Library / Aerospace / AER-06
Aerospace
Level coordinated turn
Turn radius and load factor for a banked aircraft.
- Ref
- AER-06
- Rev
- v1
- Field
- Aerospace
- Result
- r [m]
r the turn radius in m, V true airspeed, φ the bank angle and n = L/W the load factor. Constant speed, still air, level turn.
Banking an aircraft tilts the lift force so part of it pulls the aircraft sideways around the turn. The steeper the bank and the slower the speed, the tighter the turn, but the bigger the load on the airframe.
Calculator
- Load factor n = 1/cos φ1.155 g
- Turn rate3.244 °/s
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 60° of bank the load factor is 2 g, a standard limit for light aircraft. Fighters sustain 6 to 9 g.
- Turn radius depends on speed squared, so a slow aircraft can turn inside a fast one with the same bank angle.
- Stall speed rises with √n in a turn, so tight turns at low speed risk stalling.
Chart data as tables
Ranked variables
| Variable | Typical range | Lowest result | Highest result | Swing (m) | Local step | Change in result |
|---|---|---|---|---|---|---|
| V True airspeed | 20 to 400 m/s | 70.65 | 28,260 | 28,190 | +10% | +21 % |
| φ Bank angle | 10 to 75 ° | 273.2 | 5,783 | 5,510 | +10% | −11.1 % |
Sweep of Bank angle
| Bank angle (°) | Turn radius (m) |
|---|---|
| 10 | 5,783 |
| 18.13 | 3,115 |
| 26.25 | 2,068 |
| 34.38 | 1,491 |
| 42.5 | 1,113 |
| 50.63 | 836.9 |
| 58.75 | 618.8 |
| 66.88 | 435.5 |
| 75 | 273.2 |
Sweep one variable
Variables and how each one contributes
Turn radius
What the equation gives you. Everything else feeds it.
True airspeed
Speed along the turn. Radius grows with V²: doubling speed quadruples the radius.
Bank angle
Roll angle of the wings from horizontal. Steeper bank tightens the turn quickly (radius falls with tan φ) and raises the load factor.
Worked example with the values above
- tan 30° = 0.5774.
- r = V²/(g tan φ) = 100² / (9.80665 × 0.5774).
- r = 1,766 m, with a load factor of 1.155 g.
Assumptions and limits
- Constant speed and bank, still air, no sideslip.
- Level flight, so vertical lift component equals weight.
- Uniform gravity.
Common mistakes
- Using ground speed in wind.
- Entering radians in the degree field.
- Ignoring the load factor limit of the airframe.
Statistics and uncertainty
The tan φ dependence amplifies bank-angle errors at steep bank: δr/r ≈ δφ / (sin φ cos φ). At 60° of bank a 1° (0.017 rad) error produces about 2.3% error in radius.
Where it is used
- Flight planning and holding patterns.
- Missile and UAV manoeuvre limits.
- Pilot and structural g-load checks.
Maths you need
- Trigonometry: tan and cos of an angle
- Centripetal acceleration: a = V²/r