Engine theroy regarding power and economy.

Maybe this is too simplistic of an approach, but here goes:

3 engines, each with the same bore/stroke, valve size, cam profile etc. Direct injection for accurate/ consistant fuel delivery.

engine #1 is a 2.0L inline 4 cylinder turning 4000rpm

engine #2 is a 3.0L inline 6 cylinder turning 2666rpm

engine #3 is a 4.0L inline 8 cylinder turning 2000rpm

I made them inline engines to assume identical combustion chambers and intake/exhaust runners

At this speed each is pumping 8000L of air a minute and if the A/F ratio is steady at 14.7 they all are using the same amount of fuel right? Would the 8 make more power with its extra power strokes per revolution? Would one require more fuel to maintain 14.7 with the same load? So many questions!

Discuss and debate please.

It looks like what you have are a four stroke four cylinder, a six stroke six cylinder and an eight stroke eight cylinder. Sort of like taking a single cylinder capable of running on it's own and stacking it the same way people do with rotaries only the combustion events are reduced in direct proportion to the amount of cylinders present to give you a desired crankshaft speed and air volume. Given that information they would all use the same amount of fuel, though I don't think the 6 or 8 would run very well.

The engines with fewer cylinders would yield more power since they are carrying fewer cylinders through their non-firing cycles.

Pumping losses

You stated that they all had the same cam profile, but the problem is that the cam profile is a big part of what determines the engine's curve of volumetric efficiency vs RPM. A mild cam is more efficient at low RPMs, a lumpy cam more efficient at high RPMs. If they all have the same profile, but one is running 2x the revs of the other, then one of them is going to have significantly different VE than the other, and they will not all be pumping the same amount of air.

If you changed the cam profiles (and manifold lengths) so that all three were running 100% VE at the stated test condition, then they're all going to burn the same amount of fuel and generate the same amount of total force pushing down on the pistons over time. The 8-cylinder will be smoother and since it's turning lower revs it will have less friction per moving part. OTOH, the 4 cylinder has fewer moving parts to multiply that friction by. I think the lower revs will be more of a win, though.

Think I understand what you are trying to get at. Taking example of the 4-cyl and 8-cyl RPM, both have the same cylinder firing cycle in the same amount of time. 4-cyl at 4000 RPM and 8-cyl at 2000 RPM. I assume that would also mean the 6-cyl also has the same cylinder firing cycle in the same amount of time. I believe each cylinder would burn the same amount of fuel in each engine although I also believe the engines with more cylinders would burn more fuel in the same amount of time because more cylinders per RPM firing. Plus the parasitic loss would be greater due to friction, weight and rotating mass would be more in the more cylinder count engines. Would need to burn more fuel to make up for the parasitic loss. All things being equal and not taking parasitic loss into the equation then each would make the same power and burn the same amount of fuel. But factoring in the parasitic loss then more fuel would be burned to be equal. The 4-cyl would be more efficient but the higher cylinder engines would be more powerful.

Caveat - I'm not an engineer but I work with engineers and I've stayed at a Holiday Inn Express.

The fuel consumed is actually really simple. It's 4000L of air per minute (not 8000L, because it's a 4-stroke engine so you only get one intake stroke per cylinder every 2 crank revolutions), which is 4000*1.2g/L or 4.8kg of air per minute. Divide that by the quoted air/fuel ratio of 14.7:1 and you get 326 grams of fuel per minute, or about 430ccs (roughly .75 kg/L for gasoline). Back-of-the-envelope suggests all three engines are making about 90 hp, which actually matches up pretty well with random K20 dyno charts I googled. :)

Gearheadotaku wrote: At this speed each is pumping 8000L of air a minute and if the A/F ratio is steady at 14.7 they all are using the same amount of fuel right?

For this exercise, this is your answer. It ignores reality and just focuses on the few parameters you set. Based on those parameters alone, this is the answer.

Insert reality, and it changes. The degree of change depends on the degree reality is inserted.

