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THE SWEET SPOT

It's not a myth, it's real and here's the proof.

The challenge for young players is to learn where it is and why it matters - mostly in how the ball feels when hit. Why? Because if the contact is less painful, then a hitter will develop confidence, a willingness to hit the ball even on cold days! So, while this study is based on physics research, and began with a tennis racquet, it has some very practical applications in the batter's box during a game.

 

Batters know from experience that there is a sweet spot on the baseball bat, about 17 cm (6-1/2") from the end of the barrel, where the shock of the impact, felt by the hands, is reduced to such an extent that the batter is almost unaware of the collision. At other impact points, the impact is usually felt as a painful sting or jarring of the hands and forearm, particularly if the impact occurs at a point well removed from the sweet spot.

The sweet spot of a bat exists partly because bat vibrations are not excited significantly at that spot and partly because the spot is close to the center of percussion.

Actually, a baseball bat, like a cricket bat or tennis racquet, has two sweet spots. If a ball impacts at either of these spots, the force transmitted to the hand is sufficiently small that the player is almost unaware that the impact has occurred. If the ball impacts at a point well away from the sweet spots, the impact can be quite painful. One of the sweet spots is the vibration node; the other sweet spot is called the center of percussion (COP).

These and some other significant spots on a tennis racquet are shown here. Contrary to popular opinion, the two sweet spots do not coincide with the point at which the ball rebounds with maximum speed, nor do they define the spots where the force on the hand is zero. Forces on the hand arise from three independent motions of the handle, namely rotation, translation and vibration.

The vibrational component is absent when a ball strikes the vibration node. The rotational component, arising from recoil of the racquet head, exerts a torque on the hand, causing it rotate about an axis through the wrist. As a result, a force is always exerted on the upper part of the hand, and a force in the opposite direction is always exerted on the lower part of the hand. The two forces are equal and opposite for an impact at the COP, with the result that there is then no net force on the hand or forearm. This means that there is no sudden jarring of the arm for an impact at the COP.

 
A bat is similar to a racquet but there are some obvious differences. For a tennis racquet, only the fundamental mode of vibration is excited by the impact since the impact duration, about 5 msec, is too long to excite higher frequency modes of the racquet. The impact on a baseball bat is shorter (since the bat and ball are harder or stiffer), about 1.5 msec.

As a result, the fundamental and second vibration modes are both excited with about the same amplitude. These modes are shown in the bat diagram. Hence, there are two vibration nodes in the barrel. An impact at the fundamental node will not excite that mode, but it will excite the second mode. Similarly, an impact at the node of the second mode will not excite the second mode but it will excite the fundamental mode. The ideal spot to hit the ball is half way between the two nodes since both modes will be excited but only with small amplitude. This spot is also close to the center of percussion.

 


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