Aspect ratio is the wingspan squared divided by the wing area, which for a rectangular wing is simply span divided by chord. At equal lift, the drag caused by making lift (induced drag) is inversely proportional to aspect ratio, so doubling the aspect ratio halves it, while the longer span raises the root bending moment and the spar’s weight. A 10 m span with a 1.3 m chord gives 7.7, which sits inside the carrier’s target of 7-8.
Part of Aerodynamics and Flight
The ratio of span to chord, why long narrow wings glide better, and what the longer span costs in structure.
Definition And A Worked Value
AR = b² ÷ S. For a rectangular wing S = b × c, so AR = b ÷ c. A 10 m span with a 1.3 m chord: S = 13 m², AR = 100 ÷ 13 = 7.7. The carrier targets 7-8 for a first powered aircraft and describes 4-6 as low, 7-9 as medium and 10 or more as high, which is a convention, not a threshold of physics.
Why Induced Drag Falls With Aspect Ratio
A wing makes lift by leaving air moving down; at the tips, air flows round from the high-pressure side to the low and trails behind as a vortex. The downwash tilts the lift backward a little, and the backward component is induced drag. The standard result is CD,induced = CL² ÷ (π × e × AR), where e is a factor of 1 or below that measures how close the lift distribution is to elliptical (Wing Planforms). The formula is the textbook one and not a corpus figure.
Two consequences follow from the formula alone, with no numbers needed. At equal CL, doubling AR halves the induced drag coefficient. At equal AR, halving the speed (so CL rises fourfold) raises the induced drag coefficient sixteen-fold; the dynamic pressure has fallen to a quarter, so the induced drag force itself rises fourfold. That growth at low speed is why induced drag dominates at the slow end of flight.
What A Longer Span Costs
Keep the area fixed at 13 m² and double the span from 10 m to 20 m: the chord falls to 0.65 m and AR goes from 100 ÷ 13 = 7.7 to 400 ÷ 13 = 30.8, four times as large. The root bending moment from the lift grows roughly in proportion to the span (Structural Spars), so the spar is about twice as loaded and must be deeper, while the shorter chord leaves less depth to put it in. A long thin wing is also more flexible, which brings twist and flutter concerns (Control Surfaces).
Where The Trade Settles For A First Aircraft
Choose the lowest aspect ratio that gives acceptable performance and then add a margin of strength. A low aspect ratio is stiffer, lighter for its strength and less prone to flutter, at the price of drag. A high one saves power, which matters when the engine is salvage. The carrier’s 7-8 sits in the middle. It remains a recommendation, not a measurement for your aircraft.
Aspect Ratio And The Stall
A low aspect ratio wing generally stalls at a higher angle of attack than a high aspect ratio one and its lift slope is lower, both of which come from the same tip effects. The values depend on the section and cannot be given here.
Common Mistakes
- Using span ÷ chord on a tapered wing — the formula b²/S is the general one; span over a single chord misleads when the chord varies.
- Stretching the span to save power without redoing the spar — the load increases faster than the span looks.
- Expecting an aspect-ratio rule of thumb to apply to a different section — the numbers come from different wings.
Safety
A longer wing is a longer lever on the root
The bending moment at the root is the lift times the distance to where it acts, so span is a lever. A wing lengthened after the spar was sized is the same wing with a new, unchecked load.
What’s Next
- Learn next: Structural Spars, where the span’s cost is paid
- Combine with: Wing Twist, needed once the planform is chosen