Navigation NAU 102 Lesson 17

Interpolation Much of navigation uses tables. e.g. What is the deviation when heading 300°M? Ans: 3°E DEVIATION TABLE MAG HDG DEV 300° 3°E 315° 0° 330° 1°W

Interpolation What if the value we are looking for falls between table values? We must interpolate. Definition: to estimate the value of a function between two known values.

Interpolation e.g. What is the deviation when heading 305°M? 300°M = 3°E DEVIATION TABLE MAG HDG DEV 300° 3°E 315° 0° 330° 1°W 315°M = 0° 305°M = ?

Interpolation Step 1: Determine intervals between known table values 300° 3 ° E 315° 0° 305° ?15°3° e.g. What is the deviation when heading 305°M?

Interpolation Step 2: Determine interval between base table values and desired values 5° X e.g. What is the deviation when heading 305°M? 300° 3 ° E 315° 0° 305° ?15°3°

Interpolation Step 3: Compute the ratio to solve for X. = X X = 1° e.g. What is the deviation when heading 305°M? 5° X 300° 3 ° E 315° 0° 305° ?15°3° 15° 5° 3°

Interpolation Step 4: Apply resulting interval (X) to base value. e.g. What is the deviation when heading 305°M? 5° 1° 300° 3 ° E 315° 0° 305°15°3° 2°E

Interpolation e.g. What is the deviation when heading 160°M? Magnetic Heading DeviationMagnetic Heading DeviationMagnetic Heading Deviation 0°4.0° W120°2.0° W240°6.0° E 15°4.0° W135°1.5° W255°4.5° E 30°3.5° W150°0.5° W270°3.0° E 45°3.0° W165°1.5° E285°0.5° E 60°2.5° W180°4.5° E300°1.0° W 75°2.5° W195°5.5° E315°2.5° W 90°2.0° W210°6.5° E330°3.5° W 105°2.0° W225°6.5° E345°4.0° W

Gyrocompass An Electronic Compass Points to true North Works on the principle of the gyroscope.

Gyroscope Components Wheel (or Rotor) Mounted on a spin axis. Supported by gimbals: Torque axis Precession axis

Gyroscope Gyroscopic Inertia When the wheel spins at high rpm, it will tend to maintain its orientation in space.

Gyroscope Gyroscopic Inertia Unfortunately, for our purposes, it doesn’t maintain its orientation relative to the Earth.

Precession The Gyroscope must be forced to point to true north. When a force is applied to a gyroscope, the movement is 90° from the direction of the applied force. The force is called “torque”. The movement is called “precession”.

Precession The torque is provided by the rotating Earth. Since the Earth rotates East-West, the gyro is precessed 90° to the North-South axis. Weights are added to the axes to keep the rotor horizontal to the Earth and to cause the gyrocompass to seek true north.

Errors Latitude Error – torque caused by Earth’s rotation is greatest at the equator. Higher the latitude = less precession. Therefore, the gyro tends to fall off of true north. Gyrocompasses need to be adjusted for latitude changes. Manual or automatic adjustment, depending on the model. Accuracy decreases above 75° latitude.

TSGB Master Gyro

Errors Speed Error – torque (weights, etc) are applied based on Earth’s East-West rotation. When the ship’s heading has North-South components, the compass settles off of true north. The faster the North-South change, the larger the error.

TSGB

Gyrocompass One or more north- seeking gyroscopes. Housing, electrical supply and control elements.

Gyrocompass Must spin up and settle on the meridian. Takes up to four hours to settle. Typically left on unless in port for long periods.

TSGB Master Gyro

Advantages Over Magnetic Seeks true meridian. No need to apply variation. Can be used near the magnetic poles. Not affected by ship’s magnetism. Deviation corrections are unnecessary. Output can be sent to other electronic devices (e.g. automatic pilot, radar, etc.)

Gyrocompass Repeaters A remote indication of the reading of the master gyrocompass. Usually on bridge wings and helm console.

Disadvantages Expensive Maintenance and repairs are more complicated. Needs electricity If operation is interrupted, requires several hours to settle.

Gyros Can Fail! Regularly compare the gyro and magnetic compasses. Insert Sea Story here. “the failure of a ship’s gyro went undetected for a period of over twelve hours, with the result that, at the time of grounding the vessel was more than 110° off course and more than 200 miles out of position” – Dutton’s, pg. 82

Introduction to Navigation Questions?