Special Celestial Techniques

This category describes some techniques that 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.

Introduction to Special Celestial Techniques

Determining Availability of Celestial Bodies

By doing a quick comparison of Greenwich hour angle (GHA) to the observer’s position, it is easy to determine the availability of celestial bodies. For example, the observer anticipates being at 18°N 135° W at 0015Z on 28 September 1995. There are several bodies listed in the Air Almanac, but not all of them are available for observation. To determine availability, take the observer’s longitude and look 80° either side of it. Within this range, compare the GHA of a body. Looking at Figure 12-1, we see that the sun, moon, Venus, and Jupiter are within the 80° range and are therefore usable. Saturn is outside of the 80° range, so it is not usable. The declination (Dec) of a body is not normally a factor; however, at high latitudes a body may not be available when its subpoint is near the pole opposite the observer.

Figure 12-1. A quick check of body availability. [click image to enlarge]

Latitude by Polaris

Polaris is the polestar, or North Star. Because Polaris is approximately 1° from the North Pole, it makes a small diurnal circle and seemingly stays in about the same place all night. This fact makes Polaris very useful in navigation. With certain corrections, it serves as a reference point for direction and for latitude in the Northern Hemisphere. Latitude by Polaris is a quick method of obtaining a latitude line of position (LOP); only the tables given in the Air Almanac are needed.

Obtaining Latitude by Polaris

A latitude by Polaris LOP is obtained by applying the Q correction to the corrected observed altitude. [Figure 12-2] This adjusts the altitude of the pole, which is equal to the navigator’s latitude. The Q correction table is in the back of the Air Almanac. The entering argument for the table is exact local hour angle (LHA) of Aries. The effect of refraction is not included in Q correction, so the observed altitude must be fully corrected. When refraction is used for a latitude by Polaris LOP, it is applied to the observed altitude and the sign of the correction is negative. A Polaris LOP can also be plotted using the intercept method. In this case, the Hc is computed by reversing the sign of the Q correction and applying it to the assumed latitude (rounded off to the nearest degree). Refraction is positive when applied to get an Hc for the intercept method.

Figure 12-2. Polaris Q correction and azimuth tables from the Air Almanac. [click image to enlarge]

Obtaining Azimuth of Polaris

For either method, the azimuth of Polaris is obtained from the Azimuth of Polaris table found in the Air Almanac or in the Pub. No. 249. [Figure 12-2] Whether plotted as an intercept or a latitude, the assumed position should be corrected for Coriolis, or rhumb line, and precession, or nutation. The resulting LOPs should fall in the same place for either method. To plot the LOP using the latitude method, choose the longitude line closest to the DR and plot perpendicular to the longitude line. For the intercept method, use the assumed latitude and plot the intercept normally using the azimuth of Polaris.

Latitude by Polaris Example

On 18 April 1995 for Greenwich mean time (GMT) 1600 at 23° 10′ N 120° W, with an observed altitude 23° –06′ at 31,000′. When doing a latitude by Polaris you must use the exact latitude and longitude. See Figure 12-3 for plotting.

Figure 12-3. Plotting the Polaris LOP.

NOTE: If the Q correction table in Volume 1 is used, precession and nutation (P/N) and Coriolis, or rhumb line, must be used in plotting the LOP. This is because the Pub. No. 249 covers a 5-year period, and the further the years get from the Epoch year, the greater the error is when using the Polaris table. P/N compensates for this error.

Intercept Method Example

Refer to the previous problem and Figure 12-3 for plotting. NOTE: Applying 10A to assumed latitude gives 22° –50′ N, which is the same the answer in the latitude by Polaris example.

NOTE: In these examples, all information was taken from the Air Almanac. No P/N is required.

LHA Method of Fixing

LHA Method of Obtaining Three-Star Fix

The LHA technique allows you to solve the motion problem for a three-star fix by applying a correction to the assumed position rather than computing a numerical solution on the precomp. This eliminates mathematical motion calculations, therefore reducing the chance of math errors on the precomp. To accomplish a three-LHA fix, you must plan 4 minutes between the midtime of each shot. [Figures 12-4 and 12-5] Because LHA changes 1 degree for every 4 minutes, the precomp has three successive LHAs, 1 degree apart. To correct for off-time motion, adjust the assumed position based on true course (TC) and groundspeed (GS). If a shot is planned earlier than fix time, the assumed position is advanced (down-track). For shots planned later than fix time, the assumed position is retarded (up-track).

