Forces in Flight: Four Forces, Load Factor, Manoeuvring and Gust Loads, Turning, Climb and Descent
This domain converts aerodynamics into aeroplane performance: the balance of forces, the load factor in manoeuvres and gusts, and the geometry of turns, climbs and descents. Numerical items on load factor, bank angle, turn radius and rate are common.
The four forces
- In straight, unaccelerated flight: L = W and T = D. Any acceleration requires an unbalanced force.
- In a steady climb, L = W cos γ and T = D + W sin γ; climb gradient = (T − D)/W.
- In a glide, tan γ = D/L = 1/(L/D). Minimum sink speed is not maximum range speed.
Load factor
- n = L/W. In a level turn, n = 1/cos φ.
- Stall speed scales with √n, so an aeroplane can be stalled at any speed if the load factor is high enough.
- Gust load rises with TAS, gust velocity and lift-curve slope, and falls with wing loading.
Turns
- Rate of turn (deg/s) = 1091 tan φ / V, with V in knots.
- Radius = V²/(g tan φ), with V in m/s.
- Rate and radius depend on speed and bank angle, not directly on weight.
Worked example
At 100 kt (51.4 m/s) and 45° bank: n = 1/cos 45° = 1.41, so the stall speed rises by √1.41 = 1.19, or about 19%. Rate of turn = 1091 × tan 45° / 100 = 10.9 °/s. Radius = 51.4²/(9.81 × 1) = 269 m. In still air the same turn at the same bank and speed has the same radius regardless of weight; only the lift required, and hence the load on the structure, changes.
Traps
- In a steady climb the load factor is about 1, not greater than 1; only a pull-up or a turn increases it.
- A 60° bank gives n = 2 and a stall speed 41% higher; a 30° bank gives only 1.15.
- Vx and Vy converge at the absolute ceiling; Vx is always the lower speed.
- Turn radius is not independent of bank angle.
- Glide range depends on L/D, not on weight; weight changes the speed for best glide, not the angle.