At the request of Lincoln Ellsworth, the writer investigated the various methods for accomplishing celestial navigation on the proposed 1933 antarctic flight. The simplest practical method for fixing the plane’s position was sought. While the chosen method described below has been mentioned by Mr. G. W. Littlehales and others, the technique and auxiliary tables are original. The table (Fig. 2) for rectifying lines of position was computed by Mr. H. F. Freeman and the writer.
Special problem.—The proposed flight is scheduled for December, 1933, between the Bay of Whales and Weddell Sea. To see how the problem will work out, the following data are assumed:
Air speed 150 m.p.h.
Point of departure lat. 78o30’S., long. 164o30’W.
Destination lat. 78o30’S., long. 40o00’W.
Time of take-off 1800 G.C.T.
The following celestial navigation equipment will be carried:
2 second-setting navigational watches rated and set to G.C.T. Bureau of Standards type (or a German type) aircraft sextant. Navigational chart of the Antarctic, prepared by the American Geological Society.
Aircraft plotter (designed by the writer).
Air Almanac, 1933.
Specially prepared data described below.
Method of reducing sextant observations to positions.—Positions will be determined by assuming the south pole to be the observer’s position and by plotting lines of positon directly on the chart without the necessity of computing the altitude and azimuth. To accomplish this, the inaccurate “lines of position” must be rectified to the true “circles of position.” The operation of making these corrections and of plotting the accurate results eliminates the usual tedious process of solving the astronomical triangle. The basic principle on which this method rests is that for an observer at the pole the azimuth is identical with the hour angle; and the altitude is identical with the declination. This is true in this special case because the observer’s zenith and horizon coincide respectively with the pole and equinoctial.
Since the altitude for an observer at the pole is equal to the declination, the difference between these values of altitude and declination gives at once our old friend, “altitude difference,” which is handled exactly the same as the altitude difference found by computing the altitude and by comparing it with the corrected observed altitude. For high latitudes and for long distances from the Sumner, or computed, point, H.O. No. 203 and other publications provide means for rectifying lines of position to allow for their curvature. When the pole is used as the observer’s assumed position, the altitudes are usually smaller and the distances along the line of position from the computed point are usually greater.
Not only does the line of position have curvature, but its direction is different for different distances from the computed point. Referring to Fig. 1, the distance from the computed point to the observer is D, the correction to the azimuth is AZ and the correction to the altitude is AH. Figure 2 is a table giving AZ and AH for altitudes from 10° to 35°, and for distances from 100' to 700'.
Figure 3 is a small scale representation of the assumed problem using both the sun and the moon. Thanks to the new Air Almanac, the moon becomes practically as easy to handle as the sun. The principal difference between the work for the sun and that for the moon is that the G.C.T. gives at once the approximate G.H.A. (and hence, the azimuth) without reference to the Air Almanac, while in the case of the moon, the G.H.A. is taken from the Almanac for the corresponding G.C.T. The declination for both bodies, which is also the true altitude for an observer at the pole, is taken from the Almanac.
Figure 4 is a condensed table for both the sun and for the moon, showing for every two hours of G.C.T. the G.H.A. (azimuth), the declination (altitude for observer at the pole), the distance from the computed point, and the corresponding corrections for azimuth and for altitude, for the problem stated. Most of these data may be recorded for convenient use directly on the navigational chart.
With the data assembled, the actual operation of fixing a position is as follows:
(a) Measure the sun’s altitude and correct it for parallax and refraction to get the true altitude.
(b) Find the difference between the declination and the true altitude. This is the altitude difference.
(c)Plot the sun line, using the south pole as the assumed position, the G.H.A. as the azimuth, and the difference between the altitude and the declination as the altitude difference.
(d) Measure the distance from the computed point to the observer’s approximate position and, with this distance and the altitude, find from Fig. 2 the corrections for azimuth and for altitude, and plot the corrected line of position.
(e) Do the same for the moon. The intersection of the corrected lines of position is the observer’s position.
The observations for the sun and moon should be taken as close together as practicable, or else the run between the two sets of observations should be allowed for in plotting the observer’s position.