Moving the LOP
One method of converting LOPs to a common time is to move the LOP along the best-known track for the number of minutes of GS necessary for the time conversions. This method is similar to that used in correcting for Coriolis or rhumb line and precession or nutation. For example, suppose the track is 110° and the GS is300 knots. LOPs are for 1500, 1504, and 1508, and a fix is desired at 1508. This means the 1500 LOP must be moved to the time of the fix using the track and 8 minutes of the best known GS. The 1504 LOP must be moved to the time of the fix using the track and 4 minutes of GS. The 1508 LOP is already at the fix time, so it requires no movement. Figure 11-9 shows the method of conversion as it is completed on the chart.
If, at any time, the LOP has to be retarded (moved back) to the time of the fix, use the following procedures. Using the reciprocal track and GS, obtain the correction in the regular manner for the number of minutes of difference. For example, suppose the fix is at 1800 and the last shot is at 1802.
Retarding the LOP 2 minutes of GS on a track of 70° would be the same as advancing it 2 minutes of GS on a track of 250°.
Motion of Observer Tables
A second method of conversion of LOPs to a common time is with a Motion of the Observer table such as the one in Pub. No. 249. This table gives a correction to be applied to the Ho or Hc so that the LOP plots in its converted position. The correction obtained from Table 1 in all volumes of Pub. No. 249 is for 4 minutes of time. An additional table allows you to get the correction for the number of minutes needed. For example, suppose the LOP needs to be advanced for 11 minutes and the Ho of the body is 33° 29′ and Zn is 080°.
The track of the aircraft is 020o and the GS is 240 knots. In Table 1, Correction for Motion of the Observer for 4 minutes of Time [Figure 11-10], the entering arguments is Rel Zn and GS. Rel Zn is azimuth relative to course (Zn minus track or track minus Zn). Subtract the smaller angle from the larger and enter the table with the answer. In this case, Zn – track = 080° – 020° = 060° (Rel Zn) and GS is 240 knots. Entering this table with these arguments, the correction listed is +08′ for 4 minutes of time.
Use the whiz wheel to calculate the total motion for 11 minutes. In this case, the 11-minute correction totals 22′. By applying any other correction (refraction, sextant correction, etc.), a total adjustment is derived. By changing the sign, this total may be applied to the Hc. To apply the correction to the Ho, the sign of the adjustment would remain the same. Apply the adjustment to the intercept as the rules state in Table 1. In each case, the resultant intercept would be the same.
Suppose the Hc was 33° 57′. Applying the correction –22 yields 33° 35′. Comparing this with our Ho 33°29′ results in an intercept of 6 NM away. If you decide to apply the correction to the Ho, 33° 29′ + 22′ yields 33° 5l’. Comparing this to the Hc 33° 57′ yields the same result, 6 NM away. When using the Motion of the Observer table and when the fix time is earlier than the observation (LOP to be retarded), the rule for the sign of the correction is also printed below Table 1.
Moving the Assumed Position
Another method of converting LOPs to a common time is to move the assumed position. This method is recommended for shots 4 minutes apart computed to give all three bodies a single assumed position. However, it is not limited to that type of computation. The assumed position is moved along the best-known track at the best-known GS. For example, again suppose the track is 330° and the GS 300 knots. LOPs are for 1500, 1504, and 1508 and a fix is desired at 1508. [Figure 11-11] Since the first LOP would have to be advanced 40 NM (8 minutes at 300 knots), the same result is realized by advancing the assumed position 40 NM parallel to the best-known track. The 1504 LOP must be advanced 20 NM; therefore, the assumed position is advanced 20 NM miles parallel to the best-known track. The third shot requires no movement, and it is plotted from the original assumed position.
It should be noted that the first shot is always plotted from the assumed position, which is closest to destination. In this method, if observations are precomputed and the assumed position is moved prior to shooting, the following procedure is used when shooting is off schedule. For every minute of time that the shot is taken early, move the assumed position 15 minutes of longitude to the east. For every minute of time that the shot is taken late, move the assumed position 15 minutes of longitude to the west. In addition, the affected LOP must be moved along the best-known track for the number of minutes of GS the observation was early or late. If the shot was early, advance the LOP; if the shot was late, retard the LOP.