# Why Does the Torque Curve Drop Off at Low RPM in a Typical Piston Engine?

1. Jul 10, 2008

### MESIMPSON

I’ve been searching for an answer to this question on the web for 3 hours. Thought I would find it quickly, but, noooooo.

I’m trying to understand why crankshaft torque falls off at low RPM in normally aspirated piston engines. I think I understand the high end of the torque curve OK. At high RPM, torque drops off primarily from intake and exhaust flow restriction. Volumetric Efficiency declines because the engine can’t breathe any faster. Mechanical efficiency also declines at higher RPM, due to increased frictional resistance. This further reduces torque at the output. As RPM declines from high levels these limiting factors diminish, allowing torque to increase.

Unfortunately, the description above doesn’t seem to explain or apply to the low end of the torque curve. As RPM declines below the rate where the engine has peak torque, intake and exhaust flow resistance as well as frictional resistance should continue to decrease. Also, with variable valve and ignition timing, it seems like it should be even easier at lower RPM to generate higher peak pressure in the cylinder and focus it on the optimal crank angle. These things seem to suggest that torque should continue to increase as RPM falls to near zero. Instead, torque and combustion efficiency both decline at lower RPM. Why?

Any direction to a good reference that explains the basic science of low end torque drop off would be appreciated.

2. Jul 10, 2008

### marcusl

The relation between torque, power and angular speed is

$$\tau=\frac{P}{\omega} .$$

Power falls off below a peak located at high engine speed, because less fuel/air (energy source) is brought in and burned per second. If that were the only factor, then power output would be proportional to angular speed

$$P\sim\omega$$

and torque would remain constant down to idle. In fact passenger car engines have a fairly broad and flat torque curve. See the curves at, e.g.
http://en.wikipedia.org/wiki/Power_band" [Broken]

However engine efficiency drops with at low speeds since combustion chamber shape, bore/stroke ratio, manifold runner shape and length, valve lift and intake/exhaust valve overlap, to name just a few factors, are tuned for best performance at higher engine speeds. Thus torque eventually falls. In racing cars, the tuning is "peakier," that is, they produce far more peak power but only over a narrow RPM range. As you might expect, the torque curve isn't as flat in this case, and it falls off more rapidly. See Fig. 3 here
http://www.corvetteactioncenter.com/tech/hp_torque.html" [Broken]

Vehicles that are optimized for very high torque at very low vehicle speed either have no high end to speak of (road graders, bulldozers) or, if they need both, use different systems (diesel-electric locomotives).

Last edited by a moderator: May 3, 2017
3. Jul 11, 2008

### MESIMPSON

Good Stuff Marcusl. I was guessing it’s probably a combination of things.

One thing I was wondering is whether the average volume of the combustion chamber has something to do with combustion completeness (efficiency). Assuming combustion occurs in the same time interval for a given fuel mix, the average volume of the cylinder during combustion is less at low RPM than at high RPM.

Any thoughts on that?

4. Jul 11, 2008

### marcusl

Sure, combustion chamber volume and shape are both big factors. I don't have enough knowledge to directly answer your question, though. Here are some general observations: Concerning shape, work in the 1950's resulted in hemispherical ("hemi") and wedged shape combustion chambers that optimized power output. In the 70's, Honda was the only car sold in California that met emissions standards without a catalytic converter. They had introduced an extra intake valve and an angled port that introduced swirl and turbulence, resulting in more complete burning. Turbulence, volume, shape, valve overlap and speed all affect efficiency.

5. Jul 17, 2008

### Cornellian

The behavior of Torque and Power vs. RPM depends on many things. However, there are only 2 ways the analysis of an engine can be broken down. 1) Thermodynamic Analysis 2) Dynamic Analysis.

Some of the members have mentioned some variables from thermodynamic point of view. But, having designed my own engine using MatLab, I've found out that the dynamic analysis is way more interesting since, it shows why shape of the Torque/Power graph is the way it is. Not to go into the details too much and to explain in simple terms, the main dynamic variables are simply the geometry of the engine components (i.e. Conrod, bore/stroke, crankshaft radius, etc). The other key variable is the angle of rotation of between the conrod and crankshaft. And as the other member has mentioned, timing (speed) of the piston moving up and down also has a key effect.

6. May 18, 2009

### rdurden

You forgot the most basic thing. An engine has a throttle which limits the amount of air/fuel that can enter the cylinders at low speed/low loads. Less air fuel/less torque. Less cylinder filling also lowers the compression ratio. Compression ratios are calculated assuming 100% cylinder filling.

7. May 18, 2009

### Bob S

There are three primary reasons torque drops off at low RPM:
1) As you are aware, when the air-gas mixture is compressed, especially at WOT (wide open throttle), the mixture gets hot. This also raises the mixture pressure more. This is the physics of adiabatic compression. When this mixture is ignited, you get higher BMEP (brake mean effective pressure). At low RPM, the compressed gas convects much of this heat away to the walls of the combustion chamber before the mixture is ignited, as well as during the power stroke, and you get lower BMEP.
2) Leaky valves and piston rings.
3) valve timing and ignition timing at low RPM

Last edited: May 19, 2009
8. May 18, 2009

### Bob S

You are correct, but not for the reasons you imply. If you read my post directly above, at low RPM, heat convection to the combustion chamber walls is the primary loss of BMEP at low RPM. If you had a 4 cylinder 2.5 liter engine and an 8 -cylinder 2.5 liter engine side by side, with every thing else the same, the 4 cylinder engine would have better low end torque. The reason is that the combustion chamber volume is twice as large in the 4-cyl engine, and it takes longer for the compressed mixture to convect the heat away.