One reality insertion starting point would be the volumetric differences of the cylinders between the three engines. Burn time, quench, flame propagation, etc.

Another reality insertion starting point would be the rotational mass differences between the three engines.

A third reality insertion starting point could be what do you mean by power? Plow pulling grunt (the inline 8 would win) or screaming race car power (the 4 would win). Win being overly simplified from the parameters you've defined.

The straight 8 won't fit in the engine bay.

All things being equal, all things are not equal.

In reply to Gearheadotaku:

In theory 1 is better than the other. In reality, you mis-spelled "theory".

Gearheadotaku wrote: Direct injection for accurate/ consistant fuel delivery.

That part makes me chuckle....

One of the confusing things about friction, especially aero spinning friction is it's non-linearity. So given the pumping frictions of the 3- to me, it's probable that the 4 cylinder has more losses do to spinning friction, so it's net brake power will be less.

May not be a huge difference, but big enough to be noticed.

The other thing that has been touched on is the valve timing- but not just the cam timing part of it- but it's interaction with the intake and exhaust. To make this equal- one needs to assume individual cylinder runners for both the intake and exhaust, otherwise the cam timing has a big impact on pushback, scavenging, etc- and the manifold shape influences that a lot, too- will there be a lot of cross talk between cylinders?

But the other big question to ask- what is the usage of the engine? If this is a simple single speed generator, I'd choose the lower speed of the 3. But for a car, for most of us, making 5-20 hp is just as important as making max power. And that's where the 4 cyl will do better- as it will have less pumping losses at the low power, be a little higher in it's load range (normally better on it's overall efficiency), and have less spinning friction due to the less parts.

There are a lot of compromises that go into engine design choices.

Gearheadotaku wrote: Maybe this is too simplistic of an approach, but here goes: 3 engines, each with the same bore/stroke, valve size, cam profile etc. Direct injection for accurate/ consistant fuel delivery. engine #1 is a 2.0L inline 4 cylinder turning 4000rpm engine #2 is a 3.0L inline 6 cylinder turning 2666rpm engine #3 is a 4.0L inline 8 cylinder turning 2000rpm I made them inline engines to assume identical combustion chambers and intake/exhaust runners At this speed each is pumping 8000L of air a minute

No, they are not. Only at WOT, if the engine is capable of 200% volumetric efficiency at that speed.

If they are all in the same vehicle, they will all be pulling in the same amount of air, roughly, no matter what engine size or displacement or RPM. Roughly. That is what the throttle plate is for.

from what I have been led to believe, a smaller engine spinning it's heart out to make the same power a big engine makes at half the speed is more efficient simply due to pumping losses, friction, and volumetric efficency.

too many assumptions left to accurately answer your question.

But based on each cylinder on each engine is operating at the same volumetric efficiency at the given rpm in the original post.

Each engine is running the same bore and stroke on each cylinder and the load is at the same percentage of maximum engine output (e.g. 50% of peak available power, different for each engine)

the the 4 cylinder wins as the internal friction and pumping losses of each additional cylinder will add up.

Flight Service wrote: too many assumptions left to accurately answer your question. But based on each cylinder on each engine is operating at the same volumetric efficiency at the given rpm in the original post. Each engine is running the same bore and stroke on each cylinder and the load is at the same percentage of maximum engine output (e.g. 50% of peak available power, different for each engine) the the 4 cylinder wins as the internal friction and pumping losses of each additional cylinder will add up.

The problem with that is that the number of events per min is exactly the same, and since the manifold pressure is the same- and IF the pumping is the same- then there's no pumping difference between a 4 cyl at twice the speed of the 8.

If the speeds were the same, you are right.

And then some of the spinning friction and losses are non-linear- so twice the speed is 4x that particular loss.

