Spindoc.. I looked up your scores and it looks like your two favorite planes, for this tour at least, are the Typhoon and the F4U-1D.
Neither one really turns well, so you have to be careful when you are fighting the N1K2.
From your description (him diving on you head on) it is fairly safe to say he was going faster than you. The best way to counter this is to climb into the attack, but not directly Head-On (so you did good there I think).
After you make the initial evasion, check to see what the N1K2 is doing. If he is racking his plane around hard, I'd turn back into him nose to nose. The reason for this is that for a nose to nose merge (and that is what you are doing, even though the 'initial merge' has passed) speed plays a larger role in turning 'inside' another plane than turn rate (because speed has a great effect on turn radius, which is more important than turn rate for nose to nose turns). Since you were going about 250 (if I recall correctly), you'd pop a notch of flaps, and turn back into him fairly hard. Not hard enough to black out, but as hard as you can without stalling or blacking out. If he does the same (pulls as hard as he can without stalling or blacking out), you WILL get your nose pointed at him faster than he gets his pointed at you.
Now, this is where it gets interesting. If it were me in your shoes, I'd hose him down good, and then try to disengage. If you are in a Tiffie, you probably just killed him. If you are in the F4U, he is probably still kicking and very pissed off at you now
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Now, since you just went nose to nose again, he has probably burned off some speed trying to pull his nose around for the shot after the initial miss. This should leave you somewhat above him , albiet with probably slightly less speed than him (even after the inital hard turn, if he started at 400 or so he'll be around 250- and you'll probably be at around 200. The good news for you is that you've managed to (somewhat) equalize your energy state with him. If you fail to kill him after you get inside of him off the first turn, I'd disengage by flying as close to a opposite course to him as you can (I hope that is easy to understand, I am not explaining it very well). You may want to dive some to improve your acceleration. If he continues around in a 360 turn to come after you, he will burn off even more speed and hopefully lose all of the excess energy he started with. At that point you can, erm.. extend (
) with impunity, since the Tiffie and F4U are both faster than the N1K2 is. If he continues to chase you, start a very gently climb (keep your speed up) until you've got a two or three thousand foot altitude advantage on him, then go vertical. If he follows you up, he will stall- if he doesn't you have just placed yourself on his high 6, which is an ideal place for you to be.
You will have a very tough time 'dogfighting' a N1K2 in the traditional sense in the F4U or Tiffie, but you can BnZ at will. You can also try your hand at "E-fighting", but that is much more difficult to master than BnZ or traditional angles fighting (think dogfighting), and you will get killed. Hell... I get killed trying to E-fight Spits in 190s and 109s. It is more fun than BnZ though.. a LOT more fun.
Hope this helps, sorry for that one monster paragraph
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