Given the specifics of aircraft operation, large amounts of available coolant air, extra mass of cooling gear with available materials etc., I wouldn't be surprised if the result of that optimization problem is always against liquid cooling; at least for ICE engines where you can only achieve limited efficiency gains with higher temperatures and power densities.
More generally: all heat engines need high temperatures for efficiency. By Carnot's Theorem the best energy conversion efficiency you can hope for is (T_hot - T_cold) / T_hot
Where T_hot is the temperature of your combustion, and T_cold is the lowest temperature you can cool it too, ie ambient temperature at best.
If the metal walls of your combustion chamber are cold, there will be more heat transferred and more entropy generated. Looking more physically, heat lost after combustion reduces the temperature and therefore pressure of the gas on the power stroke, reducing power output for a given heat input (i.e. less efficient).
In practice, you can easily do much worse. Eg via heatloss as you say.
However, you can never do better.
To an extent yes, but the US certainly produced liquid cooled aircraft engines as well, like the Allison's and Packard Merlins powering many famous WWII aircraft. If they would have considered liquid cooled engines obviously superior, I'm sure they would have preferred those in post-WWII piston aircraft.
> neither the german nor the UK ones did (mostly, exceptions always exist).
The UK produced nearly 60000 Bristol Hercules radials, practically all used in multi engined aircraft (Beaufighter, Wellington, Stirling, Halifax being the major ones AFAIK). Sure, a much lower production numbers than the famous Merlin at 150000 engines, but far from insignificant.
Similarly, Germany produced over 60000 BMW 801 radials, mostly used in the FW190A fighters but some were also used in some Ju88 variants. In comparison the DB 600 engines powering mostly Bf 109 was about 60000 as well, and about 70000 Jumo 21X series used mostly in bombers.
So very broadly speaking, of total aircraft engine production, both UK and Germany produced about 1/3 radials and 2/3 liquid cooled.
Briston Hercules was fitted to sever plane types due to lack of production capability for the more complex liquid cooled engines, this was specifically a case with Beaufighter which suffered badly for it.
I can think of plenty of reasons the simpler design with one less failure mode might dominate production during the war, without being the obviously better choice given peacetime applications and seventy years of technical advances.
Distilled impression.
Water cooled inline engines. Small frontal area means lower drag. Water cooled provides a forgiving flexible operating envelope. What you want in a fighter. Downside, more complicated. Upside better performance means kill enemy better.
Air cooled radials. The drag penalty is less as the engine size increases. More reliable as long as you stay inside the design envelop. Scales up better than inline water cooled engines. Better suited for multi-engined bombers with a well defined mission profile.
At the end of the war though it was obvious that turbojets were the future for fighters. Which is why water cooled engines went away. Radials though are more efficient at lower speeds than early turbojets which is why they persisted.
Further, I'd say in history there's a lot of path dependence here (in aviation engine development as well as elsewhere, obviously) as well rather than 'pure' arguments based on the best option for a from scratch design. As it wasn't clear at the time which engine type would 'win', major powers developed both lines in parallel, if for no other reason but to not be so much behind their competitors in case some development would cause one of the engine types to clearly pull ahead.
WWII showed that both air cooled radial and water cooled inlines could be used for top of the line fighters for the entire conflict. After the war, it was clear that for speed jets were going to be the future and there wasn't the wartime pressure to keep any and all production lines going at maximum capacity, so aircraft designers had more leeway in choosing powerplants. Perhaps it was because US multi-engine aircraft designers were familiar with radials and it was clear to them they were plenty good enough, perhaps it was better reliability, but radials they chose (with some exceptions, obviously).
Mostly it was due to end to end design of entire engine pod which made all operations better. Meanwhile USA had, well, a lot of radials and radial making manufacturing lines and people who had experience with radials but little idea about much more complex liquid cooled engines.
Presumably you mean the Merlin and not, say, the Sabre? :)
But anyway, that's interesting, haven't heard of that before. Do you have some more information on this topic?
From what I've read Americans were shocked to find out how 'hand built' the Merlins were, with pretty large differences between each engine, engines being delivered with metal filings in the crankcase requiring inspection and cleaning and whatnot. So a large part of the work Packard did for the license produced Merlin was tightening up the design so it could be mass produced much faster on production lines. Of course this doesn't prove the RAS point you made one way or the other, but it seems strange that if Americans put so much more emphasis on efficient production that they wouldn't have put similar effort into serviceability?
As for serviceability, the difference was in design - American engines were effectively "thrown over the wall" to airplane designers, resulting in such beautiful designs like B-17, where IIRC inspecting or changing a sparkplug started by removal of propeller because apparently even good idea fairy was out drinking when they designed it.
In comparison Rolls Royce designed a standard "pod" for the engine that would be then minimally adapted by plane designer, with an eye towards servicing and commonality.
So the tolerances might have been tighter on US production lines, but little thought was placed at least in some designs on how to support operations on the planes instead of just building them. (Something that arguably is present today with F-16 at least, and possibly F-35 too)
Not too familiar with the maintenance requirements of the F-16, but admittedly having a hydrazine powered APU is a pretty WTF design choice.
The difference between the Thompson M1928 and the M1A1 isn't that the M1A1 is superior, and yet they cranked the handle on the latter as hard as they could during the war.
So "If something were better than something else, why did they make more something else during WWII?" doesn't persuade me. Nor does it eliminate other arguments which would make sense.
Well, let me clarify that as "superior in whatever dimensions the designers of those post-WWII piston engined planes considered important". Hope that helps.
> I can think of plenty of reasons the simpler design with one less failure mode might dominate production during the war, without being the obviously better choice given peacetime applications and seventy years of technical advances.
To be clear, I was writing about the immediate post-WWII environment before jets made piston engines obsolete except for the lowest end of the market. Aviation piston engine development pretty much stopped then.
Sure, a "modern" aviation piston engine for the GA market will quite likely be a water cooled design, if for no other reason that there is so little R&D money available for piston aviation engine development that most likely it's going to be based on a car engine.
Or to put it another way, the surface area of the cooling fins is not proportional to the surface area of the cylinders without any fins, but to the power output of the engine.
B) combat aircraft have to deal with bullet holes
Well, how do you define high performance? Judging by speed at least, Tempest Mk II, Sea Fury, Bearcat, and P-47M are among the fastest piston engined planes ever made.
> B) combat aircraft have to deal with bullet holes
Sure. But an engine that lacks a critical subsystem by design (say, a liquid cooling system with pumps, pipes, radiators etc.), all else being equal, is less failure prone than an engine that has it. Whether that failure happens due to shells or mechanical failure.
You could have liquid cooling, but it could be different from a car liquid cooling. For example, maybe you don't need pumps and could rely on a sturdy passive convection system. (Also include some fail-safe aspects)
Much like the transition motorcycle engine manufacturers made, moving away from air cooling in the late 70's. The first innovation being under piston oil jet cooling and then moving progressively to water cooling.
Oil cooling offers little additional risk or complication over air cooled designs, but there are limitations on liner/piston temperatures and additional vapors which increase maintenance that don't exist with water cooling.
It really comes down to whether it seems reasonable to trade on some risk for economy, but ultimately recip engine flight isn't efficient anyway