Determining a line of position from an observation of a celestial body. Using the Nautical Almanac and the Sight Reduction Tables for Marine Navigation, Pub NO.229. The steps involved will be covered in the order in which they are 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 arguments for the tables are local hour angle (LHA) expressed in whole degree. This is done by using an assumed longitude, not a DR longitude; assumed latitude in whole degree, and declination. Values of Hc and Z are tabulated for each whole degree of each of the entering arguments. Tables inside the front and back covers of each volume allow for interpolation of Hc and Z for the exact declination. No interpolation is necessary for LHA or assumed latitude.
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 observation by interpolation by using the interpolation tables or using the formula that the tables are based upon. I use the formula method.
To find the intercept distance (a), this final Hc is compared to the observed altitude (Ho). If the computed altitude Hc is greater than observed altitude Ho the intercept is AWAY from the direction of the GP of the body.
Steps in Working a Sight
We will take a situation and work out the celestial observation step by step. A form should be followed when working out a sight, so that there will be less chance for leaving out information.
Sample Problem
On 8 August 1981, at 0545 ZT, morning stars were observed, and the vessel's position was determined to be LA T26° 16.0' 5, LONG 94- 16.0' E. Your vessel is steaming at 20.0 knots on a course of 346° T. A sextant observation of the Sun's lower limb is made at 0905 ZT. The chronometer reads 03h 02m 52s, and the sextant altitude (hs) is 32° 07.5'. The index error is 5.2' off the arc, and the chronometer error is 2m 17s slow. Your height of eye on the bridge is 72 feet. Compute and plot the line of position?
BODY SUN (lower limb)
DATE 8 August 1981
DR LAT 25° 07.0' S
DR LONG 93° 58.0' E
Hs 32° 07.5'
IE + 5.2' off
Hs 32° 12.7'
Dip 72ft - 8.2'
Ha 32-04.5'
ALT CORR + 14.5'
Ho 32° 19.0'
ZT 0905
ZD - 6
GMT 8th 0305
CT 03h 02m 52s
CE + 2m 17s slow
CCT 8th 03h 05m 09s
GHA 223-35.6'
M&S 1- 17.3'
SHA --------
V ---------
GHA 224-52.9
A LONG + 94°07.1'E
LHA 319-00.0'
TAB DEC N16°11.7'
d corr (0.7) - 0.1
DEC N16°11.6'
STEP 1
Setup plotting sheet, and DR ahead
from 0542 to 1220 and get your DR position and enter it in your format: 0905
0545
3 20 x 20 kts = 66.7 miles
STEP 2
Apply your IE, in this case it is on the are, so we subtract it.
STEP 3
Using the DIP Table on the inside cover of the Nautical Almanac, enter with your height of eye 30 feet = - 5.3'. Dip correction is always a minus correction
STEP 4
On page A2 "Altitude Correction Tables 1 0° - 90° Sun, Stars, Planets" under the Sun - April September -(because our problem is in August). Enter with your Ha and find the ALT Corr under the Lower Limb column: Remember that Lower limb are always + corrections and upper limbs are - corrections.
STEP 5
Compute your corrected chronometer time STEP 6
Using GMT, and Greenwich date of observation, enter the Nautical Almanac and record tabulated hourly value of GHA and TAB DEC. in your format
STEP 7
At the foot of each declination sUb-column, get the"d corr". This number is called the "d", hence, in this case"d 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 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 yellow pages of the Nautical Almanac, and find the "5 minute page," enter with "9seconds." Then under the Sun and Planets column find the increase in the sun's GHA since the last tabulated (hourly) value, hence 1° 17.3' is your M&S correction and enter this in your format. Always add the GHA and "m & s ''tabulated value together to get the total GHA.
STEP 9
While on the 5-minute page under the "v" or "d" correction column, find the "dO 0.7 on the left hand side. This is equal to 0.1', enter this in your format and in this case subtract. This will be the declination (dec) of the sun at the time of sight.
STEP 10
Previous celestial problems we brought down our DR longitude and enter it in our form and followed the rule.
In full sight reduction, LHA has to end in the whole degree and YOUR ASSUMED LONGITUDE has to be within 30' of your DR Longitude
Our Problem
DR Long. 93° 58.0' E
GHA 224-52.9
A Long + 94- 07.1 E
LHA 319-00.0
If it was west longitude we would subtract
STEP 11
Enter-PUB 229 with LHA 319, ALat 25 S, and Dee 16 N. Then extract the tabulated He, base Z, Z for the next whole degree of declination, and the Rule for converting Z to Zn and enter this into your format. Make sure to note the sign of the differences. Then using the formula:
Difference x declination increments + 6'0= correction.
STEP 12
Add or subtract your corrections to your Tab He and base Z to get the He and Z
STEP 13
Fill in your Ho. Find the difference between He 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, Coast guard Academy -computed greater away! If not then it is towards the bearing.
STEP14
Compute the Zn by following the rule.
STEP 15
Fill in your assumed latitude (ALat) and assumed longitude (ALong).
Now we plot the line of position
Actual plotting of the line of position is as follows:
1. Plot the AP (assumed latitude & longitude)
2. Layoff the Zn line from the AP toward or away from the AP, depending on whether the observed altitude is greater or less than the computed altitude. In our 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 intercept (a), hence 18 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 a line of position.
5. Label the line of position with the time of observation and the name of the observed body 0905.
