Center of Percussion
The center of percussion is the impact location which produces no reaction force at the pivot. It is only by coincidence that the COP is often located near the so-called “sweet spot” of the bat. While early bat performance tests prescribed impacts at the COP, modern methods do not use the COP.
The center of percussion (or COP) of a bat is the impact location that produces no reaction force at the pivot point. It may be distinguished from the balance point with a simple test (a kick). If a bat placed on the floor is kicked at its balance point, it will move forward, but not rotate in the plane of the floor (although it may roll about its long axis). If the same bat (still on the floor) is kicked at its COP, it will tend to rotate about the pivot point conjugate to the impact location. In bat testing, the pivot point from which the COP is defined, is usually 6 inches from the knob. (The pivot point, however, may be defined at any location of interest along the length of the bat.)
In physics or dynamics courses a bat impact is sometimes incorrectly cited as an example to explain the COP. It is argued that when a ball strikes the COP, the hands feel no reaction force, providing the so called “sweet spot.” The sting a player feels in the hands from a poorly hit ball is due to bat vibration, however, not a reaction force. It is only a coincidence that the COP of a bat is often close to the location that minimizes bat vibration. In spite of experimental and theoretical evidence supporting the independence of the COP and sweet spot, some maintain its significance. ASTM F1890, for instance, measures bat performance at the COP which is reported as BPF (described below). The COP, relative to the pivot point, is found from
(6.1)
where t is the average period (in seconds) of the bat swinging freely about its pivot point (Fig. 6.1), and g is the gravitational constant (386 in/s2). A detailed method describing how the COP is measured can be found in ASTM F2398. The COP will typically lie between 21 and 22 inches from the pivot point of a 34 inch long bat.
Fig. 6.1 Schematic of bat swinging freely about its pivot point.