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perpendicular lines at the correct point on the respective Zn line. This greatly reduces the time necessary
to plot the fix.
10.10. Summary. Celestial precomputation methods have been brought to the forefront with the
proliferation of high-speed aircraft. Aircraft speeds make it necessary to minimize the time between
shooting and fixing. Since the sextant may be the only means of viewing the body, it is necessary to
precompute the altitude and azimuth of a body in order to locate it. Remember corrections may be
applied to the Hc, Ho, or intercept, and pay close attention to the sign of the correction. In addition to
precomputation, the fix may be resolved faster by preplotting the true azimuths of the bodies.
238 AFPAM11-216 1 MARCH 2001
Figure 10.5. Fix Can Be Plotted Quickly.
AFPAM11-216 1 MARCH 2001 239
Chapter 11
PLOTTING AND INTERPRETING THE CELESTIAL LINE OF POSITION
Section 11A— Introduction
11.1. Basics. This chapter explains the methods that transform the tabulated and in-flight observation
values into an aircraft position. The navigator is faced with two tasks: plotting the resultant information
onto a chart and resolving this information into an aircraft position. There are two basic methods of
obtaining a line of position (LOP): the subpoint method and the intercept method.
11.2. Subpoint Method (Figure 11.1). A detailed explanation of the theory concerning this method is in
Chapters 9 and 10.
Figure 11.1. The Subpoint Method.
11.2.1. Here is a summary of the steps involved:
11.2.1.1. Positively identify the body and measure the altitude using a sextant.
11.2.1.2. Because no tabulated information for azimuth or elevation is required for this method,
corrections for refraction, parallax, semidiameter, wander error, and sextant correction are applied
directly to the Ho.
11.2.1.3. The resultant measurement is subtracted from 90o to obtain the co-altitude (co-alt). To convert
to NM (1o=60 NM), multiply the number of degrees times 60. Any fractional portion of degrees is added
to the previous value.
11.2.2. Example: Vega is observed at an altitude (Ho) of 88o23'. Sextant correction is -03'.
88o23' – 03' = 88o20'
90o – 88o20' = 1o40'
1o 40' = 60' + 40' = 100 NM
240 AFPAM11-216 1 MARCH 2001
11.2.3. In this example, 100 NM represents the distance from the observer's position to the subpoint of
the body. The coordinates of the body are its corresponding declination (Dec) and Greenwich hour angle
(GHA). For this example, Vega's Dec is N38o46'. The GHA is obtained by applying the sidereal hour
angle (SHA) of Vega to the GHA of Aries.
EXAMPLE:
SHA = 080o59'
GHA Aries = 039o18'
GHA Vega = 120o17'
11.2.4. Subpoint of Vega is located at 38o46' N l20o17' W. The observer is now ready to apply the
information:
11.2.4.1. Plot the subpoint on an appropriate chart.
11.2.4.2. With dividers or compass, span the co-alt distance; in this case 100 NM.
11.2.4.3. Use the body's subpoint (38o46' N l20o17' W) as the center and 100 NM (co-alt) as the radius.
The circle is called the circle of equal altitude and the observer is located on that portion of the circle
nearest the DR position. There are definite advantages to this method. It requires no precomp values and
plotting is very simple if the observer and body are reasonably close together. When the observer and
body are separated by great distances, some disadvantages appear.
11.2.5. If a body is observed at 20o above the horizon, the observer is 4,200 NM from its subpoint. To
swing a LOP from this subpoint, the subpoint and the arc must be plotted on the same chart. To permit
plotting of any LOP, the chart must cover an area extending more than 4,000 miles in every direction
from the DR position. This means that the chart must be either of such large size that it cannot be spread
out on a table in the aircraft, or of such small scale that plotting on it is inaccurate. To cover an area
8,000 miles across, a chart 4 feet square must be drawn to a scale of about 1:10,000,000. Furthermore,
measuring would be difficult because of distortion.
11.2.6. Since a celestial LOP cannot always be drawn by the subpoint method, the intercept method,
based on the same principles, is often used.
11.3. Intercept Technique:
11.3.1. Intercept Method (Figure 11.2). You can eliminate the need for plotting the body's subpoint
and still draw the arc representing the circle of equal altitude. By using the following formula, you can
calculate the altitude and azimuth of the body for the DR position:
Hc = SIN-1 [SIN (DEC') SIN (LDr)
+COS (DEC')COS (LDr) COS (LHA)]
Z = COS (Z) = [SIN (DEC')
– SIN (LDR) SIN (HC)]/[COS (Hc COS (LDr)]
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