Figure 12-4. Typical example of the three LHA method. [click image to enlarge]Figure 12-5. Plotting three LHA.

The example in Figures 12-4 and 12-5 shows the LHA method for a 12-8-4 early shooting schedule. This shooting schedule allows the fix and/or MPP to be resolved before the fix time. To adjust the assumed positions, plot the fix time assumed position and then advance it for 4 minutes of track and GS for each body. This satisfies motion of the observer. When shooting the selected bodies, take care to shoot them exactly on the prescribed times. This eliminates motion of the body.

A variation of advancing the assumed position is to use half motions. This enables you to plot all three LOPs from one assumed position. Table 1 from Pub. No. 249 lists corrections to position of the observer. Each correction is for 4 minutes of time. To use it, enter with your relative Zn (Zn-track) and GS. Now, look at the bottom of the table and note you can apply this correction to your tabulated altitude or observed altitude. It does not matter which you choose, but note that the sign changes dependent on where you apply it. Now, take the number and multiply it by the 4-minute increment of the shot. For example, Figure 12-6 shows the precomp for a 0300 fix using 3 LHAs and half motions. The 0248 shot, Alpheratz, relative Zn, and groundspeed were used to extract a +20 correction from Table 1. Because this shot is 12 minutes early, we need to multiply +20 by three before we apply it to the shot. Note the +60 correction was applied to the observed altitude and, therefore, kept its positive sign. The benefit of doing this is a reduction in plotting. See Figure 12-7 for the plotted LOPs. This technique can be applied to day celestial as well.

Figure 12-6. Half motions three LHA format.

Figure 12-7. Plotting a half motions observation. [click image to enlarge]

Daytime Celestial Techniques

Daytime fixing, using celestial techniques, is rather limited because often only one body, the sun, is visible. Ordinarily, three LOPs cannot be obtained for a fix from one body, because the LOPs plot nearly parallel to each other.

The Sun Heading Shot at High Noon

The azimuth of the sun changes very rapidly when the subpoint of the sun is directly over the longitude of the observer, which is called the time of transit. The LHA at transit time is 360°. This phenomenon is more pronounced at lower latitudes as the subpoint of the sun passes closer to the observer. This makes it extremely difficult to get an accurate celestial heading shot at the transit time. Therefore, if you need a heading shot near the time of transit, you must take extra precaution to get the heading observation exactly at the precomputed fix time. If the moon or Venus is available, consider using these bodies for an accurate celestial heading. If using the sun, you should weigh the increased possibility of an inaccurate heading shot. If the accuracy is questionable, get another heading shot as the sun’s rate of azimuth change slows enough to allow a more accurate shot.

Intercept Method

The intercept method is normally used in obtaining a noon day fix. If the sun passes close to the observer’s position, within about 4°, the subpoint method of plotting the fix may be used. This method differs from normal procedures in that three different precomps for three different times are computed. Because of the rapid change of the sun’s azimuth at or near transit, this variation is necessary. The procedure is:

1. Determine the time of transit.
2. Select the LHA before and after transit for which the change in azimuth is 30° or more. Since 1° of LHA is equal to 4 minutes of time, the difference in transit LHA and the new LHA can be converted to time in minutes. Thus, the time preceding and following transit can be determined.
3. Plot the DR positions for times determined in 12.7.2. Select the appropriate assumed positions necessary for the computation and plotting of the LOPs. The assumed position for time of transit is also plotted.
4. Determine the intercepts and azimuth for each LOP. Plot these data from the respective assumed positions.
5. Resolve the LOPs to a common time, preferably that of the transit LOP.

NOTE: At 30° N latitude, the linear speed of the sun is approximately 780 knots. Thus, on westerly headings in highspeed aircraft, the DR distance involved before encountering a 30° change in azimuth is considerable.

Subpoint Method

When the observer is within approximately 4° of the subpoint of the body, the subpoint method of solution is normally used. This is because the radius of the circle of equal altitude is so small that a straight line does not approximate the arc and a straight line does not give an accurate LOP. The procedure is:

1. Plot the subpoints of the body for the time of the observations (using GHA and/or Dec).
2. Find the co-altitude of the shots and convert it to NM (90° – Alt × 60 NM).
3. Advance the first subpoint and retard the third along the DR track, using best-known track and GS.
4. Set the distance found from the co-altitude and strike it off from the resolved subpoints (with a compass or pair of dividers). Do this for each observation.

NOTE: The resulting intersection, or triangle, gives one ontime fix. If the LOPs form a triangle, the aircraft position is probably within the triangle.

