Turorial

Question 1

State the two characteristics of a free gyroscope

Answer 1

Rigidity in space

Precession

Question 2

Explain Free Gyro

Answer 2

• A free gyro is a spinning wheel that can tilt and turn in different directions.
• It stays pointing in the same direction unless an outside force moves it.
• when you push it, it moves in a way that’s different from the direction you pushed.
• This behaviour makes it useful in devices like gyroscopes and navigation systems.

Question 3

Explain Gimbal lock

Answer 3

• Gimbal lock happens when a gyro’s spin axis aligns with the outer gimbal axis, causing uncontrolled and rapid movements.
• This can result in violent, high-frequency precessional motions.
• To prevent gimbal lock, stops can be installed to limit gimbal movement, or a fourth gimbal can be added to maintain a large angle between the inner roll and yaw gimbal axes.

Question 4

Explain Caging

Answer 4

Caging a gyro involves locking it in place to prevent it from moving until it reaches the correct operational speed.
- This is important because when the gyros angular momentum is low, any small torques can cause high precession rates, potentially leading to gimbal lock.
- Caging ensures that no precessional forces affect the gyro during startup or slowdown phases.

Question 5

Explain Nutation

Answer 5

Nutation occurs when a sudden force or torque is applied to a gyro, causing the spin axis to wobble or oscillate.

The amplitude of these oscillations decreases as the speed of the gyros wheel increases.

over time, friction in the gimbal bearings naturally dampens the oscillations.

Nutation can be minimised by using shock-proof supports or friction dampers on the gimbals.

Question 6

In which direction does a gyro precession if a force is an applied to it and why?

Answer 6

When a force is applied to a gyroscope, it precesses 90 degrees from the direction of the applied force due to its angular momentum. This means if you push it forward, it will turn sideways instead of tilting directly forward. This happens because the torque created by the force causes the gyroscope to move at a right angle to the applied force.

Question 7

What factors is precessional rate dependant upon?

Answer 7

1. Direction of Wheel Rotation: Reversing the direction of the gyro wheel’s rotation reverses the direction of precession.
2. Magnitude and Direction of Applied Force: Increasing the force applied increases the rate of precession proportionally. Reversing the direction of the force changes the precession direction but maintains the same rate.
3. Angular Momentum: The rate of precession is inversely proportional to the gyroscope’s angular momentum. Higher angular momentum results in a lower precessional rate.
4. Torque: The precessional rate is directly proportional to the applied torque .

Question 8

Define the meaning of degrees of freedom of a gyro

Answer 8

Degrees of freedom in a gyroscope refer to the number of independent ways in which the gyroscope can move.

For a typical free gyroscope, it has two degrees of freedom: it can tilt around the horizontal axis and turn around the vertical axis. This means it can move freely in these two directions without any external constraints.

Question 9

State in general terms, what affects the earths rotation have on a free gyroscope and how we compensate for them

Answer 9

1. Horizontal Earth Rate (HER): This causes the gyroscope’s spin axis to tilt over time. The effect varies with latitude, being maximum at the equator and zero at the poles. To compensate for this, we use control systems to detect the tilt and apply corrective forces to keep the gyroscope stable.
2. Vertical Earth Rate (VER): This causes the gyroscope’s spin axis to turn or drift over time. The rate of this drift also varies with latitude, being zero at the equator and maximum at the poles. To counteract VER, we apply a compensating force that precesses the gyroscope in the opposite direction to the drift.

By detecting these movements and applying appropriate compensating forces, we can maintain the gyroscope’s stability and accuracy in navigation systems.

Question 10

State, in general terms, what affects the vehicle velocity in both N-S and E-W directions have on a free gyro and how we compensate for them.

Answer 10

Vehicle velocity affects a free gyroscope in the following ways:

1. North-South (N-S) Movement: When a vehicle moves north or south, the spin axis tilts due to the curvature of the Earth. The rate of this tilt is proportional to the vehicle’s speed and can be calculated as ( V \cos(C) ), where ( V ) is the speed and ( C ) is the course angle. To compensate, a force equal and opposite to the tilting effect is applied to keep the gyro stable.
2. East-West (E-W) Movement: As a vehicle moves east or west, the spin axis drifts away from the meridian due to the curvature of the Earth. This drift rate is proportional to the speed and latitude, calculated as ( V \sin(C) \tan(\text{latitude}) ). Compensation involves applying an equal and opposite precessional force to maintain alignment with the meridian.

Question 11

Describe the effect of a loss of VER compensation with the gyrocompass operating in the southern hemisphere.

Answer 11

If a gyrocompass operating in the southern hemisphere loses its Vertical Earth Rate (VER) compensation, the spin axis will drift westward at a rate of 15° per hour times the sine of the latitude. This drift causes the gyrocompass to misalign from the meridian, resulting in an error in the heading output. The gyro will continue to tilt and be subject to damping until it settles, but it will not correctly align with the meridian without the VER compensation, leading to navigational errors.