9. May 18, 2009

### WhoWee

Sometimes the answer is that simple...less efficient burn yields less power.

10. May 19, 2009

### Ranger Mike

good stuff to ponder but the answer is even simpler

a 4 cylinder engine at 1500 RPM is popping each piston 375 times per minute
when you spin it up to 5000 RPM each slug is lighting off 1250 times per minute

11. May 19, 2009

### Bob S

The attached pdf of the BSFC (brake specific fuel consumption) performance of a 2.7 liter engine shows that the wide-open-throttle torque (minimum intake manifold vacuum) is nearly the same at 2000 and at 5000 RPM. The maximum is at about 3900 RPM. The drop off at low RPM is due in part to the cooling of the compression-heated air-fuel mixture by convection to the combustion chamber walls.
Adiabatic compression of air obeys the relation

T v(gam-1)= constant, where T= temperature in kelvin, v = volume, and (gam-1) = 0.4

So air at 293 kelvin (20 deg C) compressed a factor of 10 is heated to about 730 kelvin (450 deg C). The walls of the combustion chamber are at about 80 deg C (water cooled).

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12. May 19, 2009

### brewnog

Excellent post Bob, this was the list I was going to put up.

13. May 20, 2009

### Ranger Mike

Original question- "I’m trying to understand why crankshaft torque falls off at low RPM in normally aspirated piston engines"

At low rpms you use very little fuel ( which means less torque & HP) and each cylinder is firing the least per RPM.
force x distance / time???

ifin you are charting fuel consupmtion for torque, you should chart HP too...it takes a lot of fuel to make HP..BSFC is the " new " trick of the day but is not real world at WOT since 99 percent of all door slammers never use it.. note the chart for a Jaguar V12 HE, the ‘HE’ indicating the use of high swirl heads.

The red line shows power – all the way to about 220kW in this graph. The green line shows torque (although here it is expressed as Brake Mean Effective Pressure). And then we have SFC, shown by the purple line. As can be seen, the SFC curve doesn’t initially appear as you might have imagined it would.

At idle it’s about 280 g/kWh, then as revs rise, it drops to be at its lowest at about 2500 rpm (at say 270 g/kWh). From there it rises steeply to reach 350 g/kWh at 6000 rpm.

Now why should the SFC be lowest at middle RPM? Or, to put this another way, what causes an increase in fuel used per kW at both low and high revs?

At low revs, SFC suffers because there’s increased time for the heat of combustion to escape through the walls of the cylinders and so not do useful work. At higher engine speeds, the frictional loses of the engine rise alarmingly (especially in this case with 12 cylinders!) and so the energy of combustion is again being wasted, this time in heating the oil.

There’s another reason that SFC is lowest at ‘middle’ rpm. Because the engine is tuned to develop best cylinder filling (ie to produce best torque) at middle RPM range, the engine’s breathing is at highest efficiency at these speeds.
THIS is critical...The engine is a giant AIR PUMP. Unless you monitor AIR Consumption as well..SFC is only HALF the story. Fuel/Air being the whole sotry! But don’t fall into the trap of saying that SFC is always at its best at peak torque – that’s not usually the case.

But the real trouble with diagrams like the one above is that in many ways, they’re irrelevant to real-world fuel consumption. Why? Because these graphs are drawn for full throttle!

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Last edited: May 20, 2009
14. May 20, 2009

### Staff: Mentor

It sounds to me like you are mixing up a few things. As others said, the torque curve is relatively flat over a relatively wide range of rpm. It is only when it gets really low that it starts to drop. And as you note, the curves are drawn at full throttle, so that means the fuel and air intake per stroke isn't very rpm dependent - you don't use less fuel per stroke at low rpm than at high rpm. Power is linearly dependent on rpm because torque is roughly constant with rpm over a certain range. Power is a function of rpm, but torque is not. And I also wouldn't say they are irrelevant to real world fuel consumption, they are just one case out of many: they show why high acceleration means poor fuel economy.

Last edited: May 20, 2009
15. May 20, 2009

### Ranger Mike

Thanks Russ..good point...
I think a better way of phrasing the original question would be..why is torque low at low RPM.
the graph I posted shows a relatively (though not totally) flat torque curve between 2000 and 4500 RPM ..then it falls off..I think we agree??
can we agree that RPM is dependent on fuel and air? You won't get more revs unless you step on the gas pedal.
so if this is true then are not Power and Torque directly dependent on fuel and air?
IMO. Power = Force x Distance / Time... and since the distance is fixed ( bore and stroke) only two things can be change in the equation. Force ( fuel and air) and time (RPM)
The SFC on the graph shows a very linear correlation between SCF and torque and HP, I think.
Granted high acceleration can mean poor economy but acceleration was not addressed.

16. Jun 3, 2009

### aaron_

What do you mean by "high acceleration"?