Gyro.docx

**Gyro** **ROUGH // HANDOUT // Compiled from Internet //References provided** https://www.youtube.com/watch?v=bvO4froSGSc&t=707s - In **marine navigation**, a gyro compass is a type of direction-finding equipment that utilizes afast-rotating disc called a gyroscope to find **the true No...

**Gyro** **ROUGH // HANDOUT // Compiled from Internet //References provided** https://www.youtube.com/watch?v=bvO4froSGSc&t=707s - In **marine navigation**, a gyro compass is a type of direction-finding equipment that utilizes afast-rotating disc called a gyroscope to find **the true North.** - Unlike magnetic compasses that rely on the Earth's magnetic field, gyro compasses detect true north using gravity and the rotation of the Earth. - A compass dial is connected to the gyro, determining the ship's heading as the vessel navigates across the seas. -  **Gyroscope**   A drawing of a machine Description automatically generated **Gyro Compass - Intro** A gyro compass basically consists of a gyroscope. earth\'s incessant rotation and the force of gravity. incessant = continuing without pause or interruption. **Gyroscope** **The gyroscope consists of a mass in the form of a wheel or rotor (yellow part)** - **which is suspended in such a way that it is free to spin about an axis passing through its centre of mass (the brown rod) and perpendicular to the plane of the rotor.** - **in this diagram, the YELLOW part is the rotor,** - **the brown rod passing through the middle of the rotor is the spin axis.** - **This spin axis is connected to a BLUE horizontal gimbal ring through ball bearings.** - **\'These ball bearings provide the \"freedom to spin\" to the rotor.** - **\'This BLUE horizontal gimbal ring is connected to a vertical RED ring through a second set of ball bearings, at two points, which are perpendicular to the spin axis.** - **This second set of ball bearings permit the spin axis to tilt freely in up and down direction.** - **\'The vertical RED ring is connected to an GREEN outer member at right angles to the horizontal axis through a third set of ball bearings,** - **Pso that the spin axis can drift or turn in the horizontal plane.** - - Ideally the spin axis bearings should be frictionless so that any rotation imparted to the rotor is maintained, - However practically there will be some amount of friction resisting the spin, - This friction is counteracted by putting in an electric motor on the rotor just like a normal ceiling fan. - With this arrangement gyroscope is not constrained in any way so as to alter the direction of its spin axis. - \'It is then said to have **three degrees of freedom & is called a Free Gyroscope.**  **Three degrees of freedom consists of ability of the rotor** - **To spin about spin axis** - **To spin about horizontal axis** - **To spin about vertical axis** **Earth is Free gyroscope** - All 3 degrees of freedoms - Earth is the best example of free gyroscope in nature, because *It* Is freely suspended in space having no friction and thus having three degrees of freedom, - It is heavy and well balanced with the equatorial mass corresponding to the plane of a rotor. And Earth rotates at considerably high speed about its axis. (Equivalent to spin axis of rotor) **The earth too may be compared to a free gyroscope.** - Earth is freely suspended in space. The earth's spin axis lies in the direction of the 'pole star', i.e. always pointing in same direction. If we disregard the negligible gravitational forces of other heavenly bodies, the earth may be considered free of any external forces **Properties Of free Gyroscope** - A free gyroscope consists of a rotor and a spin axis having three degrees of freedom. - As soon as the rotor is imparted some angular velocity it starts exhibiting these special properties, - **Gyroscopic Inertia** - **Gyroscopic Precession** Precession is a change in the orientation of the rotational axis of a rotating body. **Gyroscope inertia :** - Gyroscopic Inertia defines that a freely spinning gyroscope will maintain its axis of spin in the same direction with respect to **space** **irrespective** of how its supporting base is turned and - It resists any attempt to change the direction of its spin axis - Thus a free gyroscope has high directional stability. This property is called - GYROSCOPIC INERTIA or - RIGIDITY IN SPACE or - DIRECTIONAL STABILITY. All three meaning the same,  Important : the supporting base or the gimbals are turning but the spin axis maintains its direction because of Gyroscopic Inertia**.Turn the supporting base , turn the gimbles**. but the spin axis maintains sits direction in space. **this happens due to gyroscopic inertia** - The gyroscopic inertia of a rotor can be quantified **by its angular momentum(L)** - **Greater the Angular Momentum** **greater is the Gyroscopic Inertia** of the Gyroscope. **Gyroscopic Precession** - if a force is applied on spin axis The way in which the Spin Axis moves is quiet surprising. - We would expect it to move in the direction of the applied force but the motion is at right angle to the Applied force in the direction of the spin of the rotor - As you can see in the diagram a force is being - applied to the Spin Axis in **the upward direction in the vertical plane** but the motion of the Spin Axis is in the Horizontal - **Force applied vertical direction /vertical plane** - **Spin axis moves horizontal plane**   Precession is the resultant action, or deflection, of a spinning rotor when a deflecting force is applied to its rim. As can be seen, when a force is applied, the resulting force takes effect 90 degrees ahead of and in the direction