Gyro Compass PDF

Fig (4) 4) If a free gyroscope is situated at the North/South geographic Pole with its spinning axis vertically. If the free gyroscope spin axis were started vertically at one of the earth's poles, it would remain in that position and produce no apparent m...

Fig (4) 4) If a free gyroscope is situated at the North/South geographic Pole with its spinning axis vertically. If the free gyroscope spin axis were started vertically at one of the earth's poles, it would remain in that position and produce no apparent motion (no tilt no drift).  Conclusion:-  Maximum rate of tilting occurred at the geographical equator.  No drift occurred at the geographical equator.  Maximum rate of drifting occurred at the geographical poles.  No tilt occurred at the geographical poles. 5- Relation between rate of tilt and latitude & azimuth The rate of tilt = 15°/ h sin Az. Cosine latitude 5.1 Relation between rate of tilt and latitude To prove the relation between rate of tilt and latitude, we will fix (AZ) and change lat. 1- The free gyroscope at the equator and its axis horizontal, then we have maximum rate of tilt (150 / hour) 54  2- The free gyroscope at the magnetic pole and its axis horizontal, then we have no tilt (rate of tilt equal zero) Fig (5) From fig (5): The rate of tilting α Cos latitude (1) 5.2 Relation between rate of tilt and azimuth (AZ) To prove the relation between rate of tilt and azimuth, we will fix lat. and change azimuth (AZ): 1- The free gyroscope at the equator and its axis horizontal, then we have maximum rate of tilt (150 / hour) 2- The free gyroscope at the equator and its axis vertical (N-S), then we have no tilt (rate of tilt equal zero) Fig (6) From fig (6): Rate of tilt α sine AZ (2) From 1&2 then: The rate of tilt α sin Az. Cosine latitude The rate of tilt = 15°/h sin Az. Cosine latitude 55 6- Relation between rate of drift and latitude Rate of drift = 15º/ h sine latitude To prove the relation between the rate of drift and latitude, we must fix (AZ) and change lat. 1- The free gyroscope at the equator and its axis horizontal, then we have no drift so rate of drift equal zero 2- The free gyroscope at the magnetic pole and its axis horizontal, then we have maximum rate of drift Fig (7) From fig (7): Rate of drift α sine latitude Rate of drift = 15º sine latitude 7- Combined tilt and drift At any latitude excluding the equator and any of the geographic poles, the free gyroscope spin axis will exhibit an apparent motion. That apparent motion is partly of tilt and partly of drift (as in fig 8) 56  Fig (8) 8- The Cases which the spin axis of a free gyroscope does not make any apparent motion: 1- If it is on the equator and its spin axis is horizontal and parallel to the meridian. 2- If it is at the pole and its spin axis is vertical on the horizontal plan. 3- On any north latitude the north end of spin axis tilts upward with an angle equals to the latitude “in the plan of the meridian”. 4- On any south latitude the south end of spin axis tilts downwards with an angle equals to latitude “in the plan of the meridian”. 9- Control of the Free Gyroscope to Produce a North Seeking Instrument It has been stated that a free gyroscope suffers an apparent movement in both azimuth and tilt of the rotor axis depending upon location in latitude. It is possible to calculate the necessary force required to produce, reverse action to correct the effect of apparent movement. A force can be applied to the gyroscope, which will cause both azimuth and tilt precession to occur in opposition to the unwanted force (drift &tilt) caused by the gyroscope position of the earth. Although the gyroscope is now stabilized to a terrestrial point it is not suitable for use as a navigating compass, because it is not north seeking (meridian seeking). So to use the gyroscope as a navigation compass (gyro compass), it must be converted to north seeking or meridian seeking gyroscope. 10 - North seeking gyroscope The gyro spin axis can be made meridian seeking (maintaining the spin axis parallel to the earth’s spin axis) by acting on gyroscope by directing moment which bring the main axis to meridian plane. The directing moment is gained by gyroscope due to displacement of gravity center of gyroscope below the point of suspension is the simplest way of such limitation, gyro compass with this manner is called the pendulum gyro compass Under the influence of earth gravity, the pendulum causes a force to act upon the gyroscope assembly that will precess under its influence. Precession enables the gyroscope to become north seeking. 57 The gravitational force acting downward on the spinner axle causes the gyroscope to precess horizontally to maintain the axle pointing towards true north. The two main ways of achieving processional action due to gravity are to make the gyro spin axis either bottom heavy control or top heavy control , (as in fig 9) Bottom-heavy control top - heavy control Fig (9) Methods of gravity control: bottom-heavy and top-heavy control 11- Bottom-heavy control The bottom heavy control system used a gyroscope rotate at clockwise direction when viewed from the south end ,this done by adding a weight to the bottom of the rotor casing.this weight make a displacement to the center of gravity bellow the center of suspension. This pendulous weight will always seek the center of gravity, Because of the earth’s rotation and gyro rigidity; the pendulum will cause the gravity control to move away from the center of Gravity, caused pendulum moment. Fig (10) Principle of bottom gravity control 58 The resulting will cause a torque about the horizontal axis. This in turn causes precession about the vertical axis and the spin axis will move in azimuth towards the meridian (this manner used by S.G brown marine company). 12- Top - heavy control Other manufacturers design their gyrocompasses to be effectively top-weighted and use an anticlockwise spinning rotor, by adding a weight to the top of the rotor casing. This weight makes a displacement to the center of gravity above the center of suspension. An ‘apparent’ top weighting is achieved by the use of a mercury fluid contained in two pots. As shown in Figure (11), each pot, partly filled with mercury, is mounted at the north and south sides of the rotor on the spin axis. A small-bore tube connects the bases of each pot together providing a restricted path for the liquid to flow from one container to the other. When the gyro tilts, the fluid will also tilt and cause a displacement of mercury. This action produces a torque about the horizontal axis with a resulting precession in azimuth. Fig (11) top heavy control Consider a controlled gyroscope to be at the equator with its spin axis east west, as the earth rotates from west to east the gyroscope will appear to tilt about its horizontal axis and the east end will rise forcing mercury to flow from pot A to pot B. The resulting will cause a torque about the horizontal axis. This in turn causes precession 59