Explain Gimbal lock, Caging and Nutation
Gimbal Lock:
Gimbal lock happens when the spin axis of a two-degree-of-freedom gyro aligns with the outer gimbal axis, causing uncontrolled, violent precessional movements..
Caging:
Caging is the process of preventing gimbal lock by ensuring no precessional forces are applied to a gyro until it reaches its correct speed during startup or slowdown.
Nutation:
Nutation is the oscillation or wobbling of the gyroscope’s spin axis caused by a sharp blow or step-function torque, which can be minimized by shock-proofing the gyro support system or using dampers.
Pr = torque / angular motion
State in general terms what affects the following have on a free gyroscope and how we compensate for them:
-Earth Rotation
-Vehicle velocity in both N-S and E-W direction
Earth Rotation:
- Effect: Causes apparent tilt (HER) and turn (VER) of the gyroscope’s spin axis.
- Compensation: Apply an equal and opposite precessional force to counteract these effects.
- N-S Direction:
- Effect: Causes the gyroscope’s spin axis to tilt.
- Compensation: Apply a force equal and opposite to the tilting effect to maintain the spin axis level.
- E-W Direction:
- Effect: Causes the gyroscope’s spin axis to turn due to the curvature of the earth and its rotation.
- Compensation: Calculate the turn and apply a compensating force to precess the gyroscope in the opposite direction.
What is horizontal earth rate?
what is its equation?
What happens if gyro is aligned east to west?
Definition:
Horizontal Earth Rate (HER) is the apparent tilting movement of a gyroscope’s spin axis caused by the Earth’s rotation. It varies with latitude and the alignment of the spin axis relative to the meridian.
Equation:
HER (ø) = 15cos(lat) sin(ø)
East-West Alignment:
maximum tilt effect when the gyro is aligned East-West at the equator, gradually reducing to zero at the poles.
State the characteristics of a free gyro
Rigidity in space - Property of spin axis to remain pointing to a fixed position in space regardless of any movement of framework supporting it.
Precession - Resulting angular velocity acquired by the spin axis when a torque is applied to the gyroscope in a plane perpendicular to the plane of the rotor.
In which direction does a gyro precess if a force is applied to it and why?
How Precession Works:
- When you apply a force to a gyroscope, it will precess (move) 90 degrees from the point where the force is applied, in the direction of the wheel’s rotation.
Why This Happens:
- The force creates a torque that is perpendicular to the rotor’s plane.
- This torque causes the spin axis to move due to the combined effect of the applied force and the gyroscope’s angular momentum.
Simplified Effects:
- Tilting Force: If you try to tilt the spin axis, the gyroscope will turn.
- Turning Force: If you try to turn the spin axis, the gyroscope will tilt.
What factors is precessional rate dependant on?
- Direction of Wheel Rotation:
- Reversing the wheel’s rotation direction = reverses the precession direction. - Magnitude and Direction of Applied Force:
- Increasing the applied force = increases the precession rate.
- Reversing the force direction = reverses the precession direction. - Angular Momentum:
- Higher angular momentum = decreases the precession rate.
What happens when the gyro spins at low speeds and how is it prevented?
Low-Speed Spinning Effects:
- When a gyro wheel is spinning at low speeds, its angular momentum is low. Small torques can then cause relatively high precession rates, which may lead to gimbal lock.
Prevention:
- To prevent this, the gyro is “caged”. Caging ensures that no precessional forces are applied to the gyro wheel until it has reached its correct operating speed.
What is the ideal gyro position?
Ideal Position:
- The ideal position of a gyro is when the spin axis is aligned with the meridian (North-South direction) and level. This alignment ensures that the gyro can accurately seek and maintain true north.
What is the Horizontal Earth Rate equation and explain it.
Definition - The apparent tilting movement of a gyroscopes spin axis caused by the earths rotation.
Equation - HER(ø) = 15cos(Lat)sin(ø)
15 = represents earths rotation rate in degrees per hour
Cos(Lat) = Accounts for the effect of latitude on the tilt rate.
Sin(ø) Accounts for the angular displacement of the spin axis from the meridian.
What are the Transport Wonder N-S and E-W equations?
N-S - Causes the gyroscopes spin axis to tilt when the vehicle moves north or south.
Vcos(Course)
E-W - Causes the gyroscopes spin axis to drift E or W when the vehicle moves E or W.
Vsin(Course)tan(Lat)
What are the 4 types of accelerometers corrections
1. Gravity: Accelerometers senses gravity as upward acceleration.
2. Centripetal Effect: Earth’s rotation causes centripetal acceleration towards the center.
3. Coriolis Effect: Moving in a rotating frame (like Earth) causes an apparent force.
4. Convergence: Meridians converge as you move towards poles, causing path curvature.
What is the output of rate and rate integration gyros?
Rate Gyro:
- Output: Provides a signal proportional to the rate of rotation (angular velocity).
Rate Integration Gyro:
- Output: Provides a signal proportional to the angle of rotation (integral of the angular rate).
Summary:
- Rate Gyro: Measures how quickly an object is rotating.
- Rate Integration Gyro: Measures the total angle through which an object has rotated over time.
What information is needed to turn a city into gloss?
1. Initial Launch Position:
- Submarine’s current location and depth.
2. Target Coordinates:
- Exact latitude and longitude of the target.
3. Navigation Data:
- Submarine’s position, speed, and heading updates.
4. Environmental Data:
- Information about ocean currents and water conditions.
5. Gyroscopic Data:
- Orientation and movement data from gyroscopes.
6. Inertial Navigation System (INS):
- Position and velocity data from accelerometers and gyroscopes.
7. Earth’s Rotation Compensation:
- Corrections for Earth’s rotation effects.
How does INS work in a weapon system?
Inertial Navigation System (INS):
INS uses gyroscopes and accelerometers to provide continuous data on the position, velocity, and orientation of a weapon system without relying on external signals.
Key Components:
1. Gyroscopes:
- Measure rotational movements and maintain orientation.
- Accelerometers:
- Measure acceleration to determine changes in velocity and position.
Process:
1. Initialization:
- INS is initialized with the weapon’s starting position and orientation.
- Data Collection:
- Gyroscopes track the rotational movements, while accelerometers measure the linear accelerations.
- Integration:
- The system continuously integrates the accelerations to calculate velocity and further integrates velocity to determine position changes.
- Navigation and Guidance:
- The INS uses this data to continuously update the weapon’s current position and adjust its path to ensure it follows the planned trajectory towards the target.
Corrections:
- Earth’s Rotation: INS accounts for the Coriolis effect and other factors to maintain accuracy.
- Environmental Factors: Adjustments are made for factors like ocean currents (for submarine-launched missiles).
What are the advantages and disadvantages of INS?
Advantages:
- Independent Operation:
- INS functions without needing external references like GPS, making it reliable in all weather conditions.
- Immunity to Jamming:
- Since INS does not rely on external signals, it is immune to jamming and other forms of electronic interference.
- Stability and Accuracy:
- Provides stable and accurate data for platform and weapon stabilization.
Disadvantages:
- Initial Fix Required:
- INS needs an initial geographical location input to start operating accurately.
- Accuracy Degrades Over Time:
- Errors in the system accumulate over time, leading to increasing uncertainty in the platform’s current location. Periodic updates or fixes from external sources like GPS are required to maintain accuracy.
