Lecture Notes on Compass Error Question Using Amplitude Method

Introduction

• Topic: Solving a compass error question using the amplitude method.
• Example celestial body: Sun.

Problem Statement

• Date: 23rd September 1992.
• Conditions: Sun was rising.
• Compass bearing of the Sun: 094 degrees.
• Dead reckoning position: 0 degrees latitude (equator) and 120 degrees 27 minutes West.
• Chronometer time: 01:54:00.
• Chronometer error: 3 minutes 12 seconds fast.
• Variation: 2.7 degrees West.
• Objective: Find the deviation using the amplitude method.

Chronometer Time Correction

1. Chronometer Time Possibilities:
   • 01:54:00 (morning)
   • 13:54:00 (afternoon)
2. Apply Error:
   • Subtract 3 minutes 12 seconds from both possibilities:
     • 01:50:48
     • 13:50:48
3. Finding Correct GMT:
   • Calculate Local Mean Time (LMT) using longitude correction: LMT = GMT - (Longitude/15)
   • Longitude: 120 degrees 27 minutes (120.45 degrees) / 15 = 8 hours 1 minute 40 seconds.
   • Both GMT possibilities:
     • 17:49:00 (not valid, as Sun is rising)
     • 05:49:00 (valid)
4. Correct GMT:
   • 23rd September, 13:15:48.
   • Note: Use GMT for further calculations, not LMT.

Declination Calculation

• Nautical Almanac Reference: For 23rd September, 13:00 hours:
  • Declination: 0 degrees 17.8 minutes South.
• D Value: 1 (increasing).
• Calculate correction for time: 50 minutes and 48 seconds:
  • From increments page, find correction value (D correction value): 0.8.
• Corrected Declination:
  • 0 degrees 18.6 minutes South (adding correction).

Amplitude Calculation

1. Formula:
   • Amplitude = sin(Amplitude D) * cos(Declination) / cos(Latitude).
2. Values:
   • Latitude: 0 (equator).
   • Corrected Declination: 0 degrees 18.6 minutes.
3. Calculate Amplitude:
   • Amplitude = 0.0000541.
   • Amplitude Value (Sine Inverse): 0.3.

Naming the Amplitude

• Rising vs. Setting: Since the Sun is rising, it’s East.
• Declination: South (0 degrees 18.6 minutes).
• True Bearing: 090 degrees 0.3 minutes.
• Compass Bearing Given: 094 degrees.
• Calculation of Compass Error:
  • Compass Error = Compass Bearing - True Bearing = 094 - 090.3 = 3.7 degrees West.

Variation and Deviation

• Variation: 2.7 degrees West.
• Deviation Calculation:
  • Deviation = Compass Error - Variation = 3.7 - 2.7 = 1 degree West.

Conceptual Understanding

• Visualization:
  • True Bearing: 090.3.
  • Compass Bearing: 094.
  • Compass Error: 3.7 degrees West (Compass lies to the West).
  • Variation: 2.7 degrees West (Magnetic lies to the East).
• Deviation as the angle between compass and magnetic: 1 degree West.

Conclusion

• Understanding the use of amplitude method for compass error calculations using the Sun as a celestial body is crucial.
• Ensures accurate navigation.

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