Check out this new video posted by casting guru Jon Cave of Florida. It demonstrates the acceleration phase of the casting stroke for distance casting (using the double haul). Take notice of where his arm is during the entire stroke - low and relaxed with a final push out to deliver maximum speed (the stop then causes strong negative accleration causing the fly line to sail out).
A Jon Cave fly casting instructional. Performance Fly Casting: The Acceleration Phase of the Casting Stroke