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The centre of percussionCOP is not a unique point on& q! ?) K" x" U. Q
the barrel since it is defined in terms of a conjugate point in7 i6 q: j8 X0 e, [
2,6,7
8 s0 a2 Y; L$ z8 \the handle. Each point in the handle is associated with a
1 j. Z6 A( E4 T0 Bdifferent COP in the barrel. When a ball strikes a freely# D& p# l* P8 W g" H" n/ n
suspended bat, the bat will translate in the direction of the% a8 F+ Z6 M! v- r; L
incident ball and it will also rotate about the centre of mass.
8 r9 x1 j0 f! ?3 LThe combined effects of translation and rotation result in a2 y" G4 v% P( g" _! o, s: m. y
shift of the actual axis of rotation, away from the centre of' ~: E, P$ B; N. O/ @- m! P& I) V1 a
mass toward the handle. The axis passes through the conju-
; N4 P- H! v9 [. q/ U9 a) Ggate point for that particular impact. If b is the distance from* z! }0 C: n( F9 j5 E1 [" U
the impact point to the centre of mass, and x is the distance: N% I: f' i- r9 X
from the centre of mass to the conjugate point, then xIcm/(Mb) where Icm is the moment of inertiaof the bat
2 w! V' v+ ~! s4 x" ~2 \( `, d& K4 q. [about its centre of mass and M is the mass of the bat. Con-
" T) I8 B2 G2 }& Ssequently, if the bat is pivoted about an axis through the
% T8 O' V+ a j( C: X0 Y3 d' u' tconjugate point, and if the ball strikes the corresponding
4 g6 H) |, E* BCOP, then there is no reaction force at the pivot point. It is
8 k1 f5 K9 ]3 t; R( }0 z" `therefore reasonable to expect that every point under the' p& @, p4 y) P. G
hands will have its own COP and that an impact at any given
3 G# m7 \$ v& |- eCOP will generate zero reaction force at the corresponding" f3 @7 ^! g/ z' P* ]- N
86 q; i& V0 @3 B: d0 @& `2 ^; b7 b
conjugate point under the hands. Brancazio has suggested/ i8 S3 S" ]9 e
that the sweet spot zone might therefore encompass all cor-
3 f5 W4 X$ {* t( u. ]responding COP points along the barrel. There is, however,+ M5 q' W. T( J7 H
an uncertainty in this argument since a hand-held bat is not
" I% @. V T) E( q$ nfreely suspended, nor is it pivoted about a single axis, and
8 {7 c9 }6 _. R4 Y& `; I0 Vmay behave differently as a result of the reaction forces ex-
! w" {# m- E" n5 }8 y, l; V: Verted by the two hands. Furthermore, the axis of rotation may
* b* I1 B/ i" S- t/ aeven shift as a function of time since the ball remains in
% U! z, q8 v9 O# l4 econtact with the bat for about 1.5 ms, the transmission time8 f: A% h, ]/ t1 | u
of the pulse from the impact point to the hands is about 1 ms,+ C! ?2 t1 u% ^: B
and the impact forces on the hands last for about 20 ms as a1 K5 p$ z& b4 O7 b0 t4 F% ~* i
result of the induced vibrations and the induced motion of
+ B1 }- m0 p& G+ r8 g Nthe bat. |
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