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seconds of time.
11.15.1. In a two-LOP fix, the ideal cut of the LOPs is 90o. In Figure 11.12, a 90o cut with a 5 NM error
in one LOP will cause a 5 NM error in the fix. If the acute angle between the LOPs is 30o, a 5 NM error
in one LOP will cause a 10 NM error in the fix. Thus, with a two-LOP fix, an error in one LOP will
cause at least an equal error in the fix; the smaller the acute angle between the LOPs, the greater the fix
error caused by a given error in one LOP. Of course, if both LOPs are in error, the fix may be thrown off
even more. In a three-LOP fix, the ideal cut of the LOPs is 60o (star azimuths 120o apart). With this cut,
a 3 NM error in any one LOP will cause a 2 NM error in the fix. With any other cut, a 3 NM error in any
one LOP will cause more than a 2 NM error in the fix. In a three-star fix, the cut will be 60o if the
azimuths of the stars differ by 60o or if they differ by 120o. If there is any unknown constant error in the
observations, all the Hos will be either too great or too small. Notice in Figure 11.13 that, if stars are
selected whose azimuths differ by 120o, this constant error of the Hos will cause a displacement of the
three LOPs, either all toward the center or all away from the center of the triangle. In either case, the
position of the center of the triangle will not be affected. If you use any three stars with azimuths outside
a 180o range, any constant error in observations will tend to cancel out.
252 AFPAM11-216 1 MARCH 2001
Figure 11.12. Effect of Cut on Accuracy of a Fix.
Figure 11.13. Effect of Azimuth on Accuracy of Fix.
11.15.2. The three-star fix has two distinct advantages over the two-star fix. First, it is the average of
three observations. Second, selecting the stars carefully can counteract the effect of constant errors of
observation. There is also a third advantage. Each pair of two LOPs furnishes a rough check on the third.
In resolving an observation into a LOP, you might possibly make a gross error; for example, obtaining
AFPAM11-216 1 MARCH 2001 253
an LHA which is in error by a whole degree. Such an error might not be immediately apparent. Neither
would such a discrepancy come to immediate attention in a two-LOP fix. However, this third advantage
does not apply when a single LHA is used in solving all LOPs, such as is done when precomputing and
using motion corrections to resolve all LOPs to a common time. Because of these three advantages, it is
evident that a three-star fix should be used, rather than a two-star fix, when possible.
11.15.3. Whatever the number of observations, common practice, backed by logic, is to take the center
of the figure formed unless there is reason for deviating from this procedure. Center is meant as the
point representing the least total error of all lines considered reliable. With three LOPs, the center is
considered that point, within the triangle equidistant from the three sides. It may be found by bisecting
the angles, but is usually located by eye.
11.16. Summary. Because of all the factors involved, a certain amount of judgment is necessary, along
with the proper use of the mechanics comprising celestial navigation. When using a single LOP or a fix,
you have to take into consideration the existing conditions and weigh the DR information against the
information obtained from the LOP. An accurate DR position should always be computed.
11.16.1. The C-Plot formula helps place the MPP with a single LOP, but you might want to make further
adjustments to the final position. The formula is:
11.16.2. Remember, d is the distance measured along a perpendicular from the DR position to the LOP.
In the case of the two- or three-star fix, planning plays a very important part. Selecting stars whose
azimuths differ by 120o for a three-star fix will minimize errors in the fix position. In two-star fixes, the
ideal azimuth separation is 90o. Also, when dealing with more than one LOP, it is necessary to resolve
the LOPs to a common time. This adjustment can be accomplished by moving the assumed position, by
moving the LOPs, or by applying a correction factor to the Hc or Ho.
254 AFPAM11-216 1 MARCH 2001
Chapter 12
SPECIAL CELESTIAL TECHNIQUES
Section 12A— Introduction
12.1. Basics. This chapter has some techniques which may not be used every day and under all
circumstances but are valuable alternatives from normal precomping procedures. Most of these
techniques save time by eliminating either some extractions or computations. Some navigational
techniques and planning procedures are also discussed.
12.2. Determining Availability of Celestial Bodies. By doing a quick comparison of GHA to the
observer's position, it is easy to determine the availability of celestial bodies. For example, the observer
　
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