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Browning machine guns in the UK fighters were a US design.
With the last sentence, I disagree: the engines from Pratt&Whitney and Wright were quite capable of providing power for world-beating fighters. USAAF preference for liquid-cooled inlines was more due to fashion (they looked more streamlined, more modern) than to aerodynamics (the zero-lift drag coefficient of almost all fighters ranged between 0.02 and 0.025, whether powered by in-lines or radials: the Spitfire and the Corsair had quite similar zero-lift drag coefficients). There were also, of course, development efforts that were not being heavily funded, like the "Hyper" project, that could have been funded more heavily, and there were liquid-cooled engines under development by Wright and P&W.
Back to our regularly scheduled programing... What if there was no Allison V-1710.
The Packard V-2500 (dismissed as a 'PT boat' engine) could have been developed into something comparable to the Daimler Benz and Jumo 211 engines. Seemed to have been reliable enough at 1350 HP in naval service, and was developed to 1500 HP later in the war, again for naval service. Before you jump on weight issues, most references will quote the weight for the naval version, with likely some of the major casting being iron rather than aluminum, and heavy water cooled exhaust manifolds, etc. Don't know what an aviation version would have weighed. Biggest problem would be reliability. What I think I know is that Packard's aviation engines in the 1920s and early 1930s were none too reliable.
Maybe but for some reason they didn't stack the flat 12s but flipped them on their sides. Engine was about 2400lbs before they tried playing with two speed propeller drives.Another tact would have been to 'go big' and build something like the Hawker Typhoon with the doubled H-24 version of the Lycoming O-1230. That actually might have been do-able rather that the effort wasted on the proposal R-40C pushers and unconventionals.
Finally, discussions always seem to forget the Hispano Suiza 12Y. Start with the 12Y and then spring off with some American thinking to get rid of that horrible multiple carb induction system, and a general strengthening to run at higher rpm and boost, ala the 12Z. The Klimov gang in the Soviet Union got more out of the 12Y than the French did, no reason the US could not have. For a real "outside the 9 dots" idea, license the Milukan AM-38. Having said all that, I agree 110% with earlier posters that a foreign engine would heve been a no go.
We don't have to wonder about the the P-36, I have posted this before.
View attachment 241259
This plane achieved 389mph at 22,700ft in Sept of 1942. It is a very early P-40 airframe, please note no visible guns and the production batch it was taken from may mean no armor and no self sealing fuel tanks. Please note that that speed at that altitude with an indicated 1100hp form the engine works out to 8% more drag than the XP-40 doing 366mph at 15,000ft with 1090hp. (last modifications)
Please note that this plane used the last version of the two stage supercharged R-1830 and also appears to have a decent exhaust thrust set up for a radial engine. I don't know if the exhaust thrust was figured into the power or not.
Please look at the both the Curtiss XP-42 and the Vultee Vanguard to see the numerous ( 14 different tries for the XP-42?) attempts to get inline streamlining for a radial engine in 1939-41.