The subpoint method is convenient because Pub. No. 249 is not used—only the Air Almanac. This method can also be used with a star near your assumed position and may be necessary if, for some reason, your Volume 1 is unavailable. The stars Dec and GHA are needed to determine if the observer is within 4° of the subpoint. The Air Almanac may be used to find the Dec and sidereal hour angle (SHA) of the star. The SHA of the star is added to the GHA of Aries to find the GHA of the star.

Eliminating Motions with the Bracket Technique

For sun observations, you can eliminate motion calculations by using a shooting schedule of 3 minutes early, on fix time, and 3-minutes late. With this schedule, the 3-minute early and 3-minute late shots have the same magnitude of motion but an opposite sign. Therefore, these motions cancel each other out and do not need to be computed. The on-time shot has no motions. Therefore, the three intercepts can be averaged for a single LOP. At night, shooting the same star 4 minutes early and late, with a different star shot on time, can employ a similar method. In this case, the intercepts for the same star’s 4-minute early or late shots can be averaged. This reduces workload, but only two LOPs are obtained.

DR Computer Modification

Rather than eliminating motions, your DR computer can be modified so both observer and body motions can be computed at one time, without entry into the Pub. No. 249. Make a GS and latitude scale. [Figure 12-8] After constructing these, the DR computer can be modified for quick and accurate computations of 1-minute motion adjustments.

Figure 12-8. MB-4 motions modification.

Tape the GS scale (0 through 900) along the centerline of the grid scale. Match zero to zero, 300 to 50, and 600 to 100 as shown in Figure 12-8. Then, tape the latitude scale along the zero grid line so that 90° falls on the centerline and the scale extends to the left as shown. Check the accuracy of your placement: 30° latitude should fall 13 divisions left of centerline. Juggle the scale as necessary to provide the greatest accuracy between 30° and 45°.

To use the modified MB-4 computer for motion adjustments:

• Set true north under the index. If computing for grid, set polar angle (PA) under the index. In the NW and SE hemisphere quadrants, PA equals convergence angle (CA). In the NE and SW quadrants, PA = 360 – CA. Next, place the grommet over the zero grid line. Mark a cross (+) at the assumed latitude. [Figure 12-9]

Figure 12-9. Celestial motions–step one.

• Set track (or grid track) under the index and position the slide so the GS is under the grommet. Place a dot on the zero point of the grid scale. [Figure 12-10]

Figure 12-10. Celestial motions–step two.

• Place the Zn (or grid Zn) of the body under the index. Position the slide so the cross or the dot, whichever is uppermost, is on the zero line of the grid. [Figure 12-11]

Figure 12-11. Celestial motions–step three.

NOTE: The vertical distance between the zero line and the low mark is the combined 1-minute motion. Each line of the grid equals 1 minute of arc (1 mile). If the cross is on the zero line, the motion is positive. If the dot is on the zero line, the motion is negative. When solving for motions using grid, all directions must be grid directions.

EXAMPLE: Given the following information, find the combined 1-minute motion adjustment.

Combinations of Sun, Moon, and Venus

The moon or Venus is often visible during daylight hours and can be used to obtain an LOP. Always consider fixing using these bodies during daylight celestial flights. When planning the flight, use the sky diagrams in the Air Almanac to determine the availability of the moon and Venus. If the bodies are available, they can be readily found by accurately precomputing their altitudes and azimuths.

When looking for Venus, take all the filters out of the sextant and point it at the precise location of the planet. A bright, small pinpoint of light is visible but hard to detect, unless sky conditions and separation from the sun are ideal. With practice, acquisition should become easier and you will be familiar with those conditions conducive to successfully making a Venus shot.

During the day when the sun is high, the moon or Venus, if they are available, can be used to obtain compass deviation checks. In polar regions during periods of continuous twilight, the moon and Venus are available if their Dec is the same name as the latitude.

Duration of Light

Sunrise and sunset at sea level and at altitude, moonrise and moonset and semiduration graphs will not be discussed in detail in this chapter. It is imperative; however, to preplan for any flight where twilight occurs during the course of the flight, especially at the higher latitudes where twilight extends over longer periods of time. An excellent discussion, with appropriate examples, is provided in the Air Almanac and should be sufficient for those missions requiring detailed planning.

