Calculate the compass error using the Amplitude method - Celestial Navigation

Summary

In this video, the instructor demonstrates how to solve a compass error question using the amplitude method, with the Sun as the celestial body. The process involves determining the correct GMT by adjusting for chronometer error and applying time correction based on longitude. The declination of the Sun is then calculated using the nautical almanac. The final step is calculating the compass error and deviation through a series of mathematical steps, all while emphasizing conceptual understanding. This tutorial is especially useful for those learning to find compass error in navigation, with a focus on celestial body-based methods.

Takeaways

• 😀 The video explains how to solve a compass error question using the amplitude method, with the Sun as the celestial body.
• 😀 The question is based on the 23rd of September, 1992, with the Sun rising at a specific bearing of 0°9.4′.
• 😀 Chronometer error is taken into account, with the chronometer being 3 minutes 12 seconds fast, and this error must be subtracted to determine the correct GMT.
• 😀 Two possible GMT times are calculated (1:50:48 AM and 1:50:48 PM) after adjusting for the chronometer error.
• 😀 The local mean time (LMT) is calculated using the longitude of 20°27′W, giving two possible LMTs based on GMT.
• 😀 The correct GMT is identified by determining that the Sun was rising, indicating a morning time (13:50:48 for GMT).
• 😀 The GMT time is used to find the Sun's declination for September 23rd, with a correction applied based on the increment page of the nautical almanac.
• 😀 The Sun's corrected declination for 13:50:48 is found to be 0°18.6′ South, and this value is used in the formula to find the amplitude.
• 😀 The amplitude method formula involves using the sine and cosine of the declination and latitude, resulting in an amplitude of 0.541.
• 😀 The final compass error is calculated by comparing the compass bearing (0°94′) with the true bearing (0°90.3′), giving a compass error of 3.7° west, and the deviation is found to be 1° west due to the magnetic variation of 2.7° west.
• 😀 The explanation emphasizes the importance of conceptualizing the process, understanding the relationships between the compass, magnetic, and true bearings to calculate deviation correctly.

Q & A

What method is used to solve the compass error in the video?

The amplitude method is used to solve the compass error in the video.

What is the significance of the date and time provided in the question?

The date and time (23rd September 1992, 01:54:00) are crucial for calculating the correct GMT, which is needed to determine the Sun's declination at that specific time.

How do you handle the chronometer error in this calculation?

The chronometer error is subtracted from both possible times (AM and PM), since the chronometer is 3 minutes 12 seconds fast. This gives two potential GMT times, from which the correct one is selected based on local time considerations.

What is the purpose of calculating the Local Mean Time (LMT)?

The LMT is used to determine the correct GMT. By applying the longitude time correction, you can figure out which GMT time corresponds to the correct local time for the Sun’s rising.

Why is the morning time chosen as the correct LMT in this problem?

Since the Sun is rising, the correct LMT must be in the morning. The afternoon time (17:49:48) is discarded as it contradicts the fact that the Sun is rising.

How is the declination of the Sun calculated in the video?

The declination is found from the nautical almanac for the 23rd of September. The time is adjusted for 13:50:48 GMT using the increment page, which adds a correction of 0.8' to the original declination.

Why is the corrected declination 0° 18.6' South?

The corrected declination is 0° 18.6' South because the original declination for 1300 hours was 0° 17.8' South, and a correction of 0.8' was added due to the time difference.

What formula is used to calculate the amplitude of the Sun’s position?

The amplitude is calculated using the formula: sin(amplitude) = sin(declination) / cos(latitude). With a latitude of 0° (Equator), this yields the amplitude of 0.3°.

How is the compass error determined from the true bearing and compass bearing?

The compass error is calculated by finding the difference between the true bearing (090° South) and the compass bearing (094°), which results in a compass error of 3.7° West.

What is the final value of the deviation, and how is it calculated?

The deviation is calculated by subtracting the variation (2.7° West) from the compass error (3.7° West), resulting in a deviation of 1° West.