I  have a sling casting style which I believe is unique, in that I don't know of anyone else who does it this way, or of anyone who has learned from me and does it successfully.  
 
But, I think it could be the most powerful casting style, since it relies on the law of conservation of angular momentum to work.
 
If you remember watching a ice skater spinning on one toe, then pulling in her arms, and begin spinning faster until the eye cannot keep up with her movement, then you can grasp the principle.
 
To perform this, you must first put your left foot (assuming right-hand slinger) as far away from your slinghand as you comfortably can.  
-Holding your sling out to the right side, step over and around with your right foot, so your right foot lands on the opposite side of your left foot, and you pivot on your left.  
-Step over and around with your left foot in the same way, going in the same direction.  
-You have been keeping the slingarm down, now raise it up over your head and describe the smallest circle overhead with your sling, and release when you have made about one circle.
 
When I do this, I really feel a pull on my finger, and that's with a fairly short sling. It feels like the finger's about to be pulled out of its socket!  
 
And the stone simply disappears.

Douglas
 
   That is the way, more or less, that I use when slinging rocks way to heavy for my normal slinging style. You can throw a very big rock that way. The only difference is that I still try and put in lots of whip at the end of the throw. I can attest to the fact that even a big rock can be chunked suprisingly far using that technicue. Next time I get the chance I'll try it exactly the way you have written with a smaller stone, and see how it works.  
 
Thanks, it's good to know I'm not the only one doing a spinning windup!
 
WalkingBird
 

Ah! So I am not alone!  
 
I have a background in a few eastern martial arts involving spinning kicks, although alas I am no master.
 
WalkingBird, by whip do you mean that you surge back and forth just before the release? I never just "let go", but rather surge back and forth...
 
Light stones, up to 3 or 4 oz, short sling, like Jesus' forearm length sling...
 
For distance I think you want to incline your throw to about 45 degrees...
 
Like to get ahold of a police radar and really get an idea of velocity...

Douglas,
 
I hit you website last summer. I tried this technique. Indeed, that one gives an extra power. But after a few shots I felt like a drunken slinger
 
Jurek

A hardie Slingers Welcome Thomas!
 
I have slung hard balls over the backstop from mid- center field. They make good ammo if the pouch is big enough.
 
You've been slinging a long time. Tell us some stories and send some pictures.
 
Douglas,
 
You or someone has to send a video of that style! It is too late for me to think through your explanation, but tomorrow I need to give it a try.
 
So, who is going to video this one for us to view??