of requirements. In a race engine environment, the demands can be extreme, calling for various combinations of high strength and high fatigue resistance at high temperatures, and the minimum weight which will meet the stress and life requirements.

The perfectly-designed race engine component would operate at its design level until just after the checkered flag of the last race it was designed to run. The engineering challenge in material selection is complicated by the highly statistical nature of strength and fatigue ratings, as well as the practical problems of cost and availability. Simply stated, what is the point of specifying a 400 ksi material if it has limited availability and/or a cost that makes the target product unaffordable?

That trade-off provides the motivation to solve component-life problems by modifying the design to suit materials which are available in commercial quantities and/or for reasonable costs. The word ‘reasonable’ is highly ambiguous in the context of costs in the racing world. The 300-M which EPI, Inc. uses for highly-stressed aircraft components costs over $5 per pound, or nearly $1900 for a 10-foot bar of 2-inch round. The exotic nitriding steel (32CrMoV13) used for certain high-end crankshafts can cost over $20 per pound in the very high purity (VIM-VAR) form; over $5000 for a 26' bar of 7' round suitable for a Cup crankshaft, for example. Certain high-end PM alloys can cost over $24 per pound. Some titanium alloys cost over $60 per pound. In the nether-worlds where cost is no object (Formula One, Cup, factory Le Mans teams and the like) those numbers might not seem important, but at other levels of racing, the costs can be prohibitive.


In the article on Crankshafts, I briefly discussed the ultra-high-strength steel known as 300-M (AMS 6419). This alloy has been used in a variety of high-strength applications including crankshafts, con rods, torsion bars and gears (not to mention various critical aircraft applications such as landing gear components). This alloy is interesting because, although it has a remarkable combination of properties (strength, fatigue life, impact resistance and ductility), it has somewhat fallen out of favor, primarily because it has been misused.

Here is an example. Suppose a company has been making successful con rods from 4340, and it decides to add a higher strength product. The engineers at the company have heard that 300-M is a great material, so they decide to use it for the new con rod. At a hardness of 44-46 HRc, their 4340 con rod has good strength (220 UTS / 200 YS) and impact resistance (22 ft-lb CVN). However, although the strength of 4340 increases at hardness values above 46 HRc, the impact resistance becomes quite poor, so 44-46 HRc is the typical compromise hardness for 4340 cranks and con rods.

While developing their 300-M con rod, some designers have incorrectly reasoned that since 300-M is a 'modified' 4340 (see Table 1), the 300-M part should be tempered back to the same hardness used for 4340 (46 HRc) to achieve good toughness. The resulting con rod has issues, and 300-M gets a bad rap.

The problem is that even though the strength of 300-M at 44-46 HRc is higher than 4340, its notch sensitivity at 46 HRc is very poor (10 ft-lb CVN).

Properties of Certain Steel Alloys

In fact, the peak value for 300-M notch sensitivity occurs at a hardness of 53 HRc, where the value (22 ft-lb CVN) is the same as for 4340 at 46 HRc, but the 300-M has far greater strength (289 UTS / 245 YS).

At 53HRc, it is a bit more challenging to machine, but that is not a significant problem. Further, the extra carbon in 300-M allows a 60HRc surface to be produced on 53HRc through-hardened parts by induction hardening and tempering at 300°F, making it useful for some challenging gear and shaft applications. (Boeing uses lots of 300-M at 52-53 HRc in landing gear components.)

Recently, I heard about a new high-strength steel product from Bohler-Edelstahl, which offers potential for improvements in gearing and shafting applications. This steel, known as W-360, is a high-strength chrome-moly-vanadium alloy, having somewhat different chemistry (see Table 1) than the exotic chrome-moly-vanadium crankshaft alloy (32-CrMoV-13) discussed in my Crankshaft Design article. W-360 achieves post-heat-treat UTS/YS values of 290 / 270 ksi, with a through-hardness of 56HRc, by austenitizing at 1925°F (1050°C), oil-quenching and triple tempering at 1075°F (580°C). The alloy exhibits extremely low distortion after heat treating.

At 290 / 270 ksi UTS/YS, W-360 exhibits a 50% reduction of area (ROA) during tensile testing. As an aside: careful examination of Figure 2 reveals the ‘necking-down’ a tensile specimen undergoes just before failure. The reduction in cross-sectional area provides a quantitative measurement of a material's ductility. This phenomenon is discussed further on the Stress and Strain page.

Although W-360 already has 50 points of carbon, it can be successfully carburized, but a non-standard carbon potential is required. The high tempering temperature allows post-heat-treat nitriding and the application of PVD coatings while retaining the high core strength. With this steel, it is possible to produce a component having carburized gear teeth on one end and nitrided splines on the other.

Gears made from W-360 alloy have been successfully application-tested in an extremely-brutal form of high-end motorsport. In these applications, the best 300-M and carburized 9310 gears were failing in root fatigue from impact loading, while similar gears from W-360 survived a much longer exposure to that environment. Limited axial fatigue testing of AirMelt-PESR samples shows an endurance limit of 10^7 cycles at 138 ksi (951 mpa). One cannot help but wonder how a VIM-VAR version of this steel would perform in fatigue testing.....


There are some unique material selection challenges in the design of very-high-strength threaded fasteners. High-grade fasteners are exposed to high stress concentration in the thread roots caused by the tensile stresses produced from extremely high clamping loads, on top of which are superimposed any fatigue loads (as in the case of a con rod bolt).

A thread with a sharp-cornered root would be doomed to a quick failure. High-grade fasteners typically use the large full-radius fillet ‘UNJ’ thread form to minimize the stress concentrations there. Nevertheless, those radii are very small in relationship to the other dimensions of the fastener (minimum radius = 0.155 / threads-per-inch, so a 20-thread-per-inch fastener has a 0.0077' minimum radius in the root).

In order for a highly-loaded fastener to survive, the thread must be rolled with a die, producing the full-fillet thread root with a high residual compressive stress, which counteracts applied tensile stresses and adds dramatically to the fatigue life of the part.

There has been lots of research and experimentation with making ultra-high-strength threaded fasteners out of 280+ ksi quenched / tempered and maraging steels, but there have been problems with notch sensitivity, stress corrosion, fatigue, and other issues.

To solve those problems, producers looked to exotic alloys. One of the best solutions was the alloy AMS-5844 (also known as MP35N), which was initially developed for extreme corrosion resistance and strength required in hot, corrosive oil and gas drilling operations. AMS-5844 is a multiphase nickel-cobalt based alloy containing significant amounts of chrome and moly but almost no carbon or iron (Table 2). It can be work-hardened, then aged to strength levels as high as 300 ksi. The work-hardening feature lends itself to the production of very-high-strength rolled threads. Fasteners made from AMS-5844 are routinely specified for aerospace applications and in the highest levels of motorsport.

Because of the large amount of cobalt in AMS-5844, the material cost is quite high (currently around $80 per pound). To find a more economical solution that provides the same performance, a leading US fastener manufacturer (ARP) worked with Carpenter Technology to develop Custom-Age-625-PLUS (a modification of Carpenter's CA-625 chemistry).

Custom-Age-625-PLUS is a nickel-based alloy with a significant chrome and moly content, but with no cobalt, virtually no carbon and a small amount of iron. It can be work-hardened, then aged to strength levels around 270 ksi. (NOTE: Other superalloys shown in Table 2 are discussed in the article on Turbochargers.)

Superalloys Chemistry

Table 2


Lots of ink has been used on discussions of aluminum piston material. Forged 2618 was used for piston material in Second World War aircraft engines. In certain piston engine applications, forged 4032 was preferred because of its lower coefficient of expansion. Alloy 2618 is often described as having higher strength than 4032, but at elevated temperatures (where pistons tend to operate), the strength distinction becomes quite small (Table 3). In fact, at 400°F, the 32 ksi YS of 4032 alloy is 18% higher than that of 2618 (27 ksi) at the same temperature. However, 2618 has an impressive resistance to weakening with prolonged exposure to elevated temperatures. 2618 is a copper-magnesium alloy with low silicon, but it expands with temperature about 15% faster than the high-silicon 4032 alloy. Currently, piston manufacturers seem to prefer the 2618 alloy, and many have done slight modifications either to the chemistry or to the tolerances to produce 'proprietary' alloys.

There is a new family of high-strength extruded aluminum alloys currently under development by a major US titanium valve manufacturer (Del West). The members of this family are derived from existing 2000 and 7000 series wrought alloys, by a proprietary process in which existing chemistries are modified by the addition of spheroidized aluminum oxide, with the volume percentage varying between 5 and 20% depending on the targeted properties of the new material.

When compared to the base alloy, this process yields substantial improvements in the yield and ultimate stress values (10-15%) and in the fatigue performance across the usable temperature range of the base alloy, plus a significant reduction in the thermal expansion rate, and a dramatic increase in stiffness, with the elastic modulus increased as much as 40% (to nearly the value of titanium).

For example, comparing the new 2000-based alloy (‘DW 2-15’) to 2618 at 400°F, the yield strength of 2618 is 26.8 ksi, while the yield strength of the 2-15 is 32.6 ksi, an improvement of more than 21%. But that's not all. The coefficient of thermal expansion of the 2-15 alloy is 24% lower than 2618, and is even 8% lower than the 'low expansion' 4032 alloy.

Fatigue testing on the 7000-based alloy (‘DW 7-15’) showed a tremendous improvement in fatigue performance compared to the very-high-strength 7075-T6. As an aside: Table 3 contains some interesting information on several often-used alloys, both wrought and cast.

The fatigue testing of the 2000-based alloys has yet to be completed. However, preliminary indications are that the results will show strength and fatigue improvements similar to the improvements realized in the 7000-series. If the expected results are verified, that will present the opportunity for yet another improvement in piston technology: strength and fatigue properties exceeding 2618 with expansion less than 4032. The materials will be available in extruded bar and plate form, with planned release in late 2008.

Aluminum Properties

Table 3
Chemistry and Physical Properties of Some Interesting Aluminum Alloys

Table 3 contains the chemistries and some physical properties of the alloys discussed above, as well as properties of several other popular wrought and cast aluminum alloys. Of particular interest are the room temperature and elevated temperature strengths of some of the cast alloys, making them applicable to such demanding applications as turbocharger compressor wheels. Note, for example, how the strength of the famous high-strength alloy 7075-T6 drops to 37% of its room temperature value at 300°F and to less than 20% at 400°F. Also, note how the strength of 7475-T61 drops to about 26% of its room temperature value at 400°F.


Magnesium is the eighth-most abundant element in the earth's crust (2.7%). Although sometimes perceived as exotic, magnesium alloys have been used for decades in both motorsport and production vehicles. For example, VW began using cast magnesium crankcases for its 1961-model, 40 horsepower flat four, air-cooled engine.

It is generally accepted that it is more difficult to successfully cast magnesium alloys than aluminum alloys, for reasons which include (a) the melt must be covered with either an inert atmosphere or with a special flux to keep oxygen away from the molten metal and (b) magnesium has a relatively low heat of fusion, which can distinctly increase the problems encountered with gating and feeding.

Certain contemporary sand-casting magnesium alloys are ideal for high-strength cast housings which are exposed to operating temperatures up to 400°F (204°C). High-strength magnesium alloys are currently used in aircraft gearboxes, WRC transmission components, and (allegedly) in Formula One engine ancillaries. A low-creep die-casting magnesium alloy is used in a new BMW production engine block.

Corrosion issues have often been seen as intimidating, but recent metallurgies plus combinations of contemporary technologies (chromating, anodizing, sealing, painting) have made the atmospheric corrosion issues much less significant. Since magnesium is highly anodic, there are galvanic corrosion issues to be dealt with, but they can be designed out.

Magnesium alloys are approximately 35% lighter than aluminum alloys, and certain alloys can be heat-treated to UTS values approaching 43 ksi, making them attractive because of their high strength / weight ratio. The stiffness of magnesium is generally only about 63% of aluminum alloys, so components being switched from aluminum to magnesium will require larger cross-sections and section moduli to achieve the same stiffness as the aluminum part, and can result in a weight saving of 20-25% depending upon the design.

There are two major magnesium alloy systems (and several others less frequently used). The first system (aluminum-zinc) is primarily targeted at high-volume die-casting requirements. These alloys contain from 3% to 10% aluminum and smaller percentages of zinc and manganese. These alloys They are widely available and modest in cost. Their mechanical properties are good to approximately 220°F, but beyond that point, begin to diminish rapidly. In the early eighties, it was discovered that if the quantity of iron, nickel and silicon (contaminants to these alloys) were kept very low, the corrosion properties of the Al-Zn alloys became quite reasonable.

