Aspect ratio (aeronautics)

In aeronautics, the aspect ratio of a wing (AR) is a measure of its length relative to its width. Mathematically, it is defined as the square of the wingspan divided by the wing area. For wings of constant chord, this simplifies to the ratio of span to chord. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio.

Aspect ratio and other features of the planform are often used to predict the aerodynamic efficiency of a wing because the lift-to-drag ratio increases with aspect ratio, improving the fuel economy in powered airplanes and the gliding angle of sailplanes.

Definition

The aspect ratio

AR

{\displaystyle {\text{AR}}}

is the ratio of the square of the wingspan

b

{\displaystyle b}

to the projected wing area

S

{\displaystyle S}

, which is equal to the ratio of the wingspan

b

{\displaystyle b}

to the standard mean chord

SMC

{\displaystyle {\text{SMC}}}

:

AR

≡

b

2

S

=

b

SMC

{\displaystyle {\text{AR}}\equiv {\frac {b^{2}}{S}}={\frac {b}{\text{SMC}}}}

Mechanism

As a useful simplification, an airplane in flight can be imagined to affect a cylinder of air with a diameter equal to the wingspan. A large wingspan affects a large cylinder of air, and a small wingspan affects a small cylinder of air. A small air cylinder must be pushed down with a greater power (energy change per unit time) than a large cylinder in order to produce an equal upward force (momentum change per unit time). This is because giving the same momentum change to a smaller mass of air requires giving it a greater velocity change, and a much greater energy change because energy is proportional to the square of the velocity while momentum is only linearly proportional to the velocity. The aft-leaning component of this change in velocity is proportional to the induced drag, which is the force needed to take up that power at that airspeed.