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

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

(OP)
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!

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

Hi, I don't think the two things you mention are necessarily conflicting with each other - yes, the 6 cylinder will have 3 small firing events per rev whereas the 4 cylinder will have 2 bigger ones, so on an instantaneous basis you would have higher torque from a single cylinder ... but the firing events happen very frequently and the torque output of the engine as a whole is averaged over time because of the inertia of the rotating assembly (particularly the flywheel). If you wanted less variability in torque output and less torque recoil, the 6 cylinder would likely be a better choice. The average torque from each will scale with BMEP, displacement, and rpm.

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

You are thinking about this wrong.

Imagine the engine being a continuous process stream of air and fuel going in, exhaust and heat and useful mechanical power coming out. It converts the input stream (a mass flow rate) into a power output. That power output is a product of a speed and a force ... but it is not important what combination of speed or force, only that the product of the two is the power output.

If it so happens that this process is chopped up into one-cylinder chunks at a time superimposed on each other ... so be it.

If it so happens that this process is chopped up into four smaller-sized chunks superimposed ... so be it. Doesn't matter.

Six times one-sixth equals four times one-fourth. It doesn't matter.

Now, look up the term "BMEP" or "brake mean effective pressure". This is an effective equivalent pressure inside the cylinders that would produce the corresponding torque output. Number of cylinders does not factor into this. A four stroke normally aspirated spark ignition gasoline engine will have BMEP in a certain range regardless of how big or small the cylinders are.

Practical reality ...

A 6 cylinder engine will, if one assumes same bore to stroke ratio, have smaller cylinders than a same-power-output 4 cylinder and may be capable of spinning faster because it has smaller individual chunks of metal moving around inside.

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

Your post contains a lot of information and various questions... So I'll try and summarize with just a few points.

1) When you're talking about similar engines (i.e. engines with similar design goals) Torque is (approximately) a linear function of displacement- regardless of cylinder area, stroke, etc etc.

You have to think of torque production as a 3D problem- not a 2D one; it is produced as the fuel burns and expands inside the cylinder- so overall torque production is a function of not just some instantaneous pressure value across the cylinder area- it's a function of how that pressure gradient builds inside the cylinder and how and how long it takes to peak and then decay. When you compound this over time, it becomes a relatively simple function of the mass flow rate of air through the engine.

It's important to remember that engine parameters like BMEP, IMEP, and FMEP, and their relationships, are used to estimate conditions inside cylinders at any given set of conditions- but they are representations of much more complicated functions and physical interactions.

2) Your assumption that torque would be related directly to the energy released in a single combustion event is a start in the right direction- but if you want your thought process to reflect real-world test results, you have to consider the efficiencies involved. You approached this when you talked about valve count and valve area increases with more cylinders. A smaller engine can beat a larger one all the way across the map if it has much better VE- which is why modern 4 cylinders make as much power as older V8s with twice the displacement..

3) When you think about comparing two engines, it can be difficult to just look at simple peak torque values and compare them directly.

For example- comparing an F1 engine and the S54 in your M3 (which, by the way, I'm intimately familiar with! I've owned E30, E36, and E46 M3s and expect to take delivery on an F80 in August or September.. let's just say I'm a fan!). They make similar torque numbers from comparable displacments- if you knew nothing else, this would lead you to believe that they are operating in similar RPM ranges and with similar MEP values.

Your S54 makes ~260 ft-lb at 3900 RPM. The 3,000 cc BMW P82, which was a 3.0L V10, made ~940 HP at 19,000 RPM, which also equates to about 260 ft-lb at the crank.

The difference though is in the efficiencies and losses involved. What really matters in torque production is maximizing MEP- mean effective pressure. That is done a number of ways, including CR changes and heads designed for high VE etc.

But what you're looking at on a torque plot is NOT MEP- it's BMEP; brake mean effective pressure. The difference between BMEP and MEP is a little devil called FMEP- friction mean effective pressure. This is basically a measurement of the mean effective pressure required to overcome internal friction and move the engine. It's a devil because it increases with RPM, as a linear function of mean piston speed.

So, in essence, the F1 engine at 19,000 RPM has the same output torque as your S54, but the actual torque produced by the cylinders is much higher because the FMEP of the F1 engine is almost 5x as high (19,000/3900). All of that extra torque is consumed within the engine to turn the rotating assembly and valve gear.

This means that from a BMEP standpoint, the two engines are reasonably comparable- but the true MEP of the F1 engine will be much, much higher than the S54, because of the difference in FMEP. In order to produce that extremely high MEP, the F1 engine has to be very efficient, and isn't directly comparable to your S54.

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

(OP)
Thanks for the responses guys.

I had a feeling I was thinking about it all wrong... I'm actually taking internal combustion engines right now so I know about BMEP and whatnot, I guess the thing I missed is that the torque at the flywheel is resulting from the continual running of the engine and therefore the torque of a single explosion doesn't really mean anything in terms of the total engine torque. It was just confusing for me as to how the total engine can develop more twisting force than that which comes from a single explosion, but the fact is its a running engine with a bunch of explosions happening in close succession, acting on a single crank/flywheel.

Kinda a dumb question for a first post haha, thanks for the help.

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

Your question was a good one, for a student. But this demonstrates why student posting is not allowed here.

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

#### Quote (Compositepro)

Your question was a good one, for a student. But this demonstrates why student posting is not allowed here.

Student posting is only forbidden if the post is a request for help with coursework- which this does not to me appear to be.

Lighten up. We all started somewhere.

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

(OP)
Wow, thanks for the info jgKRI! Have fun with the new M3! My dad has an e92 M3 ZCP 6MT... that v8 is a bit of a gem. I absolutely love the S54 though. Gotta drive an e30 one day...

