Sailing by the Stars: Compass Error by Amplitude — Celestial Navigation
Despite modern technology one of the many traditional seamanship skills that all navigators need to maintain is checking the vessel’s compass accuracy (or Compass Error as it’s referred too) regularly using the stars, planets, moon or the Sun.
In this article that accompanies my YouTube video series, I’ll explain how to quickly check the compass error via the Amplitude method at sunrise or sunset.
Difference between Amplitude and Azimuth
Whereas the Azimuth Method of determining compass error can be used at any time of the day or night, the Amplitude Method provides a simpler and much faster calculation with the downside being that it’s only possible when the body being observed is situated on the celestial horizon.
For this reason, it is only practical to use the Amplitude Method with the Sun or on very clear nights with a clearly defined horizon the moon can also be used.
Celestial Horizon
Due to the curvature of the earth, the Celestial Horizon is not the same as the visible horizon.
The Sun is deemed to be on the Celestial Horizon when it’s lower limb is located 2/3 of its diameter above the visible horizon.
The Moon is deemed to be on the Celestial Horizon when it’s upper limb is touching the visible horizon. As this would only give you a few seconds it’s normally preferable to only use the Amplitude with the Sun.
Taking the Observation
The first step in calculating our compass error is to take an observed bearing of the celestial body, traditionally this would have been done with an azimuth ring on the vessels’ magnetic compass but on modern vessels with gyro-compasses, it’s more common to be taken using a bridge wing gyro repeater with sight.
This method will give us the vessels gyro error which we can then use to calculate the vessels’ magnetic compass error if desired.
It’s important that we take our observed bearing as accurately as possible, we also need to record the exact time we have taken our bearing to the nearest second — the most common method of ensuring the time is accurate is to use the clock on a GPS unit but you can use whatever timekeeping system you have onboard.
Lastly, we also need to know the position of our vessel at the time the observation was taken.
If you also wish to calculate the vessels’ magnetic compass error we need to record the gyro and magnetic compass headings at this time.
The Calculation
I’m going to show the calculation using an example, in this case, we’re calculating the gyrocompass error using an amplitude of the Sun and we’ll make use of a Pro-forma I created to match my video series which can be downloaded as a PDF from here.
After filling in the known information, which is our ship’s position, gyro heading, observed bearing of the sun and the date/time of our observation converted to UTC (all celestial calculations are carried out relative to UTC / GMT).
We only need one piece of additional information which is the declination of the Sun at the given time. In order to obtain this, we need to use a nautical almanac. The photo below shows the appropriate daily page from the 2016 British Admiralty Nautical Almanac.
Looking down the Sun column we can find that the declination for 20:18 on the 9th of April 2016 is North 7 degrees, 57.9 minutes, and we can see that the declination between 20:00 and 21:00 is increasing.
We now have a correction to apply to this declination value, to obtain the correction we need to make a note of the ‘d’ value which is shown at the bottom of the column in the Nautical Almanac, which in this case is 0.9.
With this information we need to turn to the yellow coloured pages in our British Nautical Almanac which contain “Increments and Corrections” and locate the page for 18 minutes, we then locate our ‘d’ value of 0.9 in the “v/d corr” column. This gives us a correction value of 0.3.
We said that the declination between 20:00 and 21:00 was increasing, therefore we add this 0.3 onto our original 20:00 declination value giving us our correct declination for 20:18 of North 7 degrees, 58.2 minutes.
Amplitude Formula
We now have all the information we need to work out the true bearing of the Sun using the amplitude formula.
Amplitude = SIN-1 ( SIN Declination / COS Latitude )
If we enter this into any scientific calculator you’ll get the answer of 8.9, we also need to name it, as our declination was North and the Sun was setting we name it North 8.9 West which to be useful to us we convert to a true bearing by adding it to 270, giving us a true bearing of 278.9 degrees.
To convert our amplitude to a true bearing we use the helpful table on the Pro-forma. If it had been sunrise and our amplitude was named North 8.9 East then we would subtract the 8.9 from 90.
Completing the Compass Error
The final step if we are working out our compass error is to compare the observed bearing of the Sun we took earlier with our calculated true bearing of the Sun. The difference between these is our gyro compass error.
In the case of our example, our gyro error is 0.1 degrees high.
