Calculator Inputs
Choose a solve mode, enter known values, and submit. The result appears above this form with derived turn metrics and export buttons.
Formula Used
Bank from speed and radius: tan(φ) = V2 / (g × R)
Bank from speed and turn rate: tan(φ) = ω × V / g
Turn radius: R = V2 / (g × tan(φ))
Turn rate: ω = g × tan(φ) / V
Load factor: n = 1 / cos(φ)
Turning stall speed: Vstall,turn = Vstall,level × √n
These relations assume a coordinated steady turn. They are widely used for aircraft path studies, vehicle cornering approximations, maneuver planning, and preliminary engineering checks.
How to Use This Calculator
- Select the solve mode that matches your known values.
- Enter speed, radius, rate, bank, or stall speed as required.
- Choose the correct units for each entry.
- Adjust gravity only when you need a custom value.
- Submit the form to display the result above the calculator.
- Review derived metrics such as load factor and turning stall speed.
- Use the CSV or PDF buttons to save the result.
Example Data Table
| Case | Speed | Radius | Bank Angle | Turn Rate | Load Factor |
|---|---|---|---|---|---|
| Trainer aircraft turn | 60.0 m/s | 800.0 m | 24.650° | 4.297 deg/s | 1.100 g |
| Inspection orbit | 80.0 m/s | 1000.0 m | 33.150° | 4.584 deg/s | 1.194 g |
| Steeper maneuver | 95.0 m/s | 900.0 m | 45.635° | 6.048 deg/s | 1.429 g |
FAQs
1. What is bank angle?
Bank angle is the tilt of a vehicle or aircraft relative to level. In a coordinated turn, it generates the horizontal force needed to curve the path.
2. Why does higher speed need more bank?
At a larger speed, more centripetal acceleration is needed for the same turn radius. That extra sideways acceleration usually requires a larger bank angle.
3. What does load factor mean?
Load factor is the ratio of lift or apparent weight to actual weight. It increases as bank angle rises, which also raises turning stall speed.
4. Can I use this for aircraft only?
No. The equations also help with preliminary engineering estimates for vehicles, tracked motion, and other steady turning systems where coordinated assumptions are reasonable.
5. Why is turning stall speed higher?
A banked turn increases load factor. When load factor rises, the wing must create more lift, so the stall speed increases by the square root of load factor.
6. What is a coordinated turn?
A coordinated turn is a steady turn without sideways slip. The horizontal component of lift provides the needed turning force while the motion remains balanced.
7. Does gravity matter much?
For most standard engineering work, normal gravity is adequate. A custom gravity value is useful when you are modeling nonstandard environments or sensitivity cases.
8. Which mode should I choose first?
Choose the mode based on what you already know. Pilots often know speed and desired rate, while design studies often start with speed and path radius.