Motor theory: More cylinders is better
 

This is entirely theory, but I think it's a good one.

Given a fixed displacement, say, 2.0L, we have 3 engines. First is an I-4. Second is a V-8. Third is a W-12 (for compactness).

I theorize that the V-8 will produce more usable torque at lower RPM's than the I-4, and the W-12 will likewise "lower" the bar over the V-8.

I imagine a small displacement V-12 spinning at 1,100-1,200 RPM, or even less, on the highway.

It's giving me thoughts about building an engine from scratch.

My theory comes from reading the charts in the following page: Torsional Characteristics of Piston Engine Output, by EPI Inc.

Lets assume that all three engines have a Stroke to Bore ratio of unity. The Stroke for the three engines would be as follows

4 cyl - 86mm
8 cyl - 68.2mm
12 cyl - 59.6mm

As short stroke engines do not produce as much torque at low speeds as longer stroke engines, the four cylinder engine will produce more torque than the eight and twelve cylinder engines.

Another disadvantage of the 12 cylinder engine is the greater surface area to volume ratio of the combustion chamber compared to the four cylinder engine. This will result in larger heat losses and thus inferior fuel economy compared to the four cylinder engine.

The twelve cylinder will certainly be smooth running but low speed torque and fuel economy will be inferior!

Wouldn't the additional friction and pumping losses of the extra cylinders mean that overall the I-4 would use less fuel and probably not be too far behind in terms of power ?

4 cylinders are the norm in non-North American markets for engines in the 1.3 to 2.5 litre capacities mainly as a compromise between smoothness and capacity. There are/were some exceptions such as the 2.0 i-6 used by BMW for a long time. They didn't have much more torque than their 4-cylinder rivals but did use more fuel and were bulkier and heavier. They were much smoother though.

How about an I-5 as a compromise, as used by Audi ?

The four cylinder will indeed use less fuel as I have said above. It will be particularly noticed at low loads and low engine speeds where heat losses are most pronounced.

It is the bore/stroke ratio that is important. A recent discussion on these matters had a link that I posted talking about the expansion ratio of a higher compression ratio, which is similar to a low bore/stroke ratio.

Yes. The bore/stroke ratio is important. But for the comparison of a 2.0l engine, one with 4 cylinders and one with 12 cylinders it is necessary to use the same bore/stroke ratio in order to compare the engines. I have choosen a bore/stroke ratio of 1.0 but could of picked any sensible ratio. The result would be the same for a 2.0l engine running at 1200 revs/min.

1/ 12 cylinder engine has less torque than the 4 cylinder engine.
2/ 12 cylinder engine has poorer fuel consumption than a 4 cylinder engine.

agreed, the place that the 12 cylinder makes up is when a smaller stroke is used and a higher rpm. with a larger VE, higher RPMs would give a multiplier of the torque that would equal higher HP. All in all, this is not what one would be looking for if they were interested in FE. Do a small displacment turbo engine, gain the benefits of both worlds.

Few cylinders is more efficient due to thermal conduction losses. A one cylinder engine would be most efficient, just look at specific fuel consumption of engines and you'll see the larger the engine, the better.

Basically the same thing arcosine stated.

While there are many factors that would influence efficiency, the best argument for fewer cylinders is the combustion chamber volume in relation to the surface area of the cylinder walls exposed to combustion gasses and conducting heat that would otherwise be available for expansion and useful work.

3.1416 X diameter gives the circumference of the cylinder wall, while 3.1416 X radius (half the diameter) squared gives the area of a circle.

Most efficient large diesels have a bore of 3 feet and a stroke of 9 feet and run at less than 100 RPM. Low RPM, long stroke, and less cylinder wall area to absorb the heat of combustion.

4 cylinders give you a power stroke every 180 degrees of crank revolution so its easier to make them run soothly compared to less than 4 cylinders.

The area being a function of the square of the diameter means the area increases exponentially in relation to the circumference.

regards
Mech

Mech is right, and I'll add that the frictional losses go up by the square of the engine speed. Half the power produced while cruising at 3000 RPM in a 1967 Olds 400 V8 engine is lost in engine friction.