Stall speed, load factor and bank angle
Stall-speed questions look different on the surface: a turn, a heavier aeroplane, a limit load factor. Underneath they are the same relationship. Lift has to carry the load, and the stall speed grows with the square root of that load. Learn that one idea and the numbers follow.
The load factor in a turn
In a level, coordinated turn the vertical part of the lift must still equal the weight. Lift therefore has to be larger than the weight by a factor 1 / cos φ, where φ is the bank angle. That factor is the load factor n:
n = 1 / cos(bank angle)
| Bank angle | Load factor n | Stall speed × √n |
|---|---|---|
| 0° (level flight) | 1.00 | × 1.00 |
| 30° | 1.15 | × 1.07 |
| 45° | 1.41 | × 1.19 |
| 60° | 2.00 | × 1.41 |
The stall speed in a turn
Stall speed is proportional to the square root of the load factor. So the stall speed in a turn is the 1 g stall speed times √n. Example: a 1 g stall speed of 60 kt in a 60° level turn gives 60 × 1.41 = 85 kt. The bank angle that gives a load factor of 2 is 60°, which is worth knowing both ways round.
Mass
The stall speed is also proportional to the square root of the mass. The two common exam numbers are chosen so that the square root comes out even:
- Mass up 21 %: √1.21 = 1.10, so a stall speed of 100 kt becomes 110 kt.
- Mass down 19 %: √0.81 = 0.90, so a stall speed of 100 kt becomes 90 kt.
Limit load factors and the manoeuvring speed
CS-23 gives a limit load factor of +3.8 g for the normal category and +4.4 g for the utility category. The design manoeuvring speed follows from the same square root:
VA = VS × √n(limit)
With a 1 g stall speed of 60 kt and a limit load factor of 3.8, VA = 60 × 1.95 = about 117 kt. Below VA the wing stalls before the structure reaches its limit; above it, a full control deflection can overload the airframe. Because the stall speed falls with the mass, VA decreases when the mass decreases.
Where students lose marks
- Square root, not linear. A load factor of 2 raises the stall speed by 41 %, not by 100 %.
- The factor 1.41 appears twice. It is both the load factor at 45° and the stall-speed factor at 60°. Read what is being asked.
- VA moves with mass. A lighter aeroplane has a lower VA, which surprises people who think “lighter is safer”.
- Indicated stall speed does not change with altitude. The true airspeed at the stall increases, the indicated one stays about the same.
Study aid, not the regulation or your flight manual. The relationships hold for a level, coordinated turn.
Quick answers
What is the load factor in a 60-degree level turn?
2.0. In a 45-degree turn it is 1.41, and in a 30-degree turn it is 1.15.
How much does the stall speed increase in a 60-degree turn?
By a factor of 1.41, the square root of the load factor 2. A 1 g stall speed of 60 kt becomes about 85 kt.
How does mass affect the stall speed?
The stall speed changes with the square root of the mass. 21 % more mass raises it by 10 %, and 19 % less mass lowers it by 10 %.
What is the manoeuvring speed VA?
VA equals the stall speed multiplied by the square root of the limit load factor. It decreases when the mass decreases.
Make it stick
Fly the Load Factor & Stall drill: every item is a streak you have to land.