Game Development Reference
In-Depth Information
Modeling the Jump Shot
The jump shot is the most common shot in basketball. The shooter jumps in the air and the ball
is released above the shooter's head towards the basket. In this section, we develop a model to
simulate the flight of a jump shot. Creating a basketball simulation is similar in some ways to
creating a golf or soccer simulation. When a basketball leaves the shooter's hand, it becomes a
projectile and may be subject to the forces due to gravity, aerodynamic drag, wind, and spin.
However, the velocities and spin rates of a basketball are significantly lower than those experi-
enced by golf or soccer balls. Before we can create a jump shot model, we need to evaluate
which forces need to be considered.
Evaluating the Forces on a Basketball in Flight
Let's compute the forces experienced by a basketball traveling through the air at 7.5
m/s
, approx-
imately the velocity one would use when trying to make a jump shot from a distance of 5
m
. The
mass and radius of the ball are 0.62
kg
and 0.12
m
respectively, and the density of the air is
1.2
kg/m
3
. We'll assume that the coefficient of drag for the basketball is 0.5 and that the ball is
spinning at 1.5
rev/s
when it leaves the shooter's hand. The lift coefficient for the Magnus force
due to spin is set equal to the rotational spin ratio, which is equal to 0.15.
The forces and accelerations due to gravity, drag, and spin can be computed using the
equations presented in this chapter. We'll ignore the effects of wind by assuming that the
basketball game is being played indoors. The results for the theoretical jump shot are shown in
Table 7-7.
Table 7-7.
Force and Acceleration Components Acting on a Basketball
Force Type
Acceleration Value (
m/s
2
)
Force Value (
N
)
g
Fmg
==−
6.08
g
ag
==−
9.81
Gravity
1
FCv A
=
r
2
=
0.76
a
=
1.23
Drag
D
D
D
2
1
FCv A
=
r
2
=
0.23
a
=
0.37
Spin
M
L
M
2
Under these conditions, the acceleration on the basketball due to aerodynamic drag is
equal to 12.5% of the gravitational acceleration value. Some basketball simulations ignore the
effects of drag on the ball. Since we already have the
DragProjectile
class written, we will
include drag in our basketball simulation.
The acceleration due to spin, on the other hand, is less than 4% of the gravitational accel-
eration, so it can safely be ignored. Even though spin doesn't really affect the flight of the
basketball, there are two reasons spin is put on a basketball during a jump shot. The first reason
is that the spin is a natural consequence of the one-handed jump shot where the ball rolls off
the fingers. The second reason is that spin can help “soften” the bounce off of the top of the
