Tuesday, December 18, 2007


At times between sunrise and sunset, the gyro error may be abtained by computing the true azimuth of the sun by means of tables designed for azimuth computations or the use of the Sight Reduction Tables No. 229. I generally prefer PUB 229 for obtaining the true azimuth, inasmuch as these tables are widely available, and they are good for reducing a standard sight as well.

To use Tables No. 229 for computation of the exact azimuth of the sun, it is necessary to interpolate in the tables for the exact values of DR latitude, LHA, and declination of the sun for the time of the azimuth observations. The DR latitude is, obtained from the DR plot, while the LHA and declination of the sun are from the Nautical Almanac. I use a sight form designed for use in performing the triple interpolation in PUB 229.

Entering arguments for the tables for the exact azimuth determi­nation are the whole degrees of DR latitude, LHA, and declination smaller than the exact calculated values. The tabulated azimuth angle Z corresponding with these integral arguments is first extracted and entered on the form as "Tab. Z". Next, the amount of change in the value of the tabulated azimuth angle, or "Z difference," is found between this tabulated azimuth angle and the value corresponding to the next higher integral degree of each of the three entering argu­ments. The Z difference for a one-degree increase of latitude, for example, is found by comparing the tabulated azimuth with the value contained in the next adjacent latitude column to the right, while keeping the LHA and declination the same. Likewise, the other two Z differences are found by successive comparisons of the tabulated azimuth angle for the next higher degrees of LHA and declination. All three Z differences are recorded on the azimuth form.

Using the exact minutes of each of the three entering arguments, each Z difference is then interpolated for the exact value of its corre­sponding argument; the result of each interpolation is the correc­tion for the tabulated azimuth angle for the minutes of the argument. All three corrections are added to form the total correction to the tabulated azimuth angle. This total correction is then applied to obtain the exact azimuth angle corresponding to the exact values of the three entering arguments. As the final step, this exact azimuth angle is converted to a true azimuth, using the conversion formula printed on the azimuth sight form.

Comparison of the true azimuth computed with the observed azimuth of the sun yields the gyro error.

1. Obtain and record the DR latitude, exact LHA and declination of the sun for the time of the azimuth observation.

2. Using the integral degrees of these three quantities as entering arguments in Tables No. 229, extract the corresponding tabulated azimuth angle Z.

3. Obtain and record the three Z differences between this tabulated Z and the tabulated values for the next higher degree of each of the entering arguments.

4. Interpolate each Z difference for the correction corre­sponding to the exact minutes of its entering argument.

5. Add all three corrections to the form for total correction to tabulated Z.

6. Apply the correction to obtain the exact azimuth angle.

7. Convert the exact azimuth angle to a true azimuth.

8. Compare the true azimuth with the observed azimuth to get the gyro error.