Theoretically could a propeller-driven plane exceed Mach One Could a P-38 do this in a dive?

Answer 1

Theoretically, yes. But practically, making a propeller that can transition through the speed of sound is difficult. Note that due to its spinning, the airspeed over the propeller blades increases the further out the blade you go. Thus, different parts of the blade would transition through the speed of sound at different times. This doesn't make things any easier.

Since you bring up diving, the easiest way to get a propeller driven craft past the speed of sound would likely be to climb high, then stop and feather the propeller (or better yet, retract it inside the airplane) and dive through the speed of sound using only gravity.

I don't think the P-38 could survive passing the speed of sound. First, it likely doesn't have the structural strength. It would likely break apart as it neared the speed of sound.

Even if it initially held together, it would become uncontrollable. There are a number of things that would cause loss of control. The structure would probably start flexing wildly (sort of like a flag in a stiff breeze) it wouldn't be stiff enough for the large forces involved. I couldn't find the video I was looking for, but this one shows how the lift changes drastically from positive to negative with very small changes in angle of attack.

http://video.Google.com/videosearch?q=p-38&ie=UTF-8&oe=utf-8&rls=org.mozilla:en-US:official&client=firefox-a&um=1&sa=N&tab=iv#emb=0&q=aerodynamic%20oscillation

Also, sub-sonic flight controls usually become inoperative near the speed of sound. Or you can even get a reversal of control. For example, moving an aileron up will normally reduce the lift of the wing (move the wing down). But, at high speeds, moving the aileron up can cause the wing to twist a little, increasing the angle of attack of the wing. As the video above shows, a slight change in the angle of attack can have a big change in the lift. So, the slight increase in the angle of attack will increase the lift (move the wing up) - the opposite of what happens at slower speeds. Having the controls reverse direction is not good for staying in flight. :O