Game Development Reference
In-Depth Information
Figure 5-7.
The force diagram with gravity and drag effects
The value of drag force for a given object can be computed from Equation (5.12). What is
required to evaluate that expression is the density of the fluid, a characteristic area, the velocity
magnitude of the object, and the drag coefficient. The velocity magnitude, or speed, of an
object can be found by taking the square root of the sum of the square of the velocity components.
vvvv
=++
2
2
2
(5.15)
x
y
z
To include aerodynamic drag in the projectile equations of motion, the overall drag force,
F
D
, determined from Equation (5.12), is split into directional components. Because drag acts in
the opposite direction of velocity, the x-, y-, and z-components of drag force will be in the same
proportion relative to each other as will the x-, y-, and z-components of velocity, but the signs
will be reversed. As shown in Equation (5.16), the drag force in any coordinate direction will be
equal to the overall drag force multiplied by the ratio of the directional velocity component
divided by the velocity magnitude.
v
FF
v
v
FF
v
v
FF
v
y
x
z
(5.16)
=−
=−
=−
Dx
D
Dy
D
Dz
D
The negative signs in Equation (5.16) indicate that drag force acts in the opposite direction
to velocity. The drag force component equations as shown in Equation (5.16) can be added to
the projectile equations of motion to include the effects of aerodynamic drag.
Force and Acceleration Equations
One of the big changes when aerodynamic drag forces are added to the equations of motion is
that the horizontal force components in the x- and y-directions are no longer zero. Instead
aerodynamic drag forces will act in the x- and y-directions, and they will be proportional to the
x- and y-components of velocity. The force acting on the projectile in the vertical direction will
include both gravitational and drag components. The force equations in the x-, y-, and z-directions
including aerodynamic drag effects are shown in Equation (5.17)
