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Aviation History
1910
1910 - 0792.PDF
JQCHT OCTOBER I, 1910. HOW THE ALTITUDE OF AN AEROPLANE IS MEASURED. By MAJOR F. LINDSAY LLOYD. THE simplest method of measuring the altitude of an aeroplane in flight is to take, by means of theodolites, simultaneous observations of the machine, as it passes across an imaginary line the length of which is carefully measured and forms a "base" for calculation. The observers are situated at opposite extremities of this base, and in order to ensure accuracy they should be placed as far apart as possible and their stations must essentially be on the same level. A theodolite is a device in the nature of a telescope, which part of the instrument is mounted on a swivelling bracket carrying a scale divided so as to measure the angle from the horizontal to which its line of sight is tilted. The observer brings the aeroplane into focus and keeps it in sight across the line ; as it passes over the base he makes a note of the angle recorded on the scale, and from the figures thus obtained, the altitude of the machine is calculated from the following very simple formula :— Altitude = ;=r^ ,,-,.?. (where a and fi are the Lot a. + Lot p observed angles). From the nature of the above expression it will be obvious that in any installation of this character intended for permanent employment on a flying ground, it would be a great convenience to have the vertical arcs of the theodolites marked off in the natural cotangents of the degrees of altitude, as this would save reference to a table book and thus reduce the calculation to a simple division sum. Another point of practical importance is that the theodolites employed should have reflecting eye-pieces so that the observer is not inconvenienced by having to get right under the instrument in order to sight a machine that is almost directly overhead. As a check upon the mathematical calculations it is exceedingly useful to plot the observed angles graphically on a sheet of squared paper. The angles are laid off at opposite extremities of a horizontal line, representing the base, to scale. The intersection of the angle lines graphically represents the exact position of the aeroplane at the moment of crossing the line, and the vertical height of the triangle thus drawn corresponds, to scale, to the altitude of the machine above the ground. There are several difficulties and objections to this method of observing altitudes, which may be summarised as follows:— (a) The difficulty experienced by the aviator in locating the base of observations when he is at a great height. This can be diminished by making the base line very long, even to the extent of placing its extremities outside the flying ground. This latter provision is especially beneficial from the aviator's point of view, for he can generally distinguish the flying ground itself amidst the surrounding land and is probably able to steer a fairly true course over some part of it. (b) The fact that although the aeroplane may be perfectly visible from the ground, the ground is some times invisible from the aeroplane, so that the difficulty mentioned in paragraph (a) becomes exaggerated. A recent instance of this occurred in a flight made by Morane at Bournemouth. (c) The difficulty that the observer at one end of the base has of knowing whether the aeroplane as it apparently crosses the line is really crossing the line itself, or whether it is beyond the other observer and, therefore, only crossing a prolongation of the line. In this case the calculation of height is possible, but the shape of the triangle is likely to militate against accuracy in the graphic method. This difficulty can be avoided by having the two stations of observation in telephonic communication, which is practically a necessity, for although, theoretically, the observed angles can be taken and the time of their observation noted and recorded independently at each end of the base, there are many other points on which constant communication is required. This is particu larly the case where several machines are flying at the same time or when quick results are required and the observed angles have to be communicated for the purpose of immediate calculation. (d) It is quite likely that the point at which the aeroplane attains its greatest altitude is some way from the base line, consequently the recorded altitude may not be the greatest height attained. (e) At great heights the aeroplane is frequently hidden behind clouds, as for example happened when Latham was flying at Rheims and also when Drexel was flying at Lanark. These two last mentioned objections are the most serious drawbacks to terrestrial observations of altitude, but the difficulties referred to in paragraph (d) may to some extent be overcome by taking a series ot simultaneous measurements when the aeroplane is at any convenient point for observation from both ends of the base. In this case, however, it is necessary to record both the horizontal and vertical angles ; moreover the subsequent calculation is more complicated and tedious. The process consists of calculating the two sides of a horizontal triangle formed by the base and the two observed horizontal angles, the formula for which is ——r = —^p. = —r—~ (where a, b, c are the sides and sin A sin B sin L A B L are the angles). The apex of this triangle defines a point situated vertically beneath the aeroplane at the moment ot observation and either of the two sides of the triangle thus calculated serves as a new base for a further calculation to determine the altitude. This latter is performed by the aid of the formula for altitude first mentioned; one of the new bases and its adjacent vertical angle, as measured by the theodolite being the two factors. The other angle is, in this instance, a right angle, which having a zero cotangent can, therefore, be eliminated from the expression. Taking each of the new bases with their respective adjacent vertical angles, two separate calculations for the same altitude can be made and the agreement between the results is an automatic check on the accuracy of the observation. The graphic method can also be employed as a further check on these calculations if it is considered desirable. The method just described is much better suited to the needs of aviators owing to the difficulty explained in paragraph (a), but there is the objection that it requires considerable personnel to carry out. Not fewer than two observers and one telephone operator are required at each end of the base, and the difficulty of taking these simultaneous observations accurately is so great as to 790
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