Game Development Reference
In-Depth Information
Figure 5-15.
The projectile force diagram including gravity, drag, and Magnus force
The Magnus force effect is very important in the sporting world. Golfers make use of back-
spin to increase the length of their golf shots. Putting the proper spin on a baseball is what makes
curveballs curve and sliders slide. Tennis players, on other hand, make use of topspin to cause
the tennis ball to “drop” into their opponent's court. We'll revisit some of these phenomena in
Chapter 7 when we take up the subject of sports.
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Tidbit
In the early 1920s, a German engineer named Anton Flettner proposed a sailing ship that instead
of using sails would generate propulsion from two large spinning cylinders placed vertically on the deck. The
idea worked, but the propulsive force generated by the cylinders was less than if the motor spinning the cylin-
ders had been connected to a standard propeller.
Programming Spin Effects into the Projectile Trajectory Model
Adding spin effects to the projectile trajectory model is a bit tricky because the equations for
Magnus force are geometry dependent. You have to know beforehand if you are dealing with a
sphere or cylinder, for example. Another complication lies in the fact that the Magnus force
vector is perpendicular to both the axis of rotation and the velocity vector, so the axis of rotation
must be precisely defined. The direction of the Magnus force vector can be obtained by taking
the cross product of the velocity and spin-axis vectors. Using the cross product relation devel-
oped in Chapter 2, the directional components of Magnus force are shown in Equation (5.31).
v
⎛
v
⎞
y
F
=
r
−
z
r
F
(5.31a)
⎜
⎟
Mx
z
y
M
v
v
⎝
⎠
⎛
v
v
⎞
F
=−
x
r
−
z
r
F
(5.31b)
⎜
⎟
My
z
x
M
v
v
⎝
⎠
v
⎛
⎞
v
y
F
=
x
r
−
r
F
(5.31c)
⎜
⎟
Mz
y
x
M
v
v
⎝
⎠
