Gyroscopes 3
in its single gimbal, pivoted on the aircraft fore and aft axis and compresses or extends a spring. When the spring force balances the precessed force the gyro remains tilted away from the aircraft vertical as the instrument yaws with the aircraft. The gimbal moves a needle that indicates the rate of turn. Do not worry about the derivation, but remember this phrase:
The direction of rotation of the gyro is chosen so that when the aircraft banks into a balanced turn the gyro precesses in the opposite roll sense to keep its axis more or less horizontal and therefore keep it more sensitive to turn rate. If the gyro rotated in the opposite direction it would only work satisfactorily at very low yaw rates and small angles of bank.
The spring force produces a secondary precession equal to and in the same direction as the yaw.
Note this practical reason for choosing the direction of rotation of the gyro If the air or electrical supply fails the instrument will read zero rate of turn, as the gyro will stop. Any leaks in the system, or reductions in voltage, tend to make the turn indicator under read. The slip indicator is not subject to any errors.
The turn indicator could be described as having one degree of freedom or two planes of freedom The slip indicator is either a ball in a curved liquid filled tube or a damped pendulum free to move in the same axis. In straight balanced flight the force of gravity keeps the ball or pendulum in the central position and no slip or skid is indicated. Similarly in a balanced turn the combination of gravity and centrifugal force acts through the aircraft vertical and no slip or skid is indicated. If the bank angle is too great or too small the resultant force will not be through the aircraft vertical and the ball is displaced. Figure 3.16 shows some of the indications that might be seen.
Calculation of Rate and Radius of Turn Rates of turn are standardised. A rate one turn is 180° a minute or 3° a second. A rate two turn is twice that, 360° a minute or 6° a second, and a rate three turn is three times as much, 540° a minute or 9° a second. The angle of bank required to achieve a given rate of turn increases with the TAS. A useful formula to calculate the bank angle in degrees for rate 1 turns is:
Errors The turn indicator is mounted with the gimbal axis on the aircraft fore-and-aft axis, and the gyro axis horizontal. In this position the gyro measures yaw rate. If the gyro was mounted with its axis vertical the instrument would measure pitch rate. It is inherent in the design of the instrument that in any yaw condition the gyro axis will tilt, and the gyro will become sensitive to pitch rate. If the aircraft is then rapidly pitched nose up, as in a loop or recovery from a spiral dive, this pitch input can deflect the gyro to read maximum turn rate. This is called looping error. This pitch rate error also affects the instrument readings in normal turns. To compensate for this and for the difference between yaw and turn rates the indicators are calibrated to show rates of turn correctly in balanced turns for rate 1, 2 and 3 turns at specific angles of bank and TAS. Although the indicated rate of turn will be incorrect at speeds away from these datums the errors are not significant in normal operation.
Instrumentation
v6.1.5
TAS Angle of bank = 10
+7
To calculate the radius of turn in nautical miles use the following: Radius of turn =
TAS rate of turn x 60 π
Where π is the constant for circles, 3.142, and rate of turn is rate 1,2,3 etc.
Turn Coordinator A turn coordinator is a development of a turn indicator. The gimbal is raised at the front by 30° and the instrument is sensitive to both roll and yaw, and begins to indicate a turn as soon as the roll in begins. As the yaw rate builds up the roll must be reduced to keep the indicator on its datum, so the idea is that a smooth entry to a turn can be achieved using only one instrument. The turn coordinator only indicates rate one 3.13