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For Britain I think you have 2 choices. First choice employ a man to whack Roy Fedden on the knuckles with a ruler every time he mentions sleeve valves. Eventually the bruising and scar tissue will persuade him to design a 14 cylinder twin row engine with a chunky three bearing crank and enclosed valve gear.
Second choice is throw a hand grenade into the design office at Armstrong Siddeley. A new batch of engineers come in and design a 14 cylinder twin row engine with a chunky three bearing crank and a modern cylinder head design.
Do either or both in 1932 and you could have two 1350hp Radials available for aircraft production in 1937. Sunderland's, Whitley's, Wellington's and Halifaxes could all use the engine/engines. Merlin's can cover everything else.
'Mercury 14' will be about 2350 cu in.
So you can play games with cooling (more fins) and RPM (center bearing, stronger crankshaft, etc) but basically you have 90.5% of the displacement of an R-2600 or 92% of the displacement of a BMW 801. You need either higher rpm or higher boost pressure to get the same power.
R-2600 was making 2400 rpm (for 'base' power of 1600 HP), 2600 rpm (for 1750 HP) and 2800 (for 1900 HP). No ADI, but hi oct fuel. No great shakes in boost, better versions used up to 42-43.5 in Hg (1750 HP versions) or 48 in Hg (1900 HP). At altitude it was around 44 in Hg; for reasons unknown to me, R-2600 was not allowed for max RPM beyond certain altitude (cooling problems?), something shared with a number of engines.
Me - I'd try to gain the most from a technology the companies are most fluent, in order to combine power, availability and reliability in a single package. Eg. the Germans might indeed look at both direct F.I. and the K.gerraet, while Japanese might start adding F.I in the later war years? For the UK and USA, rather pick the a good pressure carb, while staying away from the float type carb.
The R-2800 C series were mostly outfitted with 1-stage supercharger, only the F4U-4 seems to use a 2-stage supercharged C series. R-2800 was making a lot of power, fuel consumption will be high.
As for the 'power section', I'd go with a 14 cyl type, again for availability early enough after the short development time specified (3-4 years before service use), and to keep the weight down. Engine size and dry weight should ideally be kept in check, so that removes R-2600 (size) and BMW 801 (weight). Granted, BMW was capable for making the best power of the lot, but still - the TANSTAAFL rule applies as ever.
The smallest but still powerful 14 cyl engine early on was the Nakajima Ha 41, making 1260 CV at 3700 m (BMW 801C doing 1380 CV at 4800 m, but at 2/3rd more weight; granted, there was a 2-speed S/C on the 801C). It was modified into the Ha 109 with a 2-speed S/C, bigger impeller (diameter of 12in now), turned better RPM, and gained some weight, now at 720 kg; 1440 HP at 2100m or 1220 HP at 5200m. Not too bad on 91 oct engine and 37.5L. Impeller of
Next Japanese engine in size was the Mitsubishi Kasei, that was about as powerful as the ~30-50% heavier BMW 801 of the day. One of earliest adopter of water-alcohol injection among the aero engines, circumventing the lack of hi-oct fuel by a lot. A bit too wide at 1340 mm? Nice, big S/C, started with 11in impeller, moved to 12.6in quickly.
tl;dr - I'd probably want the Kasei-lookalike with a bit shorter stroke for a smaller diameter and better RPM, and then add country-specific bits & pieces. Dry weight of probably 750-800 kg. For the USA, a 2-stage S/C or turbo. Germans - fuel injection, K.gerraet, better exhausts early on. Hi oct fuel when available, ditto for ADI. Historically, both Japanese and Soviets were getting on the F.I. for the radials by late war.
Was the BMW 801 really that heavy? The Smithsonian quotes 880kg dry for their example but wiki quotes 1070kg Dry.
BMW 801, Radial 14 Engine | National Air and Space Museum
I suggest the oil cooler is being included.
Look here: link
There is nothing wrong with the BMW 801 apart from two thjngs
1 it not being in service earlier.
2 a two stage 4 speed (independent drives) inter cooled version not becoming available by early mid 1943. Such an engine would have been the BMW 801R but this was thwarted by successfully allied bombing in 1944. Corsairs and Hellcats both had two stage Super Chargers. The BMW 801R would have transformed the performance of the Ju 88, Do 217 and Ju 290