The prototype P-39 was designed with a turbosupercharger, which gave high-altitude performance above 20,000 feet of around 390mph...excellent performance for the day.
As we all know, the Army made a disastrous decision to remove the turbosupercharger, leaving the Airacobra with only an integral single stage, single speed supercharger. Performance remained excellent below 12,000 feet, yielding 360mph, but fell off rapidly above that altitude. In effect, the P-39 was a dog at high-altitude.
Of the 9500 Airacobras built, about 7000 were of the late-model N and Q Versions, which had increased engine performance above 12,000 feet. These models could attain 375 mph up to 20,000 feet before speed fell off at higher altitudes.
The early P-39D could climb at a rate of about 2400-2500 fpm up to 12,000 feet, after which the climb performance fell off sharply, falling to under 1000fpm at 25,000 feet. Late Q models had rates of climb well over 3000 fpm to 12,000 feet, reducing sharply after that.
Rate of roll was only mediocre, attaining a peak rate of about 75 degrees per second at speeds near 250 mph, thereafter falling sharply to about 50 dps at speeds in excess of 350 mph.
The P-39 had extreme control sensitivity. A P-39 fore-aft stick movement of only one inch would change the wing lift coefficient from a high speed value of 0.20 to a near stall 1.40 with a normal airplane center of gravity location. In effect, if the stick was handled carelessly the aircraft could be thrown into a stall before the pilot was aware what was happening, for stalls occurred with no warning.
The Airacobra could be dived to a maximum Mach number of 0.80 and an IAS of 475 mph, or a true airspeed of 560 mph, as measured at 15,000 feet.
The above information was gleaned from "America's Hundred-Thousand" by Francis Dean.
I have another source somewhere, which I can't lay my hands on at present, which showed test results of a P-39D against an early Zero. The Airacobra outperformed the Japanese fighter by quite a margin in speed, climb, and acceleration at altitudes below 15,000 feet. Above that altitude, the Zero could fly circles around the P-39.
Regards, Shuckins