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Aerospace
Span station of the trapezoidal mean aerodynamic chord
Distance from the centreline, measured outward along either semi-wing, at which the mean aerodynamic chord sits, for full span b and taper ratio λ = ct/cr.
- Ref
- AER-21
- Rev
- v1
- Field
- Aerospace
- Result
- yMAC [m]
The mean aerodynamic chord lies at the spanwise centroid of the half-wing area, at distance yMAC = (b/6)(1 + 2λ)/(1 + λ) from the centreline. For a rectangular wing (λ = 1) it is b/4, the middle of the semi-span; with strong taper it moves inboard toward b/6. The leading edge of the MAC is then used to place the centre-of-gravity range.
Distance from the centreline, measured outward along either semi-wing, at which the mean aerodynamic chord sits, for full span b and taper ratio λ = ct/cr. It is the conventional planform centroid station for a straight tapered wing.
Calculator
- Semi-span, b/26 m
- Station as a fraction of the semi-span0.4444
- Station for a rectangular wing, b/43 m
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 sits 2.6667 m out from the centreline, 44.44 % of the way to the tip.
- For a rectangular wing it would be at 3 m, so this taper moves it 0.333 m inboard.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| b Full span | 2 to 80 m | 0.4444 | 17.78 | 17.33 | +10% | +10 % |
| λ Taper ratio ct/cr | 0.1 to 1 | 2.182 | 3 | 0.8182 | +10% | +1.61 % |
Sweep of Taper ratio ct/cr
| Taper ratio ct/cr | Span station of the MAC (m) |
|---|---|
| 0.1 | 2.182 |
| 0.2125 | 2.351 |
| 0.325 | 2.491 |
| 0.4375 | 2.609 |
| 0.55 | 2.71 |
| 0.6625 | 2.797 |
| 0.775 | 2.873 |
| 0.8875 | 2.94 |
| 1 | 3 |
Sweep one variable
Variables and how each one contributes
Span station of the MAC
What the equation gives you. Everything else feeds it.
Full span
The full span, in m. Scales the station in direct proportion. Raising it by 10 % (to 13.2) moves the result by +10 %, from 2.667 to 2.933 m.
Taper ratio ct/cr
The taper ratio ct/cr. More taper (smaller λ) moves the MAC station inboard toward b/6. Raising it by 10 % (to 0.55) moves the result by +1.61 %, from 2.667 to 2.71 m.
Worked example with the values above
- Numerator: 1 + 2λ = 1 + 2 × 0.5 = 2; denominator: 1 + λ = 1.5.
- Ratio: 1.33333; b/6 = 2 m.
- yMAC = 2 × 1.33333 = 2.66667 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