Comprehensive Study Guide to Gyroscopic Instruments and Compasses

Gyroscope Terminology and Fundamentals

• Rigidity (Gyroscopic Inertia): The characteristic of a gyroscope that allows it to maintain its spin axis constant relative to a fixed point in space, provided no external force is applied. It is also known as the property that resists any force tending to change the plane of rotation of the rotor.

  • Factors Affecting Rigidity:         (i) Speed of the rotor.         (ii) Weight (Mass) of the rotor.         (iii) Distance of the mass from the axis of spin (radius of gyration).

• Precession: The angular change in the direction of the gyroscopic spin axis resulting from an applied external force.

  • 90-Degree Rule: The change in direction does not occur in line with the applied force, but at a point $90^{\circ}$ away in the direction of rotation.

  • Factors Affecting Precession Rate:         (i) Strength and direction of the applied torque/force.         (ii) Rigidity of the gyroscope (inversely proportional; greater rigidity results in a smaller rate of precession).         (iii) Moment of inertia ($I$) of the rotor.         (iv) Angular velocity ($\omega$) of the rotor.

• Apparent Precession (Apparent Wander): The apparent movement of a gyroscope relative to an earth-bound observer caused by the earth’s rotation. The gyro remains fixed in space while the earth turns beneath it.

• Tied Gyroscope: A gyroscope with one or more of its degrees of freedom controlled by an external force (e.g., maintain horizontal axis).

• Earth Gyroscope (Vertical Gyroscope): A gyroscope utilizing external torques to maintain its spin axis vertical relative to the earth's surface.

• Degrees of Freedom:

  • Two-degree Freedom Gyroscope (Rate Gyroscope): Utilizes one gimbal ring. It has spinning freedom and tilting freedom. It responds in one plane only and indicates rate of turn ($\text{distance/time}$).

  • Three-degree Freedom Gyroscope (Free Gyroscope): Utilizes two gimbal rings. It has spinning freedom, tilting freedom, and veering freedom. Based on rigidity, it indicates displacement from a null position.

Classification and Mechanical Properties

• Physical Construction: A gyroscope is a rotating mass with freedom in one or more planes at right angles to the plane of rotation. This is achieved by mounting the rotor in pivoted frames called gimbal rings.

• Three Freedom Axes:     (i) Spinning Freedom: Rotation about the spin axis $XX1$.     (ii) Tilting Freedom: Rotation about a horizontal axis at right angles to the spin axis (axis of tilt $YY1$).     (iii) Veering Freedom: Rotation about a vertical axis perpendicular to both spin and tilt axes (axis of veer $ZZ1$).

• Space Gyroscope: A gyroscope whose spin axis continues to point in the same fixed direction in space.

• Ceasing Precession: Precession continues as long as the force is applied. It ceases when the plane of rotation becomes coincident with the plane of the applied force.

Types of Gyroscopic Instruments

• Rate Gyroscope (Turn Indicator):

  • Consists of one gimbal ring with restraining springs.

  • Used in Turn-and-Slip Indicators.

  • Detects turn rate about the aircraft's vertical axis.

• Vertical/Earth Gyroscope (Attitude Indicator/Gyro Horizon):

  • Free gyroscope with a vertical spin axis.

  • Maintains a vertical reference relative to the earth’s surface.

• Directional/Tied Gyroscope (Direction Indicator):

  • Space gyroscope maintained in a horizontal position by external means.

  • Provides a stable directional reference.

Detailed Precession and Drift

• Real Precession: Deflection caused by external forces such as $G$-forces or acceleration/deceleration during aircraft maneuvers. A force attempting to turn the axis will cause it to tilt; a force attempting to tilt the axis will cause it to turn.

• Apparent Precession/Wander Details:

  • Earth rotates at an angular velocity of one revolution every $24$ hours ($15^{\circ}/\text{hour}$).

  • At the equator, a horizontal spin axis gyro appears to tilt $45^{\circ}$ in $3$ hours and $90^{\circ}$ in $6$ hours.

  • Geography: Maximum at the equator; zero at the North and South Poles.

• Gyro Drift (Random Precession): Caused by internal mechanical imperfections.

  • Major Causes: Unbalanced rotors and bearing friction.

Turn-and-Slip Indicators

• Purpose: Indicates lateral attitude in straight flight, direction/rate of turn, and tendency to side-slip or skid.

• Turn Indicator Construction (Air-driven):

  • Rotor axis is horizontal and athwartships (lateral).

  • Gimbal ring pivoted fore and aft.

  • A tension spring holds the gimbal horizontal.

  • Dash pot: A friction-free air or liquid damper linked to the gimbal to prevent pointer oscillation.

  • Mechanism: Pointer linkage moves the tip opposite to gimbal rotation. For a right turn, the gimbal rotates left and the pointer deflects right.

  • Rates: Rate 1 ($180^{\circ}/\text{min}$), Rate 2 ($360^{\circ}/\text{min}$), Rate 3 ($540^{\circ}/\text{min}$).

• Slip Indicator (Inclinometer):

  • A black glass ball in a curved glass tube filled with "white spirit" (liquid).

  • Straight/Level Flight: Gravity centers the ball.

  • Corrected Bank: Balance between gravitational force and centrifugal force; ball stays centered.

  • Underbanked (Skidding): Centrifugal force predominates; ball rolls to the outside of the turn.

  • Overbanked (Slipping): Gravity predominates; ball rolls to the inside of the turn.

• D.C. Operated Turn-and-Slip Indicator:

  • Electrically driven rate gyroscope ($24\,\text{V}$ D.C. nominal).

  • Rotor forms the armature of a small permanent magnet motor with a brass rim for inertia.

