The sweet spot is near the label on a Louisville Slugger. An experienced batter knows its location well, but the scientific definition is unclear, because different locations can have differing effects.
One possible sweet spot is the center of percussion, which is the location where the ball may impact the bat without causing a reaction force on the hand. An impact at any other location can cause the handle to feel like it is jumping in the hand.
Another possible sweet spot is a location called a vibrational node. The impact of the ball causes the bat to vibrate in waves that have dead spots, or nodes. Multiple waves occur at the same time, but the two largest waves both have nodes close to each other about 6.5 inches from the bat's end. Hitting the ball here results in small vibrations. Large vibrations can potentially take energy away from the ball and be painful to the hand.
A third location of interest is the bat's center of mass, which is located by balancing the bat horizontally. The sweet spot is usually located not at the center of mass, but somewhere between it and the end of the bat. The center of percussion, vibrational node, and center of mass are not generally the same location, but all are determined by the geometry, mass distribution, and material properties of the bat. The sweet spot preferred by batters appears to be close to the center of percussion and the vibrational nodes.
Reference: http://www.kettering.edu/~drussell/bats-new/bend-sweet.html Different batters have different opinions. Personally, my sweet spot is about 4 inches down from the far end of the bat.
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