The Steady Turn - ATPL 081 — Principles of Flight

A turning aircraft is an accelerating aircraft: its speed may be constant, but its direction is changing every second, and changing direction takes force. In a steady, coordinated turn that force comes from the only large force the pilot can point: the lift, tilted by the bank to do two jobs at once. From that single idea flow the load factor, the raised stall speed, the turn radius formula and the rate of turn — the calculations this lesson works through one by one.

The forces, resolved

Bank the aircraft and resolve the tilted lift. Vertically: the lift's vertical share must still carry the whole weight, $L \cos\varphi = W$ — which is why the lift must grow in a level turn. Horizontally: the lift's inward share is the centripetal force that curves the path, $L \sin\varphi = \tfrac{W}{g}\cdot\tfrac{V^2}{R}$ . Divide the second by the first and the turn's master equation appears:

Read what is not in it: the mass. Weight appeared on both sides of the division and cancelled, so for a given TAS and radius, every aircraft needs the same bank angle, the light trainer and the heavy freighter alike. And rearranged for the radius, $R = V^2 / (g\tan\varphi)$ : at a given bank, the radius is set by the airspeed alone — and by its square, which is why fast aircraft turn in such wide circles.

Coordinated and uncoordinated

A turn is coordinated when the aircraft flies it with no sideslip: bank and rate matched, the slip ball centred, the occupants pressed straight into their seats. Uncoordinated comes in two flavours:

Slipping turn — too much bank for the rate (or too little rudder): the aircraft slides toward the inside, and the ball falls to the inside of the turn.
Skidding turn — too much rate for the bank (too much rudder): the aircraft slides toward the outside, ball to the outside.

The correction reads straight off the turn indicator and slip ball (or turn coordinator, the same needle logic, though it also answers to roll rate): match the bank to the rate the needle shows, and centre the ball with rudder on the side it has fallen toward — the instructor's 'step on the ball'.

What the bank costs

The tilted lift must still carry the whole weight with only its vertical share, so the total lift, and with it the load factor, grows with bank:

At 30°, n = 1.15; at 45°, 1.41; at 60°, exactly 2: the aircraft and everyone in it weigh double. The consequences chain through everything the course has taught: more lift at the same speed needs more α; more α means more induced drag, so holding speed in the turn needs more thrust; and the accelerated stall arrives early — the stall speed rises with the square root of the load factor, exactly as the stall module derived.

Rate of turn

Two definitions close the toolkit:

Angular velocity — the rate of rotation: angle turned per unit time, in degrees or radians per second.
Rate of turn — the aircraft's angular velocity in the horizontal plane: how fast the heading changes.

The standard reference is the rate-1 turn: 3° per second (180° in one minute, a full circle in two), the rate procedures and holding patterns assume. And the influence of speed (the syllabus asks it directly): at a given bank angle, the rate of turn falls as TAS rises — the centripetal acceleration is fixed by the bank (g tan φ), and the same inward pull bends a faster path more gently, so the fast aircraft turns both wider and slower. To hold rate 1 at higher speed needs more bank (the rough rule: bank ≈ TAS in knots ÷ 10, plus 7).

Radius and safety

The square law is operational, not academic, and the syllabus asks where it bites. Instrument procedures are built inside protected areas sized for the turn radii of the aircraft flying them: exceed the maximum speeds printed on departure and arrival plates and the aircraft's wider circle can carry it outside the protection the designer drew — toward terrain and obstacles the procedure was built to miss. The same logic sorts aircraft into approach speed categories (A to E): faster categories get procedures drawn with bigger protected areas, and flying a procedure of a lower category than your speed is the same trap by another route. Turn radius is one of the few aerodynamic quantities with obstacle clearance on the other side of the equation.

Rudder in the turn: the swept-wing hazard

The closing warning: trying to hurry a turn with extra rudder instead of bank. The rudder does yaw the nose faster, but it does it by creating sideslip, a skidding turn, and on a swept wing sideslip is never free: the stability module showed sweep's powerful dihedral effect, so the skid rolls the aircraft strongly into the turn: an over-banking tendency that builds while the pilot's feet hold it in. Slow, the situation sharpens: the skidding yaw slows the inner wing, and if the stall arrives it arrives on the inner wing first — a roll into the turn and toward a spin, the classic final-turn accident. Fast, the large sideslip loads the fin that the control module's rudder-limiting section protected. The rule the syllabus wants: rate comes from bank, not rudder; the rudder's job in a turn is to keep the ball centred, nothing more.

What the exam asks

The radius, load-factor and stall-speed calculations are certainties in the bank. The overview, following the learning objectives:

Describe and resolve the forces of the steady coordinated turn (tan φ = V²/gR)

Distinguish coordinated from uncoordinated turns and correct them with the turn and slip indicator

Explain the bank angle's independence of mass, the radius's dependence on airspeed alone, and calculate the radius

Explain bank's effects on load factor (1/cos φ), α, thrust and drag, and calculate load factor and stall speed in the turn

Define angular velocity, rate of turn and the rate-1 turn, and the influence of TAS on rate at a given bank

Explain where turn radius matters for safety: plate speed limits and approach categories

Describe the hazards of excessive rudder to increase turn rate in a swept-wing aeroplane