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Aviation History
1938
1938 - 1643.PDF
JUNE 9, 1938. FLIGHT. and of the G.P. of the body) is, however, tabulated, at short intervals of time, in the Air Almanac as " Greenwich Hour Angle." Hence, to find the G.P. of X (or of the projection of any other heavenly body catered for in the Air Almanac) at any time, all that it is necessary to do is to look up the data given for that instant. We will find the position given as Dec. (Declination) and G.H.A. (Greenwich Hour Angle). Now we can make use of the imaginary spot by comparing the Theoretical Distance of the spot from our D.R. position (this is quite quickly and easily obtainable either by a short mathematical calculation based on data contained in tables, or by quick-working tables, of which there are a large variety) with an Actual Distance we find by observing the altitude of the celestial body above the horizon. How the theoretical and actual distances are obtained is explained later. Suppose our dead reckoning position is " Z " on the chart, and that we are able to calculate the distance and bearing of X, which is off the chart, from Z. Let us say that we find it is 3,000 nautical miles, and that the bearing is 100°, T. (How to obtain the Calculated Distance is shown later.) Fig. 2. From Z draw the bearing, ioo°. Suppose, again, we are now able actually to measure the distance from where we are to X. And suppose we find it is 2,980 nautical miles, the bearing being the same. (How to obtain the Observed Distance is shown later.) We therefore know that we are (3.000-2,980), or 20 miles nearer X than we thought we were, along the same bearing. We can then make use of the information on the chart by plotting a position line AA', at right angles to the bearing, 20 nautical miles nearer or " towards " X on the bearing already laid down. Fig- 3- Strictly speaking, the position line should be a portion of the circumference of a " circle of position." As, however, the radius of the circle is large, and we are only dealing with the small portion of it near our D.R. position, there is no appreciable error in making the position line a straight line. If we have observed only one body, we can lay down only one position line. If, however, we had observed another body, whose G.P. is X' and which is at a suitable angle from X, and had obtained another position line in the same way, we can obtain a " fix." Let us assume that the second set of calculation and observa- tion gave us an Observed Distance 15 miles greater than the Calculated Distance, and that bearing was 045°. We are therefore 15 miles away from Z, on that bearing. Plot a position line BB' at right angles to 0450 and 15 nautical miles away from Z. The chart will look as in Fig. 4 : earth and the celestial sphere, let us take a cross-section through any celestial great circle, i.e., a circle whose plane passes through the centre of the earth (Fig. 5) : Fig. 4. As you know you are somewhere along BB', and also some- where along AA', it follows that where AA' and BB' intersect at Y is your position, or " fix." This is, of course, assuming that your original D.R. position Z has not changed much during the interval. If this should be the case, the 1st position line AA' would need to be transferred. To obtain the Observed Distance we require a sextant, which, for air navigation work, is used for measuring the angular distance above the horizon, in degrees and minutes, of the body being observed. The horizon may be either natural (with a marine sextant) or artificial (with a bubble sextant). Let us see how this instrument helps. Going back to the Fig- 5- Let x be a star somewhere on the celestial sphere. The observer is at Z, anywhere on the surface of the globe. Immediately above him is the zenith, z, on the celestial sphere. All around z the observer sees the horizon, h, at 900 from z. Somewhere above the horizon is the star x. The celestial great circle passes through z and x and is at 900 to the horizon. The observer can, with his sextant, measure the altitude of x above the horizon, h, along the celestial Great Circle. As the earth is so small, and the star is so far away, it is exactly as if he were measuring the angle from C, the centre of the earth. The error, Horizontal Parallax, is negligible in practice for all heavenly bodies except the moon, when allowance has to be made. It is quite easy to find the correction in tables, and to apply it. Hence xZh is the Observed Altitude. • Now zCh = Zenith to Horizon = 900. , - Then xCz = 90° — Observed Altitude. . . = Angular distance from x to z. = Zenith Distance, in degrees and minutes. Now look at what is happening on the globe. Z to X, in degrees and minutes, is the same as z to x ; Z is where you are, on the surface of the globe ; and X is the sub-stellar point, on the surface of the globe. WTe know that on the surface of the globe 1' of arc is 1 nautical mile ; hence Z to X (or XCZ in minutes of arc) is the Observed Distance between yourself and the sub-stellar point X, in nautical miles. The Observed Distance is usually known as Observed Zenith Distance, or Obs. Z.D. in navigation text-books. The Observed Altitude has to be corrected for some minor corrections such as Index Error, Refraction, etc., depending on the type of sextant used. These, however, are fully explained in any text-book, and are very easy to apply. A variety of correction tables is available for the purpose of finding the necessary correction. To summarise. By observing, with a sextant, the altitude of the body in degrees and minutes above the horizon, applying small corrections, and subtracting the Observed Altitude from 900, you have found the Observed Distance in nautical miles between yourself and the sub-stellar point. How is Calculated Distance obtained ? Fig. 6. Let us go back to our celestial sphere, our globe, with the observer at his estimated position of Z and the heavenly body at x. As you will see from Fig. 6, the triangle pxz on the
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