Aspect ratio (aeronautics)

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 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.

It is important to keep in mind that this is a drastic oversimplification, and an airplane wing affects a very large area around itself.

However, as the flow becomes transonic and then supersonic, the shock wave first generated along the wing's upper surface causes wave drag on the aircraft, and this drag is proportional to the span of the wing.

However, the extra weight and complexity of a moveable wing mean that such a system is not included in many designs.

By contrast, birds which require good maneuverability, such as the Eurasian sparrowhawk, have wings of low aspect ratio.

For most wings the length of the chord is not a constant but varies along the wing, so the aspect ratio AR is defined as the square of the wingspan b divided by the wing area S.[10][11] In symbols, For such a wing with varying chord, the standard mean chord SMC is defined as The performance of aspect ratio AR related to the lift-to-drag-ratio and wingtip vortices is illustrated in the formula used to calculate the drag coefficient of an aircraft

It is a better measure of the aerodynamic efficiency of an aircraft than the wing aspect ratio.