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Declination of the Sun Declination
(d)
of the sun is tabulated for O hours universal time of each day (Greenwich date)
in table 15-5. You can interpolate for at the UT1 time of observation by using
the following equation:
A negative declination indicates that the sun is south of the equator, and a negative value must be used in the above equation and in the azimuth (Z) equation. The Greenwich hour angle (GHA) of the sun is tabulated for 0 hours universal time of each day (Greenwich date) in the ephemeris. Interpolation is required at the UT1 time of observation and can be accomplished by using the following equation:
NOTE: The value at the beginning of the day of observation is 0h. The value 24 hours later at the beginning of the next day is 24h.
Table 15-5.GHA for the Sun and Polaris for O Hours Universal Time Now that you know how to compute for the GHA and eventually the LHA, the declination of the sun, and the latitude and longitude of your location, you are ready for the field procedure for determining the azimuth of a line. Horizontal angles from a line to the sun are obtained from direct and reverse pointings taken on the backssght mark of the sun. It is suggested that repeating theodolites be used as directional instruments, with the sighting sequence being as follows: direct on mark direct on sun, reverse on sun, and reverse on mark. Times are recorded for each pointing on the sun. Since a large difference usually exists in vertical angles between the backsight mark and the sun, it is imperative that both direct and reverse pointings be taken to eliminate instrument errors. WARNING DIRECT VIEWING OF THE SUN WITHOUT A PROPER FILTER WILL CAUSE SERIOUS EYE DAMAGE. You must NOT observe the sun directly through the telescope without using an eyepiece or objective lens filter. If you do not have a filter, you can project the image of the sun and the cross hairs of the instrument onto a blank white surface held approximately 1 foot behind the eyepiece. The eyepiece and the telescope focus must be adjusted to obtain a sharp image. Usually only that position of the cross hair system situated within the suns image is clearly visible. Although this method of sun observation works, viewing the sun with the aid of a falter is more convenient and slightly improves pointing accuracies. (When using a total-station instrument, you must use an objective lens filter to protect the electronic distance meter (EDM) components.)Accurate pointings of the telescope cross hairs in the center of the sun is impractical. Rather than pointing to the center, you may take direct and reverse pointings on opposite edges (fig. 15-13). Pointings are made with the single portion of the vertical cross hair without regard to the location of the horizontal cross hair. You point the trailing edge of the sun by allowing it to move into the vertical cross hair. You point the leading edge by moving the vertical cross hair forward until the cross
Figure 15-13.Pointing the sun.
Figure 15-14.Sun-observation example field notes. hair becomes tangent to the suns image. Averaging the direct and reverse angles results in an angle to the center of the sun. Since the sun travels on a curved path, averaging the angles introduces a systematic error-the magnitude being a function of time between pointings. This error can be eliminated by computing an azimuth for each pointing and averaging the azimuths. An alternate procedure is to take both direct and reverse pointings on the same edge (usually the trailing edge). A correction, dH, is calculated from the suns semidiameter and is applied to the average horizontal angle. The semidiameter of the sun is tabulated in the ephemeris. The correction dH (a function of the suns altitude), should be computed by using the following formula (both observations, direct and reverse, should be made within 4 minutes):
When you are pointing the left edge (left when facing the sun), add dH to an angle right. When pointing the right edge, subtract the left edge, which is always the trailing edge at latitudes greater than 23.5N; the left edge is always the leading edge at latitudes greater than 23.5S. The number of sets of data varies, depending on accuracy requirements. For most applications, a minimum of three sets should be taken and an azimuth of the line (ZL) computed for each. A general equation for ZL is
ZL can be normalized to between 0 and 360 by adding or subtracting 360. After azimuths of the line have been computed, they are compared and, if found to be within an acceptable limit, averaged. In working through the following example, refer to the field notes shown in figure 15-14. These notes illustrate the standard procedure of incrementing horizontal circles and micrometer settings for a directional theodolite. EXAMPLE: Determine the true azimuth of a line AB) on the ground from a celestial observation.1. Set the transit at station A and train it on B.2. Adjust the horizontal circle at zero and lock the lower motion. 3. Train the telescope on the sun and record the time at the instant the vertical cross hair is aligned on the edge of the sun. 4. Read and record the horizontal angle. 5. Invert the telescope and take another reading. 6. Repeat Steps 3 and 4 until all the necessary sun shots are completed. 7. Proceed with the computation The following calculations are for the field notes shown in figure 15-14:
Solving for Z,
Note that LHA is between 180 and 360 and that Z is positive; therefore, the normalized correction equals 0. Solving for h,
As shown in figure 15-14, the left edge of the sun (indicated by the symbols in the "point" column) was pointed both direct and reverse. That being the case, the correction dH is added to the average horizontal angle as follows:
Solving for the azimuth of line AB (Set 1), you obtain the following:
Now, if you use the same calculation procedures to obtain the azimuth of line AB for Sets 2 and 3, you find the following:
If you desire a bearing, you know that an azimuth of 912403 equates to a bearing of S883557E. |
 
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