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I've been reading about WW2 planes lately. Some of them have 12 or even more pistons in their engines.

But if your goal is to increase power, why would you add more pistons instead of simply increasing the size of the cylinders?

Example: The P-51 Mustang had a V12 engine with a total displacement of 27 liters. So that's 2.25 L per cylinder. Instead, why not have a V4 engine with the same total displacement, which would have been 6.75 L per cylinder?

Correct me if I'm wrong, but...

Such "collectivizing" of the cylinders would be more efficient for a number of reasons. The friction of piston rings scraping the cylinder would be less, meaning less oil and more power. The crankshaft and related things could be shorter. I believe it would be lighter for another reason too: the surface area goes up less than the volume (squared versus cubed). Probably the engine as a whole would be simpler.

I believe this concept can be applied to radial engines as well as inline engines. I made an assumption that 4-stroke engine needs a minimum of 4 cylinders. Today that is not true but during WW2 with the technology of the time, I'm not sure. There were radial engines with 3 cylinders. I'm unaware of any 4-stroke engines with 2 or less cylinders in that era.

Anyway, why not just make the cylinders bigger?

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    $\begingroup$ This isn't really specific to aviation. The same thing is done in car engines. $\endgroup$ – reirab Dec 8 '16 at 6:48
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    $\begingroup$ @reirab I would argue it's more specific to aviation just because it would save weight. Weight is more important for aircraft than, say, car or train engines. Nevertheless, if it applies to aviation, I hope it's on topic here regardless if the principle applies to other fields. $\endgroup$ – DrZ214 Dec 8 '16 at 6:51
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    $\begingroup$ One reason is that you can build a larger engine just by adding more cylinders, using the same pistons, rods, &c. So a 4-cylinder O-360 becomes a 6-cylinder O-540. Other (possible - I'm not an aviation engineer) reasons might include things like rotating inertia & volumetric efficiency. Consider the difference between the V-twin of a Harley-Davidson, and the high-revving 4 & 6 cylinder engines used by most of the competiton. $\endgroup$ – jamesqf Dec 8 '16 at 6:56
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    $\begingroup$ @jamesqf your motorbike analogy is a good one. Bigger cylinders means a lot of torque at low rpm. More cylinders generally gives a nicer torque distribution. Also there's the vibration issue, a few big cylinders won't counter each other a nicely as several smaller cylinders. $\endgroup$ – Notts90 Dec 8 '16 at 7:26
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    $\begingroup$ @DrZ214: WW2 era motorcycles tend to be 1 cylinder $\endgroup$ – slebetman Dec 9 '16 at 6:52
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Constraints

Different applications have different constraints:

  • Aviation: very light weight, highly reliable
  • Marine: very high endurance
  • Automotive: moderately light weight, responsive
  • Motorcycle: very light weight, very compact, very responsive

Different technology ages yield different solutions due to additional constraints, always limited by the then contemporary technology:

  • Pioneer era: make it work
  • World War I/II era: as fast as possible
  • Post-war era: further, faster, better
  • Fuel crisis era: as efficient as possible

Aircraft Engines

The question is about the optimization of number of cylinders versus displacement volume per cylinder for engines used for aviation. This narrows the scope to “internal combustion reciprocating piston engines” (plus the Wankel engine as a very special case).

Obviously, rockets, pulse jets, turbine-powered, and electric engines have no cylinders, and steam engines were never (successfully) used in aircraft.

Number of cylinders and the cylinder displacement are two out of countless parameters that go into the design of any engine. Both may be used to increase the power output.

Power Increase

The power output of an engine may be increased either through the number of cylinder or through increasing the cylinder displacement (or both).

Each change of parameters causes the gain or loss of certain wanted characteristics. These are listed further below under (N), (n), (D), and (d).

  • Increasing the number of cylinders means gaining (N) and losing (n)
  • increasing the cylinder displacement means gaining (D) and losing (d)

Adding cylinders is easier than increasing the size of the cylinder. The cylinder geometry does not change. Identical engine parts can be used multiple times in the same engine design (cylinder banks, cylinder heads, or complete engine blocks).

Tradeoff shift

Starting from one engine configuration, the same power output may be achieved by

  • gaining (N) and (d), and losing (n) and (D) or
  • gaining (n) and (D), and losing (N) and (d).