Anyway, I appreciate the response. I've been learning about friction and what the brake output actually means compared to whats going on inside of the engine. It's all very interesting for me as someone who knows quite a lot about cars and the different engines available now (at least for a 21 year old..), I'm really glad to finally get to delve into the science behind IC engines, even if much of the class is somewhat second nature to me. I'm still learning a lot!

I hadn't really thought about how much friction the F1 engine had to overcome to output the same 260 brake ft lb, although I knew about that concept. So in reality the F1 engine makes a lot more twisting force with combustion. Makes sense as it has a bunch more cylinders to do so, relatively big bore and tiny stroke to flow as best as possible.

Really makes me want to import a Honda CBR250RR. 250cc inline 4 that does 20k rpm. Sounds amazing!!

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

I am trying to be helpful. The OP will get banned for asking such questions because he has already admitted to being a student.

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

(OP)
To be honest I knew it was a bit of a stupid question to begin with. For as long as I can remember I've related displacement and torque output to estimate relative engine efficiency (NA) in my head, just when looking at production cars. I know a BMW S1000RR will make as much torque as VW Up 3 cylinder (likely more), I was just trying to understand the science a little better.

When registering on Eng-Tips today, student was an option in the occupation section. What's the problem? I've had multiple internships and will graduate in 2018..

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

It wasn't a stupid question at all- it was/is a good question, and it's the type of thing you should be thinking about beyond what you're learning in class.

You're allowed to be a student and post on this forum- just don't ask for help with your homework and you won't get the boot.

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

(OP)
Okay, understood. I for sure won't be asking about homework.

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

Read the posting guidelines at the bottom of the page.

"To be honest I knew it was a bit of a stupid question to begin with." This is why. Hundreds of engineers have now spent time on your question, as I am doing now. Don't be selfish, and don't dig your hole any deeper. You have teachers and fellow students to have these discussions. We are not a substitute, otherwise the target audience of this website will get bored and leave.

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

#### Quote (eng-tips.com Posting Guidelines)

Student posting in Eng-Tips forums for help with theses or coursework is forbidden. This is considered cheating. Offending posts will be removed from the site and offending members will lose their membership privileges.

Students post here every day of the week, and when they're asking interesting questions that don't break the rules, they get interesting responses.

Keep learning Imola.

And keep polishing that red E46.

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

(OP)

#### Quote (Compositepro)

This is why. Hundreds of engineers have now spent time on your question, as I am doing now. Don't be selfish, and don't dig your hole any deeper. You have teachers and fellow students to have these discussions. We are not a substitute, otherwise the target audience of this website will get bored and leave.

It's a forum right? People spend time here at their own will. It's not like the thread was inappropriately titled to draw in views.

#### Quote (jgKRI)

Students post here every day of the week, and when they're asking interesting questions that don't break the rules, they get interesting responses.

Keep learning Imola.

And keep polishing that red E46.

Thanks!! :D Very stoked to drive the car again when I get home in August. Plan on keeping the car indefinitely

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

Don't be discouraged OP, I regularly see far worse questions posed here by licensed engineers. ;)

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

In the old days in the aircraft engine world, the simple way to make more power was simply to add more cylinders.
Not bigger cylinders just more, bigger cylinders would be less efficient as well as having to redesign the wheel of sorts.
And you can do all the calculations you wish, in the end the true answer is what the dynamometer reports.
Equal displacement 4 and 6 cylinder engines? Equal output? Depends on all the variables.

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

Same approach is being used nowadays in the automotive world. Many companies have been zeroing in on using somewhere near 500cc cylinder displacement, thus one will see a 1.5 litre three, 2.0 litre four, 3.0 litre six, and 4.0 litre V8 with design similarities and in many cases, shared parts. It just works out nicely in terms of emissions, power output, durability, noise and vibration, etc.

Obviously the 500cc is plus or minus a fair bit depending on specific objectives for a given design (It is not a magic "line in tne sand").

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

Optimum cylinder size depends a bit on your assumptions, the lowest figure for automotive gasoline naturally aspirated I can remember is 350cc, the highest 600. That isn't much of a range considering the range of factors involved, including what you need the engine to do. That is the optimum for fuel efficiency may not be the optimum for max bmep which may not be the optimum for max specific power.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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

Now hold on thar, you're overlooking the vast majority of american engines produced from the 50s through the 70s. Even today, there is a sizable segment of automotive engines on the market with well over 600cc/jug. The upper limit, when referring to modern passenger car engines, as far as I'm aware, was defined by the Cadillac 500 CID V8, with over 1000cc/cyl, offered from 1970 to 1976 .

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

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

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.

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

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

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

600cc per cylinder is not far from 500cc. It isn't a "line in the sand" situation - not even close.

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

Sorry I was thinking about theoretical 'optimums' I've seen calculated, not what people use in practice.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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

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

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

Aero piston engines came to a much larger cyl size. The hp req't was much much higher.

"Schiefgehen wird, was schiefgehen kann" - das Murphygesetz

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

I am not sure about the 'sweet spot' without looking at other limitations. There's a nice diesel that 1,820 liters per cylinder.

see http://www.amusingplanet.com/2013/03/the-largest-a...

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

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.

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

" Scale an engine dimensionally and the physics remain largely the same"

Speed of air through the valves?

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

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

(OP)

#### Quote (CWB1)

Don't be discouraged OP, I regularly see far worse questions posed here by licensed engineers. ;)

Hah, thanks

#### Quote (CWB1)

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?

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

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.

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

(OP)
Ahhh, that^^ makes a lot of sense

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

Around 155 cid per cylinder was one aircraft engine manufactures favorite combo, and too bad they weren't getting, 2hp / cu in back then.

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

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

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

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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