Library / Aerospace / AER-20
Aerospace
Mean aerodynamic chord of a trapezoidal wing
Chord of an equivalent rectangular wing with the same area, zero-lift moment and lift as the actual one, for a symmetric linearly tapered wing with taper ratio λ = ct/cr.
- Ref
- AER-20
- Rev
- v1
- Field
- Aerospace
- Result
- c̄ [m]
The mean aerodynamic chord is the chord of a rectangular wing that has the same area, the same lift and the same zero-lift pitching moment. For a tapered trapezoid with λ = ct/cr it equals (2cr/3)(1 + λ + λ²)/(1 + λ). It is the reference length for pitching moment coefficients, and the centre of gravity is usually given as a percentage of it. It is longer than the mean geometric chord S/b.
Chord of an equivalent rectangular wing with the same area, zero-lift moment and lift as the actual one, for a symmetric linearly tapered wing with taper ratio λ = ct/cr. It is the reference length for pitching-moment coefficients, and it differs from the mean geometric chord S/b.
Calculator
- Mean geometric chord, cr(1 + λ)/21.5 m
- Tip chord, λcr1 m
- MAC as a fraction of the root chord0.7778
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 MAC is 1.5556 m, 77.78 % of the root chord and 0.0556 m longer than the mean geometric chord of 1.5 m.
- A moment coefficient defined on this length gives the same pitching moment as the real wing, so use it for balance and stability.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| cr Root chord | 0.5 to 10 m | 0.3889 | 7.778 | 7.389 | +10% | +10 % |
| λ Taper ratio ct/cr | 0.1 to 1 | 1.345 | 2 | 0.6545 | +10% | +2.44 % |
Sweep of Taper ratio ct/cr
| Taper ratio ct/cr | Mean aerodynamic chord (m) |
|---|---|
| 0.1 | 1.345 |
| 0.2125 | 1.383 |
| 0.325 | 1.44 |
| 0.4375 | 1.511 |
| 0.55 | 1.594 |
| 0.6625 | 1.685 |
| 0.775 | 1.785 |
| 0.8875 | 1.89 |
| 1 | 2 |
Sweep one variable
Variables and how each one contributes
Mean aerodynamic chord
What the equation gives you. Everything else feeds it.
Root chord
The root chord, in m. Scales the MAC in direct proportion. Raising it by 10 % (to 2.2) moves the result by +10 %, from 1.556 to 1.711 m.
Taper ratio ct/cr
The taper ratio ct/cr (1 is rectangular). A higher taper ratio (less taper) raises the MAC toward the root chord. Raising it by 10 % (to 0.55) moves the result by +2.44 %, from 1.556 to 1.594 m.
Worked example with the values above
- Numerator: 1 + λ + λ² = 1 + 0.5 + 0.25 = 1.75.
- Denominator: 3(1 + λ) = 4.5.
- MAC = 2 × 2 × 1.75 / 4.5 = 1.55556 m.
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