Most alloys in this family are best-suited to high-pressure die-casting methods because in those processes, the die acts as a huge chill, and causes fairly rapid freezing (just a few seconds) of the melt. The rapid cooling of the melt is what gives the Al-Zn alloys their good strength properties. Conversely, extreme skill and care is generally required to obtain good sand-castings in Al-Zn alloys. The slow cooling rate which occurs in sand-casting generally provides poor material properties and inconsistent strength between thick and thin sections unless elaborate chill systems are installed in the molds.

Typically, it takes high-volume production operations to cost-justify the investment in die-casting tooling. Motorsports, on the other hand, often need relatively small numbers of castings, and therefore, rely on the lower tooling costs of sand-casting methods.

It was the need for good sand-casting magnesium alloys which provided part of the motivation for the development of the second major alloying system. That system consists of magnesium alloyed with various combinations of other elements (rare earths, zinc, thorium, silver, but NOT aluminum) to achieve a set of desired properties. This system includes a small, but essential quantity of the grain-refiner zirconium, which produces a very tiny grain size in the metal, thus giving the alloys very consistent, homogeneous properties, without the need to rely on a fast cooling rate.

These Rare Earth containing alloys have some highly desirable properties: (a) they can be sand-cast, investment-cast and extruded, (b) many of them have excellent tensile and yield values, (c) they do not depend on fast freezing rates to achieve good strength, and (d) very important is the fact that these alloys retain their room temperature strength values much better than Mg-Al-Zn and aluminum alloys at higher temperatures (see Table 4).

Magnesium Chemistries

Table 4
Chemistry and Physical Properties of Some Magnesium Alloys

The alloy WE-43B is a high-strength, corrosion-resistant casting alloy specifically developed to maintain its high mechanical properties up to 570°F without using silver (which degrades the corrosion properties) or thorium (which is radioactive). When this alloy is extruded, the mechanical properties are uniform in all directions (isotropic). In the -T6 condition, it has reasonably-high room temperature properties, but the way it maintains almost constant properties up to and above 400°F is highly desirable for certain applications (see Table 4). This alloy was originally developed for the aerospace industry, and it is currently used for several helicopter transmission housings, the propeller gearbox housing on a new, very-high power turboprop engine, and in several high-end motorsport applications.

There is a recent high-strength sand-casting alloy (Elektron-21) which has room-temperature and high-temperature (to 400°F) strength properties similar to WE-43B (Table 4), but which has been specifically developed for better casting properties than WE-43B.

I was told that it is typically quite difficult to investment-cast magnesium alloys to obtain thin-wall therefore very lightweight parts. The developers of Elektron-21alloy reasoned that (a) if they could provide a high-strength alloy from which it is easier to cast successful parts,, then (b) it will be easier to make design changes, (c) the scrap rate will be lower, so (d) the overall cost of parts will decrease. Elektron-21is a high-strength alloy which is highly suitable for investment casting as well as sand-casting technology, and I have heard that it is now being used more regularly in military aircraft applications as well as WRC, MotoGP and other forms of high-end motorsport.

Elektron-675 Properties

Figure 3
Elektron-675 Properties

An interesting new wrought mag-nesium alloy is currently under development. This alloy (Elektron-675) represents a step-change upward in mechanical properties. The tensile / yield values are listed as 62 / 47 ksi respectively, with initial tests showing excellent fatigue properties. The chemistry, thus the alloying system, is presently undisclosed while the patent is being sought. The strength versus tem-perature properties are shown in Figure 3, constructed from data provided by the manufacturer. This material, being in the early stages of life, is not yet available in production volumes.

BMW Magnesium Block

Figure 4
BMW Magnesium Block

The alloy AJ-62A is a recently developed high-pressure die-casting alloy based on the Noranda-developed magnesium-aluminum-strontium ternary alloy system, with the specific goals of providing excellent high-temperature creep resistance and excellent high-pressure die casting properties in order to avoid the problems of hot tearing, cold shuts, porosity and difficult removal from the dies.

Using this alloy, BMW developed a composite inline-6 engine block (Figure 4) which uses AJ-62 for the external block, and an aluminum alloy for the liners, coolant passages and main bearing bulkheads. This block is reported to be 24% lighter than a conventional aluminum block and contributes to BMW's claim that the R6 engine, at 161 kg, is the lightest 3.0 litre inline-six in the world.


Titanium based alloys have been commercially available for just a little over 50 years. However, they have achieved widespread use in aerospace and various forms of motorsport. The valves and con rods in Formula One engines and the valves in NASCAR Cup engines are made from titanium alloys. It is used in various other applications including springs, torsion bars, fasteners, flywheels and clutch components.

Titanium is alloyed with combinations of other elements (mainly aluminum, vanadium, molybdenum, silicon, chromium, iron, zirconium and niobium) to produce titanium-based alloys metals with various physical properties. These alloys have densities which range between 0.158 - 0.175 lb/in³ (4.37 - 4.84 gm/cc), making them 56% to 62% of the weight of steel, and stiffnesses which vary between 53% to 61% of steel (15.5 to 17.7x10^6 psi). Certain alloys can be heat-treated to strengths exceeding 215 ksi (1480 mpa) UTS. Regardless of the strength levels, applications which have stiffness requirements would require a redesign to take best advantage of titanium. Unlike steel alloys, where the basic melt is an air-melt process, all titanium melting must be done in a vacuum, so the basic grades are VIM; high purity grades are VIM-VAR, and in extreme aerospace cases, there are triple-melt versions.

There are several manufacturers producing aftermarket titanium conrods. I was told by one major titanium supplier that the most frequently used alloy for conrods is the old standby Ti-6Al-4V (6% aluminum, 4% vanadium), also known as Grade 5 titanium. This alloy can be solution heat-treated and aged up to tensile strengths of 181 ksi (1250 mpa). It is interesting to note that the nomenclature '6Al-4V' has become nearly a generic, because there are more than 20 different variations available, all having the same basic chemistry but with differing melt practices, impurity tolerances, inspection requirements, etc.

I was told (by Allegheny Technologies Ltd.) about a new alloy under development that achieves a step-change in titanium material properties. This alloy was developed from the old existing alloy known as Beta-C (grade 19: Ti-3Al-8V-6Cr-4Mo-4Zr).

Whereas the commercial manufacture of Beta-C required a lengthy solution treatment and ageing cycle to achieve a tensile strength of 181 ksi (1250 mpa), this new material, using a patented process, can be cold-worked then direct-aged to a UTS over 220 ksi (1517 mpa). Even more interesting is the fatigue performance of this alloy. While the S-N (fatigue) curve for 6Al-4V continues downward as cycles increase, the curve for this material in fully-reversing fatigue (R = -1) appears to go flat at a stress level of about 93 ksi (640 mpa) at 1x10^6 cycles. This new Beta-C alloy was initially developed as a cold-winding spring alloy, but has evolved into favored usage for shafts, torsion bars and high-strength fasteners (where titanium is allowed).

Yet another interesting titanium based material is the alloy known as 15V-3Al. This is a cold-formable beta alloy produced in sheet form (1.0 - 1.5 mm thickness). Unlike many titanium alloys, this one is easily bendable to form complex fabricated sheet metal parts. When fabrication is complete, the part can be solution treated and aged, and the net result is a very high-strength, lightweight fabricated part. Imagine the possibilities for a fully-titanium monocoque chassis……

Making titanium valves survive in the harsh operating environment of a Formula One or Cup engine was a substantial challenge, especially in the case of exhaust valves, which are exposed to extremes of temperature and corrosive gasses along with high levels of fatigue loading (zero-max-zero plus bending), with quasi-impact compressive loads on the tip and seat.

To meet the challenge, the metallurgists at a major US titanium valve manufacturer (Del West) developed a proprietary, precipitation-hardening titanium alloy which begins with the tightly-controlled chemistry and melt processes of a ‘rotary’ (turbine blade) grade of Ti-6242 (6Al-2Sn-4Zr-2Mo) and the requirement for 100% virgin input (no scrap, no recycled metal). To that base, they add an undisclosed amount of silicon, which significantly improves the strength at elevated temperatures. (If there is any doubt regarding how much a small change can alter the properties of a material, compare the chemistries of 300-M and 4340 in Table 1.)

Some manufacturers make DLC-coated intake valves and spring retainers from 6AL-4V, but this manufacturer makes both its intake and exhaust valves from its proprietary version of Ti-6242. The heat treatment process is quite different for each type. The intakes are heat-treated below the beta transus temperature and subsequently quenched to form a martensitic titanium structure. That is followed by a stabilization / aging cycle at a lower temperature to achieve the desired strength properties.

The exhaust valves are heat-treated above the beta transus to produce an acicular, Widmanstätten structure (a ‘basket weave’ microstructure), which substantially improves the fatigue properties at elevated temperatures.

It has been discovered through experience that this microstructure also has crack-arresting properties. Sample exhaust valves which had been subjected to extreme mechanical and thermal loads have been found during teardown to have hundreds of tiny cracks in the stem-to-head transition area, but they had not failed in service.

These titanium valves are PVD-coated with chromium-nitride to provide the wear-resistant surfaces. Other hardcoating processes have been tried, such as controlled oxidization of the outer surface to form a hard layer of titanium-oxide. However, contrary to what was predicted by papers on that process, users of valves with that coating reported a huge loss of fatigue life, which would be expected since the TiO layer is an extremely brittle case.

More materials technology is presented in the article on turbochargers, including the use of titanium in high-temperature compressor wheels.

- Turbochargers -

How They Work, and Current Turbo Technology


This article first presents the basics of turbocharger operation, and then explores some of the current thinking in turbo-supercharger technology as applied to competition engines.


Since the power a piston engine can produce is directly dependent upon the mass of air it can ingest, the purpose of forced induction (turbo-supercharging and supercharging) is to increase the inlet manifold pressure and density so as to make the cylinders ingest a greater mass of air during each intake stroke. A supercharger is an air compressor driven directly by the engine crankshaft, and as such, consumes some of the power produced by the combustion of fuel, thereby increasing BSFC and engine wear for a given amount of produced power.

A turbocharger consists of a single-stage radial-flow ('centrifugal') compressor (air pump), as shown on the left side of Figure 1, which is driven by a single-stage radial-flow turbine, as shown on the right side of Figure 1, instead of being driven directly by the crankshaft. The turbine extracts wasted kinetic and thermal energy from the high-temperature exhaust gas flow and produces the power to drive the compressor, at the cost of a slight increase in pumping losses.

Borg-Warner VGT Turbo

Figure 1
Borg-Warner Turbocharger with Variable Geometry Turbine

The performance of a radial-flow compressor is defined by a chart known as the ‘map’, as illustrated in Figure 2. The map defines, based in on inlet conditions, the usable operating characteristics of a compressor in terms of airflow (pounds-mass per minute, lbm/min) and pressure ratio (absolute pressure at the compressor outlet divided by absolute pressure at the compressor inlet). The compressor RPM lines show, for the stated compressor speed (in thousands of RPM), the pressure ratio delivered as a function of airflow. The compressor efficiency lines show the % of adiabatic efficiency (AE) the compressor achieves at various combinations of pressure ratio and airflow.

Garrett GT3582R Compressor Map

Figure 2
Garrett GT3582R Compressor Map

The odd-shaped line up the left side of the map is the surge line. It defines, for each pressure ratio, the minimum airflow at which the compressor can operate. Airflows to the left of the surge line cause the air to separate from the blades and experience a 'stall' phenomenon similar to the stall of an aircraft wing. This is an area of instability in which the airflow moves in a chaotic manner, causing snapping and popping, and potential blade damage. Surge can occur with a downstream-throttled installation when the throttle is suddenly closed if there is no blowoff valve or other device to vent airflow.

The dotted line up the center of the map is the peak efficiency operating line: the maximum available efficiency for each combination of airflow and pressure ratio.

Note from the map that, for a given compressor RPM, the available pressure ratio reaches a point where it begins to drop quickly as airflow increases. This effect is less severe at lower rotor RPM, but with higher rotor RPM (therefore higher available pressure ratio), the pressure ratio drops dramatically with a slight increase in airflow. This phenomenon is known as 'choke'. The choke condition is defined differently by different manufacturers: sometimes by a specific percentage reduction in pressure ratio, sometimes by reaching a specific efficiency (Garrett uses 58%).

A single basic compressor wheel casting or turbine wheel casting can have the periphery of its blades machined (‘trimmed’) to provide a variety of different gas flow capabilities and to mate with differently-configured housings. The term trim expresses the area ratio between the inlet and the outlet of a radial flow wheel. Is it calculated by the equation:

Trim = 100 x (inducer diameter² / exducer diameter²).

