Gyro Numerical - Free Gyro | Part - 1

Summary

The lesson reviews gyroscope properties and explains how a free gyroscope appears to move when observed from the rotating Earth. Understanding tilt and drift is essential for later gyrocompass calculations.

Main ideas

• Rigidity in space: A spinning rotor tends to keep its spin axis pointed in the same direction in space unless an external force acts on it. This tendency is associated with gyroscopic inertia and angular momentum.
• Precession: When torque is applied to a gyroscope, it responds with precession, which occurs perpendicular to the applied torque. Precession increases with torque and decreases with angular momentum. Because angular momentum depends on the rotor’s moment of inertia and angular velocity, a faster-spinning rotor precesses more slowly under the same torque.
• Apparent motion caused by Earth’s rotation: A free gyro’s axis remains fixed in space while Earth turns beneath it. Consequently, the axis appears to move relative to an observer on Earth. Stars—and the Sun, as an illustrative reference—also appear to move across the sky because of Earth’s rotation.
• Gyro star: The point in space toward which the gyro’s spin axis is directed can be treated as a reference star, called a gyro star. It may be an actual star or an imaginary reference point.
• Describing direction: A star’s position can be described using:
  • Altitude: Its angle above or below the horizon.
  • Azimuth: Its direction in the horizontal plane, measured relative to the meridian.
• Tilt and drift of the spin axis:
  • Tilt is the angle the spin axis makes with the horizontal, measured in the vertical plane. The lesson uses T (or TG) as its notation.
  • Drift is the angle of the spin axis in the horizontal plane relative to the meridian or true north. The lesson uses D (or Dr) as its notation.
  • Tilt and drift describe different aspects of the axis’s orientation: tilt is vertical, while drift is horizontal.
• Apparent daily movement: As Earth rotates, the gyro star appears to travel around the sky, and the spin axis traces a circular path in the celestial hemisphere. The rate is 360° in 24 hours, equivalent to 15° per hour or 15 minutes of arc per minute of time.
• Tilt sign convention: Tilt is positive when the spin axis is above the horizontal and negative when it is below. This convention is independent of the observer’s latitude or hemisphere.

Speakers and sources

• Instructor: Leads the review and explains gyroscopic properties, reference directions, tilt, drift, and apparent motion.
• Unidentified students: Answer questions and participate in the classroom exchange.