Aspect ratio (aeronautics)

In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wing area. Thus, a long, narrow wing has a high aspect ratio, whereas a short, wide wing has a low aspect ratio. In aeronautics, the aspect ratio of a wing is the ratio of its span to its mean chord. It is equal to the square of the wingspan divided by the wing area. 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 fuel economy in aircraft. The aspect ratio AR {displaystyle { ext{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 { ext{SMC}}} : AR ≡ b 2 S = b SMC {displaystyle { ext{AR}}equiv {frac {b^{2}}{S}}={frac {b}{ ext{SMC}}}} Roughly speaking, an airplane in flight can be imagined to affect a circular 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. The interaction between undisturbed air outside the cylinder of air, and the downward-moving cylinder of air occurs at the wingtips and can be seen as wingtip vortices. It is important to keep in mind that this is a drastic oversimplification, and an airplane wing affects a very large area around itself. Although a long, narrow wing with a high aspect ratio has aerodynamic advantages like better lift-to-drag-ratio (see also details below), there are several reasons why not all aircraft have high aspect wings: Aircraft which approach or exceed the speed of sound sometimes incorporate variable-sweep wings. These wings give a high aspect ratio when unswept and a low aspect ratio at maximum sweep.