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General IC Engine Theory Question - effect of cylinder count on torque, displacement equal

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Imola

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Jun 8, 2017
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Hello all,

I have a little question about piston engine theory; I was hoping you all could enlighten me. For reference, I am a junior undergrad in mechanical engineering at the University of Illinois (currently studying in Munich-TUM for a semester). I'm a huge a car/motorcycle fan.

I'm curious as to the 'effect' of cylinder count on general torque (and power) output of an engine, keeping displacement and CR equal. Consider two engines, an inline 6 and an inline 4, of equal displacement (we'll say 2 liters). Assume the bore/stroke ratio is the same between them, and the inline 6's cylinders have only been scaled down in size as appropriate.

Here is where my question lies: is the output (brake) torque of the engine always correlated directly with the torque produced by one combustion event in the engine (i.e. the force of one explosion on the con-rod/crankshaft)? This makes sense to me, but if that were true, the 6 cylinder would always have less torque than the equal displacement 4 cylinder (keeping other parameters constant of course). The 6 cylinder would have more combustion events / time though, which would allow it to make relatively more power than the 4 cylinder, perhaps enough to offset the torque advantage of the 4 banger at a given rpm. Also, because of the better balance it would likely rev higher/smoother. BUT, here's an example against this claim that volume of a single cylinder determines (to an extent) the torque output. Take a 3.0 liter F1 engine (v10 or v12). It might make around 260 ft lbs of torque max. My BMW e46 M3 (S54) makes 262 ft lbs of torque in stock form, from 3.2 liters. So the F1 engine is able to make the same torque with much tinier cylinders. How? Is the 'torque' from each combustion event 'added' together to get the brake torque output? I figured that would equate more to the overall power output. I don't see how the output torque could be more than the torque produced by one cylinder (unless its a 'big bang' engine), but I could be thinking about this too simplistically. Is the answer simply that, the torque from the individual cylinders comes in such quick succession that the overall brake torque is greater than that of one explosion?

I always thought of displacement as the main factor for torque output of an engine (at a single rpm, keeping relative head flow characteristics constant) given that it represents the volume of fuel+air that can be crammed into it at atmospheric pressure for a given amount of time. Specific output of an engine is often expressed in terms of torque / liter, especially on an NA engine.

I understand that the total valve surface area will be different for the 2 configurations (more valves / probably better flow with the 6 cylinders) but I didn't really feel like doing that math at the moment. I'd just like to get a little better overall understanding.

Thank you in advance!
 
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Sure, but we are talking modern era, in which things that were tried in the past have gone by the wayside or have been optimized away from the way they were back then.

There is some tendency for the smaller displacement engines to be on the side of less than 500cc per cylinder in the interest of smoothness (my own car has a 1.4 litre 4 cylinder) and for the bigger displacement engines to be on the side of more than 500cc per cylinder in the interest of keeping cost, space, and parts count under control.

BMW, specifically, builds 1.5 litre 3 cylinder, 2.0 litre 4 cylinder, and 3.0 litre 6 cylinder engines with common engineering, if not exact parts, between them.
 
In the modern era, we have quite a few >4.8L V8s, a few >3.6L 6 cylinders, and I guess even some >2.4L 4 cylinders.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz
 
I heard once that the magic 500cc per pot comes from scaling laws. Heat transfer area scales as the square of engine linear dimension, swept volume as the cube. Optimum performance/ecomony/emissions is where curves governed by these two scaling laws cross (or cause a local maximum/minimum). Something like that anyway. It was plausible when described, even if the details were sketchy.

Steve
 
Bore/stroke is the important criteria, not displacement/cylinder. Scale an engine dimensionally and the physics remain largely the same. In a similar manner, if you develop a combustion system on a single cylinder it can easily be translated to various multi-cylinders to create an engine family.

As to efficiency, small auto engines are pretty inefficient. Not to suggest that they cant be developed to be ~45% efficient like many large stationaries but they simply dont warrant the investment.
 
CWB1 said:
Don't be discouraged OP, I regularly see far worse questions posed here by licensed engineers. ;)

Hah, thanks

CWB1 said:
Bore/stroke is the important criteria, not displacement/cylinder. Scale an engine dimensionally and the physics remain largely the same. In a similar manner, if you develop a combustion system on a single cylinder it can easily be translated to various multi-cylinders to create an engine family.

As to efficiency, small auto engines are pretty inefficient. Not to suggest that they cant be developed to be ~45% efficient like many large stationaries but they simply dont warrant the investment.

This makes most sense to me. Would you say the relative inefficiency is due to the requirement of running through a large range of revs, unlike a generator?
 
The characteristics of the load in an auto engine don't match up well with the BSFC chart.

Operating at part throttle (low BMEP) leads to high pumping losses and the various friction and thermal losses are a relatively higher part of the picture. So the engine wants to be operated at a relatively high torque output in order to be efficient, basically by varying the revs in order to match the requested power delivery.

The current trend to CVT and automatic transmissions with a large number of ratios and a wide range between the highest and the lowest ratios is an attempt to match this, but even then, drivers don't like it when the system changes ratio because they breathe on the accelerator pedal, or the vehicle has to go up a barely-perceptible hill. So even with an 8 or 9 or 10 speed transmission, there is a factor in the shift logic "stay in the current gear if possible". People also don't like it if the transmission is lugging the engine down in top gear and there is a moment of delay before accelerating because the transmission has to change ratio.

And hence ... hybrid powertrains, where a fair chunk of the propulsion comes from an electric drive, and the engine can be shut down completely under operating conditions where it would have poor efficiency if it kept running, and the engine can be operated with cam timing (Atkinson cycle) that would have unacceptable driveability characteristics if it were used alone without the electric "assist".

Some of the latest batch of spark ignition auto engines are ~40% efficient at their best operating point, but the real trick is to improve part-load efficiency so that it doesn't drop off as badly. And for that, we have variable valve timing, and direct-injection, and various forced-induction schemes combined with downsizing, etc.
 
Around 155 cid per cylinder was one aircraft engine manufactures favorite combo, and too bad they weren't getting, 2hp / cu in back then.
 
SI efficiency peaks at some relatively small displacement/cylinder - I think somewhere between 300 and 400 cc whereas diesel efficiency increases with cylinder size. The difference is mainly to do with detonation which is time dependent (heating time of end-gas) and therefore dependent on flame travel length. Go too small and friction and internal surface area (heat loss) begin to dominate.

je suis charlie
 
Aero engines grew to about 5-1/2" bore and 6" stroke. The bore was limited due to detonation and cooling, and stroke topped out I suppose due to bore/stroke ratio (e.g. valve size needed to feed the displacement), radial engine diameter, and maybe dynamics as well. Once they reached these limits, they just added cylinders for more power. Not to mention, as dicer just did, squeezing a pretty impressive number of hp/cu.in. out of the displacement.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz
 
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