Wing Aspect Ratio

Aspect ratio is span squared over area, and for a plain rectangular wing that collapses to span divided by chord — which is where the intuitive sense of a long thin wing versus a short stubby one comes from. The general form is the one to use, because almost no real wing is rectangular, and it handles taper, sweep, crank and elliptical planforms without amendment.

Everything interesting about aspect ratio is in one term of one other equation: induced drag goes as $1/AR$. Double the aspect ratio and halve the induced drag at any given lift coefficient. That is why sailplanes have the wings they do — 25 to 35 is ordinary, and open-class machines go higher — and why the albatross and the swift are shaped so differently from the sparrow.

The physical mechanism is worth having, because it explains why SPAN is what matters rather than slenderness as such. A finite wing leaks: high pressure underneath escapes around the tip to the low pressure above, rolling into a trailing vortex on each side. Those vortices induce a downwash over the whole wing, which tilts the local lift vector backward, and the rearward component of that tilted vector IS induced drag. A longer span puts the tips further from the middle, so a smaller fraction of the wing sits in the downwash, and the penalty falls. Winglets work by making the tip vortex do more of its turning vertically, which raises the EFFECTIVE aspect ratio without adding span — useful precisely when span is limited by a hangar door or an airport gate box.

Nothing stops a designer choosing 40 except that the wing has to hold together. Bending moment at the root grows roughly with the square of the span for a given lift, so the spar gets heavier faster than the drag gets lower, and the optimum lands where the extra structural weight costs more than the aerodynamic saving returns. The answer depends on the mission: a sailplane that must climb in a two-knot thermal will pay almost anything for low induced drag, and a naval fighter that has to fit on a lift and pull 7g will not.

Low aspect ratio has its own compensations, and they are not merely structural. A delta wing stalls very late and very gently, because the leading-edge vortices keep producing lift long after a straight wing would have let go — at the cost of a steep nose-up attitude on approach and a great deal of induced drag while it is there. It is a genuine design choice, not a failure to achieve slenderness.