Compressor efficiency is an important concept to understand with regard to forced induction. At standard atmospheric conditions (29.92 'hg, 59 °F) one pound-mass of air has a known density (0.0765 lbm / cubic foot) and occupies 13.07 cubic feet of volume. Compressing that mass of air into a smaller volume increases the pressure, the temperature and the density. If a compressor was 100% efficient, the temperature of the gas exiting the compressor could be calculated from the ideal gas law PV = krT (so called 'adiabatic' compression: no gain or loss of heat energy). However, real world compressors are less than 100% efficient, and so the air exiting the compressor is heated more than it would be with a 100% efficient compressor, hence the resulting density is less than would be expected.

Here is an example. On a ‘standard day’ (29.92 'hg barometer, 59 °F), a compressor having ambient conditions at the inlet, operating at an adiabatic efficiency of 100% and a pressure ratio of 2.9 would produce a compressor outlet pressure of 86.77 'hg absolute (2.9 x 29.92 = 86.77), or 2.94 bar absolute (coincidentally, the 2008 manifold pressure limit for Le Mans LM-P1 diesels). The compressor outlet temperature would be 241 °F and the density ratio (density relative to the inlet air) would be 2.15, for an air density of 0.164 lbm/ft³. (2.15 x 0.765 = 0.164).

In the real world, on a warm day with a low barometric pressure (say 85 °F and 29.10 'hg, ambient density = 0.071 lbm/ft³) with a turbo installation having a pressure drop of 0.5 psi in the inlet tract and a compressor operating at 75% adiabatic efficiency, the pressure ratio required to achieve that same outlet pressure (86.77 'hg) would be 3.087. The compressor discharge temperature and density ratio would be 358 °F and 2.057 respectively, for a density of 0.146 lbm/ft³, only 89% of the density achieved with a (dream-world) 100% efficient compressor.

If the engine designer decides that an inlet manifold temperature of 358 °F is not terribly desirable, he might decide to use a charge air cooler (correctly known as an 'aftercooler' but more commonly referred to as an 'intercooler') having, for example, an effectiveness of 85% and a pressure drop of 3 'hg. That would result in a manifold pressure, temperature and density of 83.7 'hg, 126 °F, and 0.196 lbm/ft³ respectively, for a system density ratio of 2.77 and an inlet air temperature that would dramatically improve the survival prospects of an SI engine. That is the real world of turbocharging.

(Please note that it is beyond the scope of this article to explain the details of these example calculations. Be assured they are relatively straightforward, and are presented in several excellent textbooks, including Refs. 5:12, 5:23, 5:24, 5:25 and 5:26.)


Turbochargers are becoming ever more widely used in racing, as motorsport increasingly embraces energy efficiency. It is expected that turbos will soon (2009 ?) reappear in F1 and IRL, as well as other venues. There is a considerable amount of development work currently being done on turbochargers, which is being motivated primarily by the following road-vehicle requirements:

  1. the ability to operate reliably and continuously with higher exhaust gas temperatures (EGT), and
  2. the ability to operate with higher compressor inlet temperatures and flowrates.

The demand for operability with higher EGT's comes from increasing demand for better fuel economy in spark-ignition (SI) engines, which requires that the engines run much closer to stoichiometric mixtures rather than employ the very rich mixtures used in the past to reduce EGTs.

These days, compression-ignition (CI) road car engines are invariably turbocharged and this relatively-fast developing technology is operating at ever-rising BMEPs, which means higher combustion temperatures and the resulting increases in NOx emissions. The demand for higher inlet temperatures and flowrates comes from the high percentages (30-40%) of exhaust gas recirculation (EGR) required to control NOx emissions from CI engines.

Although these motivators are coming from the production-vehicle end of the spectrum, the resulting technology is or will soon be available for application into motorsports. An SI race engine won't need to operate at stoichiometric mixtures, but the availability of turbines which can live with 1925°F (1050°C ) EGTs will provide new opportunities for greater output.

At present, competition CI engines are not required to reduce NOx emissions (but that will surely develop as political correctness further invades motorsports), so the increased compressor efficiencies, flowrates and map widths can be used to provide greater intake density at the mandated manifold absolute pressure (MAP) limits.

The increased compressor efficiencies, flowrates, and map widths developed for CI technology will certainly benefit competition SI engines in the same way.


A turbocharger lives in a terribly hostile environment. The turbine is driven by exhaust gasses that can exceed 1875°F (1025°C) and which are very corrosive. Exhaust valves experience those same corrosive, high-temperature gasses, but exhaust valves do not approach the peak temperature of the exhaust gas. An exhaust valve in a competition engine spends at least half of the time on the valve seat (production engines more like two-thirds of the time). Valves continuously transfer heat through the stem to the guide, and when they are seated, they rapidly transfer heat into the cylinder head through the valve seats. Those cooling paths keep exhaust valve temperatures well below EGTs.

The turbine wheel, however, lives in a continuous, high-velocity jet of those gasses. Although there is expansion across the turbine nozzle, therefore some cooling of the gasses, the temperature at the tips of the turbine rotor can approach exhaust gas temperatures. Further, the rotor system on many turbochargers operates well in excess of 100,000 RPM, and some approach 150,000 RPM. That imposes huge tensile loads from the centrifugal forces, as well as bending and vibratory loads. That environment requires the use of nickel-based superalloys for the turbine wheels. Those alloys can retain high strength values at these high temperatures.

The turbines in most current production turbochargers are suitable for continuous operation at an exhaust gas inlet temperature of 1750°F (950°C). Production turbines are typically investment-cast from Inconel 713 C or 713 LC (Table One). The turbine wheel castings are treated with Hot Isostatic Processing (HIP) to improve their structure and then are heat-treated to the required strength level.

Superalloys Chemistry

Table 1
Chemistries of Certain Superalloys

Honeywell Turbo Technology (Garrett) supplies the turbochargers (TR30R) used on the stunning 5.5 liter Le Mans-winning Audi CI V-12's and those of the pole-winning Peugeot CI V-12's. Those turbos have fixed turbine nozzle geometry with wastegates. The turbine wheels in those turbos must operate continuously with EGTs up to 1925°F (1050°C). Honeywell uses a superalloy material known as Mar-M-247 (developed by Martin-Marietta in the seventies for gas turbine engine blades, discs and burner cans). This material is a nickel-based alloy containing significant amounts of chrome, aluminium and molybdenum.

In order to achieve optimal properties in components cast from Mar-M-247, NASA developed the Grainex process. This process uses traditional investment casting techniques, with the additional process of mold agitation during freezing to produce homogeneous grain inoculation, resulting in outstanding uniformity of grain structure and material properties. The part is HIP'd at 2165°F (1185°C) and 170 bar for 4 hours to minimize porosity, then solution treated for two hours at the same temperature, followed by 20 hours of aging at 1600°F (870°C). That produces a room temperature UTS of 150 ksi, which increases with temperature up to 1400°F (760°C).

Variable geometry turbines (VGT) provide a substantial improvement in turbine efficiency and enable greater flexibility of operation. A large turbo with VGT can operate as if it were a smaller turbo at lower engine speeds. In many cases, the VGT can replace a wastegate.

VGT turbochargers have been around for several years, but their applications have been somewhat limited by the EGTs they can survive. At present, VGT implementations are limited to continuous EGTs of 1750°F (950°C), with an occasional spike to 1800°F (980°C) allowable, as in the Porsche 997 twin-turbo system supplied by Borg-Warner. However, current development efforts are focused on producing VGT systems which will operate successfully at the temperatures for which the newer turbines are designed (1925°F, 1050°C) .

VGT is implemented in different ways. One system uses a series of movable vanes around the periphery of the turbine wheel, as shown in Figure1 at the beginning of this article.

Each vane pivots on an axis parallel with the rotor axis. When the exhaust gas supply is low, the vanes pivot to a position which is a few degrees from perpendicular to the turbine wheel inducer vanes, as shown in Figure 3. That gives the incoming gasses a strong tangential component to drive the turbine more effectively.

VGT Position with Low Exhaust Supply

Figure 3
Low Exhaust Flow VGT Position

The angle of the blades can be varied continuously, and at high exhaust flow they are nearly aligned radially with the outer contour of the turbine blades, as shown in Figure 4, giving the incoming gasses a strong radial component to drive the turbine, while offering a relatively large flow area to reduce backpressure, .

VGT Position with High Exhaust Supply

Figure 4
Low Exhaust Flow VGT Position

Although many such systems currently use non-cambered vanes (the chord line is straight), future developments will include cambered vanes to increase VGT efficiencies at the top and bottom ends of the operating range. These VGT systems can be electrically operated, providing even greater flexibility to an ECU-managed engine system.

Another VGT system uses vanes which are attached to a ring surrounding the turbine wheel. These vanes have a have a fixed angular orientation. The ring and vanes move parallel to the rotor axis. The vanes orient the gas flow toward the turbine wheel blades, and the ring opens and closes the net nozzle area, dynamically altering the nozzle area, which changes the gas velocity therefore the turbine performance.


The compressor side of a turbocharger faces its own challenges. In most applications, the compressor is ingesting air at slightly more than ambient temperature, but the temperature rise across the compressor can be substantial (as explained in Turbocharger Basics at the beginning of this article).

With ambient inlet air and a 4:1 pressure ratio at 80% adiabatic efficiency (AE), the compressor discharge temperature can exceed 400°F (205°C). However, the low temperature of the inlet air plus the fact that most of the temperature rise occurs in the diffuser, where velocity is exchanged for pressure, typically keeps the operating temperature of the compressor wheel well below the compressor discharge temperature. A compressor wheel, often operating at over 100,000 RPM, is subjected to high centrifugal loads. High pressure ratios apply bending loads to the blades. Cycling between pressure ratios of 1.0 (no boost) to 4.0 (max boost) and back applies significant fatigue loads to the wheel. Surviving these cyclic loads at elevated temperatures can be a problem.

Currently, most production compressor wheels are aluminium investment castings, and a very popular material is the permanent-mold alloy 354-T61. The room temperature properties of this alloy rival some of the best forged piston materials, but the properties of 354-T61 cast aluminium at 400°F (205°C) substantially exceed any of the well-known wrought alloys (see Table 3 in Advanced Metals). Wheels cast from the very-high strength alloy 201-T7, using a permanent mold process, have also been successful in compressor applications, but this alloy is more difficult to pour successfully than is 354.

The compressor wheels in most performance applications, including the Audi and Peugeot Le Mans turbodiesels, are five-axis CNC machined from forged 2000-series aluminium billet. According to Turbonetics, that procedure provides wheels with optimal properties and accuracy, frees them from the costs involved in permanent mold tooling, and gives them a large measure of flexibility to experiment and modify existing designs.

However, much of the current direction in compressor improvement is being driven by the pressure ratio and flow requirements of CI engines for road vehicles, operating at high boost levels and high levels of EGR to reduce emissions of NOx. Wide-map compressors with pressure ratios of 4:1 and peak adiabatic efficiency of 80% are on the horizon.

With the 30-40% EGR systems being exploited in CI applications, there are advantages to taking the recirculated gas from downstream of the emission-control system, and feeding it into the turbo inlet to be mixed with the fresh charge air. That causes the inlet gas temperature to be well above ambient, and introduces contaminants including acid components and particulates, which can deteriorate both the structural and aerodynamic properties of the wheel.

The increase in inlet temperature from EGR, combined with the corrosive and abrasive effects of the exhaust gas, pose an increased challenge to the tensile and fatigue strength of even the best aluminium alloys. That has caused the development of titanium compressor wheels made from both CNC-billet and investment-castings. The titanium material provides stiffer blades, higher strength at elevated temperatures, and greater fatigue resistance.

Those features can be especially useful in competition applications which use two-stage turbocharging, achieving pressure ratios in the 9:1 range, with no intercooler between stages. (On a 29.92 day at 75°F, a 9:1 pressure ratio at 70% adiabatic efficiency would produce nearly 260'hg MAP and an inlet air temperature over 725°F.)

Improving the aerodynamics of a radial flow compressor involves intense modelling and simulation of the combined effects of the compressor wheel, the diffuser and the housing. One area of compressor development is the ongoing effort to provide ‘wider’ maps (at a given pressure ratio, a larger spread of airflow values between the surge line and the choke line).

The ‘widening’ of a map is illustrated in Figure 5. The blue lines in that map are the same as the map discussed in Turbocharger Basics above. The sketched-in red line shows an example of how the surge line can be moved to the left. The sketched-in green lines show how the 65, 68 and 70% efficiency lines have been extended into the new operating area. Note that at a pressure ratio of 2.75, the original operating range was from 36 to 60 lbm/minute. With the ‘widened’ map, the range at 2.75 PR now extends from 30 to 60 lbm/minute, a 25% improvement.