  • Speed Control: Two identical symmetrically opposed centrifugal cut-outs maintain $4,200\,\text{r.p.m.}$

  • Includes an "OFF" flag for power failure.

Gyro Horizon (Attitude Indicator)

• Principle: Uses an earth gyroscope ($15,000\,\text{rev/min}$) acting like a pendulum but without oscillation during attitude changes.

• Gimbals: Inner ring (rotor casing) pivoted on lateral axis $YY1$; outer ring pivoted on fore-and-aft axis $ZZ1$.

• Gimbal Lock & Tumbling: Occurs when the rotor axis coincides with the outer gimbal axis (inner ring at $90^{\circ}$). Resilient stops limit pitch to $\pm 85^{\circ}$ to prevent this. Striking the stops causes "tumbling" (precessing $180^{\circ}$).

• Air-Driven Erection (Pendulous Vanes):

  • Four discharge ports (A, B, C, D) below the rotor.

  • Four pendulous vanes bisect ports when vertical (equal air reaction).

  • If tilted, vanes remain vertical due to gravity, uncovering one port and covering another.

  • The resulting unequal air reaction torque precesses the gyro back to vertical.

• Electric Gyro Horizon:

  • Uses a 3-phase squirrel-cage induction motor ($115\,\text{V}, 400\,\text{Hz}$).

  • Speed: $20,000$ to $23,000\,\text{rev/min}$.

  • Electric Erection: Uses mercury levelling switches and torque motors. Mercury makes contact to energize specific windings in the split-field induction motors.

  • Fast Erection Switch: Applies full $115\,\text{V}$ instead of $20\,\text{V}$, increasing precession rate from $5^{\circ}/\text{min}$ to between $120^{\circ}$ and $180^{\circ}/\text{min}$.

  • Precautions: Not more than $15$ seconds (overheating risk); only in straight and level flight (acceleration errors).

Air-driven Direction Indicator

• Stability: Uses a free gyroscope to provide a stable reference against which a scale is read.

• Correction: Must be rechecked against a magnetic compass every $15$ minutes due to wander/precession.

• Caging Mechanism: A manual knob used to clamp gimbals and engage gears to align the unit with the magnetic compass.

• Erection: Air jets hit rotor buckets. If tilted, air impinges on side flanges of the rotor, creating a torque that precesses the axis back to horizontal.

Magnetic Compasses

• Principle: Interaction between a suspended permanent magnet and the earth’s magnetic field.

• Direct Reading Liquid Compass (Construction):

  • Magnet System: Annular cobalt-steel magnet and light alloy card on an iridium-tipped pivot and sapphire cup.

  • Bowl: Moulded plastic (Diakon) with magnifying front.

  • Liquid Damping/Silicone Fluid ($1.5\,\text{oz}$): Makes the compass aperiodic (no oscillation) and provides buoyancy.

  • Expansion Compensation: Bellows or corrugated diaphragm at the rear of the bowl to handle volumetric changes in liquid due to temperature.

  • Deviation Compensators: Two pairs of small magnets adjusted by N-S and E-W screws.

• Errors:

  • Variation: Difference between True North and Magnetic North.

  • Deviation: Interference from aircraft structure/electronics.

  • Dip (Acceleration Errors): On East/West headings, acceleration causes a turn toward North (Northern Hemisphere). Deceleration causes a turn toward South.

  • Turning Errors: Centrifugal force acts on the offset center of gravity, causing rotation in azimuth. Northerly Turning Error is most pronounced.

Remote-Indicating Compass System (MHRS)

• Flux Detector (Flux Valve):

  • Heart of the system, pendulously suspended ($\pm 25^{\circ}$ pitch/roll freedom).

  • Sensing Element: 3-spoked Permalloy wheel.

  • Coils: Primary winding energized at $23.5\,\text{V}, 400\,\text{Hz}$. Secondary pick-off coils sense the Earth's horizontal component ($H$).

• System Components: Detector, slaving/servo amplifier, Directional Gyroscope Unit (DGU), and Radio Magnetic Indicator (RMI).

• Calculation of Drift/Topple:

  • Horizontal axis gyro drift: $15 \times \sin(\text{Latitude})$.

  • Vertical axis gyro topple: $15 \times \cos(\text{Latitude})$.

Compass Swinging Procedure

• Purpose: Neutralize permanent (Hard Iron) and induced (Soft Iron) magnetic fields of the airframe. Required after heavy landings, lightning strikes, or radio installation.

• Coefficients:

  • Coefficient A: Mean of deviations. Corrected by rotating the compass bowl.         $A = \frac{\sum \text{Deviations}}{n}$

  • Coefficient B: Error on East/West headings ($0^{\circ}$ or $180^{\circ}$-aligned magnetism). Corrected with athwartship magnets.         $B = \frac{\text{Dev}_{E} - \text{Dev}_{W}}{2}$

  • Coefficient C: Error on North/South headings ($90^{\circ}$ or $270^{\circ}$-aligned magnetism). Corrected with fore-and-aft magnets.         $C = \frac{\text{Dev}_{N} - \text{Dev}_{S}}{2}$

  • Coefficient D: $\frac{(\text{Dev}_{NE} + \text{Dev}_{SW}) - (\text{Dev}_{SE} + \text{Dev}_{NW})}{4}$

  • Coefficient E: $\frac{(\text{Dev}_{N} + \text{Dev}_{S}) - (\text{Dev}_{E} + \text{Dev}_{W})}{4}$

• Correction Logic (Northern Hemisphere):

  • For $+B$, red poles (North) forward.

  • For $+C$, red poles (North) to starboard.