How can modern turbo-charged petrol engines have such constant torque plateaus over a broad rpm range. Does the mathematical relationship between torque and power still hold here? This looks totally different from a normally aspirated engine where torque and power increase gradually.

[BMW 650i engine performance]

  • This isn't an actual dyno graph. For one it's much too smooth. and also the big giveaway is as Paulster mentions the fact that they don't cross at the right place. Jul 22, 2015 at 15:29
  • At 5252 Drehzahl (RPM), it looks like about 550 Nm (405 ft. lbs), and 298 Kw (399 hp), which is fairly close. power (in hp) = torque (in ft. lbs) * RPM / 5252. power (in kW) = torque (in Nm) * RPM / 9549.
    – Ehryk
    Jul 22, 2015 at 18:38
  • 1
    The scales for torque and power are different. That is why they do not intersect at 5252.
    – Dmitry S.
    Jul 22, 2015 at 19:43

3 Answers 3


The engine torque produced is a function of the amount of air ingested and the air/fuel ratio combusted in the cylinder(s), combined with 'static' variables like the compression ratio, bore/stroke, crankshaft design, intake length, cam profile, intake and exhaust sizing, etc.

With all the other parameters now static (non-variable) once the engine is built and assembled, and with the ECU controlling the amount of fuel added to the mixture (air/fuel ratio), in gasoline engines torque produced in that engine is now almost entirely a function of air flow. More air in the cylinders = more torque, less air in the cylinders = less torque (speaking of mass here, not volume).

Natural Aspiration (non-variable)

Because of this, in a naturally aspirated non-variable cam non-variable intake internal combustion engine, there will be one (and only one) RPM at which the flow will peak, based on the cam profile and intake length (a hump in the graph). You can tune where this peak happens with various cams and heads and valve sizes, but there is only one. (note: this excludes variable intake length and variable cam systems, see below)

Natural Aspiration

Natural Aspiration (variable cam and/or intake)

With variable cam profiles, there can be two or more peaks (or even a continuously variable setup in theory) where each distinct cam profile or intake length experiences peak flow (greatest mass charge in the cylinders). This can vary the lift, duration, or both of the valves. Examples of this are Honda's VTEC, Toyota's VVT-i, generically known as Variable Valve Timing.

The intake length can also be varied in addition to or instead of the cam profile, for further (though usually smaller) local maxima along the graph (sub-peaks). Examples of this are Mazda's VRIS, VW's variable intake manifold on the VR6, Yamaha's YCC-I

Variable Cam

Forced Induction (regulated)

Now, let's consider forced induction. With a capable compressor (either supercharger or turbocharger), it will be capable of a variable mass charge through the RPM range. For a number of reasons, bypass/blowoff valves, wastegates, clutches, and similar devices limit the amount to a known value, typically based on pressure (say, 21 psi). At this pressure, if we can assume a constant temperature (which we can't in practice), that would yield a theoretically constant mass of air entering the cylinders under sufficient boost. With a set mass of air, and an ECU injecting a corresponding amount of fuel, the engine will produce a constant amount of torque.

Each detonation event will experience the expansion pressure of that set amount of air mass and fuel, and your torque line becomes flat as 21psi of air is forced through the pressurized intake in a constant way (unlike the variable draw of natural aspiration). This will fail to be 'flat' when the compressor is unable to produce more pressure than the regulated amount, which will happen both when the compressor isn't spinning fast enough (too low of RPM) and when the amount of air flow the engine requires at an RPM is greater than the compressor can provide (too high of RPM).

Forced Induction

Forced Induction (unregulated)

Now in theory, if your engine components were overbuilt to handle lots more torque than they would need to otherwise, you could remove the wastegate/clutch system and to deregulate the peak pressure, essentially allowing the flow characteristics of the compressor to define whatever peak it could produce, all the way until the compressor is so outside of its efficiency that it's heating the air charge (and thus expanding it) so much that it's either causing predetonation, causing components to fail, or reducing the effective air mass even with higher pressure, or some combination thereof.

