Step-by-step sight reduction
Here is the entire sight reduction sequence broken down into steps. You can use this as a guide should you get stuck on a step and need to know what to do next.
A. Sextant sight correction sequence
Overview: The reading from the sextant (Hs) needs to be corrected for index error, height of eye and the main sun correction to give Ho, the observed altitude.
1. Start with Hs, the angle that you read off of your sextant.
2. Apply the index correction.
3. Correct for height of eye using the dip table on the inside front cover of the Nautical Almanac. The dip correction is always subtracted. The result is the apparent altitude, or Ha.
4. Determine and apply the main sun correction from the inside front cover of the Nautical Almanac.
5. The final result is Ho, the observed altitude.
B. Using the Nautical Almanac
Overview: The Nautical Almanac is used to pinpoint the exact position of the sun (or other celestial body) second by second. Enter the daily pages with the Greenwich Mean Time (GMT) of the sight and leave the Nautical Almanac with GHA and declination.
1. Find the page in the Nautical Almanac with the date of your sight.
2. On the left side of the right page is a column with every hour of the three days covered on that page. Go down the column until you find the correct hour in GMT of the correct day.
3. Find the GHA and the declination of the sun in the next two columns and extract those numbers.
4. At the bottom of the declination column is a value for “d.” If the declination is decreasing during the day, then d is negative; if declination is increasing, then d is positive.
5. At the end of the Nautical Almanac is a section of colored pages labeled ”Increments and Corrections.” There is half a page for each minute. Find the page with the correct minute of GMT. Move down the far left column to the row for seconds of GMT. On that row, move to the first column to the right (for sun and planets). Add this number to the GHA for the final GHA.
6. Staying in the same box, there is a column labeled “v or d.” Go down that column until you find your value for d. The number directly to its right should be added to the declination if d is positive and subtracted if d is negative.
C. Find the LHA and assumed latitude
Overview: LHA is the combination of GHA and the assumed longitude. In the Western Hemisphere, LHA = GHA minus assumed longitude. In the Eastern Hemisphere, LHA = GHA plus assumed longitude.
1. To enter the tables, LHA must always have 00.0 minutes. Because of this, in the Western Hemisphere the minutes of the assumed longitude always equal the minutes of the GHA. Assumed longitude is not the same as DR longitude.
2. Start with GHA and then fill in the minutes of assumed longitude so that the minutes of LHA equal zero. Make the degrees of the assumed longitude as close as possible to the DR longitude.
3. To find assumed latitude, take the DR latitude and round it off to the nearest degree.
D. HO 249
Overview: The sight reduction tables are based on a set of algorithms derived from the navigational triangle. They convert the assumed latitude, declination and LHA into Zn and a calculated altitude (Hc). It is a calculated altitude because it is based on the assumed position.
1. Enter the table with assumed latitude, declination and LHA.
2. Find the correct page. First, find a page with your assumed latitude. Second, find a page with the degrees of declination (0° – 14°) or (15° – 29°). Third, determine if the declination and latitude are the same or contrary (they are the same if both are north or both are south; they are contrary if one is north and one is south). Fourth, find the page with the proper “SAME” or “CONTRARY” designation. Fifth, recheck to make sure that the page has the proper latitude, declination and sign.
3. Find the correct column for degrees of declination. Find the correct row with LHA running up and down the sides of the page. LHA is greater than 180° on the right side of the page and less than 180° on the left side. It sometimes runs over to the next page.
4. Extract Hc, d and Z. Make sure to get the proper sign for d; the sign is not printed on each row.
5. Convert Z to Zn (azimuth) using these formulas supplied on each page:
Northern Hemisphere: if LHA > 180, then Zn = Z; if LHA < 180, then Zn = 360 – Z
Southern Hemisphere: if LHA > 180, then Zn = 180 – Z; if LHA < 180, then Zn = 180 + Z
6. Use Table 5 in the back of the volume. Enter with d and minutes of declination. If d is positive, add result to Hc; if d is negative, subtract the result from Hc. This gives the final value of Hc.
E. Find the intercept
Overview: This is determining whether our position is closer to the sun than the assumed position. The larger the altitude, the closer to the sun.
1. Find the difference between Hc and Ho (subtract one from the other). Each minute equals one nautical mile.
2. Determine if the intercept is to be plotted toward or away. If Hc > Ho, plot away; if Ho > Hc, plot toward.
Overview: The plotting sheet should be used for keeping a DR track as well as for celestial information. For a sun sight, use the assumed latitude, assumed longitude, Zn and intercept to create a line of position (LOP). Remember: One sight yields one LOP, not a fix.
1. Set up your plotting sheet for your area of the ocean.
2. Plot your assumed position (AP). Assumed latitude is the whole degree of latitude used to enter HO 249. Assumed longitude is the longitude that was subtracted from GHA to get LHA, not your DR longitude.
3. Plot your Zn (azimuth). The azimuth direction needs to be plotted through the assumed position, then draw an arrow on the end of that line in the direction of the sun (e.g., if the azimuth = 129°, then on the end that points toward 129°).
4. Plot the intercept. Starting at the assumed position (AP), plot toward or away from the sun along the azimuth line and mark.
5. Plot the LOP. The LOP must be perpendicular to the azimuth. Add or subtract 90° to/from the azimuth. Plot this line through the intercept. Label one end with “sun” over the line and the time underneath it.