Reasons to increase the number of cylinders (N)

  • Torque directly scales with the number of cylinders
  • Increasing the surface-to-volume ratio is advantageous for air-cooled engines
  • Increase the power: Adding cylinders is easier than increasing the size of the cylinder. The cylinder geometry does not change. Identical engine parts can be used multiple times in the same engine design (cylinder banks, cylinder heads, or complete engine blocks)
  • Improve balancing of forces and momenta
  • Reduce the time between power strokes
  • Decrease the impact of a failing cylinder
  • Improve the flatness of the torque distribution over revolution speed.
  • Enable more flexible and more distributed form factor

    enter image description here

    Pratt & Whitney R-4360 Wasp Major, 28-cylinder, 28 l, 3500 hp, 2700 rpm, built 1944-1955.

Reasons to decrease the number of cylinders (n)

  • Simplicity: less moving parts improve robustness, decrease the need for service, thereby increase the availability.
  • Enable a more compact form factor

    enter image description here

    Mercedes 1 cylinder, 1.5 kW, 720 rpm, 84 kg, built 1888.

Reasons to increase the cylinder displacement (D)

  • Increase power through torque

    enter image description here

    BMW IIIa, 6-cylinder, 19.1 l, 200 hp, 1400 rpm, built 1917.

Reasons to decrease the cylinder displacement (d)

  • Smaller displacement means smaller pistons, shorter rods, or both. Either way, smaller displacement allows for higher revolution speed, and higher acceleration.
  • Smaller combustion chamber will increase the time required for the flame expansion (gasoline only, not diesel). This allows for higher revolution speed.
  • The valves are limiting the gas stream into and out of the cylinder. The valves are subject to the surface-volume ratio. Smaller cylinders are easier to fill and empty through the valves, allowing for higher revolution speed.
  • At a given compression rate, smaller cylinders have to withstand less total force, allowing for a lighter engine structure (less weight).

    enter image description here

    JPX PUL 212, 1 cylinder, 212 cm³, 11 kW, 6000 rpm.


Notes

  • Radial engines belong to the WW I/II era. Most of them were air-cooled. For air-cooled engines, the surface-to-volume ratio matters. Therefore increasing the number of cylinders instead of the displacement per cylinder is obvious.
  • Aircraft during WW I/II had to be as fast and powerful as possible to attack and defend. There was no good reason to go for less than 6 cylinders.
  • Four-stroke engines perfectly work with 1, 2 and 3 cylinders. They are used powered paragliders respectively ultralight aircraft.
  • Certain cylinder numbers are more preferable to due symmetry reasons

    • 6, 8, 4 for in-line engines
    • odd numbers (per row) for radial engines
  • Building radial engines with an even number of cylinders is well possible, albeit an even number in one row us not preferable. Multi-row radial engines with even cylinder number have been flown in many aircraft.

  • Automotive engine developers prefer 0.5 l per cylinder as ideal trade-off.
  • A high cylinder count would be necessary to build high power piston engines, but this segment is now occupied by jet engines.
  • Radial engines with less than 5 cylinders exist. Here is a radial 3-cylinder, built 1930 in the USA:

    enter image description here

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    $\begingroup$ It was probably easier to add cylinders (fewer design decisions to review, fewer drawings to alter, fewer tooling changes) than to increase displacement. Increasing displacement means more or less designing a new engine vs. making modifications to an existing design. $\endgroup$ – Dan Pichelman Dec 8 '16 at 14:17
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    $\begingroup$ @DanPichelman Just as with CPU power on modern mainboards. It's easier to just add more "phases" (up to 40) that can be shared with 4-phase budget boards instead of designing more powerful single "phase" to lessen problems with synchronizing them. The availability of high-power mosfets and individual cooling also plays a role. The similarities to engine cylinders is striking ; ) $\endgroup$ – Agent_L Dec 8 '16 at 14:39
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    $\begingroup$ cool photo !!!! $\endgroup$ – Fattie Dec 8 '16 at 15:15
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    $\begingroup$ "Either way, larger displacement will limit the maximum revolution speed." Indeed, look at the opposite: a Yamaha R1 engine has tiny cylinders with a redline of 14,500 rpm! $\endgroup$ – aholmes Dec 8 '16 at 16:14
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    $\begingroup$ An easy mistake to make, but that's not a Dutch engine: the Szekely Aircraft & Engine Co was headquartered in Holland, Michigan. Also it was nicknamed the Flying Dutchman, just to confuse us :-) $\endgroup$ – TonyK Dec 9 '16 at 0:53
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Your reasoning is correct if engine mass is not important. Ships use huge engines, because increasing the number of cylinders beyond 8 will have diminishing returns in terms of smoothing out the torque ripples, and bigger cylinders help to increase efficiency. But aircraft need to keep the mass of the engine down.

