Vertical force balance yields

whereas horizontal force balance gives

Let us assume that the angles and are both small. According to Equations (9.108) and (9.109), and . Thus, and . Moreover, it is clear from Equations (9.111) and (9.112) that and . Thus, to lowest order in , Equation (9.111) yields

whereas Equation (9.112) gives

Expression (9.113) relates the angle of attack to the ratio of the aircraft's weight to its (theoretical) maximum lift (at a given airspeed). Expression (9.114) relates the aircraft's angle of controlled (i.e., at constant airspeed) ascent to the thrust developed by its engine. An unpowered aircraft, such as a glider, has zero thrust. For such an aircraft, Equation (9.114) reveals that the angle of controlled decent--which is usually termed the

(9.115) |

At fixed airspeed, , and wing surface area, , (which implies that is fixed) this angle can be minimized by making the wing aspect-ratio, , as large as possible. This result explains accounts for the fact that gliders (and albatrosses) have long thin wings, rather than short stubby ones. For a powered aircraft, the critical thrust to weight ratio required to maintain level flight (i.e., ) is

(9.116) |

Hence, this ratio is minimized by minimizing the glide angle, which explains why long-haul aircraft, which generally need to minimize fuel consumption, tend to have long thin wings. Finally, as we saw in Section 9.4, if the angle of attack exceeds some (generally small) critical value then boundary layer separation occurs on the back sides of the wings, giving rise to a greatly increased level of drag acting on the aircraft. In aerodynamics, this phenomenon is called a

(9.117) |

In other words, a stall can be avoided by keeping the airspeed above the critical value , which is known as the