Pumping losses would only be different if the engines were being throttled down to less than max power. Since they're running at > 100% VE, we can assume the throttle is wide open, intake manifold is at ambient pressure, and there will be no difference in the pumping losses between the engines.

codrus wrote: Pumping losses would only be different if the engines were being throttled down to less than max power. Since they're running at > 100% VE, we can assume the throttle is wide open, intake manifold is at ambient pressure, and there will be no difference in the pumping losses between the engines.

can't make that assumption. Most engines don't run at 100% VE at WOT, especially these days of fat powerbands.

Peak combustion efficiency doesn't happen at WOT.

which is essentially what you are talking about.

In reply to alfadriver:

I still think the extra piston, bearings, valvetrain, total friction losses would be more for the larger engines.

Flight Service,

Think of the bearings as little centrifugal pumps. The power required to drive them goes up with the cube of the speed. If you can halve the speed but need twice as many bearings, you're still ahead by a factor of four.

Flight Service wrote: can't make that assumption. Most engines don't run at 100% VE at WOT, especially these days of fat powerbands.

It's not an assumption that they're running 100% VE, it's stated in the original question. Well, actually he says they're running 200% VE, but I'm assuming that's a "forgot to divide by 2 because 4-stroke" error.

alfadriver wrote: And then some of the spinning friction and losses are non-linear- so twice the speed is 4x that particular loss.

Which is a lot of why a large, low-revving engine can get unexpectedly good fuel economy. I'm thinking here of the GM sixes that could get over 30mpg highway in an aerodynamic brick of a car. 3100, 3400, 3800, they were all good for that.

Flight Service wrote: In reply to alfadriver: I still think the extra piston, bearings, valvetrain, total friction losses would be more for the larger engines.

At equal speeds, sure. Could even say half for the 4 cyl. But then double the speed, and then the linear friction power doubles, and the non linear friction power goes up even more.

chaparral wrote: Flight Service, Think of the bearings as little centrifugal pumps. The power required to drive them goes up with the cube of the speed. If you can halve the speed but need twice as many bearings, you're still ahead by a factor of four.

right, and that curve is linear (and has a slope less than 1) so because the size of the boundary layer, as RPM goes up as does the boundary layer (once it hits a point it goes exponential). So I would agree with your statement if we were running at a very high RPM but we aren't. We are running at 4k down to 2k. Which I would say is on the lower end of the curve.

I found us an answer!!!!

Also please remember I said in my assumption same percentage of load not the same load.

But that does't matter as according to my information I am wrong. The V8 would get better slightly better fuel economy at full load and no load. The V6 seems to be the loser in the charts.

      4 cylinder   8 cylinder

Full 1.4 bar ~1.8 bar in losses
None 1.1 bar ~0.85 bar in losses at their respective RPMS

codrus wrote:

Flight Service wrote: can't make that assumption. Most engines don't run at 100% VE at WOT, especially these days of fat powerbands.

It's not an assumption that they're running 100% VE, it's stated in the original question. Well, actually he says they're running 200% VE, but I'm assuming that's a "forgot to divide by 2 because 4-stroke" error.

No he didn't you did in your first post.

Flight Service wrote:

codrus wrote:

Flight Service wrote: can't make that assumption. Most engines don't run at 100% VE at WOT, especially these days of fat powerbands.

It's not an assumption that they're running 100% VE, it's stated in the original question. Well, actually he says they're running 200% VE, but I'm assuming that's a "forgot to divide by 2 because 4-stroke" error.

No he didn't you did in your first post.

Go read the first post again, it states: "At this speed each is pumping 8000L of air a minute"

codrus wrote:

Flight Service wrote:

codrus wrote:

Flight Service wrote: can't make that assumption. Most engines don't run at 100% VE at WOT, especially these days of fat powerbands.

It's not an assumption that they're running 100% VE, it's stated in the original question. Well, actually he says they're running 200% VE, but I'm assuming that's a "forgot to divide by 2 because 4-stroke" error.

No he didn't you did in your first post.

Go read the first post again, it states: "At this speed each is pumping 8000L of air a minute"

ok