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Aviation History
1909
1909 - 0355.PDF
JUNE 19, 1909. LANCHESTER'S HYPOTHESIS, LANGLEY'S ERROR AND A REVIEW OF THEIR THEORIES. OUR article entitled " Flight according to Lanchester," which appeared in the issue of May 22nd, has aroused a very considerable amount of interest and not a little correspondence, some of which has led us to believe that a few further remarks on the subject might be appropriate. In the first place it is necessary to correct an impression that Mr. Lanchester himself wrote the article in question, in case there should be in that article any word or sentence which is not strictly expressive of Mr. Lanchester's own point of view. We were particular to point out in our introduction that the basis of the article was a lecture delivered by Mr. Lanchester from notes which were not published. In order to deal with the subject adequately it was therefore necessary to write editorially, but this, needless to say, could not have been undertaken in the manner adopted without a previous familiarity with Mr. Lanchester's line of thought, as set forth in his work on Aerial Flight. It seemed to us an excellent opportunity for putting before our readers a fairly concise summary of Mr. Lan- chester's theories, in simple language and deprived of their mathematical analysis. It was hardly to be expected, and certainly not to be desired that any such summary should be completely satisfactory to. readers of very serious and enquiring minds, who must of necessity go to the author's own work for the complete solution of their difficulties. At the same time it has been possible, as we imagined it would be, to introduce our readers to an extremely interesting method of investi- gating the underlying principles of flight. Mr. Lan- chester's theories are a little apt to be assailed by unfair criticism because they do not happen to be deduced from a man-lifting flyer, and do not resolve themselves into a series of cut-and-dried rules for the construction of a practical machine. There is no doubt that Mr. Lan- chester has in his time been as keen as anybody upon achieving flight on a full-sized scale, but being of a scientific turn of mind he thought it would not be a bad idea to find out one or two things about the air before he trusted his life to it. . • Still Air Experiments. In accordance with all properly conducted scientific investigations, Mr. Lanchester commenced with the •simplest possible state of affairs. He assumed the air to be absolutely still, and he took a plane which was abso- lutely flat. From his experiments and investigations of the behaviour of the plane, he deduced that advantages would accrue by the use of an arched aerofoil instead of a flat surface. Neither the one nor the other was in itself a complete flying machine regarded from the man-carrying point of view. But it represented the behaviour of one of the most important parts of a flying machine, viz., its supporting surfaces considered by themselves. If a man cannot fly on a supporting surface without a lot of attendant complication associated with his accommodation and that of the machinery, it does not in any way invalidate the researches as to the behaviour of the elementary plane or aerofoil by itself. It does, of course, very considerably complicate the appli- cation of the knowledge thus gained, but it cannot reason- ably be supposed that with such knowledge it should be more difficult to design a successful machine. The Wright brothers, at any rate, did not despise the theoretical aspect of the problem, although it is sometimes forgotten now that they devoured books and made laboratory experiments* When it comes to dealing with the open air, theory as directly applied from indoor work fails, not because that theory is inaccurate, but because it does not neces- sarily apply to the new hypothesis. If it were possible to define exactly the state of the atmosphere during any particular period under consideration, it would be possible to apply indoor theory with considerable exactitude. But, unfortunately, the atmosphere is such a turbulent fluid that it is impossible to give any such exact definition, and consequently all the latter stages of experiment have to be made by trial and error, with a view to achieving the result which has the best all-round value. An Equation for Stability. ! In connection with the question of automatic stability, for instance, Mr. Lanchester has given a formula which defines the conditions which will enable the machine to avoid falling if struck by a gust. This formula, however, not only specifies the machine, but it specifies the wind gust also, and it is very difficult, not to say impossible in practice, to have gusts made to order. On the other hand, however, it is by no means without interest to be made aware of the conditions required, because even if they cannot be exactly realised, it can throw light on other points which may result in practical improvement. The equation in question, for instance, is as follows.:— tan 7 I (1, * V Where cCe <x ft are as given on page 297 of FLIGHT, May 22nd, and / is the length of tail, H,,, is the height of fall which would give rise to the natural velocity of the machine under consideration, K is defined as a constant by the equation W = KV2, I is the moment of inertia of the machine about its transverse axis, and p is the density of air. Since for stability the expression must be greater than unity, it follows that the factors in the numerator are advantageous when large, and of these the factor, Hn, is a function of velocity, and being present as H2, has an enhanced effect when altered, compared with similar alterations in the other factors. Some Practical Deductions. It is on this that Mr. Lanchester bases his argument that safety lies in high speeds. Another factor in the- numerator is the length of the tail, that is to say, its distance from the main surfaces measured between centres of pressure. A long tail is indicated as advan- tageous, but it will be noticed that the factor, I, for moment of inertia appears in denominator, where it contributes to instability, so that in making the tail long it is necessary to guard against increasing the moment of inertia. In fact the designer might consider it advisable to have a short tail for this reason. If the tail is discarded altogether, the expression becomes zero, and automatic stability vanishes under the conditions of the hypothesis. These do not, it should hardly be necessary to point out, include provision for the hand manipulation of an elevator, so that when Mr. Lanchester says that the Wright flyer is unstable, he is not attempting to dispute the fact that it flies, as some few people appear to imagine. Admittedly the investigation 357 c 2
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