Why airplanes bank
Tilt the wings and the lift tilts with them. Explore how a coordinated, level turn changes the forces on an aircraft and the path it follows.
Set the turn
Left bank, wings level, or right bank.
Speed through the air, held constant.
- Load factor
- g
- Turn radius
- m
- Rate of turn
- °/s
- Stall speed multiplier
- ×
Coordinated, constant-altitude flight · no wind · unchanged weight and configuration
Tilt the lift, keep the altitude
At 30.0° of bank, the wings must generate 1.15 times the aircraft’s weight in lift to maintain altitude. The vertical component still equals weight; the horizontal component pulls the aircraft into the turn.
Change the airspeed while keeping the bank fixed. Load factor stays the same. Turn radius grows with the square of speed, and the heading changes more slowly.
The stall speed multiplier compares this turn with wings-level flight at the same weight and configuration. The model does not evaluate stall, available power, or an aircraft’s operating limits.
One force, two components
In a steady level turn, the vertical component of lift balances weight: L cos φ = W. The horizontal component supplies the centripetal force: L sin φ = mV²/R.
Load factor: n = 1 / cos φ
Turn radius: R = V² / (g tan φ)
Turn rate: ω = g tan φ / V
Here, φ is bank angle, V is true airspeed, and g is 9.80665 m/s². The model uses the magnitude of bank for radius; its sign sets the turn direction.
What the diagram shows
The Warrior is held in place so you can compare the force directions. Arrow lengths are relative to weight, W. The separate top view plots 20 seconds of motion using the calculated turn rate.
See NASA Glenn’s explanation of banked turns, the FAA’s aerodynamics chapter, and the Instrument Flying Handbook for the underlying force balance, load factors, and standard-rate turns.