NavList:

Feedback, or a layman's explanation of "amplitude."

 

Amplitude is a special case bearing problem.  Basically you are taking a bearing when the Ho is 0 degrees. You are eliminating the "altitude" portion  of the celestial triangle and therefore greatly reduce the formula to determine Azimuth.  All you need to do is know Latitude and Declination and take a bearing.  It is a very easy shot to shoot and reduce, much easier then an Azimuth, even of Polaris (unless you use a computer which renders all the math moot).  It also has the advantage of not needing a precise time or latitude to get a reasonably accurate number.  My example demonstrates this with the vague DR Lat and time that is given.  This will not significantly affect the outcome of the compass error.

 

The formula Sin A = Sin Declination / Cos Latitude will give you "A" which is the degrees between the prime vertical (90 and 270 deg) and where the sun is actually crossing the celestial horizon.  A is 0 at the time of equinox and increases as we head towards the solstice.  You can see it in effect by observing that the sun will rise north of East in the summer and south of East in the winter (northern Latitudes).  Amplitude will tell you the exact amount north or south of east or west the sun will be when it crosses the celestial horizon given the declination of the body and the observers latitude.  Does this help?

 

My solution to the problem is here:

 

Declination of the Sun is N 16 deg 41'.  Latitude is 14 degrees north.

 

Sin A = Sin 16.7/Cos 14 (notice I am rounding even here)

A= 17.2

 

Since the sun is observed bearing 288 deg, we can see that it is a PM amplitude so we start at the Western Prime vertical or 270 deg.  Since the sun's declination is North, we know it is setting north of 270 so we use the terms  W 17.2 N or 270 +17.2 = 287.2.  This is the calculated bearing of the sun.

 

We shot the sight on a gyro compass and got 288.0 deg pgc (per gyro compass).  Finding the difference between the observed bearing of 288.0 and the calculated bearing of 287.2, we find a gyro error of 0.8 degrees W (compass best error west).

 

Apply the Gyro Error to the gyro heading of 208 and we get a true heading of 207.2 degrees. 

 

T         V    M        D         C    (add west)

207.2   2E  205.2  1.8W     207

 

Compass error is the difference between True and Magnetic compass and is 0.2 deg E.

 

Jeremy