True Heading Celestial Observation

The periscopic sextant, in addition to measuring celestial altitudes, can be used to determine true headings (TH) and true bearings (TB). Any celestial body, whose azimuth can be computed, can be used to obtain a TH. Except for Polaris, the appropriate volume of Pub. No. 249 is entered to obtain Zn (true bearing). In the case of Polaris, the Air Almanac has an azimuth of Polaris table. It does not require information from the Pub. No. 249 tables. There are two methods used to obtain TH with the periscopic sextant. The TB method requires precomputation of Zn. Postcomputation of Zn is possible with the inverse relative bearing (IRB) method. The procedures follow.

True Bearing (TB) Method:

1. Determine GMT and body to be observed.
2. Extract GHA from the Air Almanac.
3. Apply exact longitude, at the time of the shot, to GHA to obtain exact LHA.
4. Enter appropriate Pub. No. 249. table with exact LHA, latitude, and Dec. Interpolate if necessary and extract Zn and Hc. [Figure 12-12] If Polaris is used, obtain the azimuth from the Azimuth of Polaris table in the Air Almanac and use your latitude instead of Hc. [Figure 12-13]
5. Set Zn in the azimuth counter window with the azimuth crank, and set Hc in the altitude counter window with the altitude control knob.
6. Collimate the body at the precomputed time and read the TH of the aircraft under the vertical crosshair in the field of vision. If you are using precomputation techniques, a TH is available every time an altitude observation is made. NOTE: Shot must be taken at precomp time.

Figure 12-13. True bearing method (including Polaris). [click image to enlarge]

Inverse Relative Bearing (IRB) Method:

1. Set 000° in the azimuth counter window with the azimuth crank. [Figure 12-14]
2. Collimate the body. At the desired time, read the IRB under the vertical crosshair in the field of vision.
3. Compute Zn of the celestial body and use the formula: TH = Zn + IRB

Figure 12-14. Inverse relative bearing method. [click image to enlarge]

Celestial Navigation in High Latitudes

Celestial navigation in polar regions is of primary importance because it constitutes a primary method of determining position other than by DR, and it provides a reliable means of establishing direction over much of the polar regions. The magnetic compass and directional gyro (DG) are useful in polar regions, but they require an independent check that can be provided by a celestial body or other automatic system, such as inertial navigation system (INS) or global positioning system (GPS).

At high latitudes, the sun’s daily motion is nearly parallel to the horizon. The motion of the aircraft in these regions can easily have greater effect upon altitude and Zn of the sun than the motion of the sun itself.

At latitude 64°, an aircraft flying west at 400 knots keeps pace with the sun, which appears to remain stationary in the sky. At higher latitudes, the altitude of a celestial body might be increasing at any time of day, if the aircraft is flying toward it and a body might rise or set, at any azimuth, depending upon the direction of motion of the aircraft relative to the body.

Bodies Available for Observation

During the continuous daylight of the polar summer, only the sun is regularly available for observation. The moon is above the horizon about half the time, but generally it is both visible and at a favorable position with respect to the sun for only a few days each month.

During the long polar twilight, no celestial bodies may be available for observation. As in lower latitudes, the first celestial bodies to appear after sunset and the last to remain visible before sunrise are those brighter planets, which are above the horizon.

The sun, moon, and planets are never high in polar skies, thus making low altitude observations routine. Particularly with the sun, observations are made when any part of the celestial body is visible. If it is partly below the horizon, the upper limb is observed and a correction of –16′ for semidiameter (SD) is used in the SD block of the precomputation form. During the polar night, stars are available. Polaris is not generally used, because it is too near the zenith in the arctic and not visible in the Antarctic. A number of good stars are in favorable positions for observation. Because of large refractions near the horizon avoid low altitudes (below about 20°) when higher bodies are visible.

Sight Reduction

Sight reduction in polar regions presents some slightly different problems from those at lower latitudes. Remember, for latitudes greater than 69° N or 69° S, Pub. No. 249 tables have tabulated Hc and azimuths for only even degrees of LHA. This concerns you in two ways. First, it is necessary to adjust assumed longitude to achieve a whole, even LHA for extractions. This precludes interpolating. Second, the difference between successive, tabulated Hc is for 2° of LHA, or 8 minutes of time, so this difference must be divided in half when computing motion of the body for 4 minutes of time.

For ease of plotting, all azimuths can be converted to grid. To convert, use the longitude of the assumed position to determine convergence, because the Zn is for the assumed position, not the DR position. On polar charts, convergence is equal to longitude.

In computing motion of the observer, it is imperative that you use the difference between grid azimuth and grid track, or Zn and true track, since this computation is based on relative bearing (RB). Zn minus grid course does not give RB.

