Level turn

Level Turn

In a level turn the aircraft flies a circular arc at constant altitude. From the lift vector a centripetal component for the curve motion is derived.

Forces in the turn

Lift vector decomposition

At bank angle φ:

• Vertical component: L · cos(φ) — must balance weight.
• Horizontal component: L · sin(φ) — acts as centripetal force.

Equilibrium conditions

1. Vertical: L · cos(φ) = W
2. Horizontal: L · sin(φ) = m · v² / r

From (1): L = W / cos(φ)

→ Lift must be greater than weight, so the vertical component balances weight!

Load factor

n = L / W = 1 / cos(φ)

Stall speed in turn

Since CL_max is constant and the turn needs n · W of lift:

Vs(n) = Vs · √n = Vs · √(1/cos φ)

→ In a 60° bank turn the aircraft stalls at 71 KIAS instead of 50 KIAS in straight flight!

Practical pilot technique

Coordinated turn

1. Aileron for bank initiation.
2. Rudder coordinated (against adverse yaw).
3. Elevator for pitch — slight yoke pull to maintain altitude.
4. Power increase if needed in steep turns (compensates higher drag).

Power requirement

• Bank > 30°: power increase needed (more induced drag from higher CL).
• C172 at 45° bank: typically +200-300 RPM for altitude hold.

Roll-out procedure

1. Aileron opposite (against roll direction).
2. Rudder coordinated (against adverse yaw of aileron motion).
3. Elevator relax (pitch back to cruise).
4. Power back to cruise setting.

Standard bank values

Steep turn exercise (skill test): typically 45° bank, 360° rotation, altitude held ±100 ft.

Safety aspects

Spiral dive from the turn

• In an uncoordinated turn with too much pitch-up: bank automatically tightens without further aileron input.
• Wrong reflex: pulling more yoke → bank amplifies → graveyard spiral.
• Correct: aileron for wings-level, then relax pitch.

Spin from stall in bank

• At too low speed in bank: one wing stalls first → spin.
• Classic accident: base-to-final stall-spin in too tight bank.
• Prevention: speed reserve = at least 1.3 × Vs for the bank angle.

Worked example

Aircraft: Cessna 172. Bank angle 30°. Weight 1043 kg.

• n = 1/cos(30°) = 1.155.
• L required = n · W = 1.155 × 1043 × 9.81 ≈ 11,825 N.
• In level flight (n=1): L = 1043 × 9.81 ≈ 10,234 N.
• Lift increase by 16 % → more CL → more α → more induced drag → more power needed.

CG position and turns

• CG forward: higher yoke force for pitch hold in turn.
• CG aft: lower yoke force but less stable.

Altimeter correction in turn

• In steep bank (>60°) the pitot/static system can show small errors — usually minor.
• Consult POH for specifics.