Bank Angle, Load Factor and Stall Speed in a Turn Calculator
Load factor, raised stall speed, turn radius and rate of turn for an aircraft in a banked level turn, plus the bank angle that gives a standard-rate turn.
Results
The dashed line marks the value you entered.
What this tool does
In a level turn the wings must carry more than the aircraft's weight, by a factor of 1 ÷ cos(bank): 1.15 g at 30°, 1.41 g at 45°, and 2 g at 60°. Stall speed rises with the square root of that load factor, so a steep turn at 60° stalls at about 41 % above the level-flight figure, which is why steep turns near the ground, at slow speed, are dangerous. The turn radius depends on speed squared and the tangent of the bank, so slowing down tightens a turn far more than steepening the bank does.
Formula
n = 1 ÷ cos φ · V_stall,turn = V_s × √n · R = V² ÷ (g × tan φ) · rate = g × tan φ ÷ V
Variables
| Symbol | Meaning | Unit |
|---|---|---|
va | Speed through the air in the turn | kt |
vs | Stall speed in level flight (1 g) | kt |
ph | Bank angle | ° |
N | Load factor in the turn (g) | g |
VT | Stall speed in the turn | kt |
R | Radius of the turn | m |
RT | Rate of turn | °/s |
T3 | Time for a full circle | s |
BS | Bank angle for a standard-rate turn (3° per second) | ° |
Worked example
- Speed through the air in the turn100 kt
- Stall speed in level flight (1 g)50 kt
- Bank angle45 °
- Load factor in the turn (g)1.41 g
- Stall speed in the turn59.5 kt
- Radius of the turn270 m
- Rate of turn10.92 °/s
- Time for a full circle33 s
- Bank angle for a standard-rate turn (3° per second)15.4 °
Limitations
- The formula assumes ideal conditions: no friction losses, no air resistance and no efficiency losses unless you enter them.
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.