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the accuracy of the celestial information is unaffected by the time from the last fix, it would, in this case,
be most likely that the actual position is closer to the LOP than to the DR position.
11.10.2. A formula has been devised to position the observer along the perpendicular to the LOP
according to the time factor. The formula is:
AFPAM11-216 1 MARCH 2001 247
where t is time in minutes, p is the perpendicular distance between the DR position and the LOP and d is
the distance from the DR position for the time of the MPP measured along the perpendicular to the LOP.
Look at B and C of Figure 11.7 and see how the formula works for the two problems cited above if the
perpendicular is 20 NM in length. In B of Figure 11.7, t is 15 minutes and p is 20 NM, so the MPP
would be located along the perpendicular about 8½ NM from the DR position.
11.10.3. Now, consider C in Figure 11.7 where t is 1 hour 25 minutes or 85 minutes, p is 20 NM and in
this case, the MPP would be over 16 NM away from the DR position along the perpendicular to the
LOP.
11.10.4. If you prefer not to use the formula, a simple table can be easily constructed to solve for d with
entering arguments of t and p as shown in Figure 11.8. The table could easily be enlarged to handle
larger values of t and p. In most fixes, the DR position is so close to the LOP that the midpoint between
these two can be considered the MPP. A good rule to use is to take the midpoint of the perpendicular if
the total distance between the DR position and the LOP is 10 NM or less. If the value of p is greater than
10 NM, use a table or the formula to determine the MPP. Up to this point, determination of the MPP has
been rather mechanical. Experienced navigators will frequently further adjust the position of the MPP
for other factors not yet considered. For example, if the LOP is carefully obtained under good conditions
or if it is the average of several LOPs, you may further weight the MPP in the direction of the LOP by
an amount that judgment dictates. However, the reverse may be true if the LOP is obtained under
adverse conditions of rough air. In the latter case, you might move the MPP closer to the DR position by
some amount determined by sound judgment.
Figure 11.8. To Solve for Distance.
248 AFPAM11-216 1 MARCH 2001
11.10.5. Further, consider the validity of the DR position in relation to factors other than time. A DR
position at the end of 40 minutes would be more reliable with Doppler drift and GS versus one based on
metro information. These factors may also adjust the original MPP closer to or farther away from the
DR position, along the perpendicular. However, these last mentioned factors are judgment values that
come only with experience. In fact, with experience you may mentally calculate all the factors involved
and arrive at the final position of the MPP without recourse to a formula or table.
11.11. Finding a Celestial Fix Point. Up to this point, only the single celestial LOP and what to do with
it have been considered. Now, the celestial fix should be considered. To establish a fix, two or more
LOPs must be obtained. Since, in most cases, two or more LOPs cannot be obtained simultaneously,
they must be converted to a common time. For example, a LOP obtained at 1010 must be converted to
the LOP obtained at the fix time of 1014. There are several methods for making this conversion, which
are discussed in this chapter. Consideration is also given to the planning of the fix and the final
interpretation of the fix itself.
Section 11C— Conversion of LOPs To A Common Time
11.12. 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 for correcting for Coriolis or rhumb line and precession or nutation. For example,
suppose the track is 110o and the GS 300 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.
Figure 11.9. Conversion of Lines of Position to a Common Time.
11.12.1. 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.
AFPAM11-216 1 MARCH 2001 249
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