was based on the assumption that a single stage, 2-speed Supercharger might have been quickly developed for the P-40 that would have incrementally improved its high altitude performance in the time-frame of 1941-42. Instead, the USAAF fielded the P-40K in the Summer/Fall of 1942, which did nothing to improve the aircraft's high altitude performance but did provide additional performance for the overweight aircraft to get off the ground.
That's pretty funny that a P-40 is overweight but the P-38 and P-47 aren't?
P-40K used the low altitude power, especially when overboosting to 60" (which was secretly agreed to by Allison before Dec 1942) gave them ~1,500 + hp at 2,000 feet so that was quite useful in Theaters like the Russian Front (which is why so many Soviet pilots did so well with the P-40E and the P-40K in particular) and also in North Africa, and to some extent Burma.
In the Pacific, like at Darwin when the Japanese level bombers were sometimes coming in at 30,000 feet the altitude limit on the P-40s was a major problem, though they did work out effective tactics anyway. It did a lot better against tactical aircraft like dive and torpedo bombers such as at Milne Bay.
As Shortround noted, the V-1710-73 in the P-40K had a strengthened (first peened, then tempered) camshaft which allowed overboosting at higher levels and for longer periods. The gasoline quality also made a big difference though I don't understand precisely by what mechanism. From reading Allison memos it sounds like they are saying the better fuel didn't run as hot which seems counter-intuitive.
The later P-40 engines with the 9.6-1 gear ratio such as the V-1710-81 on the P-40M etc. had a bit higher altitude rating but were riskier to run at high manifold pressure.
SR6 has provided the rationale for why it wasn't pursued: little benefit to be achieved, and of course the fact that at about the same time, the single staged, two-speed variant of the Packard-Merlin engined P-40(F) was coming on line which was perhaps a far simpler solution to the problem than a dedicated Allison development.
The Packard Merlin P-40F raised the effective ceiling of the P-40 to 20k feet, which helped somewhat in North Africa but was still generally insufficient in terms of altitude performance. tey did use them to escort medium bombers like the A-20s, B-25s and B-26s, but escorting the heavy bombers was left to P-38s. Interestingly Packard strengthened the V-1650-1 / Merlin 28 used for the P-40F/L by coating the bearings with super hard iridium, and these too were overboosted quite a bit in the field.
P-38s however, while they found a niche early on in the Pacific, and were the best high altitude escort available in the Med and Europe until the P-51, more generally simply did not live up to the hopes of USAAF planners in the Med which is one of the reasons why the P-40 continued in use for so long. That along with the range limitation on Spitfires and the almost complete failure of P-39 units in the Med forced the USAAF and RAF to keep equipping units with P-40s until 1944 (and 1945 for RAF and in the Pacific / CBI Theater). The P-47 was what ultimately replaced the P-40 in the Med. As a radial engined plane it with a heavier bomb load it was a better fighter-bomber in many respects and it also had the altitude capacity to escort heavy bombers in theory, though in practice they still used the P-38s for that mostly I think until the P-51s were available.
The decision to use the single stage Merlin XX as the basis of the P-40's "Merlin 28" instead of something more like the Merlin 60 series is allegedly why Don Berlin quit Curtis aircraft company. I do think it was a major mistake though it's basically a question of quantity vs quality. Merlin 61 were not being produced by Rolls Royce until March 42 and I'm not sure when the V-1650-7 became available from Packard I'm guessing a bit later that year. 1942 was a very tough year for the Allies and the V-1650-1 powered P-40, for all it's limitations, was definitely needed and played a crucial role in the capture of Tunisia, the reduction of Pantellerina, the invasion of Sicily and the invasion of Italy through Anzio. The Spit V was a better interceptor but didn't have the legs for most escort missions. The Spit IX was the best air superiority fighter they had by far but there weren't enough of them, and all Spits were a bit too fragile for ground attack.
I think the Russians actually preferred the P-40K though with the Allison engine because they were fighting down low for the most part. They got about 100 P-40Fs but sent them right to PVO units (air defense). Allison engine P-40s seem to also have been preferred in the CBI.
One question I have is why weren't the Allison engined P-51s a bit more widely used in the Med? They did have them but were using them as dive bombers and recon planes mostly.
It seems like one answer to the 'supercharger dilemma' would have been to produce some V-1650-1 / P-40Fs while also diverting at least some of the V-1650-7s to P-40s along with the P-51s. The P-51s were better in many ways but a P-40 with a V-1650-7 probably would have been a pretty dangerous opponent for the Luftwaffe. I guess it was basically a question of prioritizing Strategic bombing over the (stalled out) Tactical campaign in Italy.
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