Friday, October 8, 2004
1:00pm – 2:00pm
Professor Mont Hubbard
Department of Mechanical & Aeronautical
Engineering
University of California at Davis
ÒMechanics of Ball SportsÓ
Abstract:
As an illustration of the research work in our laboratory, this talk
focuses on and contrasts the mechanics of two popular American ball sports;
baseball and basketball.
Improved models for the pitch, batting, and post-impact flight phases
of a baseball are used in an optimal control context to find bat swing
parameters that produce maximum range. The improved batted flight model
incorporates experimental lift and drag profiles (including the drag crisis).
An improved model for bat-ball impact includes the dependence of the coefficient
of restitution on the approach relative velocity and the dependence of the
incoming pitched ball angle on speed. Undercut distance and bat swing angle are
chosen to maximize range of the batted ball. The sensitivity of the maximum range is calculated for all
model parameters including bat and ball speed, bat and ball spin, and wind
speed. Post-impact conditions are found to be independent of the ball-bat
coefficient of friction. The lift is enhanced by spin produced by undercutting
the ball during batting. Contrary to popular opinion, an optimally hit curve
ball will travel farther than an optimally hit fastball or knuckleball due to
increased lift during flight.
In contrast, the motion of a basketball is much less affected by
aerodynamics. A dynamic model is presented for basketball motion that may
contact the rim, the backboard, the bridge between the rim and board, and
possibly the board and the bridge simultaneously. The model is used to
investigate free throw success near the sagittal plane. Non-linear ordinary
differential equations describe the ball angular velocity and ball center
position. The model includes radial ball compliance and damping and contains
sub-models describing slipping and no-slipping contact and purely gravitational
flight. Switching between the sub-models depends on contact point velocity and
friction forces. Interesting limiting dissipation-free families of trajectories
allow the ball to pass below the rim plane before being ejected rather than
captured. The combination of dynamic models of basketball-rim and
basketball-backboard interaction allow simulations for a single point ball-rim
or ball-board contact, as well as the possibility of two-point contact on both
board and bridge. In this talk, the model is used to study free throw release
angles, velocity, and angular velocity that maximize the probability of
success.