Monday, November 22, 2010

Celestial Navigation made Easy (Complete Sun Sight)

This was designed to help you complete a solution for a sun line or if you are just interested in learning celestial navigation. I have written this with two ideas in mind.

1. Make it as short as possible.
2. Make the math simple and keep it in a form that is easy to use.

Tools you will need: 1981 Nautical Almanac, Pub. 229 Volume 2 (15°- 30°) Sight Reduction Tables for Marine Navigation, Parallel Rulers, Triangles, Dividers, Calculator, and Pencil.               

This is the complete solution for a Sun Sight using the Nautical Almanac and Pub. 229 Sight Reduction Tables for Marine Navigation. The steps involved are in the order in which they should be taken.

Pub. 229 Method
Pub. 229 Sight Reduction Tables for Marine Navigation is a set of six volumes of pre-calculated solutions for the computed altitude (Hc) and the azimuth angle (Z) of the navigational triangle. Entering the arguments for the tables are local hour angle (LHA) expressed in whole degree, and declination. Values of Hc and Z are tabulated for each whole degree of each of the entering arguments.

Working Sights with Pub. 229
To work a sight with Pub. 229 you enter the tables by selecting the proper volume and turning to the page with the appropriate LHA. Using the assumed latitude and declination extract the tabulated values for Hc and Z. You then determine the exact value of Hc and Z corresponding to the time of the observation by interpolation using a formula that the tables are based on.

To find the intercept distance (a), this final Hc is compared to the observed altitude (Ho). If the computed altitude Hc is greater than the observed altitude Ho the intercept is AWAY from the direction of the GP of the body.

I will take a hypothetical situation and work out the celestial problem step by step. A form should be followed when working out a sight so there will be less of a chance for leaving out any pertinent information.

Step 1: Setup your plotting sheet and DR ahead from 0542 to 1220 and get you DR position and enter it in your format.

09h 05m
05h 45m
3h 20m x 20 kts = 66.7 miles

Step 2: Apply your IE, in this case it is on the arc, so you would subtrack it.

Step 3: Using the DIP Table on the inside cover of the Nautical Almanac enter with your height of eye 72' feet = (- 8.2). Dip correction is always a minus correction.

Step 4: On page A2 "Altitude Correction Tables 10°- 90° Sun, Stars, Planets" under the Sun - April - September (because our problem is in August). Enter with your Ha and find the Lower Limb column. Remember that Lower Limbs are always + corrections and Upper Limbs are - corrections.

Step 5: Compute your corrected chronometer time.

Step 6: Using GMT and Greenwich date of the observation enter the Nautical Almanac and record the tabulated hourly value of GHA and Tabulated Declination in your format.

Step 7: At the foot of each declination sub-column find the "d correction". This number is called the "d", which in this case is (0.7) this is the average over the three day period that the declination changes per hour of GMT. The "d" is recorded on the d corr line off to the side. This is a correction, as with any correction, it is either a + or -. If the declination is increasing (getting larger) then it is a plus (+) correction, if the declination is decreasing then it is a minus (-) correction.

Step 8: Turn to the Increments and Corrections pages of the Nautical Almanac and find the "5" minute page and enter with "9" seconds. Then under the Sun and Planets column find the increase in the Sun's GHA since the last tabulated (hourly) value, which is 1°17.3, this is your minutes and seconds (M & S) correction, enter this in your format. Always add the GHA and M & S values together to get the total GHA.

Step 9: While on the 5 minute page under the "v or d" correction column, find the "d" which is 0.7 on the left hand side. This is equal to 0.1, enter this in your format and in this case you would subtract. This is the declination (Dec) of the Sun at the time of the sight.

Step 10: In full sight reduction LHA has to end in the whole degree and your Assumed Longitude has to be within 30' minutes of your DR Longitude.

GHA 224°52.9'
A Long. +94°07.1' E
LHA 319°00.0'

Step 11: Enter Pub. 229 with LHA 319°, A Lat. 25° and Dec. 16° N. Then extract the tabulated Hc, base Z, and Z for the next whole degree of declination, and the Rule for coverting Z to Zn and enter this into your format. Make sure to note the sign of the differences. Next, using the formula, (Difference x declination increments ÷ 60 = correction).

Step 12: Add or Subtract your corrections to your Tab. Hc and base Z to get your corrected Hc and Z.

Step 13: Fill in your Ho, find the difference between Hc and Ho, this will give your altitude intercept (a). Next, you must determine if (a) is (A-away or T-towards the bearing Zn).

You say to yourself this little ditty, "Coast Guard Academy" computed greater away, if not then it is towards the bearing.

Step 14: Compute the Zn by following the rule.

Step 15: Fill in your assumed latitude (A Lat) and assumed longitude (A Long).

Click Here to View: Solution to the Problem

Now you plot the line of position, actual plotting of the line of position is as follows.

1. Plot the AP (assumed latitude and longitude).

2. Lay off the Zn line from the AP toward or away from the AP depending on weather the observed altitude is greater or less than the computed altitude. In this case it is away from 048.4° T.

3. Measure in the proper direction along the Zn line the difference between the observed and the computed altitude in miles and tenths of miles. This distance is called the altitude (a), which is 18.0 miles away.

4. Draw a line at the extremity of altitude intercept (a) perpendicular (90°) to the azimuth line. At the time of observation this is your line of position.

5. Label the line of position with the time of observation and the name of the observed body, "0905 Sun".

Tables that you will need are shown below