Widened Garrett GT3582R Compressor Map

Figure 5
Widened Garrett GT3582R Compressor Map

Production Compressor Ported Shroud

Figure 6
Production Compressor Ported Shroud

One contemporary method which has been successful in widening the map is the ‘ported shroud’ feature. It moves the surge line to the left by allowing a small amount of airflow to bleed off the low-velocity portion of the wheel and recirculate, to ward off blade stall. This feature is illustrated schematically in Figure 6.

A method which I have used in the past (before ported shrouds) is to install a sonic nozzle and an on-off valve in the compressor outlet plumbing. The sonic nozzle is sized to choke at a small percentage of the usable airflow (approximately 20%), and the on-off valve is controlled to open below an appropriate com-bination of RPM and MAP.

A contemporary example of this technology is shown in the compressor section of the turbocharger pictured in Figure 1 at the beginning of this article. In that implementation, the nozzle is controlled by an integrated servo-valve on the compressor housing, and the bypasses flow is recirculated to the inlet..


The bearing system which supports the rotor assembly (turbine, shaft and compressor) resides in the turbocharger center housing. That bearing system must reliably position and support the rotor from zero up to speeds that can approach 150,000 RPM. In addition to the rotating loads on the bearings, there can be substantial thrust loads in either direction, depending on operating conditions. The bearing system also has an influence on critical rotor speeds, vibration and shaft instability.

The temperature of the turbo environment also presents a challenge to the bearing system. If the engine is shut down immediately following a run at high power output, the turbine and turbine housing temperatures are toward their upper limits, and suddenly all gas flow through the turbine stops and all oil flow through the center housing stops. All that heat must go somewhere, and an easy path is into the center housing. The resulting temperatures can easily cook the oil to a solid with potentially disastrous results on the next run.

The bearing system has evolved from the early days, when most were hydrodynamic sleeve and face bearings which required uninterrupted oil supply to avoid damage from loss of fluid film and from overheating.

Today's turbos feature dual ball bearing systems with very high bi-directional thrust capacities and reduced frictional drag, allowing faster spool-up times. To combat flat-spotting of bearings during heat-soak, an upgrade in bearing material from 52100 to M2 tool steel is also available.

The centrifugal force at very high speeds can cause steel balls to lift off the inner race, and to skid on the inner race during acceleration. To combat that issue, some manufacturers have switched over to bearings having ceramic balls, and others are moving in that direction. The ceramic ball bearings are also reported to be more resistant to damage from high temperatures.

Garrett Bearing Cartridge

Figure 7
Garrett Bearing Cartridge

Garrett uses an integrated dual ball bearing cartridge (Figure 7) which contains an angular-contact ball bearing at each end, providing a huge bi-directional thrust capacity, and which adds bending stiffness to the shaft system, helping to prevent critical speed issues.

Borg-Warner is developing a two-ball-bearing system which is expected to be fully ceramic.

Turbonetics now provides a ceramic ball bearing at the compressor end of all its turbos.

Some production turbos incorporate liquid-cooling provisions in the center housing to combat lubrication and heating issues, but several turbo suppliers told me that racers don't like the cooled housings because of the added complexity in the racecar. However, liquid-cooled center-housings are very appropriate for turbocharged, liquid-cooled aircraft engines, and have been used successfully in several instances.

There have been applications where compound turbo systems have been used, in which one turbo feeds pressurized air to the engine, and a second turbine downstream extracts more energy from the exhaust system, but instead of running a compressor, it is geared directly to the engine output shaft. That has worked well in aircraft applications, but it presents several complex problems in an automotive application.

Energy Efficiency and Greening

The emerging PC emphasis on 'green' racing provides an excellent opportunity to use a second turbine in the exhaust stream to extract otherwise wasted thermal energy from the exhaust stream and store that energy in a number of different ways, including a KERS-like flywheel, or for an IC-electric hybrid vehicle, to run a generator which charges the battery system.

That would increase the overall thermal efficiency of the powerplant in a real sense, as opposed to the imbecilic notion that electric cars which plug into the wall sockets to recharge their batteries somehow get their energy for free.

The heavy-thinker proponents of such nonsense conveniently overlook the fact that that a huge percentage of available electric energy in the developed world comes from the combustion of petroleum and coal-based fuels, producing huge amounts of the carbon dioxide with which they are so obsessed. (By the way, carbon dioxide was, until recently, known as a gas essential to life. Now, however, in classical PC doublespeak, it has been reclassified as a 'pollutant'.)

While on the subject of 'greenery', it is interesting to note that, in addition to wholesale manipulation of the basis data they use to support the PC thesis of 'Global Warming', and in addition to widespread demonizing and extortion (both financial and professional) of non-confirming scientists, the GW fanatics also conveniently overlook the fact that burning ANY hydrocarbon (yes, Ethanol, C2-H5-OH is a hydrocarbon) produces carbon dioxide and water.

Yet ethanol has been decreed to be envro-friendly, thereby justifying immense subsidies from the delusionals in government to enable the production of ethanol from corn, in the face of undeniable evidence that the net energy balance (energy required to plant, cultivate, grow, and harvest the corn, transport it to the conversion site, convert it into ethanol, and transport it to the blending site, compared to the energy it delivers in an IC engine) IS A BIG NEGATIVE. And there is also no mention of the huge economic impact on the nation's food supply that the diversion of corn crops into ethanol production is having. They also conveniently ignore the huge impact that the production of ethanol from corn is having on the entire water table un the nation's midwest, a major source of our food.

If the government braindeads were actually serious about effectively using ethanol to be an efficient biofuel, they would allow and encourage the production of ethanol from sugar cane rather than corn (a policy being followed in Brazil with great effectiveness).

- Exhaust System Technology-

The Sound and The Fury


All too often the engine exhaust is an afterthought for the engine and chassis builders, yet its design and construction impacts significantly upon car performance. The exhaust system can be a vital tool for optimizing the performance of the engine, through the way in which its design manipulates the pressure waves that can crucially assist cylinder filling and scavenging. On the other side of the coin, the exhaust system presents many challenges. It is a major loss-path for thermal energy; and it can be a car packaging nightmare.

The environment which a competition exhaust system, and particularly engine headers, must survive, can only be described as a brutal combination of temperatures, stresses, corrosion and vibration. Contemporary exhaust technology can help reduce the problems and help to maximize the potential gains of the system.

BMW Formula-One Engine at Full Power

Figure 1
BMW Formula-One Engine at Full Power

It is interesting, from having spoken to several highly-placed and well recognized experts in this field, that while there is general agreement about what features cause improvements to happen, there are varying opinions about the reasons why those improvements occur.


The computation of what actually goes on during an exhaust cycle is a highly complex problem in compressible fluid flow, the details of which are explained in detail in several texts, my favorite being Professor Gordon Blair's Design and Simulation of Four Stroke Engines. For the purposes of this article, the following overly-simplified explanation will serve to illustrate the principles.

There are two separate components to the exhaust event. The first is the removal of exhaust gasses from the cylinder, which occurs as a pulse of hot gas exiting the cylinder and flowing down the header primary tube. The second is the (much faster) travel of the pressure wave in the port caused by the pressure spike which occurs when the exhaust valve opens, and the various reflections of that wave. Taking proper advantage of these pressure waves (component two) can produce dramatic improvements in clearing the cylinder (component one) and can strongly assist the inflow of fresh charge.

Considering component one, when the exhaust valve first opens in a 4-stroke piston engine, the in-cylinder pressure is still well above atmospheric. In a normally-aspirated spark ignition engine burning gasoline and operating at high BMEP, the pressure can be 7 bar or more, and the pressure in the exhaust port at the valve is somewhere near 1 bar (atmospheric). As the valve opens, the pressure differential across the rapidly-changing valve aperture (pressure ratio of approximately 7) starts exhaust gas flowing through the opening, and the outrush causes the pressure in the port (behind the valve) to increase rapidly, or 'spike'.

The instantaneous velocity of the exhaust gas flow at any point is determined by the pressure gradient and the cross-sectional area at that point. In the header, a smaller tube diameter will increase the velocity at a given RPM, which might enhance the pressure wave tuning (the second component) and can be beneficial with regard to inertia effects. However, if the diameter is too small, there will be flow losses and consequent pressure gradient increases which can offset any tuning gains. So the selection of proper tubing diameters is an important part of the design.

In the early part of the exhaust cycle, the pressure difference across the valve is high, so the instantaneous gas particle velocity through the small exhaust valve aperture is very high. Sometime past mid-exhaust stroke, the majority of the exhaust gas has left the cylinder. At that time, the valve aperture area is quite large and the cylinder pressure is approaching atmospheric, which causes the instantaneous particle velocity across the valve to be much lower. It is at that phase of the exhaust cycle where the second component becomes important.

To help with the explanation of the second component, Figure Two shows traces of in-cylinder pressure (black), port pressure at the intake valve (light blue) and port pressure at the exhaust valve (red), taken from a simulation of a high BMEP engine operating near the optimum tuning point for both intake and exhaust.

Intake Port, Exhaust Port and In-cylinder Pressures with Effective Tuning

Figure 2
Intake Port, Exhaust Port and In-cylinder Pressures with Effective Tuning

The second component is the result of the pressure 'spike' which occurs at EVO, shown by the peak in the red line in Figure Two, just after EVO. That pressure spike, or pressure wave, moves down the pipe at the sum of the local sonic velocity plus the particle velocity of the gas flow. Whenever the pressure wave encounters a change in cross-sectional area of the pipe, a reflected pressure wave is generated, which travels in the opposite direction. If the change in area is increasing (a step, collector, the atmosphere), the sense of the reflected pressure wave (compression or expansion) is inverted. If the change in area is decreasing (the end of another port having a closed valve, or a turbocharger nozzle, for example), the sense of the reflected wave is not inverted. The amplitude of the reflected wave is primarily determined by the proportionate change in cross-sectional area (area ratio), but the amplitude is diminished in any case. For purposes of approximation, the particle velocity can be ignored because its effect is self-canceling during the round-trip of the wave. However, highly-accurate simulations must take it into account. These waves are sometimes called finite difference waves, because of the finite difference numerical modeling techniques used to calculate their propagation characteristics.

In the case of the currently-flowing header primary, the EVO-initiated positive pressure (compression) wave is reflected back as a negative pressure (expansion) wave. If the arrival of the reflected negative pressure wave back at the exhaust valve can be arranged to occur during the latter part of the exhaust cycle, the resulting lower pressure in the port will enhance the removal of exhaust gas from the cylinder, and will reduce the pressure in the cylinder so that when the intake valve opens, the low pressure in the cylinder begins moving fresh charge into the cylinder while the piston is slowing to a stop at TDC.

Note in Figure Two, how the cylinder pressure (black) and exhaust port (red) pressures go strongly negative from approximately mid-exhaust stroke to TDC). Note also how the second-order reflected positive pressure wave in the intake tract (light blue) reaches the back of the intake valve just before IVO, and works together with properly-timed exhaust negative pressures to begin moving fresh charge into the cylinder.

If, on the other hand, the negative exhaust pressure wave arrives a non-optimal time, its effects can be detrimental to the clearing of the cylinder and ingestion of fresh charge. A reflected positive wave during overlap (from a turbocharger nozzle, for example) can push a large amount of exhaust gas back into the cylinder and the intake system.

Figure Three shows the same three pressure traces when the engine is operating well above the intake and exhaust tuning points. In addition to reduced breathing efficiency, note the additional pumping losses from the higher cylinder pressure in the latter portion of the exhaust cycle, caused in part by the late arrival of the reflected negative exhaust pulse.

Intake Port, Exhaust Port and In-cylinder Pressures with Poor Tuning

Figure 3
Intake Port, Exhaust Port and In-cylinder Pressures with Poor Tuning

The timing of the arrival of the negative wave at the back (port) side of the exhaust valve is determined by the engine RPM, the speed of sound in the pipe and the distance from the valve to the relevant change in area. Those three factors will cause the exhaust tuning to come in and out of tune over the engine operating speed range. Sophisticated designs can produce systems having more than one tuning point. The most significant example of exhaust pulse tuning is dramatically demonstrated by the operation of crankcase-scavenged, piston-ported two-stroke engines.

At the relevant tuning distance from the exhaust valves, the primary tubes from two or more cylinders are often joined together into a larger collector tube which provides the area increase to generate the reflected waves described above.

Using a 4-into-1 system as an example, the four primary tubes will ideally have the same centerline length and will sharply transition into an area having roughly three to four times the area of the primary.. The larger the cross-sectional area of the collector tube plus the area of all other tubes at the same junction compared to the area of the active primary tube (area ratio), the larger will be the amplitude of the reflected wave. However, the collector has an optimal size: too much area and the wave tuning in the collector will be diminished. The optimal length is related to the number of cylinders feeding into it.