Unregulated Forced Induction

Forced Induction - Theory vs Practice

Also note that there is a big difference between a 'theoretical' dyno chart, with perfectly flat/smooth lines, and a 'true' dyno chart as in practice. Even with a perfectly regulated forced induction system at a set pressure (21 psi in the above example, 7.5psi in the graph below), there will be slight variances due to the temperature and flow characteristics of the intake and cam system at various RPMs, which can lead to slopes and small peaks/valleys in the 'flat-ish' region.

Forced Induction - Real

Why Flat Torque?

It would be possible, in theory, to introduce artificial variable restrictions in a naturally aspirated engine to produce the same results, but it would just be wasteful. Alternatively, if you could design a perfect continuously variable cam and intake system, perhaps that system could (in theory) get to a constant air mass and thus flat curve.

The reason the pressure regulation is done with forced induction typically have to do with design constraints, such as the price to overbuild the components to handle the short torque spike, including possibly everything from fuel injector sizing to piston and rod metallurgy, and the corresponding hit that will be taken in reliability for very small gains.


horsepower = (torque * RPM) / 5252 always.

Typically engines have to suck in their air and fuel so they can only suck in an optimal amount in a certain range. With a turbo you are forcing the air in, so the engine can make more torque over a wider range. If there is a max torque the manufacturer wants to set (for torque limit on the transmission/drivetrain), they can set a boost limit so there is a flat torque line. Shelby did this with the GLHS, they made max torque over a 2000 RPM range.

  • Perhaps another reason is also to establish a clear difference between the same engine in different levels of tune. For example, the Ford Duratorq 2.2 TDCi in the previous Transit went 100/125/140 HP - but also 310/330/350 N.m, for what is basically the same engine (but different pricing).
    Jul 22, 2015 at 17:02
  • power = (torque * RPM) / 5252 only if power is measured in horsepower (hp) and torque is measured in foot pounds (ft. lbs.) (Imperial units). power = (torque * RPM) / 9549 if power is measured in kW and torque is measured in newton meters (Nm) (SI Units). Depending on the units chosen, the dimensionless 'constant' that relates power, torque and RPM will vary.
    – Ehryk
    Jul 27, 2016 at 20:15

That's not a realistic flat-torque graph. It should look more like the following in the real world:

enter image description here

Although you woold find that the horsepower v torque holds true if you apply the calculation at any point on the RPM band.

  • @Paulster2 the horsepower and torque curves will only cross at 5252 if they are expressed in the right units relative to each other (W and Nm, or hp and ft. lbs) and also if the units are the same on the Y axis. On this answer's graph, and the OP's, note that the hp and torque are graphed against different y-axes. It you note, 5252 is roughly halfway between the 4900 and 5600 lines, which reads ~300hp and ~300 ft. lbs., without 'crossing'.
    – Ehryk
    Jul 22, 2015 at 18:22
  • @Ehryk - ARGH! You are right ... throws me off every time. Thank you for pointing it out!!! I have deleted my comments for lack of reading it correctly! Jul 22, 2015 at 18:25
  • No worries, here's a good article on it brighthubengineering.com/machine-design/… and an even better video youtube.com/watch?v=fgLNO3ThGD4 to brush up!
    – Ehryk
    Jul 22, 2015 at 18:40
  • The graph is PERFECTLY realistic. The formula HP = (TQ*RPM)/5252 holds true (to the torque and HP lines crossing at 5252) when measuring torque in lb-ft and power in HP. You will note that this is in N-m and power is in Kw; this is why they do not cross at 5252.
    – user11450
    Jul 22, 2015 at 22:37
  • @Ehryk - Oh, it's not a matter of brushing up, but pulling my head out of my backside long enough to be able to read the two different scales. Again, I stand corrected. These are more than like good for others, though, so thank you for posting them! Jul 23, 2015 at 1:27

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