Well....some good advice....BUT....there's a little more to turn radius than just speed and the relationships are a bit more complicated.
Let me give you an example. Your plane has a corner velocity of 200mph. You find yourself pointed straight down at low altitude with very little room for recovery, your speed is 100mph, and your death clock (altimeter) is racing down to 0. Obviously, you're going to immediately start pulling your maximum G but what about your throttle? Do you a) throttle back, or b) go full power and WEP? 99% of all pilots will chose "a" and 99% will be wrong. This is because what you need in this situation is your absolute smallest turn radius to keep from smacking into the deck. Your smallest turn radius occurs when pulling your maximum G at corner velocity which, in this case, is 200mph. Seems counter-intuitive to the casual observer doesn't it? It's even more counter-intuitive when you're the one looking at Mother Earth reaching up to smack you in the snot locker but it's true, the answer is "b". Now, if you're in the same situation but you're at 250mph then yes, you throttle back and immediately pull max Gs to recover. This is because when you're doing a maximum performance turn at corner you're already pulling the maximum G the airplane can structurally sustain (or you black out). Above corner you can't pull any more G and excess speed increases your turn radius. Even going down hill pulling max G's can slow you down (provided you don't start too fast) and once you reach corner velocity you start to throttle back up again to sustain your best turn.
Replace the "ground" in this example with the bottom of a looping fight. As you nose over at the top you should be using full power (unless you're slow and have issues with excessive torque) and continue this as you go downhill until you accelerate to near corner velocity then throttle back to maintain corner at max G across the bottom of the loop then, as soon at your nose passes the horizon coming up hit full power again.
Now, there are times when this doesn't apply say, for instance, you're diving in on a slower low altitude target and you want to drop right into his control zone. You don't want to overshoot and you're not planning on going back up again, you want to saddle up so speed can be your enemy. In this case throttle at idle and a bit of sideslip and G can be used to control your rate of descent to arrive at your desired position with the desired closure.
How about flat turns? If you're well above corner throttle back and then get back on the throttle when near corner. That will give you your best start but you can't sustain that unless you're going down hill. Say you're locked in a sustained flat turning fight on the deck at 120mph. Do not throttle back. You can not reduce your turn radius by reducing power here because you're below corner, you can only improve it by accelerating to corner velocity and in a WWII aircraft you cannot accelerate in a flat turn at max sustained G. As a matter of fact you need all the power you have to give you your best sustained turn. About the only time you want to throttle back in this sort of turn is if you're just a bit too fast for flaps but it all depends on your strategy and the aircraft you're in. What you can do if your adversary has a better turn rate is to ease your turn a bit (throttle at max) to gain some additional speed then start to transition from a flat turn into a series of high and low yo-yo's. In the high yo-yo you can use rudder to again assist in pointing your nose and reduce your turn radius. You can actually begin to build your speed doing this provided your adversary isn't too deep into your knickers already or his airplane has a significant performance advantage on you.
There are also many occasions when the time it takes to get from point A to point B matters. Go too fast and you can overshoot and fly out in front but slow down and he'll fly out in front of you. Scissors is a great example. In this case, you're not really concerned with either instantaneous or sustained turn capability and you're not really using G to turn the aircraft, you're more pointing it. You can get well below corner and use the aircraft's pitch or yaw rate to point the nose where you want to go and end up with a very tight radius. In the flat scissors for instance, you get your nose up and throttle back to slow down to just above stall speed (flaps down!) but it's important to realize that you must then throttle back up to sustain yourself on the edge of stall. This is the backside of the power curve where it actually takes more power to fly slower. You can still "turn" but the turn is basically done by using rudder to "point" your nose and lift from your wings is primarily just keeping you in the air.
Another example is the vertical reversal. You use full power to zoom climb and, at the top you slow to just above stall then use pitch and/or yaw to point the nose down. Again, you're not using G to turn the airplane (or maybe just a bit) but, since you're so slow it's really the pitch and/or yaw being used to point the nose. In this case you use full power in the climb and, with many airplanes the torque actually assists you in yawing/rolling the aircraft around but be aware that you may need to throttle back to reduce torque effects, particularly if (for most airplanes) you want to roll/yaw right.