The effect of a straight collector is generally a very peaky tuning, in which the lengths of the primaries can be varied to produce a 'rocking' effect of the torque curve around its peak. Lengthening the tubes raises the portion of the curve below peak and reduces the portion above peak torque; shortening them has the reverse effect. Various strategies have been devised to spread the effect of exhaust tune over a wider RPM band. These strategies typically involve generating additional waves of smaller amplitude (additional, smaller steps, for example) or attempts to increase the width (duration) of the pulse at the expense of pulse amplitude by using a tapered section to extend the area change over a longer period of time.

Figure Four shows one of these devices, known in the States as a 'merge collector'. The primaries converge into a nozzle area which is larger than the primary area but smaller than the final collector size. That keeps the gas velocity up for a bit longer, helping to scavenge neighboring pipes, and the smaller area ratio reduces the amplitude of the reflected wave. The section behind the nozzle tapers up to the final collector diameter, allowing the flow to decelerate with better pressure recovery than would occur with a sharp transition, and extends the width of the reflected wave. The characteristics of the reflected wave can be tuned with different nozzle areas, different final collector diameter and length, and the length of the tapered section. The net effect is usually aimed at boosting a particular portion of the torque curve and at extending the RPM band over which that boost is effective.


Figure 4
A 'Merge Collector'

It is sometimes argued that the speed of sound is a function of pressure, density, temperature, and / or phase of the moon. Actually, the speed of sound in an ideal gas (which air emulates) is a function of the stiffness of the gas divided by the density. When one does the arithmetic necessary to create an equation which uses known parameters, the stiffness and density terms are replaced by equivalents from the ideal gas law, producing the equation: Va (acoustic velocity in meters per second) = square root ( S x R x T), where S is the ratio of specific heats (approximately 1.4 for air at 25°C, 1.35 for exhaust gas at 500°K), R is the gas constant (approximately 287 J/kg-°K for air, 291 for exhaust gas) and T is the absolute temperature (°Kelvin, which is °C + 273).

What that boils down to is that once one has the specific heats and gas constant value for a given gas (or mixture of gasses), the speed of sound varies only with the temperature. To add a bit of complexity, the instantaneous temperature of the exhaust gas varies along the exhaust path, perhaps as much as 150°C in a primary tube.

The next interesting basic is that as the pressure ratio increases across a smoothly-decreasing nozzle, the particle velocity at the smallest cross-sectional area increases with increasing pressure ratio until it reaches the local speed of sound. Once it has reached the speed of sound, no matter how much larger the pressure ratio becomes, the gas particle velocity remains at sonic ('choked'). An increase in the upstream pressure will increase the mass flow rate due to the increased density upstream of the nozzle, but the particle velocity through the nozzle remains sonic.

For air flowing in a smoothly-decreasing nozzle, the pressure ratio which just causes sonic flow (the 'critical pressure ratio') is slightly less than 2.0. For non-smooth and irregular nozzles (an exhaust valve, for instance) the critical pressure ratio is higher, but the effect is the same. That means that, for some period of time after EVO, the gas particle flow velocity across the exhaust valve is at the local speed of sound, which as shown later, is quite high at exhaust gas temperatures.

Again, it should be noted that these explanations are highly simplified. There are several very-high-end engine simulation software packages which are said to model engine performance, including exhaust system phenomena, quite accurately. These models are so sophisticated that they can take into account such esoterica as the local temperature gradients along the primary, secondary and collector tubes. For accuracy, these models rely on accurate engine data, including valve flow coefficients at various lifts. Apparently it is difficult to determine accurate flow coefficient data for the valves, particularly at high pressure ratios, which has a profound influence on the limits of computational accuracy.

That being said, several designers told me that the simulations tend to be less accurate in predicting the various effects of the collector, in terms of the real world effects of geometry, pipe angles, and the like. One approach to that problem has been to use a CFD simulation (a 3-D analysis) for the collectors, and couple those results with the 1-D simulations of the pipes.

Exhaust Materials

Usually, header systems are fabricated from welded-up collections of cuts from pre-formed 'U' bends and straight segments of tubing in the chosen material. There are several reasons for that, but the most persuasive is the fact that, in order to achieve the design configuration, there is not usually ample grip-space between bends to form the pipes from a single piece of tube. In some cases, where the bends are not too closely spaced, the pipes can be bent up in one piece using a mandrel bender which will retain the circular cross section of the tube throughout the bend and transition. The typical exhaust tube bender commonly found in automotive exhaust shops is not suitable for that duty since those benders distort the cross-section of the bends terribly and shrink the cross-sectional area.

Tubing bend radii (the radius of the plan-view centerline of the bend) are expressed in terms of multiples of the tubing diameter. For example, a '1.5-D bend' in 2-inch diameter tubing would have a bend radius of 3 inches. One fabricator described some specialized machinery he had devised for making high-quality exhaust tubing from sheet. The first machine rolls the sheets into straight tube sections of the required diameter. The second machine completes the straight section of tube with a continuous welded seam using a semiautomatic inert-gas-shielded process. A third machine does what had been thought to be impossible: bending 0.50-mm wall inconel tubes into less-than-1-D radius sections while retaining accurate cross-sectional geometry.

There are several materials commonly used in competition header and exhaust systems, depending on the requirements and operating temperatures.

For the most demanding applications, Inconel tubing is commonly used. Although the name 'Inconel' is a registered trademark of Special Metals Corp., the term has become something of a generic reference to a family of austenitic nickel-chromium-based superalloys which have good strength at extreme temperatures and are resistant to oxidization and corrosion. Because of the excellent high-temperature properties, Inconel can offer increased reliability in header systems, and in certain applications, it is the only material which will do. The high-temperature strength properties can enable weight-reducing designs, since, for a given reliability requirement, Inconel allows the use of much thinner-wall tubing than could be used with other materials. The catch, as usual, is that Inconel tubing is quite expensive.

Certain Inconel alloys retain very high strength at elevated temperatures. One of the favorites for header applications is Inconel-625, a solid-solution alloy containing 58% Nickel, 22% Chromium, 9% Molybdenum, 5% Iron, 3.5% Niobium, 1% Cobalt. It has good weldability using inert-gas-shielded-arc processes, and good formability in the annealed condition, and has a lower thermal expansion rate than the stainless alloys commonly used in exhaust systems. Weldability and formability are both important because of the somewhat limited availability of Inconel tubing sizes, which often makes it necessary to form tubing sections from sheet. The yield strength of this alloy at 650 °C (1200°F) is 345 MPa (50 ksi), while at 870°C (1600°F) it is a remarkable 276 MPa (40 ksi). As with many metals, the high-temperature strength diminishes as the amount of time the parts are exposed to extreme temperatures increases.

Inconel tubing is nearly essential in high-output turbocharged applications, and I was told by several knowledgeable players that all the Formula-One cars and a few Cup teams use Inconel for their headers, both for reliability and for weight savings.

One builder told me that some teams are routinely using headers made from 0.50-mm (0.020 inch) wall Inconel tubing. He also told me that, in view of the immense heat load imposed by the exhaust gasses of contemporary Formula One engines, he seriously doubted that a set of stainless headers, even in 1.6-mm wall (0.065 inch), would survive. Figure One, a BMW F-1 engine at full power, graphically illustrates this demanding environment.

There are several austenitic stainless alloys which are commonly used in exhaust systems. In order of reducing temperature capabilities, they are 347, 321, 316 and 304. In addition, special variations in the basic alloy chemistry (carbon, nickel, titanium and niobium) are available to enhance the high temperature strength of these alloys.

Regarding the use of stainless, I was told by a knowledgeable source that in NASCAR Cup racing, the 304 and 321 stainless alloys were used more often than Inconel, depending on the preferences of the various teams. The manager of one prominent team told me that, in view of the facts that thinwall Inconel headers are (a) very fragile and readily damaged by inadvertent mishandling, (b) 'grotesquely' expensive, and (c) provide almost immeasurable gains on a 3600 pound vehicle, his opinion is that the use of Inconel headers is not prudent stewardship of his resources. For a peek at the magnitude of the costs involved, one fabricator told that a single 1-D 'U' bend of 2-inch diameter, 0.032-inch wall Inconel tubing would cost somewhere in the neighborhood of $200, whereas the same bend in 321-stainless would be in the $65 range.

Although titanium has been made to work quite well in exhaust valve applications, the practical temperature limits for titanium alloys suitable for tubing is quoted at about 300 °C (575 °F), which makes that material suitable for lightweight tailpipes in various applications and in certain motorcycle applications as well. My favorite supplier of titanium reports that grades 1 and 2 commercially-pure (CP) titanium have been used for the exhaust systems on competition 2-stroke motorcycles for decades. For lightness, many of these systems were made using 0.50 mm wall tubing, and treated as a consumable, being replaced after every meeting.

One might ponder why the same materials used for titanium exhaust valves are not used for exhaust tubing. Apparently, the simple reason is cost vs. benefit, since the estimated cost of thin sheets of Ti-6242 were estimated at over $150 per pound in large-quantity purchases. Add to that the fact that this material lacks the ductility to be readily formed into tubes, plus the fact that there would be problems welding the seams of a rolled tube, and yet more problems forming the welded straight tubes into bends, and it becomes evident that there are more suitable materials for exhaust tubing use.

Formula One

Recently, I had the opportunity to hold in my tired, worn hands, a primary header tube which was alleged to have been for a nearly-contemporary F-1 application. Pictures of said hardware were not allowed, but the reproduction from memory, shown in Figure Five, illustrates the very interesting feature, the existence of a large-diameter step in the primary, quite close to the flange.

Formula-One Primary Header Tube

Figure 5
Formula-One Primary Header Tube

The illustration shows a single 10-mm step spaced approximately 125 mm from the flange. However, experts say that in 2008, two smaller steps (5 mm each) in the primary are more commonly seen, depending on the research and beliefs of the developers. The first step is typically between 100 and 200 mm from the flange. If there is a second step, it is typically another 100 to 150 mm beyond the first step, and in general, tubing sizes range from about 50 mm to 65 mm. (1.97' to 2.56'), although the specific designs seem to vary dramatically from team to team.

My first impression, which was shared by a number of experts with whom I spoke, was that, since these engines are operating up to 19,000 RPM, then the primary length required to achieve the negative pressure pulse during overlap was so short that, due to packaging constraints, the location of the collector would be too far away from the valves to initiate the properly-timed reflection. However, a bit more thought and a quick calculation revealed quite a different theory.

For purposes of approximation, assume that the mean temperature of the exhaust gas in the primary up near the head is 1500°F (815 °C). The speed-of-sound-in-air equation (close enough for approximations, according to Professor Blair) produces a sonic velocity of 661 m/s (2168 feet per second). At 18,000 RPM, (300 RPS) one crankshaft rotation takes 3.33 milliseconds (ms) or 3333 microseconds (µs). Therefore one degree of crank rotation takes 9.26 µs (3333 ÷ 360). If the first step in the primary is 200 mm from the back of the exhaust valves, then using the calculated speed of sound as an approximation of the propagation speed of the finite pressure wave, the 400 mm round trip from the valve to the step and back takes about 600 microseconds, or 65 degrees of crankshaft travel.

Assume that, in an 18,000 RPM engine, the establishment of enough exhaust valve opening to allow meaningful flow would occur in the neighborhood of 100° after TDC. Therefore, it is clear that this first reflection is timed to arrive back at the valves even before the piston reaches BDC. For what purpose? Recalling that during blowdown, there is sufficient pressure ratio in the cylinder to establish choked (sonic) flow through the exhaust valve orifice, then it would certainly be advantageous to maintain that gas velocity for as long as possible.

A noted engineer in the world of Formula-One confirmed that this is exactly the reason for the one-or-more large-magnitude steps in the primary: to place a negative pressure at the back of the exhaust valve timed so as to extend the duration of the critical pressure ratio.


The required Cup engine configuration (90° V8 with a two-plane crankshaft) provides an interesting challenge for exhaust system designers. Because of the firing order of this engine configuration, the exhaust pulses on each bank of the engine are unevenly-spaced. In the words of the technical director of one prominent team: 'The exhaust system design in Cup is an interesting tradeoff between minimizing flow losses while at the same time trying to optimize whatever tuning you can do with a non-equally-spaced system, which isn't a lot.'

With the GM cylinder-numbering system (1-3-5-7 on the left) and firing order {18436572; the 4-7 swap is not allowed in Cup} ), the exhaust pulse spacing on the left side (expressed in terms of degrees of crankshaft rotation) is 270°-180°-90°-180° while the spacing on the right side is 90°-180°-270°-180°. This uneven pulse spacing gravely impedes the achievement of a well-tuned exhaust system such as can be achieved with evenly-spaced pulses and a 4-into-1 collector.