Wartsila-Sulzer RTA96-C turbocharged two-stroke diesel engine

Wartsila-Sulzer RTA96-C turbocharged two-stroke diesel engine during assembly (picture source). Its size makes this engine supremely efficient: Its 14-cylinder version produces 108,920 hp at 102 rpm and has a thermal efficiency of more than 50%. Specific fuel consumption is only 0.260 lbs/hp/hour. But it weighs 2600 tons!

Engine power is the product of torque and speed. To maximize engine power, the speed must be kept as high as possible. Increasing cylinder size will limit the speed at which the engine can be run due to the speed of the combustion process inside the combustion space. If the cylinder diameter grows too big, the flame front originating from the spark plug will not have traveled far enough to have burnt most of the fuel by the time the piston moves down again. Only adding more cylinders will increase power while keeping the speed of the engine constant.

Here is a comparison of WW I aircraft engines from the excellent enginehistory.org site. Note how the figures for bore and speed correlate inversely (the Austro-Daimler 120 was a pre-war design and saw later speed increases):

Comparison table of WW I aircraft engines

Graphical comparison

Graphical comparison, the Austro-Daimler is shown with the specs of a later version.

Quote from the linked PDF (enginehistory.org):

The large bore diameter, however, pushed the upper limit of an aero-engine cylinder. Adequate cooling and fuel efficiency require a complete as possible combustion of the fuel-air mixture and this complete combustion requires that the flame fronts moving across the combustion chamber from their respective points of ignition be given time to meet. The speed of a four-stroke aero-engine with a large cylinder bore is thus actually limited by the rate of combustion of the fuel-air mixture which for a given cylinder and mixture is a constant and thus efforts to increase the output horsepower by increasing the speed of an engine with a large bore cylinder may result in incomplete combustion, over-heating and detonation.

Other limits to engine speed like loads on the connecting rods or adequate cylinder filling and flushing can be dealt with by using materials of higher strength and more valves per cylinder, respectively, but when the type of fuel is given, the hard limit for engine speed is the cylinder's bore. So the only way to increase power without hurting the power/weight ratio is to add more cylinders.

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    $\begingroup$ If the cylinder diameter grows too big, the flame front originating from the spark plug will not have traveled far enough to have burnt most of the fuel by the time the piston moves down again. If I'm interpreting this correctly, then diesel engines will not suffer this problem. No matter the volume of the cylinder, the auto-ignition conditions will be met by the entire volume once the piston moves down far enough. So there is no "speed of flame front" in that case. Is this valid? $\endgroup$ – DrZ214 Dec 9 '16 at 4:54
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    $\begingroup$ P.S., this is just an off-topic aside, by why would a huge marine engine use 2-stroke instead of 4-stroke? 2-stroke combines the exhaust phase with the fuel intake phase, and therefore some of the income fuel escapes out the exhaust without being burnt. I thought 2-strokes were only best for very small applications like small watercraft, not huge marine vessels. $\endgroup$ – DrZ214 Dec 9 '16 at 4:55
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    $\begingroup$ @DrZ214 2-stroke marine engines are diesels. They don't have a fuel intake stroke, it's just air intake (fuel is injected after compression). So fuel can't escape via the exhaust, unlike a 2-stroke petrol engine. That's why 2-stroke is a viable option for diesels, and halving the number of cylinders is a win... $\endgroup$ – Brian Drummond Dec 9 '16 at 19:30
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    $\begingroup$ @DrZ214: Fuel is injected in Diesels long after the auto-ignition conditions have been reached - otherwise no complicated high-pressure fuel injection would be needed. Fuel vapor spreads out from the nozzle and ignites at the spray penetration boundary after an ignition delay period caused by the heating of the fuel vapor. This is not an instantaneous, sudden ignition of all the fuel but a cone originating from the injection nozzle in which the outer parts ignite first and heat up the rest which burns as it mixes. See here for details. $\endgroup$ – Peter Kämpf Dec 10 '16 at 9:28
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    $\begingroup$ @DrZ214: Technically, auto-ignition conditions need both the right temperature and the right fuel-air mixture, so they can only be reached after injection. What I meant is that the compression-induced temperature is high enough before fuel is injected, or the high pressure and exact timing would not be needed. Gasoline injection is a comparable lazy process happening in the suction pipe or during the compression stroke, and gasoline compression ratios are limited by the knock limits. Diesels operate far beyond the knock limit. $\endgroup$ – Peter Kämpf Dec 11 '16 at 8:43
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When a cylinder gets bigger—

The square-cube principle states that its volume grows faster than its surface area.— Wikipedia

Pressure and mass:

Reducing the number of cylinders increases the amount of force per cylinder and per attachment point to the crankshaft.

