Game Development Reference
a rigorous treatment of these, we refer you to the Theory of Wing Sections and Fluid-
Dynamic Lift . 4
Turning back to Figure 15-6 , you'll notice that the drag coefficient increases sharply
with attack angle. This is reasonable, as you would expect the wing to produce the most
drag when oriented flat against or perpendicular to the flow of air.
A look at the lift coefficient curve, which initially increases linearly with attack angle,
shows that at some attack angle the lift coefficient reaches a maximum value. This angle
is called the critical attack angle . For angles beyond the critical, the lift coefficient drops
off rapidly and the airfoil (or wing) will stall and cease to produce lift. This is bad. When
an aircraft stalls in the air, it will begin to drop rapidly until the pilot corrects the stall
situation by, for example, reducing pitch and increasing thrust. When stall occurs, the
air no longer flows smoothly over the trailing edge, and the corresponding high angle
of attack results in flow separation (as illustrated in Figure 15-9 ). This loss in lift is also
accompanied by an increase in drag.
Figure 15-9. Stalled airfoil
Theoretically, the resultant force acting on an airfoil acts through a point located at one-
quarter the chord length aft of the leading edge. This is called the quarter-chord point.
In reality, the resultant force line of action will vary depending on attack angle, pressure
distribution, and speed, among other factors. However, in practice it is reasonable to
assume that the line of action passes through the quarter-chord point for typical op‐
erational conditions. To account for the difference between the actual line of action of
the resultant and the quarter-chord point, we must consider the pitching moment about
the quarter-chord point. This pitching moment tends to tilt the leading edge of the foil
down. In some cases this moment is relatively small compared to the other moments
4. Fluid-Dynamic Lift , by Sighard F. Hoerner and Henry V. Borst, and Fluid-Dynamic Drag , by Sighard F.
Hoerner (both self-published by Hoerner), contain tons of practical charts, tables, and formulas for virtually
every aspect of aircraft aerodynamics. They even include material appropriate for high-speed boats and