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The Arc of the Swing occurs when the ball comes down from the top of the back swing to the release point and is finished with the follow through. The full arc of the swing is like the shape of a letter U.
The key to the Arc of the Swing is to allow gravity to bring the ball down without using muscle or pulling the ball down.
As the ball reaches the bottom of the arc, it creates a flat spot where the thumb is released. When the thumb comes out, the fingers continue through the ball creating rotation. The ball should go onto the lane like an airplane going on a runway. A common mistake that many bowlers make is to release the ball just beyond the flat spot causing the ball to be released in a slightly upward direction. This will cause the ball to lose speed and direction.
Once the ball is released, the bowler finishes the arc of the swing with the follow through. The elbow must reach shoulder height to complete the letter U.
When creating the letter U, think of having a paint brush in your hand. As the ball comes from the back swing to the top of the follow through, paint a smooth letter U without splattering the paint.