Figure 5-4.  Some aircraft have the ability to change the direction of thrust.  Figure 5-5.  Coefficients of lift and drag at various angles of attack.  5-4  shift control, or gliders, air must be moving across the lifting  surface. This is accomplished by the forward speed of the  aircraft. Lift is proportional to the square of the aircraft’s  velocity. For example, an airplane traveling at 200 knots has  four times the lift as the same airplane traveling at 100 knots,  if the AOA and other factors remain constant.  The above lift equation exemplifies this mathematically  and supports that doubling of the airspeed will result in four  times the lift. As a result, one can see that velocity is an  important component to the production of lift, which itself  can be affected through varying AOA. When examining the  equation, lift (L) is determined through the relationship of the  air density ( ρ ), the airfoil velocity (V), the surface area of the  wing (S) and the coefficient of lift (C$_{L}$) for a given airfoil.  Taking the equation further, one can see an aircraft could  not continue to travel in level flight at a constant altitude and  maintain the same AOA if the velocity is increased. The lift  would increase and the aircraft would climb as a result of  the increased lift force or speed up. Therefore, to keep the  aircraft straight and level (not accelerating upward) and in a  state of equilibrium, as velocity is increased, lift must be kept  constant. This is normally accomplished by reducing the AOA  by lowering the nose. Conversely, as the aircraft is slowed, the  decreasing velocity requires increasing the AOA to maintain  lift sufficient to maintain flight. There is, of course, a limit to  how far the AOA can be increased, if a stall is to be avoided.  All other factors being constant, for every AOA there is  a corresponding airspeed required to maintain altitude in  steady, unaccelerated flight (true only if maintaining level  flight). Since an airfoil always stalls at the same AOA, if  increasing weight, lift must also be increased. The only  C$_{L }$ .  ρ  .  V 2  .  S L =  2  Stall C$_{L}$ C L$_{MAX}$ C$_{D}$ L/ D L/ D$_{MAX}$ 18  16  14  12  10  8  6  4  2  0  .2000  .1800  .1600  .1400  .1200  .1000  .0800  .0600  .0400  .0200  0  Coefficient of drag (C D )  Lift/drag  Angle of attack  0°  2°  4°  6°  8°  10°  12°  14°  16° 18°  20°  22°  C L 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0 