That tuning difficulty led (more than a decade ago) to the re-introduction of the 4-into-2-into-1 (so-called 'Tri-Y') configuration, which has been around since at least the 1960's. In the 'Tri-Y', cylinders on each bank are paired so as to provide the maximum separation between pulses. Using the above numbering scheme, the primaries of cylinders 1 & 5 and 3 & 7 would be merged into slightly larger secondary pipes, which after the appropriate length, would be merged into the larger collector. On the right side, adjacent primaries are paired (2 & 4, 6 & 8). That provides a 450°-270° separation between pulses in each secondary. An example of this configuration is shown in Figure Six.

Example of a 4-2-1 Header System

Figure 6
Example of a 4-2-1 Header System

The tuning of this type of system is not terribly intuitive. Several well-placed experts in Cup told me that their teams have consumed large amounts of modeling time using very sophisticated (and expensive) simulation software to arrive 'in the ball park', and then fine tune the designs on the dyno. And, as would be expected, there are different header designs for long tracks, short tracks, and restrictor-plate tracks.

One expert mentioned that, while it is relatively straightforward to accurately model the behavior of the primaries, it is very difficult to accurately model the secondaries and collectors, because the theoretical reflections are meaningfully altered by specifics of geometry (bend radii, intersection angles, nozzle and diffuser angles, etc.) which cause destructive interference and pulse attenuation. That being said, several experts agreed that the rules-of-thumb still apply: better low end needs smaller and longer tubes; better high end needs bigger and shorter tubes.

There are additional challenges in Cup header design and tuning. The chassis teams often impose a major set of constraints on primary length and bend location so as to not interfere with critical items such as upper control arm pivot locations. The prevailing view is that, in terms of lap times, making the car turn better is a reasonable trade-off against a small amount of power increase. The straightforward header shown in Figure Six simply to illustrate the concept, is a dyno header, built almost without regard for any packaging constraint. Consider how difficult it might be to implement that concept within the very tight engine compartment of a Cup car, constrained by intruding frame tubes, suspension pickup points, a 230-mm long external oil pump, and the like.

Given the existing packaging constraints, it is indeed fortunate that the primary lengths in the 4-2-1 system are not nearly so critical as are the lengths of the secondaries. Several experts told me that the engines are very sensitive to changes in the length of secondary sections, and that most of the development effort is focused on secondary merge, length, diameter and step issues.

Moving rearward, the NASCAR Cup rulebook provides some interesting insight into additional exhaust system challenges. The rules include the requirements that the exhaust system for each bank of the V8 engine must be completely separate and may not connect in any location except for a single 'X' or 'H' pipe in a tightly-constrained region of the tailpipes, and must end with two tailpipes which exit under the frame rails within a tightly-constrained area on the right side of the car. Further, the pipes from the collector to the exit must be magnetic steel, no larger than 101.6 mm (4.0 inches) ID, and may have a circumference no greater than 336.5 mm (13.25').

The circumference restriction provides a subtle challenge. In order to fit beneath the COT frame and still provide ground clearance, the large diameter tailpipes are reshaped into a cross-sectional form having two long parallel walls (no closer to each other than 51 mm ) and a full radius at each end, such as illustrated in Figure Seven.

NASCAR Under-Frame Exhaust Pipe Exit

Figure 7
NASCAR Under-Frame Exhaust Pipe Exit

Because of the fact that a circular section provides the most cross-sectional area for a given circumference, the necessary ovalling of the pipe exit puts an orifice at the end of the tailpipe. If the exit section is the minimum height of 51 mm, the limiting circumference (assuming 1.6 mm-wall tube) yields a cross-sectional area which is only 77% of the 101.6 mm round tailpipe. That reduced area can be a flow restriction at high RPM.

Top Fuel and Funny Car

At the top levels of drag racing, in particular Top Fuel and Funny-Car, the exhaust systems might seem very simple. The header systems, known as 'zoomies,' consist of a single pipe on each cylinder, dumping straight into the atmosphere, with each tube bent so that it faces upward, rearward, and often outward. The outward angle of bend in Funny Cars is typically larger than would be seen in an unbodied Top Fuel car, in order to eliminate bodywork damage from both temperatures and exhaust concussion forces.

In addition to the noise, a notable feature of these exhaust systems is the large volume of open, whitish flame standing just off the ends of these pipes, as shown in Figure Eight. That flame-front is the byproduct of two intersecting parameters.

Secondary Combustion

Figure 8
Secondary Combustion

First, these highly-supercharged, nitromethane-nourished engines have fuel flow rates stated to be in the 80 to 90 gallon-per-minute range. With that amount of fuel being delivered, it is clear that there will be a certain amount of fuel puddling behind the intake valve. When the intake opens, some portion of that collected fuel will be either in liquid form or in a mixture which is too rich to burn (insufficient oxygen molecules). Further, these engines apparently use a large amount of overlap in order to assist in cooling. The combination of the excess fuel and the long overlap assures that a non-trivial quantity of raw fuel and fuel mixture is short-circuited directly down the exhaust pipe, and heated during its journey. When it exits the primary, it finds an abundance of oxygen and initiates an energetic secondary combustion. The combination of the large momentum-change of the mass flow through the engine, plus this secondary combustion has been calculated by at least one aerospace engineer to generate normal reaction forces in excess of 2500 pounds (1130 kg).

Given that the pipes are angled in both the lateral and longitudinal planes, that exhaust reaction force can dramatically affect the vehicle stability. The vertical component obviously provides downforce to the chassis. The rearward component will add propulsive thrust. If everything is in balance, the sideward components generated by the left and right sets of pipes should counterbalance and net to near zero. However, I was told that the loss of one cylinder on a Funny-Car can cause the driver to have real difficulty controlling the car. That is because the loss of a single cylinder unbalances the sideward-thrust and adds a yaw-moment from the now-asymmetric rearward thrust. That same (highly-credible) source told me that the loss of two cylinders on the same bank will amost certainly render the car uncontrollable.

As might be expected, the length of the primaries plays a critical role in the engine tune. I was told by a lead engineer on a prominent Funny-Car team that there was a considerable amount of development effort required just to get the gasses out from underneath the Funny-Car bodywork.

That source also said that when they tried collector-systems, the result was that the engines ran 'horribly'. The theory is that the huge amount of exhaust gas flow into a relatively-confined space raised the collector pressure enough to create a destructive blockage in the collector pipe.

As far as the pipes themselves are concerned, it is well known that 'too sharp a bend' in the primary or 'too much length' dramatically reduces engine performance. Apparently, in supercharged nitromethane engines, any tuning on the exhaust side (cam, ports, headers) requires a substantial alteration in the fuel delivery curves. After experimenting with various exhaust system changes, then working to get the fuel system back into line with the engine changes, the net change in performance was typically considered to be not worth the time and effort. After having determined a working combination, experience has shown that development efforts in areas other than the exhaust system will be more productive.

I was told that currently, there is not a large amount of development effort on the Funny Car exhaust system, as the result of several practical and economic factors. It is hard to imagine the level of difficulty involved in doing engine development on a system which is not well suited to a dyno cell, and therefore must be tested on the track in 5-second test sessions. Without taking into account salaries, logistics, transportation, food, lodging, and other 'overhead' expenses, the out-of-pocket cost to make 'one more test run' is uncomfortably close to ten thousand dollars.


Neil Spalding, Race Engine Technology's in-house expert on motorcycles, provided me with a gallery of detailed photos showing the varied strategies employed in Moto-GP (the F-1 of motorcycle racing) to shape the engine power curves with exhaust tuning finesse, along with a wealth of information on these machines, including the fact that the use of Inconel tubing is fairly common.

In several RET articles, Neil has discussed the difficulty in getting the available power to the ground in Moto-GP, and the efforts which the manufacturers have taken to improve the available traction, including implementation of uneven firing orders so as to affect the tire contact patch in a beneficial way. The uneven spacing of exhaust pulses requires some out-of-the-box thinking to gain benefit from exhaust tuning. In order to linearize the engine power curve (flatten the torque curve) there has been widespread usage of the 4-2-1 design described above in the Cup section.

These systems use various techniques specific to the particular engine, including diverging tapers in the primary tubes just past the flange, steps in the primary tubes, converging-diverging collectors, straight collectors, diverging tapered collectors, and more.

Figure Nine shows the torturous 4-2-1 system developed for the 2005 Yamaha 990 cc irregular-fire inline 4. The picture shows the diverging taper in the primary just past the flanges. Neil told me that the current system for the 800-cc engine has substantially shorter primaries and secondaries due too the fact that the 800 cc engines turn up to 18,000 RPM, where the 990's were in the 16,000 RPM range.

2005 Yamaha 990

Figure 9
2005 Yamaha 990

Figure Ten shows the individual stacks used on an experimental Kawasaki 990 cc engine, which reportedly had a flat-plane crankshaft but which fired pairs of cylinders together. Note the very long tapered expansion pipes and reduced exit diameters, which will help reduce the extreme power-curve peakiness that occurs when a primary opens directly into the atmosphere (which constitutes an apparent infinite expansion area ratio). Note also how the lower tube has a longer centerline length and a longer tapered end. That too will help to spread the potentially very peaky tune of these pipes over a wider RPM band.

2005 Experimental Kawasaki 990

Figure 10
2005 Experimental Kawasaki 990

Turbocharged Applications

According to the turbocharger engineers, the most important aspect of designing a good header system for a turbocharged application is to maximize the recovery of exhaust pulse energy. This energy recovery has at least two components.

The first is to provide evenly-spaced exhaust pulses to the turbine. To accomplish that, it is helpful first to be working with an engine (or bank of an engine) which has evenly-spaced firing intervals. In an application in which the cylinders feeding a given turbine or turbine section have even spacing, the lengths of the primary tubes should be as close to equal length as possible.

The second component is to maximize the recovery of pulse velocity energy. For that purpose, turbine housings are available in split housing, or 'twin-scroll', configurations, in which there is a divider wall in the center of the turbine nozzle housing to separate the incoming flow into two separate streams. That allows the nearly ideal pulse separation of 240 crankshaft degrees to be achieved on an inline-6 engine by grouping the front 3 cylinders into one side of the housing and the rear three cylinders into the other side. The same effect can be achieved on a V6 engine by grouping each bank separately.

Although the split housing arrangement adds wetted area (hence boundary layer drag) to the gas flow, the advantages more than offset that drag increase. In instances where pulse energy recovery has been optimized, it is often possible, based on calculations using pressure and temperature losses across the turbine, to observe very high turbine efficiencies, which some experts say are in excess of 100%.

Pulses which are evenly-spaced but too close together will reduce the effectiveness of this pulse energy recovery. Apparently, that phenomenon is seen on even-fire inline 4-cylinder engines as well as on individual banks of flat-crank V8 engines, where the pulse separation is 180°. I was told that the ideal pulse separation was in the neighborhood of 240 crankshaft degrees, and that, on an even-fire (single-plane crankshaft) inline-4 (as opposed to the two-plane crankshafts used in some Moto-GP motorcycle engines) it is better to separate the end cylinders into one side and the center two into the other side of the turbine than to run all four together into an undivided scroll housing. The same reasoning applies to each bank of a V8 with a single-plane crankshaft.

With regard to the uneven pulse spacing of each bank of a two-plane crank V8, there is agreement that it is very difficult to organize the pulse spacing in a useful way. It has been demonstrated that where a small turbo is used on each bank, the use of a short-tube 4 into 2 system (same idea as the 4-2-1 discussed above) feeding a twin-scroll turbine could take some advantage of the resulting 450 - 270 separation in terms of pulse energy recovery. If a single, large turbo can be located in such a way that the tubing lengths from each bank can be fairly equal, then splitting the primaries to achieve 180° separation would be an advantage.

Whenever practical, reducing the heat (energy) losses before the exhaust gasses reach the turbine allows the turbine to be more effective. This has been done with double wall tubing, reflective coatings, and wraps. However, insulating the pipes to reduce heat loss will, of course, raise the operating temperature of the pipes themselves, which can require extreme-duty materials where more affordable materials would suffice in the un-insulated form.

Another important exhaust system consideration, in order to provide the most effective operation of the wastegate in controlling boost, is to position the wastegate inlet port so that it is subject to exhaust stream total pressure, rather than off to the side where it sees only static pressure.

- Torsional Output of Piston Engines -

The torsional pounding that piston engines apply to the stuff they run

In order to design machinery which will be driven by piston engines, it is necessary to understand the nature of the output those engines produce. Unlike a turbine or an electric motor, a piston engine does not produce a smooth output, but a very 'lumpy' one, the degree of lumpiness depending on the number of cylinders and the evenness of the firing order. The following subsections present an explanation of piston engine torsional excitations.