of rotation **Tilt and Drift in a Gyro compass** - **Drift **is the movement of the spin axis in the direction of azimuth. On horizontal plane - **Tilt** is elevation or depression of the spin axis above or below the horizon. On vertical plane - The **eastward or westward movement** of the North end of the axle is called **drift** - The **rising and dipping movement** of the North end of the axle is called the **tilt** - - **Rate of tilting **in degrees per hour = 15^O^ sine Azimuth \* cosine Latitude - **Rate of Drift** in degrees per hour = 15^O^ sine Latitude A diagram of a circular object **Earth movement effect : Because of earth movement ,  Coriolis force forces acting on gyroscope. Can not keep pointing to one direction ,drifts about his horizontal and vertical axis the movement of the earth having effect on the gyro scope. effect is tilt and drift** - Star is fixed - Earth is moving. - We see the apparent movement of the heavenly bodies through out the day so the stars also rise and set. apparent movement. we are moving. Stars , heavenly bodies are fixed - Earth rotation is slow and we are situated on earth for us we see an apparent motion of heavenly bodies , stars rising and setting - Now , If we make gyroscope point towards fixed star, it will continue to do so, but stars are rising and setting , it goes through the journey from east to west - Now gyroscope traces the star as the star goes - This movement is different at pole and equator A screenshot of a video Apparent movement - **Drift : Drift **is the movement of the spin axis in the direction of azimuth -. On horizontal plane - Drift : Movement around horizontal plane. Imagine. Gyroscope on pole. Spin axis horizontal,pointing towards fixed object.ideally if earth not rotating. gyroscope will pointing towards star. Gyroscope will also trace the movement of the star **At pole bodies are not rising or setting ,** all the time going round you because at pole we are on top. Therefore gyroscope is also tracing the star.movement is only one direction **. horizontal**. No movement in vertical direction At pole no rising and setting of bodies just going round and round At Pole :  A globe with a star and text Description automatically generated with medium confidence **Spin AXIS follows the Gyro star**  **Tilt :**   A screen shot of a blue planet - Gyroscope at Equator - Rising and setting takes place of gyro star - **Apparent movement of gyroscope axis about it vertical plane because it traces rising and setting**  **How to make north seeking and settling the gyro** A screenshot of a device 1. **Make the spin axis horizontal : weights to be applied to make spin axis horizontal with spin axis pointing north. during construction manufacturer does it** 2. **Make it point to geographical north : pole star can be used. real problem is not pointing but stablising there.** 3. **Drift and tilt are present due to earth rotation.** 4. **Drift maximum at pole** 5. **Tilt maximum at equator** 6. **Other latitudes having both Tilt and drift component.** **Making North seeking gyro** - force of gravity is used - Top heavy **effect -Rotor Spinning** - **AntiClock wise** - Bottom Heavy effect **\-\-\-- Rotor** - **moving Clock wise** - when viewed from south end of - spin axis Rotor spinning anti clock wise Top Heavy -------------------------------- -------------- Rotor spinning Clock Wise Bottom Heavy Viewed from south end of Axis A screenshot of a video Description automatically generated  - Black Colour casing - Spin axis connected to casing through ball bearing - Casing **is not free to spin**, casing is free to tilt up and down , casing free to drift - Thus making rotor free to spin  **When gyro star moves** - **Upward tilt & easterly Drift** - **Dealing Tilt**  - **Torque in vertical plane** - **Torque result == horizontal plane south end eastward ==North end westwards towards the meridian** - **Known as Control precession** - - **Pc** [**∝**]{.math.inline} **tilt** - **North end tilt upwards \-\-\--precession caused westerly \-\-\-\--opposes easterly motion of free gyro**  A close-up of a computer screen Description automatically generated  - **Controlled gyro weights applied** - **Follows Elliptical path in 84 minutes , free gyroscope 24 hrs** - A screenshot of a video -  - **Spin axis always below the pole** **Elliptical path movement Behavior** - **Gyro still not settled. still moving in small elliptical motion** A screenshot of a computer Description automatically generated **Controlled Gyro=weights applied =elliptical motion explained**  - **Latitude Not changed** - - **Ellipse is made below the pole** - **Drift easterly** -  - **Azimuth is zero azimuth = when the spin axis is in line with meridian OD. azimuth is zero.== tilting is zero== no red line at D and G. Azimuth = angle between spin axis and meridian** A diagram of a circle with arrows and a circle with arrows Description automatically generated with medium confidence  **Damping == reduce the elliptical motion == make spiral inwards to wards equilibrium position where axis will settle & if disturbed will return back t o position**  - **Anticlock wise rotation \-\-\-- Top heavy gyro =uses Damping in Tilt -upward or downward opposes the tilt** - **Clock wise rotation \-\-\-- bottom heavy Gyro == Uses Damping in Azimuth** - **Both Seen from South of spin axis** - **Damping Precession -- Pd** - **What damping Precession does? Bring Back the spin axis towards meridian** A white paper with blue and orange text Description automatically generated  A screenshot of a video Description automatically generated  A screenshot of a video Description