Similar to finding error by Amplitude, this method requires an observation and a correction of the sun, and can be done at
any time of day. The reductions needed to find the true bearing can be a bit more complicated though.
Beginning Steps for Either Method
Step 1: Observe the sun's bearing on the celestial horizon, noting time of observation. This is best accomplished
with an azimuth circle, or telescopic alidade for smaller bodies.
Step 2: Find time in GMT for use in NA, either converting from CT or ZT.
Step 3: Find Declination, make sure to note whether South or North and the trend in values, i.e. if the values are
increasing, the d correction is to be added; if the values are decreasing, the d correction is to be subtracted
Step 4:Find LHA. Table at right describes this process. The value of LHA is needed either to determine the page number
to be used in Pub 229, or to be entered directly into the equation to find Z.
Step 5: Compare observed azimuth to calculated azimuth.
Compass error is simply the difference between the two values, or you can plug the values into TVMDC to find deviation if
Method 1: Using Pub 229
This method is a bit tedious but allows you to easily identify any mistakes you might have made along the way.
Step 1: Open up Pub 229
Find the correct page by using LHA. For Volume 2, remember that Latitudes 15-22 are in the front of the book, and Latitudes
23-30 are in the back.
Also make sure you are on the correct page (left or right). The left hand pages are for when Latitude is Same Name as Declination.
Right hand pages are for when Latitude is Contrary Name to Declination.
Step 2:Find your Z
This is tough, and uses a Three-Way Interpolation, and I'm not quite sure if I'm describing it correctly, so I'd just use
the formulas if I were you. But here goes. Using your assumed Latitude, find the correct column on the correct page. Using
your calculated Declination, find the correct row. Where the row and column intersect you'll find a value of Hc, d, and Z.
In this problem we are only concerned with the Z value though. Next, find the Z correction for your LHA, Dec, and the next
latitude column over, either left or right depending on East or West longitude. Note this Z as well. Then, note the Z for
your LHA, Lat, and the next Dec down. Lastly, note the Z for your Lat and Dec, and the next LHA. Finally, interpolate between
all of these values for the leftover increments (e.g. minutes of Dec or LHA). This interpolated value is your actual Z.
Note this in your modified Sight Reduction Form (you won't use the whole thing, therefore it is modified).
Step 3:Find Your Z Correction
This correction is similar to the "d" correction for declination, except that there are no tables for interpolation. How you
find this correction is by noting both the Z for your Lat and Dec, and also noting the next Z down in the same Lat column.
Next, you find the difference between these values, and multiply that value by the Dec minutes that are unaccounted for. The
last step is to divide this entire value by 60. The resulting number is your Z correction, and will be either positive or
negative, depending on the trend of Z.
Step 4: Find your Zn
Simply add your Z correction to your original Z value to find your corrected Z. From here, you can always consult the inside
margin of Pub 229 for help. At the top of the left hand, and the bottom of the right hand, you'll notice some equations that
let you know exactly how to convert. Those equations are as follows:
For N Lat:
LHA greater than 180, Zn=Z
LHA less than 180, Zn=360-Z
For S Lat:
LHA greater than 180, Zn=180-Z
LHA less than 180, Zn=180+Z
Method 2: Equations only
This method may be simpler in that you don't have to look through Pub 229 to find it, but if you mistype a single
number in your calculator, you may not realize it until you get to the end, and wont be able to find it easily.
Step 1: Enter values into calculator.
This one is pretty simple. Using the equation:
Z= ((cos Dec)(sin LHA)) / (((cos Lat)(sin Dec))-((sin Lat)(cos Dec)(cos LHA)))
A lot of parenthesis, Freddy knows,
but Freddy have yet to figure out how to write equations in html format.
Some things to remember though:
-if LHA is
greater than 180, it is entered as a negative
-If Dec and Lat are contrary name, Dec is entered as a negative
is a negative in the end, add 180.
That's it, you've got Z, then see the last step in the above method for conversion