Since the surface area doesn't scale as fast, all the engine parts will have to cope with much greater pressuresforce over area.

The engine with the same energy output and fewer cylinders will be heavier and harder to cool.


Can it be built? Absolutely.

Will it fly nicely? No. Because it'll be way too heavy.

You find huge cylinders in applications where weight is not an issue, like on ships.

Streamlining:

enter image description here
(Source) Small cylinders fit nicely in a thin aerodynamic shape.

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    $\begingroup$ "Exponentially"? $\endgroup$ – pericynthion Dec 8 '16 at 20:08
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    $\begingroup$ Exponentially doesn't just mean "more than linear". It means "more than any polynomial". In this case, the scaling is probably something like quadratic, scaling with diameter squared. It's a fast-growing function, but nowhere near exponential growth for large ratios. I wish people would stop using "exponential" to mean "anything more than linear", although a linguist would probably tell you it is gaining that alternate meaning in casual English. $\endgroup$ – Peter Cordes Dec 9 '16 at 5:00
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    $\begingroup$ @pericynthion "Exponentially" perhaps came from a misunderstanding. The volume increases with the cube of the radius. The surface area increases with the square of the radius. Both of those are exponential. However, dividing them (which is what the ratio is supposed to be) gives you plain linear r, or 1/r if you do it the other way. Both of those are linear. Therefore, "surface area to volume ratio" as the graph is titled should be linear. I don't know who drew that graph or where it came from, but if it had actual numbers labeled I think we would see the error. $\endgroup$ – DrZ214 Dec 9 '16 at 5:01
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    $\begingroup$ @DrZ214: r^2 is quadratic. Exponential is 2^r (or any constant to the power r), which is a very different function. One interesting property of an exponential function is that it is its own derivative: the slope of e^r at any point is e^r. x^2 doesn't have this property (the slope is 2x). When you're trying to reason about physics / math, it's usually good to be accurate with your terminology. Normally I wouldn't nitpick about this common (mis-)use of "exponential", but we're doing physics here. $\endgroup$ – Peter Cordes Dec 9 '16 at 5:09
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    $\begingroup$ @PeterCordes Sorry. "Exponential" is a loosely used term and you have every right to clarify it. But I really do believe ymb1 made the misunderstanding based on r^2 area and r^3 volume, when really the ratio is linear. At least, that appears as the most likely explanation to me. However, I also made a mistake in that 1/r is a curved graph, so it turns out the original graph may be right after all. Sometimes pursuing these things leads to a circuitous route. $\endgroup$ – DrZ214 Dec 9 '16 at 5:13
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You said it yourself with the surface-area-to-volume-ratio. You have to get the heat out of the cylinders, and if they're too big you can't do that effectively. It's also difficult to get even, complete, rapid combustion as the volume increases.

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  • $\begingroup$ I don't think this reasoning is correct. Engines don't need cooling of the burning air/fuel charge, they need cooling of the cylinder wall and the oil film on the wall to prevent it from decomposing. For efficiency you want the charge to be as hot as possible, hot air exerts more pressure on the piston. Less heat loss to the cylinder wall is one reason why large cylinders are more efficient than small ones. Having said that, larger cylinders require thicker walls to withstand the higher total forces and that may be an issue for air cooling. $\endgroup$ – JanKanis Nov 5 '18 at 8:29
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Others have already mentioned the scaling of volume vs scaling of surface. However the most important part about the surface is valve area.

When you scale a cylinder 2 times you get 8× as much volume but only 4× bigger valves. This means that same volume of the cylinder is now served by 2 times smaller valve area. This area determines how fast you can fill and empty the cylinder. This means that you have to turn the rpm down. As more rpm means more power, that means you get diminishing returns: twice as big cylinder will deliver less than twice as much power.

Adding another cylinder, on the other hand, is almost perfectly linear: twice the cylinders mean twice more power.

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Most was already said, but I'd add following:

  • More displacement means heavier pistons which have higher inertia. This limits RPM and produces serious loads on engine components. To withstand these loads, other components have to be more rigid and thus heavier.

  • Power is the product of momentum and revolutions. Increasing rpm rate yields power faster and it is easier way to get more power (to a certain extent) rather than increasing momentum. To rise RPM, lighter internal parts should be employed. AFAIK, in aircraft applications, unlike automotive, higher RPM is preferred over higher momentum. You don't need power at the low-rpm end as much as in a car.