Piston engines are often referred to as 'Internal Combustion' (IC) engines, which is something of a misnomer. The 'IC' really stands for INTERMITTENT COMBUSTION.

As a result of that intermittent combustion and the piston motion described on a previous page, a piston engine is a vibration machine. It generates horizontal and vertical shaking vibrations, fore and aft rocking moments, and torsional excitations galore. The torsional component of the output is the subject of this discussion.


Consider how a 4-stroke piston engine operates. During each 720° of crankshaft rotation, each cylinder in a contemporary 4-cycle piston engine produces a torque output during roughly 140° of crankshaft rotation, and requires torque input during the remaining 580° of rotation. The general shape of this instantaneous torque characteristic is well-known and is illustrated in Figure 1.

Single Cylinder Instantaneous Torque Characteristic

Figure 1

Notice that the peak value of torque output is approximately 15 times greater than the mean torque output of the engine (the torque which the dynamometer measures). Also notice that the torque curve contains a negative peak (valley) which is nearly 5 times the mean engine torque. Kind of impressive that your lawnmower engine stays together, isn’t it?

Now, let’s examine the torque characteristics of various configurations of multi-cylinder engines. The following charts are representative of full throttle operation of various engine configurations, and show the waveform of the torque curve which each engine applies to whatever is connected to the crankshaft output flange. The torque values are displayed as a percentage of mean torque.

These charts were prepared by mathematically superimposing the single-cylinder data shown in Figure 1 in order to show the effect of various engine layouts. Be mindful, however, that although these curves were mathematically generated, they do not represent some form of engineering fantasy. They bear a remarkable similarity to actual data we have taken from instrumentation installed across the load cell on an engine dynamometer.

On any given engine, the shape and amplitude of the signal can vary from those shown, depending on the specific details of engine. However, the fact remains that piston engine output consists of peaks and valleys, and the peaks greatly exceed the measured torque of the engine.

You may notice that, in general, as the number of cylinders increases, the peak amplitudes decrease and the waveform tends to become more approximately sinusoidal.

This section presents 'even-fire' engines as well as a few common 'odd-fire' engines. An even-fire engine is one in which the firing of each cylinder is separated from its predecessor by the same angular travel of the crankshaft. An odd-fire engine is one in which each cylinder fires at a different rotational spacing from its predecessor. Odd-fire engines are interesting because they produce more complex excitation resulting from the uneven pulse spacing and also because closely-adjacent pulses couple in unexpected ways, which can raise the amplitudes of the excitations and of the harmonics.


In a standard inline or horizontally-opposed even-fire four-cylinder engine, one cylinder fires every 180° of crankshaft rotation. The waveform in Figure 2 the instantaneous torque curve for an even-firing 4-cylinder engine, measured at the output flange of the crankshaft.

Four Cylinder Instantaneous Torque Characteristic

Figure 2

Note that the waveform in Figure 2 contains two torque peaks which are nearly 300% above mean torque, and two torque valleys which are about 200% below mean torque. This waveform is an example of 'second order' excitation, because there are two complete up-and-down torque pulses (cycles) per rotation of the crankshaft.

Note that this waveform approximates a sawtooth, and there is a small negative 'blip' at the bottom of the valley, which means that the engine output contains a complex mixture of harmonic orders. The shape of the waveform and the torque reversals make it quite apparent that the metal-prop designers have done an amazing job.


In a standard 6-cylinder engine with inline, horizontally-opposed, or a 60° V layout, one cylinder fires every 120° of crankshaft rotation. (One variant of the GM 90°-V-6 has a split-pin crankshaft which incorporates a 30° offset between adjacent rods to implement an even 120° firing spacing). Figure 3 shows the torque waveform of an even-fire 6-cylinder engine, which is a 'third-order' excitation, one which has three peaks per revolution.

Six-Cylinder Instantaneous Torque Characteristic

Figure 3

Note that, as a result of more closely-spaced power pulses, the amount that the peaks exceed the mean is less than in the 4-cylinder example, and although the valleys still dip below zero, the negative amplitude is reduced. Also notice that the waveform still resembles a sawtooth curve, and has some irregular shaping in the negative-pulse valley, indicating the presence of complex harmonics.


An example of an odd-fire engine is the GM 90°-V6 with the 'common-pin' crankshaft (conceptually, a small-block Chevy V8 with cylinders 3 and 4 cut out). This version of the V6 is often used in performance applications because the common-pin crank is quite a bit stronger than the split-pin crank used in the even-fire GM 90°-V6 engines..

With this layout, the firing impulses are unevenly spaced and occur at crankshaft rotation intervals of 150°-90°-150°-90°-150°-90°. This engine produces a complex mixture of torque excitation, as shown in Figure 4.

Six-Cylinder Odd-Fire Instantaneous Torque Characteristic

Figure 4

From a torsional standpoint, this engine is terrible. It exhibits adjacent-pulse coupling, uneven spacing between adjacent peaks and significant dips into the negative torque range. This particular curve contains large excitation components of the 1.5, 2.4 and 4th order (and others) which can be difficult to suppress. High-output odd-fire V-6’s have been known to shatter the strongest of dynamometer driveshafts in a rather short time.


In a standard layout V8 engine, one cylinder fires every 90° of crankshaft rotation. Figure 5 shows the instantaneous torque characteristic of this type of engine. This is a 'fourth order' excitation, which at an 800 RPM idle, produces 53 pulses per second (Hz), and at 5000 RPM, produces 333 pulses per second (Hz).

Note that in this layout, as a result of the closely-spaced power pulses, the valleys do not dip below zero.

Eight-Cylinder Instantaneous Torque Characteristic

Figure 5

Figure 5 shows the peak torque amplitude to be roughly twice the mean torque of the engine. This particular engine produces a mean torque of 625 lb.-ft. at a specific RPM, but at that mean torque value, the instantaneous torque peaks are about 1235 lb.-ft. and the valleys are about 68 lb.-ft. Note that the waveform still has somewhat of a sawtooth appearance, although more rounded than previous examples.


In a 60° V-12, 120° V12, or horizontally opposed 12-cylinder engine, one cylinder fires every 60° of crankshaft rotation, producing six power pulses per crankshaft revolution. Figure 6 shows the instantaneous torque characteristic of this type of engine. Note that in this layout, as a result of even-more-closely spaced power pulses, the peaks only extend about 40% above mean and the valleys extend only 40% below mean.

Twelve-Cylinder Instantaneous Torque Characteristic

Figure 6

This waveform is the type generated by the Allison and Merlin V-12's which powered a significant number of successful WW2 aircraft (P-38, P-39, P-40, P-51, P-63, Spitfire, Hurricane, Lancaster, etc.).


Certain examples of odd-fire engines exhibit an unexpected characteristic: when one cylinder follows its predecessor very closely, the successor pulse combines with its predecessor pulse to produce a single larger torque pulse, and the output waveform changes to the order of an engine with half the number of cylinders. Therefore the excitation frequency is half what an evenly-spaced engine with the same number of cylinders produces, and the amplitude is considerably greater.

A specific example of that phenomenon is the V-12 engine being used in a certain warbird replica. That odd-fire engine is, in essence, a pair of in-line six-cylinder engines, physically separated 90° from each other, sharing a common 120° crankshaft. It has a 90°-30°-90°-30° firing impulse spacing, which produces the output waveform shown in Figure 7.

Twelve-Cylinder Odd-Fire Instantaneous Torque Characteristic

Figure 7

Notice how the cylinder which follows its predecessor by only 30° combines with the predecessor to produce a 3rd order wave-form instead of the expected 6th order of an even-fire V-12.

The torque peaks of this engine are nearly 250% of the mean torque instead of the 160% commonly expected from an even-fire V-12 (Allison, Merlyn, etc. as shown in Figure 6), and the valleys extend below zero. Also notice that the pulse shape looks less like a sine wave and more like a sawtooth wave. This shape suggests that there are some complex harmonic components in the excitation.

The substantial difference between this engine and an even-fire V-12 could lead to some very unpleasant surprises if the PSRU system was not designed with the torque signature of this specific engine in mind. The saving graces, in this case, might be the fact that (a) the PSRU on this particular engine is a knockoff of the Orenda™ PSRU, which is extremely hefty, but has begun to exhibit problems in service above 150 hours, and (b) the V-12 package is delivered with an MT 4-blade composite prop, which is quite forgiving of large amounts of torsional excitation. Only accumulated service will show whether this PSRU is up to the job. We have seen several of these PSRU's apart for inspection and repairs after only 100 or so hours. Some of the results were not very encouraging.

- The Definitive V8's -

NASCAR Cup and FIA Formula One engines:
How do they compare?


At the end of the 2006 competition season, both NASCAR Cup and FIA Formula One engines had reached pinnacles of crankshaft speed for their respective classes of motorsport: 10,000 and 20,000 RPM respectively. Although operating at these RPM levels has since been outmoded by regulation (NASCAR’s ever more stringent use of its ‘gear rule’ and the FIA’s 19,000 RPM rev limit introduced in 2007, reduced to 18,000 RPM for 2009), it seemed interesting to compare these very different engines to see what, if any, areas of commonality might exist.


In order to establish a backdrop for this article, the next few paragraphs give a brief sketch of the highlights of both engines.

A Formula One engine is certainly one of the most refined, developed, sophisticated pieces of machinery on the planet. It is a purpose-built, pure race engine, in a 90° V8 configuration, with 2.4 liters (146.4 cubic inches) of swept volume. There are fundamentally few restrictions on the implementation. Those few restrictions include the 2.4-liter, 90° V8 configuration with a 180° crankshaft, 106.5 mm bore spacing, 98 mm maximum bore, no variable-length inlet pipes, no metal-matrix composite materials, 58 mm minimum crankshaft height, and one injection nozzle per cylinder. The engines are DOHC, four-valve-per-cylinder layout with finger-followers and pneumatic valvesprings, with the ignition and fuel injection systems controlled by a sophisticated engine-management digital computer system. The engine weight is a minimum of 95 kg (209 lbs) and a center of gravity height restriction further influences the characteristics of the overall package.

The FIA required that each car must use the same engine for two consecutive practice-qualifying-race meetings or be penalized, so the design life of a 2006 engine was in the region of 1350 km (840 miles).

At the end of the 2006 season, Formula One engines typically used a 20,000 RPM redline (sometimes even throughout the course of a Grand Prix), and produced a peak power of about 755 BHP at above 19,000 RPM, with a peak torque of about 214 lb-ft (290 nm) at 17,000 RPM. Those levels of power and torque are 315 BHP/liter and 15.2 bar of BMEP respectively.

NASCAR 'Cup' engines, by comparison, are the opposite end of the regulation spectrum. Not only are they more tightly restricted with regard to allowable parts, materials, dimensions, component minimum weights, etc, they must be derived from a (nominally) production-based, iron-block, 90° V8 with pushrod valve actuation, two valve wedge heads and a single four barrel carburetor. These engines are subject to various parameters imposed by NASCAR upon the four competing manufacturers in addition to those in the published rule book.

Of particular note, the Cup V8 is restricted to a 106.3 mm (4.185 inch) maximum bore, a 5.86 liter (358 cubic-inch) maximum swept volume, a 90° crankshaft, steel conrods, a single valley-located camshaft, flat tappet cam followers of no more than 22.2 mm (0.875 inches) diameter, pushrod & rocker-arm valve actuation using steel pushrods and aluminum or steel rockers, (approved) aluminum cylinder heads with two valves per cylinder using steel helical valvesprings, a single four barrel carburetor based on a specified Holley model and a single, distributor-controlled ignition. Engine weight is approximately 260 kg (575 lbs).

Each car must, by regulation, use the same engine for one complete race meeting (practice, qualifying and the race) or be penalized. Races are typically 300 – 500 miles in length, so the design life of an engine is up to 800 miles.

At the end of the 2006 season, Cup engines made peak power of about 820-830 BHP at about 9000 RPM, and peak torque of about 520 lb-ft at about 7500 RPM. During a typical oval race, these engines continuously cycle between about 7000 and 10,000 RPM. (I have it on very reliable authority that, if it were not for the final drive gearing rule, today’s Cup engines would be operating close to 11,000 RPM.)


On the basis of the ratio of BHP to displacement, one might argue that the Formula One engine is vastly superior (315 BHP per liter versus 140 BHP per liter). However, given the design latitude, which allows the Formula One engine to operate well at 20,000 RPM, perhaps there are better criteria by which to compare these engines.

The remainder of this article examines several other criteria to compare the performance of these two engines.

