I always thought that by cork screwing your punch it added power to it, that's until i did some research on the subject and to my disappointment found out that it does add power to your punch but the amount of force is so small in the whole scheme of things its not even worth talking about.
But imo what cork screwing does do is make your punch more accurate with the ability for small changes during the flight of the punch, kind of like a heat seaking missile.
I also think that the force may enter the target in a spiraling motion instead of a straight line or cone, which means it could penetrate further, also kime of the arm and lats is made easier with the forearm in this position.
Force dispertion for straight and spiral impact
Straight punch Spiral punch
Nakayama sensei discusses all these issues in the best karate series No.2 Fundamanetals.
The other thing is its a natural motion of the human arm to to turn over palm facing down when you extend your arm over half way.
Think about fully extending your arm to reach something on a desk it turns over palm down, if it extends half way like to shake hands its in the vertical position.
Here is an article on the effects of cork screwing your punch and many other karate techniques, which explains the effects much better than i ever could.
To enlarge the document below to full screen, right mouse click on the document and select full screen mode, or press the square with the arrows pointing out on the drop down menu and same again to return here or hit escape.
On the Dynamics of Karate by Florin Diacu
http://ua-mirror.pims.math.ca/pi/issue6/page09-11.pdf
karate math -