Game Development Reference

In-Depth Information

you'll need to calculate the unit normal vector perpendicular to the plane of each wing

section. (You'll need this later when calculating angle of attack.)

These first two steps need only be performed once at the beginning of your game or

simulation since the data will remain constant (unless your plane changes shape or its

center of gravity shifts during your simulation).

The third step involves calculating the relative velocity between the air and each com‐

ponent so you can calculate lift and drag forces. At first glance, this might seem trivial

since the aircraft will be traveling at an air speed that will be known to you during your

simulation. However, you must also remember that the aircraft is a rigid body and in

addition to the linear velocity of its center of gravity, you must account for its rotational

velocity.

Back in
Chapter 2
, we gave you a formula to calculate the relative velocity of any point

on a rigid body that was undergoing both linear and rotational motion:

v
R
= v
cg
+ (ω × r)

This is the formula you'll need to calculate the relative velocity at each component in

your model. In this case,
v
cg
is the vector representing the air speed and flight direction

of the aircraft, ω (omega) is the angular velocity vector of the aircraft, and
r
is the distance

vector from the aircraft's center of gravity to the component under consideration.

When dealing with wings, once you have the relative velocity vector, you can proceed

to calculate the attack angle for each wing section. The drag force vector will be parallel

to the relative velocity vector, while the lift force vector will be perpendicular to the

velocity vector. Angle of attack is then the angle between the lift force vector and the

normal vector perpendicular to the plane of the wing section. This involves taking the

dot product of these two vectors.

Once you have the attack angle, you can go to your coefficient of lift and drag versus

attack angle tables to determine the lift and drag coefficients to use at this instant in

your simulation. With these coefficients, you can use the following formulas to estimate

the magnitudes of lift and drag forces on the wing section under consideration:

Lift = C
L
(1/2) ρ V
2
S

Drag = C
D
(1/2) ρ V
2
S

This is a very simplified approach that only approximates the lift and drag character‐

istics. This approach does not account for span-wise flow effects, or the flow effects

between adjacent wing sections. Nor does this approach account for air disturbances,

such as downwash, that may affect the relative angle of attack for a wing section. Further,

the airflow over each wing section is assumed to be steady and uniform.