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Aerospace
Stall speed under a positive manoeuvre load factor
Stall speed at load factor n = L/W, in terms of the one-g stall speed at the same weight, density and configuration.
- Ref
- AER-27
- Rev
- v1
- Field
- Aerospace
- Result
- Vs,n [m/s]
In a manoeuvre the wing must lift n times the weight, and at the same maximum lift coefficient this needs a speed √n higher at stall: Vs,n = Vs,1√n. A 2.25 g pull-up stalls at 1.5 times the one-g stall speed, and a 60° coordinated bank (n = 2) raises it by 41 %. This is why stalls occur suddenly in tight turns.
Stall speed at load factor n = L/W, in terms of the one-g stall speed at the same weight, density and configuration. Maximum lift coefficient is assumed unchanged and loading quasi-steady. In a coordinated level turn, n = 1/cos of the bank angle.
Calculator
- Bank angle in a level turn at this load factor, acos(1/n)63.61 °
- Increase over the one-g stall speed15 m/s
- Speed ratio Vs,n/Vs,11.5
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.
- At a load factor of 2.25 the aircraft stalls at 45 m/s, 50 % above the one-g value of 30 m/s.
- A coordinated level turn with this load factor needs a bank of 63.61°.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m/s) | Local step | Change in result |
|---|---|---|---|---|---|---|
| Vs,1 One-g stall speed | 10 to 100 m/s | 15 | 150 | 135 | +10% | +10 % |
| n Load factor | 0.5 to 6 | 21.21 | 73.48 | 52.27 | +10% | +4.88 % |
Sweep of Load factor
| Load factor | Stall speed at load factor n (m/s) |
|---|---|
| 0.5 | 21.21 |
| 1.188 | 32.69 |
| 1.875 | 41.08 |
| 2.563 | 48.02 |
| 3.25 | 54.08 |
| 3.938 | 59.53 |
| 4.625 | 64.52 |
| 5.313 | 69.15 |
| 6 | 73.48 |
Sweep one variable
Variables and how each one contributes
Stall speed at load factor n
What the equation gives you. Everything else feeds it.
One-g stall speed
The one-g stall speed at the same weight, density and configuration, in m/s. Scales the manoeuvre stall speed in direct proportion. Raising it by 10 % (to 33) moves the result by +10 %, from 45 to 49.5 m/s.
Load factor
The load factor L/W, a positive number. Raises the stall speed with its square root. Raising it by 10 % (to 2.475) moves the result by +4.88 %, from 45 to 47.2 m/s.
Worked example with the values above
- Load-factor ratio: √n = √2.25 = 1.5.
- Multiply by the one-g stall speed: 30 × 1.5.
- Vs,n = 45 m/s.
Assumptions and limits
- A parabolic polar CD = CD0 + kCL², constant over the speed range and with no compressibility rise.
- Steady level, unaccelerated flight with lift equal to weight, at constant density.
Common mistakes
- Using the formula with a changed maximum lift coefficient, such as with flaps deployed.
- Using the bank angle directly instead of the load factor 1/cos φ.
- Forgetting that a stall in a turn can be abrupt and may lead to a spin.
Statistics and uncertainty
The parabolic drag polar fits real aircraft well only over the middle of the lift range. Speeds from it are usually accurate to 5 % when CD0 and k come from flight tests; with handbook estimates they can be off by 10 % to 20 %, and the result moves with the one-quarter power of the drag ratio.
Where it is used
- Plotting thrust and power curves and finding best speeds for range and endurance.
- Estimating how stall speed changes in turns.
Maths you need
- Drag polar: CD = CD0 + kCL²
- Level flight: L = W and T = D
- Load factor: n = L/W