Question 12

What is meant by REAL wander? Give 4 possible causes

Answer 12

Real wander refers to the actual movement of a gyroscope’s spin axis due to imperfections or external factors. Four possible causes of real wander are:

1. Bearing Friction: Friction in the gyro gimbals produces a torque that opposes precession, requiring compensation.
2. Mass Imbalance: Manufacturing imperfections cause imbalances, resulting in constant torques that displace the spin axis.
3. Rotor Speed Variations: Changes in the gyro wheel’s speed affect angular momentum, altering the precessional rate and introducing errors.
4. Power Supply Variations: Fluctuations in power supply affect gyro speed and the precession signals, causing gyro errors .

Question 13

Explain the basic construction and operation of a rate gyro. state the relationship between input/output functions.

Answer 13

A rate gyro consists of a high-speed spinning wheel mounted in a gimbal or frame. The frame is connected to the instrument case using torsion bars and low-friction bearings. When the instrument case rotates, the gimbal turns, and a pickoff measures the gimbal’s angle, producing an electrical output proportional to the rate of rotation.

The input (rate of rotation) and output (electrical signal) relationship is linear: the electrical output is directly proportional to the rate at which the gyro is rotating. This means that if the rate of rotation increases, the electrical signal increases proportionally.

Question 14

Describe how the restraint of a rate integrating gyro differs. State the relationship between input and output functions.

Answer 14

• Restraint: A rate gyro has low damping restraint, meaning it allows free movement with minimal resistance. In contrast, a rate-integrating gyro uses minimal spring restraint, allowing it to measure displacement more accurately without significant resistance.
• Input/Output Relationship: For a rate gyro, the output signal is proportional to the input angular rate. For a rate-integrating gyro, the output is proportional to the integral of the input angular rate, meaning it measures the total angle of rotation over time.

The main difference lies in how they measure and respond to rotation, with rate-integrating gyros focusing on cumulative angular displacement and using feedback to maintain accuracy.

Question 15

Explain the requirements for a stable platform in an intertial navigation system, mentioning accelerometer corrections. What other type of interial navigation system could be employed and how does this correct for accelerometer tilt?

Answer 15

1. Gyroscopes: Maintain the platform’s orientation in inertial space.
2. Accelerometers: Measure acceleration in three orthogonal directions.

Accelerometer Corrections:
- Gravity: Correct for gravitational acceleration, as accelerometers cannot distinguish between gravitational force and actual acceleration.
- Centripetal Effect: Due to Earth’s rotation, objects experience centripetal acceleration.
- Coriolis Effect: Affects moving objects within a rotating reference frame.
- Convergence: Adjust for the convergence of meridians at the poles.

Alternative INS: Strapdown System

Strapdown System:
- Uses gyroscopes and accelerometers rigidly mounted to the vehicle.
- Requires computational corrections for accelerometer tilt.

Correction for Accelerometer Tilt:
- The computer processes data from gyroscopes to continuously calculate the vehicle’s orientation.
- This information is used to correct the accelerometer readings, ensuring accurate measurements of acceleration relative to the navigation axes.

This system avoids the mechanical complexity of gimbaled platforms and uses software to simulate the stable platform’s functions.

Question 16

Explain the principle of operation of a basic pendulous accelerometer.

Answer 16

A basic pendulous accelerometer works by having a mass suspended as a pendulum. When acceleration occurs, the mass deflects. This deflection is measured by a pick-off system, converting it into an electrical signal that indicates the magnitude and direction of the acceleration.

Question 17

A vehicle moving across the surface of the earth with constant velocity will experience accelerations, ven though it has NO acceleration with respect to earth itself. List these accelerations which must be corrected in an inertial navigation system.

Answer 17

1. Centripetal Acceleration: Due to the Earth’s rotation, any object moving over its surface experiences centripetal acceleration directed towards the center of rotation.
2. Coriolis Acceleration: This occurs because of the Earth’s rotation and affects objects moving north-south or vertically. It causes an apparent force perpendicular to the direction of motion and the axis of rotation.
3. Convergence Acceleration: This results from the convergence of meridians towards the poles, causing a deviation from a great circle path and requiring correction for accurate navigation.

Question 18

State how corrections for base motion, earth rate, and vehicle velocity are applied to a simple, single axis stable platform.

Answer 18

1. Base Motion: The platform’s gyroscope detects unwanted rotations. A torque motor driven by the gyro output corrects this by stabilizing the platform.
2. Earth Rate: Compensation is done by applying a calculated precession force to the gyro to counteract the earth’s rotation effect on the platform.
3. Vehicle Velocity: Corrections are made by adjusting the output from accelerometers, which are stabilized by the platform. The navigation computer processes this data, subtracting gravity and compensating for vehicle motion effects.

