lift of the wing actually doesn't have a whole lot to do with climb. This is counter intuitive but I believe it is true.
Best climb is achieved at the point where the induced drag curve crosses the profile drag curve.
Like this.
View attachment 596925
with the plane flying at the minimum drag speed the rest of the engines power can be used for climbing. This assumes that the minimum drag speed has a comfortable margin above the minimum control speed.
Lift goes up with square of the speed, which is why the induced drag (or drag from creating lift) goes down so quickly, at least to a certain point. However the profile or parasitic drag also goes up the square of the speed so trying to fly faster to create more lift to increase climb doesn't work very well. You have less power left to actually do the work of lifting the plane.
You can estimate climb to some extent if you have (or can reasonable guess) the power needed to fly at the minimum drag speed and figure the power to weight ratio of the plane using the excess power available.
Any of our members who know more about aeronautics ( a bunch of them) are free to correct me on this.
However we can also make the same mistakes than many designers of the 30s made. Those inaccurate estimates of drag and/or induced drag that often under estameted the power needed to fly at minimum speed (prop efficiency can also screw things up).
When you have planes that outperform similar aircraft by a large margin you really have to start looking for the answer. Not always easy to find and make sure you are comparing the same things.
The US was one of the few countries that used military power for the first 5 minutes of a climb, Both Britain and Germany used a much longer time period rating. The US also, at some point during the war on certain aircraft ran take-off power for 5 minutes and then some WEP rating for the rest of the climb unless the engine overheated.
Sometimes a Non US test did use full power for a climb but it is almost always noted.
British tests for the Spitfire for instance used 2600rpm for the early Spitfire with Merlin III engines, later Spitfires used 2850rpm for the climb. Later on some spits were allowed to use 3000rpm at the higher altitudes where the supercharger could not provide full pressure. But finding a test for a Spitfire where they used 3000rpm and full boost from the ground to 25,000 ft or more is going to be a very rare test.
The P-39N in those tests seems to outperform, and by a large margin, the P-39s that came before it and the P-39 that came after it (the Q).
It was also running over the allowable temperature limits.