Why airplanes bank
Banking tilts the lift with the wings. Only the vertical part still holds the airplane up, so the wings have to make more lift; the horizontal part is what turns it.
LiftWeightVertical componentHorizontal component
Presets
- Load factor
- 1.15g
- Turn radius
- 467m
- Rate of turn
- 6.31°/s
- Stall speed
- 1.07× wings level
Ground track
At 30.0° of bank the wings have to make 1.15 times the airplane’s weight in lift. The vertical part of that still equals the weight; the horizontal part, 0.58 W, pulls the airplane around the turn.
Airspeed doesn’t change the load factor, only the turn. At a fixed bank the radius grows with the square of the speed: twice as fast is four times as wide.
Stall speed rises with the square root of the load factor. At this bank it is 7% higher than with the wings level.
The model
In a steady level turn the vertical part of the lift balances the weight, L cos φ = W, and the horizontal part supplies the centripetal force, L sin φ = mV²/R. Solving those two gives every readout above:
n = L / W = 1 / cos φ
R = V² / (g tan φ)
ω = V / R = g tan φ / V
Vstall = Vstall, level √n
φ is the bank angle, V the true airspeed and g = 9.80665 m/s². The sign of φ only sets which way the airplane turns.
The turn is coordinated and level, in still air, with weight and configuration unchanged. The model doesn’t check stall, available power or the airplane’s limits. The Warrior is held still so the force directions are easy to compare, and the arrows are drawn in units of its weight, W.
The method follows NASA Glenn’s explanation of banked turns, chapter 5 of the FAA’s Pilot’s Handbook of Aeronautical Knowledge and, for standard-rate turns, the Instrument Flying Handbook.
Also in the lab: Wind tunnel, Flying in moving air and Density altitude at KLAF.