Question 19

What can a stable platform provide which an azimuth gyro cannot?

Answer 19

A stable platform provides a fixed reference frame for the accelerometers, keeping them level and aligned regardless of vehicle motion. This ensures accurate measurement of accelerations in the navigation axes. An azimuth gyro cannot maintain this fixed orientation, as it only measures rotation around a vertical axis and does not stabilize accelerometers to counteract vehicle tilts and movements.

Question 20

What are the basic components of an INS?

Answer 20

1. Gyroscopes: Measure angular rotation and help maintain the orientation of the system.
2. Accelerometers: Measure linear acceleration to determine changes in velocity and position.
3. Navigation Computer: Processes data from the gyroscopes and accelerometers to calculate the vehicle’s current position and velocity by integrating the measured accelerations and rotations.

Question 21

What are the advantages and disadvantages of an INS?

Answer 21

Advantages -
Independent System - Once fixed the system acts independently from external references/ systems such as GPS. (Not affected by weather conditions like GPS and Radio is)
Not Susceptible to Jamming - Independent from external inputs makes INS immune to jamming and other threats.
Can be used for Platform/Weapon Stability - The altitude data calculated by the gyro compass can be used for platform stability and weapon initialisation data.

Disadvantages -
Requires initial fix location - requires initial geographical location to determine compensations required from gyro compass to function.
Accuracy degrades over time - errors within system whilst initially very small through calibration will increase and compound overtime.

Question 22

What are the advantages of a ring laser gyro over a conventional mechanical gyro?

Answer 22

• There are no moving parts
• Simple design
• Very rugged
• Output is inherently digital
• Fast update rate
• Long and reliable lifetime
• Low total cost of ownership

Question 23

Describe the construct of a ring laser gyro

Answer 23

• A ring laser gyroscope is constructed using an equilateral triangular ring machined from a block of quartz.
• This block includes corner mirrors and electrodes.
• For stability, one of the three mirrors is concave, and the lasing medium, a helium-neon discharge tube, is placed within the cavity.
• The cavity has two circulating beams, one clockwise and one counterclockwise.
• A partially transmitting mirror extracts part of each beam, which are then combined at a detector to generate an interference pattern.
• The angular position is measured by counting the interference fringes.

Question 24

What is the SAGNAC effect?

Answer 24

The Sagnac effect measures rotation by detecting the difference in path lengths traveled by two light beams moving in opposite directions within a rotating system. This difference creates an interference pattern, with a beat frequency proportional to the rotation rate.

Question 25

Describe an operating problem associated with RLGs and how it is overcome.

Answer 25

Problem - An operating problem with ring laser gyros is “lock-in,” where the output shows zero even when there is rotation.

Fix - This is fixed by mechanical dithering, which adds a constant small rotation to keep the beams from locking together.

Question 26

How does the construction of a fibre-optic gyro differ from the RLG?

Answer 26

1. Core Structure: The fiber-optic gyro uses a coiled optical fiber, often comprising several hundred turns, with a radius of about 10-20 cm. In contrast, the RLG uses a block of quartz with a triangular ring cavity.
2. Light Source and Path: In the fiber-optic gyro, light from a laser is split and sent in opposite directions through the coiled optical fiber. The RLG, however, uses a helium-neon laser with two circulating beams in a triangular cavity.
3. Size and Cost: Fiber-optic gyros are generally smaller and cheaper than RLGs but are also less accurate.
4. Detection Mechanism: Both types measure the difference in the travel times of light beams, but the fiber-optic gyro does this through the phase difference in the coiled fiber, whereas the RLG uses a triangular cavity with mirrors.

Question 27

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Show how a free gyroscope can be made to seek, settle on and maintain the North meridian. Give diagrams to show the damped and undamped motion of the North end. How can you tell when the gyro is settled on the meridian?

Answer 27

Seeking, Settling, and Maintaining the North Meridian with a Free Gyroscope

1. Initialization: Set the gyroscope level in an arbitrary direction.
2. Earth’s Rotation: Causes the gyroscope’s spin axis to tilt.
3. Control Force (Pc): Applied to precess the spin axis towards the meridian. Upward tilt means east of the meridian; downward tilt means west.
4. Oscillation: Without damping, the gyroscope oscillates around the meridian.

Damped and Undamped Motion

• Undamped Motion: The spin axis oscillates around the meridian due to continuous HER and Pc influence.
• Damped Motion: Introduce a damping force (Pd) proportional to the tilt, reducing oscillations and settling the spin axis on the meridian.

Identifying Settlement on the Meridian

• The gyroscope is settled when tilt and precession rates (HER, Pc, and Pd) are zero, indicating no oscillation and alignment with the north-south meridian.