Accurate navigation depends on determining and correcting a ship's gyro error. This video explains how to find the gyro error through astronomical observation using the ABC method. Key data to collect includes the sun's bearing using the gyro repeater, universal time (UTC), ship's position, local magnetic variation, gyro course, compass course (PSC - Per Standard Compass), and the current date and year. GPS is useful for time and position, while charts or ECDIS provide variation.

The first step involves using a nautical almanac (e.g., 2021 edition) to find the Sun's Greenwich Hour Angle (GHA), Local Hour Angle (LHA), and declination. The video demonstrates how to locate the relevant daily page (e.g., August 24th) and extract the GHA and declination for a specific UTC. Adjustments are made for minutes and seconds using increments and corrections tables, and a declination correction (v-correction) is applied based on whether the declination is increasing or decreasing. The ship's longitude is then applied to the GHA to find the LHA, remembering to add for easterly longitude and subtract for westerly.

The second step uses Norie's Nautical Tables to find the true azimuth (or true bearing) of the sun. This involves three main tables: Table A, Table B, and Table C. Table A uses LHA and latitude to find value 'A', determining its direction based on rules provided in the table. Table B uses LHA and declination to find value 'B', taking the same direction as the declination. If 'A' and 'B' have the same name, they are added to find 'C'; otherwise, their difference is taken. Finally, Table C uses the calculated 'C' value and latitude to determine the azimuth angle. The azimuth's direction is named according to the rules, resulting in a true bearing (e.g., North 17.9 West, converted to 342.1 degrees true).

The final step is to calculate the gyro error and compass deviation. Gyro error is the difference between the true bearing and the gyro bearing. A rhyming rule (compass best, error west; compass least, error east) helps determine the direction of the error. Once the gyro error is known, it's applied to the gyro course (adding for east, subtracting for west) to find the true course. The difference between the true course and the compass course gives the total magnetic compass error. Finally, by applying the local variation to the total error (reversing the variation's sign), the deviation for the ship's heading is determined. A check is performed by correcting the compass course to verify the calculations.