Since low altitudes and low temperatures are normal in polar regions, refer to the refraction correction table and use the temperature correction factor for all observations.

In polar regions, Coriolis corrections reach maximum values and should be carefully computed.

Poles as Assumed Positions

Within approximately 2° of the pole, it is possible to use the pole as the assumed position. With this method, no tabulated celestial computation is necessary and the position may be determined by use of the Air Almanac alone.

At either of the poles of the earth, the zenith and the elevated poles are coincident or the plane of the horizon is coincident with the plane of the equator. Vertical circles coincide with the meridians and parallels of latitude coincide with Dec circles. Therefore, the altitude of the body is equal to its Dec and the azimuth is equal to its hour angle.

To plot any LOP, an intercept and the azimuth of the body are needed. In this solution, the elevated pole is the assumed position. The azimuth is plotted as the GHA of the body or the longitude of the subpoint. The intercept is found by comparing the Dec of the body, as taken from the Air Almanac, with the observed altitude of the body. To summarize, the pole is the assumed position, the Dec is the Hc, and the GHA equals the azimuth.

For ease of plotting, convert the GHA of the body to grid azimuth by adding or subtracting 180° when using the North Pole as the assumed position. When at the South Pole, 360° – GHA of the body equals grid azimuth. The result allows the use of the grid lines for plotting the LOPs. When using grid azimuth for plotting, apply Coriolis to the assumed position (in this case, the pole). Precession or nutation corrections are not necessary since current SHA and Dec are used. Motion of the observer tables may also be used in precomputation, since grid azimuth relative to grid course may be determined. Motion of the body is zero at the poles.

Note the exact GMT of the celestial observation. From the Air Almanac, extract the proper Dec and GHA. Plot the azimuth. Compare Ho and Hc to obtain the intercept. When the observed altitude (Ho) is greater than the Dec (Hc), it is necessary to go from the pole toward the celestial body along the azimuth. If the observed altitude is less than the Dec, as is the case with the sun in Figure 12-15, it is necessary to go from the pole away from the body along the azimuth. Draw the LOPs perpendicular to the azimuth line in the usual manner. Do not be concerned about large intercepts; they have no bearing on the accuracy of this type of fix. Observations on well-separated bearings give a fix that is as good close to the pole as it is anywhere else.

Figure 12-15. Using pole as assumed position.

Adjusting Assumed Position

Adjusting Assumed Position for Off-Time Shot

There are times when the observer does not start the shot at the prescribed time for various reasons. For example, the observer may struggle to find the body due to cloud cover. If a shot is taken off time, you can use the FEAST (Fast EAST) rule: a shot taken too fast or too early has the assumed position moved 15′ of longitude east for each minute early to compensate for body motion. [Figure 12-16] Apply the reverse of the FEAST rule for late shots (move the assumed position west). This adjusted position is then advanced or retarded for track and GS to account for motion of the observer, applying the same concept used in the three-LHA method. [Figure 12-5] This technique for solving motions is also discussed in the Celestial Precomputation category.

Figure 12-16. Corrections for off-time shooting.Figure 12-5. Plotting three LHA.

EXAMPLE:

Original assumed position: 23°–50′ N 120° –00′ W
Move 15′ of longitude west for 1 minute late
Retard 6 NM from track of 360° TH
New assumed position: 23°–44′ N 120 ° –15′ W

Longitude Adjustment Principle

You will occasionally make errors in your precomputations. Possibly the most common would be an extraction error of the GHA or math error while computing the LHA. If one of these numbers is incorrect, then all the extractions from the Pub. No. 249 would be based on erroneous information, and the result would be an LOP error. Fortunately there is a way of compensating for this type of error without having to reenter the table and retrieve the correct data. This method is called the Longitude Adjustment Principle (LAP). You need only adjust the assumed longitude (up to 2½°) to correct for a GHA extraction error or a math error. Moving the assumed position beyond the 2½° induces some error in the plotting LOP. Suppose you wanted the GHA for 1410Z, you extracted the value for 1400Z and applied it to the longitude. [Figure 12-17] The resultant LHA was used and the precomp completed before you realized your error. To do the LAP first, extract the correct GHA (031–20), keep the old LHA, and adjust the longitude so that the math is correct. [Figure 12-18] A math error can occur in solving for the LHA. [Figure 12-19] Once you have corrected the precomp, use the adjusted longitude for your assumed longitude to plot the LOP.

Figure 12-17. LAP using incorrect GHA.Figure 12-18. LAP using correct GHA.Figure 12-19. LAP correcting a math error.