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Aviation History
1912
1912 - 0841.PDF
SEPTEMBER 14, 1912. [/ycHf] THE X CONSTANT, By J. H. MAY I make the suggestion that instead of multiplying W \» . W HUME-ROTHERY, W H.P. W x area it might be more satisfactory to multiply |--—--| K " , as this VH.P. / area latter seems susceptible of a definite mathematical interpretation. If W be the weight of the aeroplane, S its area in sq. ft., V its velocity in ft. per sec, i the angle of attack, K a constant, so that 4 I -/• or/. K: >. • v?; W = KSV-/ approximately. Then as usual Drift = KSW2. Taking H as the coefficient of head resistance, so that Head resistance = HV°-. .-. Thrust = V-(KSr! + H) H.P^-LVfKS^+H). 550 Substituting for V from (1) we get Hi (1) J.K Hence the constant V 550 obtained Thrust^ KS, + «) (a) 1 /W If H.P.= ' ("Y(KSSi + 550VKS/ V flying at the angle of attack for minimum V KS (3) thrust we get by If flying for minimum power we differentiating (2) . 1 get from (3). /' = y/3 A/ -£L. And the H.P. required in e case is got by substituting these values of i in (3). H.P. for minimum thrust= W'-(KS) «r H.P. at minimum H.P. = »/ 3V(KS) 550 '(§)' V,- 55° VKS^ [7SW1 55o H (KS) • 4 IKS/ q.p. Now following Capt. Duchene, the factor -,- represents the propor- tion which the head resistance bears to the effective lifting power of /KS the planes and he calls its inverse square root, viz., A/ , the Oneness of the aeroplane =/. Substituting this we get ® ® M.A., B.Sc. H.P. = a(orr"Jw»(KS) 55o K = 2(or 1-75) _W_ 55o H.P. /a(ori75)\V W \« W \ 550 / VH.P./ S If t is the efficiency of the propelling mechanism, so that * \ B.H.P = H.P. as used in the above formula. 2(or 175) \'/ W \« W ; • r by multiplying (^ H p J g measures directly the product of three of the most essential factors of efficiency, the fineness of the aeroplane as a whole, the lifting efficiency of its planes per square foot, and the (efficiency)' of its propelling mechanism. In regard to this latter it seems as if one should deduct any surplus power of the motor, as shown by it* climbing power, before inserting its H.P. in the formula. [The above communication is of exceptional interest because it arrives at precisely the same results as I have obtained by the .1 and e calculations, but by another method. Thus, in order to arrive at e, the anticipated efficiency of the machine, X is multiplied by a constant -5 to produce a new factor x, which represents the speed appropriate to the design, from which, by multiplying by the weight W and dividing by the horse-power is evolved the numerical value for «. In fine, « is a function of X times the weight per h.p. or may be otherwise expressed as (.,,,) x It which precisely what our correspondent has himself suggested. His method of investigation is worked out in the most interesting manner from aerodynamic premises, whereas my own investigation into the true meaning of X, which resulted in the use of .» and t, was conducted partly by the aid of fundamental dimensions and partly from a known aerodynamic law. If, as seems hopeful, these aeroplane factors are really justifiable they should be of real use to designers, and at least they have the merit of being simple and straightforward calculations easily made and easily understood by anyone.—TECH. ED.] ® ® is FOREIGN AVIATION NEWS. France Wins the Gordon Bennett. FOR the first time France has won the Gordon Bennett Aviation Trophy, the French representative Vedrines as a matter of fact having practically a " walk-over " on his Deperdussin monoplane. Great Britain was not represented in the race as Mr. Claude Grahame-White and Mr. Hamel were both unable to go across the Atlantic, while the Americans were unable to get their specially built monoplane, which was to have been piloted by Glen Martin, ready in time. Although there was a considerable wind blowing across the ground, in the neighbourhood of Chicago, selected for the contest, Vedrines made a start about ten o'clock and with his machine running in splendid fashion be covered the 200 kiloms. in ih. 10m. 56s., the speed working out to about 105 miles an hour. His machine was fitted with a 140-h.p. Gnome driving a Chauviere propeller, and Oleo plugs were fitted. Previous winners of the Gordon Bennett have been Glen Curtissat Rheims in 1909, Grahame- White in America in 1910, and Weymann at Eastchurch last year. Garros Regains the Height Record. SINCE the Austrian officer Lieut. Blaschke succeeded in beating the height record, Garros has waited for a favourable oppor tunity to regain it. The chance came on the 6th inst., when, starting from Houlgate, near Deauville, on the special Bit-riot machine built for the purpose, he climbed until the barograph showed a height of 5,000 metres (16,405 ft.). Starting at 12.45 p.m., in ten minutes' time a height of 2,000 metres had been attained, and although the machine was flying against the wind, and was kept headed in the direction of the sea, it was steadily carried inland. Garros carried a supply of oxygen on board in order to assist respi ration at the great height, but this gave out when he was 4,000 metres high, still he kept on climbing until he had reached 5,000 metres. He tried to get beyond that, but owing to an ominous noise in the motor, he shut off and commenced to volplani down, eventually finding a landing place at Bieville-en-Auge, close to Crevecoeur, about i2| miles inland from his starting point. On examining the motor after the attempt it was found that one of the cranks had broken. Garros's previous record was 3,910 metres, while Lieut. Blaschke's height, which was attained with a passen ger was 4,260 metres. The Belgian Hydro-Aeroplane Meeting. AT the opening of the Belgian Hydro-aeroplane Meeting at Tamise on Saturday last there was a good deal of wind and rain in the morning but Train was out on his hydro-monopline, while Renaux on the Farman biplane took two, then three, and finally four passengers. This machine as well as the Nieuport with Weymann in charge, was again out in the evening carrying passengers. Sunday was the first day of the competition, but the weather was so bad that it was decided to postpone starting the tests, and to double the marks awarded in the tests on the following day. During the preceding night Renaux's machine, which had been unable to find room in the special hangars, put up for the event by Bessonmeau, had been left at anchor by the quay and was badly damaged, but repairs were put in hand at once and quickly carried through. Paulhan made several tests on a Curtiss machine and Weymann was also out on the Nieuport. On Monday morning the proceedings were enlivened by the sighting of a military officer from Antwerp on an aeroplane on which he returned without landing. In the morning Molla (R.E.P.), Paulhan (Ctirliss), Gobe (Nieuport), Weymann (Nieuport), each made the navigability test after which the proceedings were cut short by the squally wind. Beaumont (Donnet-Levque), Renaux (I-'arman), Molla (R.E.P.) and Benoist (Sanchez Besa) each started in the afternoon, but on account of the wind did not do very much. During the day Beaumont made three flights of about twenty minutes each with one passenger. Renaux took two passengers for a 16-min. trip and in another "flight for 21 mins., while four were taken for 19 mins. Chemet on a Borel made two flights of 10 and 17 mins. respectively, and Molle was up for 20 mins. On Tuesday a serious accident marred the proceedings, Busson's machine falling among some trees at Weert, about five miles from Tamise. The pilot and his mechanic were badly burnt through the wrecked machine catching fire. 84I
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