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Aviation History
1942
1942 - 1546.PDF
96 AST AV /'" '«• 4 Difficult Subject Reduced to Its Simplest Form : Position Found Whlhout Mathematics By LT. COL. A. L. MIEVILL27 D.S.O., M.C., M.I.Mech.E., M.E.I.C. ~m MULTITUDES of young men are starting to study navigation. As a rule it is only after /\/g many months of painful work, that they come to see what it is all about—many of them M rJL never get to that point at all. In none of the books on navigation have I been able to find a simple picture, defining each step in the reasoning that enables us to navigate by the Stars. Hence this effort. As set out here the principles can be grasped by anyone. There is nothing new or secret in the petftter. It is only a reduction to its simplest form of what is generally supposed to be a very complicated subject. The method was used/in 1914, later by Alcock and Brown, and others. More recently Capt. Weems of U.S.A. Navy published his charts which have been in regular use for flying. The principles are the same as those upon which the usual mathematical methods are based, but in this method there are no logarithms, no mathematics, no formulae, no difficulties—a relief to the navigator who usually must solve spherical triangles, under appalling conditions. The article is not only ageneijzl statement of principles but a precise method by which navigation has been and is now being carried on. I believe it will be developed rapidly now that its simplicity, speed, and freedom from the danger of error are becoming more appreciated. Half an hour's study of this article will shoiv the student that the subject is really simple. Then, being predisposed to find it so and having already got hold of the why and wherefore of the mathematical processes which must still be learnt for other branches of the subject) he will get through his work much more quickly, sft will form an invaluable background to which the student can constantly refer "when in difficidties and should rob the subject of all its terrors. In the air, at sea, in the desert, our job as navigators is to find out where we are. Provided that we can see two known stars, we can find our "posi tion" by the following method with out elaborate calculations. Suppose we tie a string to the top of a flagstaff and that we walk in a circle round the base, keeping the base of the flagstaff as the centre of the circle, holding the string taut. The angle formed by the string and the horizontal or ground level is, what is calledja navigation, the "altitude." Of JX& top of the flagstaff. Suppose it to be 70 deg. in this case. The string will always make the same angle or "altitude," 70 deg. with the horizontal, so long as .we keep walking on the same circle. In other words, the " altitude " of the top of the flagstaff is the same, 70 deg., from any point on the circumference of that circle and it cannot be 70 deg. from anywhere else upon the whole earth. Let us mark that circle 70 deg. in Fig. 1 (lower view). Now suppose we walk on a larger circle round the base of the flagstaff. *i£fae angle formed by the string and the horizontal will now be smaller than before. Suppose it to be 60 deg. That angle, or "altitude," will be the same 60 deg. wherever"w*e are, provided we keep somewhere upon the circum ference of that second circle, and it cannot be 60 deg. from anywhere else upon the whole earth. Let us mark that circle 60 deg. in Fig. 2 (lower view). Suppose we walk in a still larger circle round the base of the flagstaff. The angle formed by the string and the horizontal will now be still smaller, say 50 deg., and that angle, or " altitude," will be the same 50 deg. wherever we are, provided we keep somewhere on the circumference of that third circle, and it cannot be 50 deg. from anywhere else upon the whole earth. Let us mark that circle 50 deg. in Fig. 3 (lower view). In other words, the "altitude" of the top of the flagstaff remains the same, provided we remain on some one circle of which the flagstaff is the centre. If we walk on a larger circle the angle or " altitude " gets less, and so on. Let us combine Figs. 1, 2 and 3, and produce Fig. 4 thus: Let the place •^here the flagstaff enters the ground be marked A. Take A as centre and describe a circle of the same size as in Fig. 1 and mark it 70 deg. Again with A as centre, describe a second circle of the same size as in Fig. 2 and mark it 60 deg. Again with A as centre, describe a third circle of the same size as in Fig. 3 and mark it 50 deg! If we went out for a walk and took an observation of the top of the flag staff and found the angle, or "alti tude," to be 60 deg., by using Fig. 4 as a " map ''. we would know that we must be on the 60-deg. circle. A Second " Altitude " Suppose now there were a second flagstaff B somewhere near the first flagstaff A. Just as we have done with flag-staff A, we establish a series of circles upon the earth, but with the base of flagstaff B as centre. We would get a figure very much like Fig. 4, except that we have flagstaff B at the centre instead of flagstaff A. Suppose the two flagstaffs to be fairly near together; we would get some thing like Fig. 5. Now, if, during our walk, we stop and by means of a suitable instrument take an observation for the " altitude " of the top of A and find it to be 60 deg., we must be upon the 6o-deg«. circle. If, without moving our posi tion, we take another observation for the '' altitude '' of the top of the flag staff B, and find it to be 50 deg., we know that we must be upon the 50-deg. circle of flagstaff B. But we are already upon the 60-deg. circle of flag staff A. Since the 50-deg. circle of flagstaff B cuts the 60-deg. circle of flagstaff A at only two points, C and D, we must be at one or other of those two points, for C and D are the only two points on the whole earth from which the "altitude" of flagstaff A is 60 deg., while at the same time the " altitude " of flagstaff B is 50 deg. If we know that we are, say, below the line going from A to B, we know
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