automatically generated  **ROUGH** +-----------------------------------+-----------------------------------+ | Pointing towards fixed object. |  | | revolution of gyro scope | | | maintained and pointing fixed | Heavenly body rising and setting | | object |. sun is constant. we are | | | rotating | +-----------------------------------+-----------------------------------+ **Real challenge : to bring the gyro axis back to north , once drifted** **Weights are being used for that** **Weights are being used using the property of Precession** Precession is a property of gyroscope to apply a force in one direction then gyroscope moves (precess) 90 degree away from the force. Using this property gyroscope seeks north direction. Weights are used and torque is applied to bring back to north One more criteria for placing weight is the direction of the rotor movement. Weights to be placed on basis of Clockwise or anticlockwise movement **Methods** **1.Damping Mechanism:** 1. A north-seeking gyroscope needs a damping mechanism to ensure that once it points to the true north, it stays there. 2. **Liquid Damping:** The gyroscope is mounted in a liquid-filled chamber. This liquid creates resistance that dampens oscillations, helping the gyroscope to stabilize pointing towards true north. 3. **Electrical Damping**: Some systems use electronic feedback systems to apply a counter-torque to dampen the movement. 2\. To make a gyroscope north-seeking using the gravity control method, you need to apply gravity to influence the gyroscope\'s behavior so that it aligns with true north. This method is commonly used in gyrocompasses. Here's a step-by-step guide: 1\. **Set Up the Gyroscope:** Mount the Gyroscope on Gimbals: Ensure the gyroscope is mounted on a set of gimbals, which allows it to rotate freely in multiple directions. Spin the Gyroscope: Start the gyroscope spinning at high speed. The spinning creates stability, which is key for its ability to seek north. 2\. **Align the Spin Axis Horizontally:** The gyroscope\'s spin axis should be nearly horizontal. This allows the gravitational forces to interact with it effectively. 3\. Introduce Gravity Control: **Weighted Pendulum or Mechanism**: Attach a small weight or pendulum to the gyroscope\'s axis in such a way that gravity can influence the axis when it is not aligned with the north-south direction. Offset the Spin Axis: The weight should slightly tilt the axis when the gyroscope is not pointing to the correct direction (i.e., north). 4\. **Allow Precession to Occur:** Due to the Earth\'s rotation, the gyroscope will experience a torque (force causing rotation) because the weight creates a slight imbalance when not aligned with the Earth\'s axis. This torque causes the gyroscope to slowly precess towards the north-south direction. 5\. **Stabilization:** As the gyroscope nears the north-south direction, the force from the weight diminishes because it aligns better with gravity, leading to less precession. The gyroscope stabilizes when it points true north, where the forces are balanced and no further precession occurs. 6\. **Continuous Operation:** The gyroscope will continuously correct itself if disturbed. The gravity-controlled mechanism ensures it remains aligned with true north, compensating for minor shifts or movements. **Summary of Gravity Control:** Gravity Influence: A weight attached to the gyroscope's axis helps it sense when it\'s not aligned with true north. Precession: This weight creates a slight torque, causing the gyroscope to precess towards the north. Stabilization: The system stabilizes when the gyroscope is correctly aligned with the Earth\'s rotational axis (north-south direction). This method is reliable and effective, especially in applications like marine gyrocompasses, where a consistent and accurate true north reference is needed. How is the Gyro Compass System made North Seeking? North Seeking Gyro:- - In order to damp unwanted oscillation, we need to achieve damping in tilt. - This is done by means of offset slightly to the east of vertical, resulting in component of the same force producing the required torque. - The magnitude and direction of this force is pre-calculated to achieve the required damping oscillation. - The amplitude of each oscillation is reduced to 1/3^rd^ of previous oscillation. - The spin axis reaches equilibrium and settles in a position at which drifting is counteracted by control precession & the damping precession counteracts tilting. - Finally, the gyro settles in the meridian & becomes north seeking. **GRAVITY CONTROL IN GYRO** - The rotation of the earth gives us a free gyroscope, which has to be controlled with the help of precession - and we have to use the property of earth\'s gravity and rotation to create the torque. - If we place the gyro scope with its North axis pointing Eastwards, this axis will tilt upwards as the earth rotates and with the help of mercury ballastic or a fixed weight we can now create a top heavy effect which will provide us a torque. - This is achieved as shown in figure 9, where the rotor is moving in anticlockwise direction and the North end of the axle is pointing Eastwards, as the earth rotates this end tilts upwards, hence mercury from North bowl N flows to the South bowl S and as a result torque is applied to the upper end of the axle at B, which results in precessing the North end Westwards. A similar effect can be created by attaching a weight to the two ends of the axis, the weight being above the rotor as shown in figure 9. This is known as the TOP HEAVY EFFECT.  A diagram of a globe Description automatically generated