I have been told that the ballistic properties of fighter airplanes are really minor factors compared to its ratio of thrust to weight and drag as long as the engine is running, to the point that for example, a zoom climb from 400 TAS in a Pony with 25% fuel ought to be higher than a zoom from 100% fuel Pony under the same conditions, because the thrust/weight advantage more than makes up for the "ballistic" advantage of having more weight. Is that true?
No, it is not true.
Let's have a look at the math again.
For a ballistic zoom the acceleration would be:
a = -g - D/m
For a power zoom the acceleration would be:
a = -g + (T-D)/m
In both cases if you keep everything constant but the weight the heavier aircraft will zoom higher.
Let's take a closer look at your example of the two P51s in a vertical zoom at 400mph with one at 100% fuel and one at 10% fuel. Putting in values for gravity, mass, thrust and drag and calculating the deceleration for each, then using those values with the 400mph start speed we can calculate the time for each aircraft to slow to 150mph. Then we can use those times to calculate the distance zoomed during that time. What happens in both cases is that the heavier aircraft has less deceleration so it zooms for longer and zooms higher. In the first case with no power the heavier aircraft zoomed 180ft higher than the lighter one. Under maximum power of course both aircraft zoomed higher than in the first example but the difference between them was less at 140ft.
That's a difference in zoom of between 4 and 5 aircraft lengths just based on fuel load. Factor in dissimilar aircraft with big weight differences and different props and drag and the situation gets more complicated but when you have heavy American aircraft with powerful engines and paddle blade propellers the difference would be even greater in favor the heavy aircraft to the extent that it would have been tactically significant both in zooms and dives.
I can't recall specific examples right now, but I'm sure I have read a number of anecdotal accounts by WWII pilots that verifies that.
Regards
Badboy