The table at the end of this article lists those criteria and other relevant numbers in a side-by-side format, with line numbers for each item, in order to make frequently-occurring references in the text easier to spot.

The basic dimension, weight, power and torque figures were obtained from engineers operating in the respective fields and supplied under condition of anonymity.


Two of the most accepted performance-comparison yardsticks are Brake Mean Effective Pressure (BMEP, explained HERE) and Mean Piston Speed (MPS, explained HERE).

The BMEP of the Formula One engine at peak torque (table line 13) is 15.17 bar while the Cup engine produces a peak torque BMEP of 15.12 bar (0.3 % less).

At peak power, the Formula One BMEP value (table line 22) is 14.6 bar while the Cup figure is 14.0 bar (4.1% less).

It is evident that producing 15.17 bar BMEP at 17,000 RPM and 14.6 bar at 19,250 RPM are remarkable achievements, given that the ratio between Friction Mean Effective Pressure (FMEP) and BMEP is much higher at Formula One than it is at Cup RPM.

However, it is astonishing that the Cup BMEP (remember, flat-tappet cam, pushrod / rocker arm, two-valves-per-cylinder, single carburetor) is only 0.3% less than the Formula One figure at peak torque, and only 4.1 % less than Formula One at peak power.

Even more revealing, at peak power RPM (table line 19) the Formula One engine MPS (table line 23) is 25.5 m/s (5025 ft/min), while that of the Cup engine is less than 3% lower at 24.8 m/s (4875 ft/min). At redline, the Formula One MPS is 26.5 m/sec, while the Cup MPS is a stunning 27.5 m/sec. To put those numbers in perspective, Professor Gordon Blair wrote (Race Engine Technology, issue 27) that 26.5 m/sec was the highest he had seen.

While being cautious with empiricisms, it is interesting to compare the nondimensional values of BMEP x MPS (bar x m/sec) at peak power (table line 24) and at peak torque (table line 15).

At peak power, the Cup engine value is only 7% less than the Formula One engine, again showing the remarkable performance extracted from this production-based V8. There is a bigger disparity at peak torque (nearly 9%), largely due to the greater spread between peak power and peak torque in the Cup engine (15% of redline versus 11% of redline for the Formula One engine).


The net acceleration imposed on a piston is actually the sum of two independent curves: primary and secondary accelerations, shown in Figure 1 below and explained more fully HERE.

Piston Accel Components

Figure 1 - Piston Acceleration Components

The primary acceleration (the blue line in Figure 1) is a first-order curve, based on crankshaft angular velocity squared, crank angle and stroke length, while the secondary acceleration (the green line in Figure 1) is a second order curve based on crankshaft angular velocity squared, twice the crank angle, and rod / stroke ratio.

While the primary component of piston acceleration has equal magnitude but opposite sign at top and bottom, the secondary component (that which is generated by virtue of the side-to-side motion of the conrod) has a positive sign at both top and bottom, as shown by the green line. Therefore at TDC the secondary peak adds to the primary peak, while at BDC, the secondary peak subtracts from the primary, as shown by the magenta line.

Figure 2 below is a graph of piston velocity and acceleration profiles for both engines at redline (table line 28), 20,000 and 10,000 RPM respectively.

Piston Velocity and Acceleration

Figure 2 - Piston Velocity and Acceleration Comparison

There are several items of interest here. The first (perhaps surprising) is that although the Formula One redline crankshaft speed is twice that of the Cup engine, the peak piston speed (table line 30) for the Cup engine is actually 5% greater than that of the Formula One engine at redline (44.6 m/sec vs. 42.4 m/sec), as shown graphically by the yellow (CUP) and teal (F1) lines in Figure 2.

Because the Formula One engine has a greater rod length / stroke ratio (2.56 vs. 1.91, table line 5), the Formula One peak piston velocity occurs at 79.5° before and after (b/a) TDC, (closer to mid-stroke) whereas, the Cup peak occurs at 76.5° b/a TDC.

The rod / stroke ratio noticeably affects the shape of the acceleration curve in the region of BDC. Note that the Formula One curve reaches peak negative acceleration at BDC, while the Cup curve is essentially flat for 26° either side of BDC.

Even though the center-to-center distance on the Formula One rod is only 102 mm (4.016 in), the large rod / stroke ratio (2.56) produces a relatively small secondary acceleration component. That is helpful, since with a flat-plane crankshaft, the secondary accelerations produce a considerable horizontal shake.

Assuming no piston pin offset, the maximum positive piston acceleration occurs at TDC. The reciprocating assembly exerts the greatest tensile force on the rod at TDC-overlap cycle because there is virtually no cylinder pressure to offset the acceleration force, whereas at TDC-combustion, the cylinder pressure is approaching its maximum value of roughly 85 – 90 bar, which will completely cancel the tensile acceleration force and produce a large compressive load on the rod.

The large difference in Peak Piston Acceleration (PPA) between Formula One and Cup is in the direction one would expect given the crankshaft speed values. At redline, the Formula One PPA is 10,622 g compared to the Cup value of 5821 g. Note that the PPA at redline (table line 31) for the Formula One engine is 82% greater than that of the Cup engine, while both the peak and mean piston speeds (lines 29 & 30) are fairly similar for both engines.

However, comparing the force levels that those acceleration values produce is revealing. The Formula One piston package (pistons, rings, piston pin, circlips) weighs roughly 295 grams (lines 33-35). At 20,000 RPM, the PPA causes a tensile load on the piston pin bore of the conrod (table line 41) of 10622 g x 0.295 kg = 3133 kg (6894 lb), and the piston package plus the reciprocating portion of the conrod exerts a 4036 kg (8880 lb) tensile load on the cross section of the rod beam (table line 42) at the CG (approximately 1.23 inches from the big end center).

In comparison, the Cup piston package (pistons, rings, piston pin, circlips) weighs about 500 grams (lines 33-35). At 10,000 RPM, the PPA causes a tensile load on the piston pin bore of the conrod (table line 41) of 5821 g x 0.50 kg = 2911 kg (6403 lb), only 7% less than the Formula One value. Similarly, the piston package plus the reciprocating portion of the conrod exerts a 3725 kg (8196 lb) tensile load on the cross section of the rod beam (table line 42) at the CG (approximately 1.66 inches from the big end center), only 8% less than the Formula One engine.


In order to do a rough comparison of the conrod stress and deflection levels, I generated estimated models of the two conrods. Since I have not been privileged to view conrods from either engine, I used some known data about the Cup and Formula One rods (length, weight, material, crankpin diameters, and piston pin diameters) plus a few educated guesses.

The Cup rod material is required be steel, and I have been told that the 300 ksi, very-high toughness 300-M alloy is used frequently, although the use of a high nickel, high cobalt, very low carbon 350 ksi maraging alloy has been hinted at. It has an ‘H’-beam configuration, a ballpark centerline length of 157.5 mm (6.2 inches), crankpin diameter of 47 mm (1.85 inches) , piston pin diameter of 20 mm (0.787 inch) , and a minimum specified weight of 525 grams.

It has been publicly stated by one well-known supplier of such rods that a suitably strong and stiff rod can be made at well below the minimum weight. Therefore, it is safe to reckon that material has been added to the rod where it can be of most benefit.

One of the areas of greatest deformation under load is the ovalling of the piston pin bore under tensile load, which pinches the piston pin and thereby adds to the friction losses. A lighter beam section is adequate for the applied tensile, compressive and buckling loads. Therefore, to reach the minimum weight of 525 grams, I guessed the existence of stiffening ribs around the piston pin bore.

The same reasoning was applied to the Formula One rod. I have been told that the Formula One rod is an ‘H’-beam layout in titanium, with a centerline length of 102 mm (4.016 inches), 34 mm (1.34 inches) crankpin diameter, 18 mm (0.709 inches) piston pin diameter, and a stated weight in the 285 gram vicinity.

Since the stiffness of titanium alloys is roughly half that of steel, I assumed the use of the high strength, high-modulus 6Al-2Sn-2Zr-2Mo-2Cr-0.25Si Alpha-Beta titanium alloy to design our estimated Formula One rod. That material has a high Young’s modulus (17.7 million) compared to other titanium alloys, and a middle of the road density, which allows for lots of material (good stiffness) while maintaining low weight. The existence of piston pin stiffening ribs was also assumed for this rod, for the same reasons as for the Cup rod.

The resulting estimated designs are shown in the following picture (Figure 3). Having those estimated models allows the estimation of the reciprocating (small end) and rotating (big end) weight components of each rod, leading to a comparison of the loads applied to the rod beam and crankpin by the two engines.

Con Rod Comparison

Figure 3 - Estimated F1 and Cup Rods

Although the applied tensile loads are greater in the Formula One engine (table line 42), the calculated tensile stress on the rod beam (table line 44) is substantially less in the Formula One rod because of its larger cross sectional area (0.429 in² vs. 0.299 in² in the CAD models). The lower stress level in the Formula One rod reduces the TDC stretch of the less stiff titanium, and helps the rod live with the much lower ultimate, yield, and endurance limit of the titanium material as well.

However, the beam tensile and compressive stresses on both rods are not nearly as great as the stresses around the pin eye and the cap ribs. Within the time constraints placed on the generation of this article, I was able to do a few FEA studies of both rods. All the studies assumed extreme-strength, 8 mm rod bolts and used 8000 pounds of preload in each bolt, to provide a substantial cap-to-rod clamping margin.

Those studies showed that

  1. At max compressive load, the stresses and buckling margins in both rods are acceptable (although “I” beam rods have considerably more buckling margin at the same loads than “H” beam rods of similar cross section),
  2. At max tensile load, the stresses are acceptable and have margins from the respective endurance limits suitable for their design lives, and
  3. The stresses in the rod bolts are very high (over 180,000 psi) but with such a high preload, they are non-cycling, so probably not subject to fatigue failure.

The studies also showed that with both rods, more optimization in terms of moving material from lower-stressed areas to higher-stressed areas would yield more rigidity and lower stresses in critical areas. The two FEA pictures (Figures 4 and 5) show the stresses for the assumed Formula One and Cup rod configurations.

F1 Rod FEA

Figure 4 - F1 Rod FEA

Cup Rod FEA

Figure 5 - Cup Rod FEA


Stepping back to fundamentals for a moment, we know that the potential power any engine can produce is directly dependent on two factors:

  1. The mass of air it can ingest per second, and
  2. The BSFC it can coax from the fuel.

The mass airflow parameter encompasses elements including bottom-end design (RPM capability), runner, port, valve and chamber design, cam profile and valvetrain design, and others.

The BSFC parameter encompasses elements including the heat content of the fuel, best-power air-fuel ratio, thermal efficiency, mechanical efficiency, mixture homogeneity, mixture motion, chamber design, combustion quality, and others.

Mass airflow is dependent on:

  1. Air density and
  2. Volumetric efficiency (VE).

At 100% VE, the volume of air a four-stroke engine can ingest is proportional to: RPM x Displacement ÷ 2. To express that potential airflow, I will define the term Potential Airflow Number (PAN) as:

PAN = (rpm / 1000) x (displacement ÷ 2)

It is revealing to examine the relationship between power produced and potential airflow. Using the potential airflow as expressed by the PAN, I can generate an empiricism which clearly expresses that relationship. Let's name it Engine Performance Coefficient (EPC) because it provides another basis (in addition to BMEP, BSFC, MPS and BHP/Cubic-Inch) for comparing one engine to another. That factor (EPC, table line 9) encompasses all the engine design variables .

EPC = Peak Power / PAN

Combining terms and rearranging the equation produces:

EPC = (Peak Power x 2000) / (rpm x displacement)

At peak power, the Formula One engine EPC is:

EPC = 755 x 2000 / (19,250 x 146.46) = 0.536

Likewise at peak power, the NASCAR Cup engine EPC is:

EPC = 825 x 2000 / (9000 x 357.65) = 0.513

It is very revealing to consider that the EPC figure for the Cup engine is only 4.3% less than the F1 engine. Again, remember the limitations imposed on the Cup engine. Some of the most severe are the pushrod / rocker arm valvetrain, two-valves per cylinder, and the single carburetor.

Less obvious, but very significant are limitations such as the 0.875 flat tappet diameter. That restriction severely limits the lifter velocity (inches / degree) that can be attained. However, since the real goal is to achieve velocity at the valve, the Cup engine people have neatly sidestepped that limitation with large base-circle cam lobes, immense rocker ratios, and very stiff pushrods and rocker arms.

Considering the restrictions, the small 4.3% difference in EPC between Formula One and Cup gives a real insight into just how clever the Cup engine people really are.

Table of Numbers

We would like to thank EPI Engineering for allowing public access to the valuable and interesting resource posted above.