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The centre of percussionCOP is not a unique point on
8 L7 x* C8 d) U7 f/ `7 ithe barrel since it is defined in terms of a conjugate point in
$ N- [ P) |6 b. d! [2,6,76 Q$ _* c5 [8 E7 P9 s% m3 a7 j
the handle. Each point in the handle is associated with a
% B* p% V D' W, ndifferent COP in the barrel. When a ball strikes a freely
5 m6 `( Z. ^, }: \+ ?9 [suspended bat, the bat will translate in the direction of the
" F1 c* ]' ~2 ?, I' J' |6 m; p+ xincident ball and it will also rotate about the centre of mass.
8 v1 Z! T8 l3 }1 i" fThe combined effects of translation and rotation result in a
/ z5 Y* n3 q; y8 P4 N$ y( ^2 i' zshift of the actual axis of rotation, away from the centre of1 ~2 c* v2 H+ \6 X. ~3 _: n
mass toward the handle. The axis passes through the conju-) f$ H* Y6 I6 F, y0 D
gate point for that particular impact. If b is the distance from
$ {% r7 C q6 E: |2 R. y" t9 A. othe impact point to the centre of mass, and x is the distance
7 k r( @+ N/ E" N7 i( N7 |from the centre of mass to the conjugate point, then xIcm/(Mb) where Icm is the moment of inertiaof the bat$ q" _6 @5 {) L' V
about its centre of mass and M is the mass of the bat. Con-( J* _$ M% w$ [/ J
sequently, if the bat is pivoted about an axis through the
$ F, r t1 K5 @9 u; E% Gconjugate point, and if the ball strikes the corresponding3 B! S8 r9 Q! ~9 m, m# e1 [1 W' ?0 O
COP, then there is no reaction force at the pivot point. It is9 F& c4 z8 I. p# b9 J" m5 x7 K
therefore reasonable to expect that every point under the
8 ^/ E/ V2 {, T9 [% Ohands will have its own COP and that an impact at any given+ y+ r5 @0 i) ^/ s
COP will generate zero reaction force at the corresponding
d& Z% m$ u7 h- a9 d8* V( S# ]. c8 p) V4 `
conjugate point under the hands. Brancazio has suggested
* k+ j5 m) K$ W5 ?/ k. _that the sweet spot zone might therefore encompass all cor-
4 ~) [* ?0 R+ @0 Q1 ?& Z8 H7 hresponding COP points along the barrel. There is, however,2 L0 _% f" J" n: J; `
an uncertainty in this argument since a hand-held bat is not% E" R3 Q' D% X# ^7 D+ U
freely suspended, nor is it pivoted about a single axis, and: e% b5 y: ~; V8 `7 h
may behave differently as a result of the reaction forces ex-
' l1 ^+ m9 T6 T4 }$ l6 u2 werted by the two hands. Furthermore, the axis of rotation may) U: O j d2 U
even shift as a function of time since the ball remains in
$ g ~2 f, d- F8 t2 xcontact with the bat for about 1.5 ms, the transmission time
# }: v/ h! Z: L9 M- B* Sof the pulse from the impact point to the hands is about 1 ms,1 I) A" l: A" d- x7 z
and the impact forces on the hands last for about 20 ms as a% a4 R4 W4 P+ F# t* F
result of the induced vibrations and the induced motion of
! R _9 ?4 U; R4 }# athe bat. |
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