  • The more displacement one cylinder has, the more difficult it is to achieve uniform mixture formation and effective, complete combustion. That is why in automotive engine 4-cylinder engines most often limited to 2.0-2.5 liters, 6-cylinder - to 3-3.3L, 8 cylinder - up to 4-5 liters, and so on. This keeps volume per cylinder to a certain reasonable level (0.5l/cylinder).

  • Limit of volume per cylinder is also determined by combustion speed. On high RPM it may turn out that combustion is not finished when power stroke is complete, so flame shoots up from cylinders and eventually melt valves. As a variant, the engine won't be able to speed up over certain RPM at all. This issue could be partially negated by early ignition and double spark plugs, but again this is not as effective as keeping good volume/cylinder ratio.
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    $\begingroup$ @Federico Thanks for corrections! $\endgroup$ – Eugene Dec 9 '16 at 13:50
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With more cylinders, the strokes are so timed that, when one cylinder is compressing, some other gives out power, and so on. This ensures that the power output (or mean torque, as will be shown in a T-theta diagram) will remain constant over complete rotation of crank. Kinetic energy stored in flywheel is proportional to it's mass (actually mass moment of inertia). If engine requires less energy from flywheel for compression strokes, K.E. required to be stored in flywheel is less. And flywheel could be made lighter .

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  • $\begingroup$ Could you provide such a T-theta diagram? Most people probably don't know it. $\endgroup$ – Gypaets Dec 9 '16 at 19:31
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    $\begingroup$ Do aircraft engines really need a flywheel? I would have thought the propeller could serve that function. And anyway, with 6 or more cylinders, the inert strokes should be pushed through by the powered strokes so I'm not sure if a flywheel is needed to balance it out. $\endgroup$ – DrZ214 Dec 9 '16 at 20:07
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Planes need to conserve weight. In other words: it wants an engine with a high power/weight ratio. The power produced by a cylinder is proportional to the surface area of the piston (if the pressure stays the same). So, if you divide all the dimensions of a engine cylinder by 2 the power produced is 4x smaller, but the weight of the cylinder is 8x smaller. Hence, the power/weight ratio is twice as high. That's why planes prefer engines with lots of small cylinders over an engine with a few large cylinders. In engineering this is called 'dimensional analysis', see https://en.wikipedia.org/wiki/Dimensional_analysis

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  • $\begingroup$ Strictly, the force produced by a cylinder is proportional to the surface area of the piston if the surface area stays the same. To say that the power (horsepower or kW) produced by a cylinder is proportional to surface area we must add the assumption that the average velocity of the piston remains the same. Broadly, this assumption is correct and means that that the longer the stroke of a piston, the lower the RPM of the engine, which hurts power/weight ratio as you describe. $\endgroup$ – Level River St Dec 9 '16 at 12:10
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    $\begingroup$ I don't understand your reasoning. Work by the piston = Force x Distance. $\endgroup$ – key Dec 9 '16 at 15:06
  • $\begingroup$ And power = work / time = force x velocity. $\endgroup$ – Level River St Dec 9 '16 at 15:54
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    $\begingroup$ I don't understand ' Strictly, the force produced by a cylinder is proportional to the surface area of the piston if the surface area stays the same' $\endgroup$ – key Dec 9 '16 at 16:01
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    $\begingroup$ muscular FORCE (measured in newtons, lbf or kgf) is proportional to muscle area. muscular WORK is given by force times distance. Therefore to lift your friend when you are taller, you have to lift him twice as far, which is another, different way of looking at why it is more difficult. POWER is work / time. So if you run upstairs you generate more power than if you walk upstairs. When talking about the relationship between force and power (in the physics / engineering definition, which may be abused in general conversation) it is always necessary to mention both time and distance. $\endgroup$ – Level River St Dec 9 '16 at 16:32
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Early aviation was not based on very much on all these scientific or engineering concepts, but based on what they found worked. Many early aviation engine manufacturers primarily came from automotive industry, and they took what they knew worked, and doubled it to meet power requirements (flat 6 to v12). Why they tended to not simplify and reduce the number of cylinders probably had a lot to do with reliability (more cylinders, more redundancies). The British, and by alliance Americans, had the first jet engine concepts of the war but focused on more practical technology; which would have you wanted to test fly?

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    $\begingroup$ On the contrary - the Wright Bros were the first to develop an accurate and reliable science of aerodynamics, which is what allowed them to develop a working airplane. Aviation has always been based around science but is reluctant to stray too far from established and workable designs $\endgroup$ – Carlo Felicione Oct 10 '18 at 13:24

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