Game Development Reference
Figure 5-3. Example baseball and bat collision
To a reasonable degree of accuracy, the motion of a baseball bat at the instant of collision
can generally be described as independent of the batter—in other words, you can assume
that the bat is moving freely and pivoting about a point located near the handle end of
the bat. Assume that the ball strikes the bat on the sweet spot—that is, a point near
the center of percussion. 2 Further assume that the bat is swung in the horizontal plane
and that the baseball is traveling in the horizontal plane when it strikes the bat. The bat
is of standard dimensions with a maximum diameter of 70 mm and a weight of 1.02 kg.
The ball is also of standard dimensions with a radius of 37 mm and a weight of 0.15 kg.
The ball reaches a speed of 40 m/s (90 mph) at the instant it strikes the bat, and the speed
of the bat at the point of impact is 31 m/s (70 mph). For this collision, the coefficient of
restitution is 0.46. In the millisecond of impact that occurs, the baseball compresses
quite a bit; however, in this analysis assume that both the bat and the ball are rigid.
Finally, assume that this impact is frictionless.
As in the previous example, the line of action of impact is along the line connecting the
centers of gravity of the bat and ball; thus, the unit normal vector is:
n = (( r 1 + r 2 ) 2 - r 1 2 ) - r 1
r 1 + r 2
n = (0.875) i + (0.484) j
Here the subscripts 1 and 2 denote the bat and ball, respectively.
The relative normal velocity between the bat and ball is:
2. The center of percussion is a point located near one of the nodes of natural vibration, and is the point at
which, when the bat strikes the ball, no force is transmitted to the handle of the bat. If you've ever hit a baseball
incorrectly such that you get a painful vibrating sensation in your hands, then you know what it feels like to
miss the center of percussion.