The Turn and Slip Indicator

1. Overview of the Instrument

The Turn and Slip Indicator (also called Turn and Bank Indicator or TBI) incorporates two measuring devices, both indicating on the same instrument face:

• Rate of Turn Indicator — uses a rate gyro to measure rate of turn about the vertical axis.
• Slip Indicator — a simple pendulous device (ball in a curved tube) showing whether the turn is balanced (correct bank for TAS and rate of turn), or indicating slip or skid.

2. The Rate Gyro — Principle

The turn indicator is based on a horizontal-axis rate gyro with only one gimbal and therefore only one degree of freedom.

• If the aircraft banks (without turning) — the gyro axis has the freedom to remain horizontal (no effect).
• If the aircraft yaws (turns) — the frame (fixed to the airframe) applies a force (primary torque) about the ZZ axis, where the gyro has no freedom. This causes a primary precession about the YY axis, tilting the gyro.

A spring system prevents the gyro from turning all the way to the vertical. The amount of spring stretch is a measure of the rate of turn.

3. Operation — Spring and Precession Equilibrium

When the aircraft turns:

1. Primary torque acts about the ZZ axis (the aircraft yaws).
2. Primary precession occurs about the YY axis → the gimbal tilts.
3. As the rotor tilts, the spring between gimbal and frame extends.
4. Spring tension applies a secondary torque about the YY axis.
5. This secondary torque, with precession, continues until gimbal tilt gives spring tension producing a rate of secondary precession equal to the rate of turn → equilibrium.

The chain of events is virtually instantaneous — as the aircraft goes into a turn, the gimbal immediately takes up the appropriate angle of tilt. If the rate of turn changes, the tilt changes to re-establish the balance. The angle of tilt is thus a measure of the rate of turn.

4. Constructional Details and Calibration

Suction and electrically-driven types are available. For suction types, an engine-driven pump or venturi applies suction; replacement air enters via a filter and is directed as a jet at buckets on the rotor periphery.

Rotor rpm are low compared with the DGI and AH (because precession is used, not rigidity).

A damping system (piston-in-cylinder or electromagnetic device) reduces oscillation of the gimbal.

Stops limit gimbal movement to a tilt corresponding to a turn of about 20°/second. Because there is only one gimbal, the gyro will not topple when it comes against the stops.

TAS Calibration and Error

Calibration of correct rate of turn (spring tension) is optimized for a design TAS. However, only a small error is introduced even for quite large departures from design TAS. One manufacturer quotes:

5. Effect of Varying Rotor Speed

6. Errors in the Looping Plane

In a gently banked turn, the aircraft turns mainly in the yawing plane. In a steep turn there is more movement in the looping plane. Normally this means rotation about the rotor axis with no effect. However, if the gimbal is already tilted (from a preceding yaw), movement in the looping plane causes additional precession of the rotor.

In a steep turn, the usual positive movement in the looping plane will increase the gimbal tilt — causing the indicator to over-read, sometimes coming against the stops.

7. The Slip Indicator

The slip indicator indicates whether a turn is properly balanced (correct bank angle for TAS and rate of turn), or whether the aircraft is slipping in or skidding out.

Rule of Thumb for Rate 1 Bank Angle

Construction

The modern slip indicator is a 'ball-in-tube inclinometer' — a solid ball in a curved tube containing liquid that damps out oscillations. Early types used a simple metal pendulum with piston-in-cylinder damping. The heavy ball behaves like a pendulum, with the centre of curvature of the tube acting as the effective suspension point.

8. Operating Principles of the Slip Indicator

Level Flight

Weight W of the ball acts downwards; equal and opposite reaction from the base of the tube acts upwards towards the centre of curvature. Wings level → ball lies between the two etched lines.

Balanced Turn

In a balanced turn, the ball rolls outward due to centrifugal force, taking up a new equilibrium where the reaction of the tube base balances the resultant of ball weight and centrifugal force. Because both aircraft and ball experience the same TAS and rate of turn (same centripetal acceleration), their resultant force vectors are parallel. When the ball is central, the turn is balanced — lift equals the resultant of weight and centrifugal force.

Unbalanced Turns

9. Turn and Slip Displays

The turn indicator needle deflects in the direction of turn (left or right of centre). Rate 1 is indicated at the first marked graduation on each side. The ball shows balanced or unbalanced state as described above.

flowchart LR
    subgraph T[Turn Indicator - Needle]
        NL["Needle Left\n= Left Turn"]
        NC["Needle Centre\n= Straight Ahead"]
        NR["Needle Right\n= Right Turn"]
    end
    subgraph S[Slip Indicator - Ball]
        BL["Ball Left\n= Slipping In\n(left turn - too much bank)"]
        BC["Ball Centre\n= Balanced"]
        BR["Ball Right\n= Skidding Out\n(left turn - too little bank)"]
    end

10. Rate 1 Turn Calculations

Master Reference Tables

Answer Key Summary