Precomputation Techniques (Part Two)

Celestial Computation Sheets

The format in Figure 10-2 is a typical celestial precomputation and illustrates one acceptable method of completing a precomputation. The explanation is numbered to help locate the various blocks on the celestial sheets. [Figure 10-2]

Figure 10-2. Typical celestial precomputation format.

Figure 10-2. Typical celestial precomputation format. [click image to enlarge]


NOTE: Not all blocks apply on every precomputation.

  1. DATE—place the Zulu date of the Air Almanac page used in this block.
  2. FIX TIME—GMT (coordinated universal time) of the computation.
  3. BODY—the celestial body being observed.
  4. DR LAT LONG—the dead reckoning (DR) position for the time of the observation.
  5. GHA—the value of GHA extracted from Air Almanac (10-minute intervals).
  6. CORR—the GHA correction for additional minutes of time added to the GHA in block 5 and, if necessary, the 360° addition required establishing the LHA. SHA–When a star is precomped with Pub. No. 249, Volume 2 or 3, SHA is placed in this block.
  7. GHA—corrected GHA (sum of blocks 5 and 6).
  8. ASSUM LONG (–W/+E)—the assumed longitude required to obtain a whole degree of LHA.
  9. LHA—LHA of the body (or Aries).
  10. ASSUME LAT—the whole degree of latitude nearest the DR position.
  11. DEC—the declination of the celestial body (not used with Pub. No. 249, Volume 1).
  12. TAB Hc—the Hc from the appropriate page of Pub. No. 249, Volume 2 or 3.
  13. D—the d correction factor found with previous Hc. Include + or –, as appropriate. The value is used to interpolate between whole degrees of Dec.
  14. DEC—minutes of declination from block 11.
  15. CORR—the correction from the Correction to Tabulated Altitude for Minutes of Declination table in Volume 2 or 3, using blocks 13 and 14 for entering arguments.
  16. CORR Hc—this is the corrected Hc—sum of blocks 12 and 15 or extracted from Pub. No. 249, Volume 1.
  17. Zn—true azimuth of the celestial body from the formula in Pub. No. 249, Volume 2 or 3, or directly from Volume 1.
  18. TRACK—the true course (track) of the aircraft.
  19. GS—the groundspeed of the aircraft.
  20. ALT MSL—aircraft altitude.
  21. CORIOLIS—the Coriolis correction extracted from Pub. No. 249, the Air Almanac, or a Coriolis/rhumb line table.
  22. PREC/NUT—precession and nutation correction computed from the table in Pub. No. 249, Volume 1.
  23. REL Zn or Zn—the difference between Zn and track, used to determine motion of the observer correction.
  24. MOTION OF OBSERVER (MOO)—motion of the observer correction for either 1 minute (using 1-minute motion correction table) or 4 minutes (using 4-minute correction table in Pub. No. 249) of time.
  25. MOTION OF BODY (MOB)—motion of the body correction for either 1 minute (using 1-minute motion correction table) or 4 minutes (using tabulated Hc change for 1° of LHA or 4-minutes correction table in Pub. No. 249) of time.
  26. 4-MINUTE ADJUST—algebraic sum of 24 and 25; for use of 4-minute motion corrections extracted from Pub. No. 249.
  27. X-Time—time in minutes between planned shot time and fix time.
  28. TOTAL MOT ADJUST/ADV/RET—correction based on combined motion of observer and body, for the difference between the time of the shot and fix time. The sign of this correction is the same as the sign in block 26 if the observation was taken prior to the computation time. If it was taken later, the sign is reversed.
  29. REFR—correction for atmospheric refraction.
  30. PERS/SEXT—sextant correction or personal error.
  31. SD—semidiameter correction for Sun or Moon.
  32. PA—parallax correction for Moon observation.
  33. POLARIS/Q CORR—the Q correction for the time of the Polaris observation (extracted from Pub. No. 249 or the Air Almanac).
  34. Total ADJ—algebraic sum of blocks 28–33 as applicable.
  35. OFF-TIME MOTION—motion adjustment for observation other than at planned time.
  36. Ho—height observed (sextant reading).
  37. INT—intercept distance (NM) is the difference between the final Hc and Ho. Apply the HOMOTO rule to determine direction (T or A) along the Zn.
  38. LAT—polaris latitude.
  39. CONV ANGLE (W/–E)—convergence angle used in grid navigation.
  40. GRID Zn—the sum of blocks 17 and 39.

Corrections Applied to Hc

In some methods of precomputation, corrections are applied in advance to the Hc to derive an adjusted Hc. When using corrections that are normally applied to Hs, the signs of the corrections are reversed if applied to Hc. For example:

Corrections Applied to Hs

Hs 31° 05
REFR –01
Ho 30° 59
Hc 30° 40

Corrections Applied to Hc

Hc 30° 40
REFR +01
ADJ Hc 30° 46
Hs 31° 05

This demonstrates that corrections may be applied to either Hs or Hc. As long as they are applied with the proper sign, the intercept remains the same. The following sample precomp uses a common fix time (though computation times are different) and common observation times to facilitate comparison.

NOTE: Atmospheric refraction correction must be extracted for the actual Hs. It may then be applied to either Hc or Hs using the proper sign. Extracting the value for Hc may cause large errors, especially when the body is near the horizon. Figure 10-3 is a sample three-star precomputation using the mathematical format. Corrections to altitude of the body are applied to the Hc and the sign of the correction has been reversed in this process, so the fix can be plotted prior to the computation time. All shots are early shots, allowing the navigator to resolve the fix and alter at fix time. However, any minor errors in interpolation for motions are multiplied for the two earliest shots and may cause inaccuracies in the fix.

Figure 10-3. Mathematical solution.

Figure 10-3. Mathematical solution. [click image to enlarge]

Figure 10-4 shows a three-star precomputation using a three-LHA or graphical solution. The assumed position is then moved for track and GS to accommodate LOPs shot off time. Each observation is taken on time and then plotted out of its own plotting position. This precomp is easier and faster to accomplish with relatively few opportunities for math errors to occur. The three assumed positions required for this solution, on the other hand, often cause large intercepts and may make star identification difficult if care is not taken in choosing the precomp assumed position.

Figure 10-4. Graphical solution.

Figure 10-4. Graphical solution.


Precomputational methods lose accuracy when the assumed position and the actual position differ by large distances. Another limiting factor is the difference in time between the scheduled and actual observation time. The motion of the body correction is intended to correct for this difference. The rate of change of the correction for motion of the body changes very slowly within 40° of 090° and 270° Zn, and the observation may be advanced or retarded for a limited period of time with little or no error. When the body is near the observer’s meridian, however, the correction for motion of the body changes rapidly due in part to the fast azimuth change and it is inadvisable to adjust such observations for long (over 6 minutes) periods of time.

NOTE: Errors in altitude and azimuth creep into the solution if adjustments are made for too long an interval of time. Because of these errors, the navigator should attempt to keep observation time as close as possible to computation time.