Library / Aerospace / AER-19
Aerospace
Wing aspect ratio
Ratio of span squared to reference planform area.
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- AER-19
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- Aerospace
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- AR
Aspect ratio AR = b²/S is the span squared divided by the area. For a rectangular wing it equals the span-to-chord ratio. High aspect ratio wings, like those of gliders (AR 20 to 40), have low induced drag, and low aspect ratio wings, like those of fighters (AR 2 to 4), are stiff and manoeuvrable but have high induced drag. For tapered wings use the mean chord S/b, not the root chord.
Ratio of span squared to reference planform area. It is dimensionless and measures how slender the wing is. For a non-rectangular wing the root chord alone is not enough to find it.
Calculator
- Mean chord, S/b1.5 m
- Induced drag factor for an elliptic wing, 1/(πAR)0.03979
- Lift-curve slope with a₀ = 2π and e = 15.027 1/rad
What drives the result
Each variable is moved across its typical range while the others stay at the values above. The longest bar is the key driver.
- The wing has an aspect ratio of 8 and a mean chord of 1.5 m, so the span is 8 mean chords.
- The elliptic induced-drag factor is k = 1/(πAR) = 0.03979, so doubling AR would halve the induced drag at a given lift.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing () | Local step | Change in result |
|---|---|---|---|---|---|---|
| b Full span | 2 to 80 m | 0.2222 | 355.6 | 355.3 | +10% | +21 % |
| S Planform area | 2 to 200 m² | 0.72 | 72 | 71.28 | +10% | −9.09 % |
Sweep of Planform area
| Planform area (m²) | Aspect ratio |
|---|---|
| 2 | 72 |
| 26.75 | 5.383 |
| 51.5 | 2.796 |
| 76.25 | 1.889 |
| 101 | 1.426 |
| 125.8 | 1.145 |
| 150.5 | 0.9568 |
| 175.3 | 0.8217 |
| 200 | 0.72 |
Sweep one variable
Variables and how each one contributes
Aspect ratio
What the equation gives you. Everything else feeds it.
Full span
The full span, in m. Raises the aspect ratio with its square. Raising it by 10 % (to 13.2) moves the result by +21 %, from 8 to 9.68.
Planform area
The reference planform area, in m². A larger area for the same span lowers the aspect ratio in inverse proportion. Raising it by 10 % (to 19.8) moves the result by −9.09 %, from 8 to 7.273.
Worked example with the values above
- Span squared: b² = 12² = 144 m².
- Area: S = 18 m².
- AR = 144 / 18 = 8.
Assumptions and limits
- A symmetric, straight, linearly tapered wing with a planform area measured as a projected area.
- For the lift slope: attached subsonic flow, small angles and a lifting-line model.
Common mistakes
- Using the root chord instead of the mean chord to find aspect ratio.
- Mixing up semi-span and full span.
- Using the mean geometric chord to normalise pitching moment instead of the mean aerodynamic chord.
Statistics and uncertainty
Planform geometry is exact, and the aerodynamic estimate is not: lifting-line theory predicts lift-curve slope to about 5 % for unswept wings of aspect ratio above 4, and it overpredicts for low aspect ratio, swept and highly tapered wings.
Where it is used
- Setting reference geometry for coefficients, and predicting how lift grows with angle of attack.
- Locating the aerodynamic centre and the centre of gravity limits.
Maths you need
- Taper ratio: λ = tip chord divided by root chord
- Aspect ratio: AR = b²/S
- Lift-curve slope: the rate of change of lift coefficient with angle of attack