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Aviation History
1913
1913 - 0326.PDF
1/jJGHT because we have more complete theories available. Theories of hydrodynamics and aerodynamics are, however, very incomplete, and in naval architecture are rejected in favour of experiments on models. The particular problem is here, to find the resistance due to waves. Obviously, the waves depend on the earth's attraction, on tl e leng h of the model, its velocity, and the density of the fluid, and, so far as is known, on nothing else to any appreciable extent. The most general expression for resistance which contains all these «*»©. quantities and has the right dimensions is : Resistance = Now J i* a general unknown function, and at first sight it might appear to be impossible to make any use of the equation. A little analysis, however, shows how to avoid the difficulty, if only we are in a position to test a model of the ship. On the model earth $ is constant, and if we make vljl have the same value for the model and ship, then /Q has the same value ; this is just the statement at Froude's law of corresponding speeds. Now go further. We have used f as being the earth value for both model and ship. Suppose that the ship was for use on Mars and the model test was to txr made on the earth, then the equation tells us that, since the attraction on Mars is less than that on the earth, the model must be towed faster in a given proportion. The reason for this extension of Froude's law is easy to see—since the earth attracts the water more atrongly than Mars, it requires a greater disturbing force, and there fore greater speed, on the earth to create waves as big as those on Mars at the lower speed. It has been known for a long time that frictional resistances do not follow Froude's law, and these forces are calculated separately. Suppose, however, that we are deeply submerged, then the surface does not matter, and we are left entirely with friction. What is the law in this case ? Experimental evidence now says, the resistance depends on the speed, the length of the model, the velocity and on the density and viscosity of the fluid. As before we find Resistance • fPPfi J is the only possible relationship between the above quantities which has the correct dimensions, v is the mathematical coefficient of viscosity. The models will now produce similar disturbances in the vt fluid if — is constant. This might be called the law of corresponding speeds for fluid friction, and was first stated by Osborne Reynolds. It differs from Froude's law of corresponding speeds in one particularly important respect. If we take two models of different sizes, the friction law says that the velocity past the bigger of the two must be the smaller, whilst Froude's law says exactly the opposite. Turning now to an ex|>eriment in which the earth's attraction, and therefore, presumably, Froude's law, doesn't matter, we can see (Fig. 2) in a striking way how the mathematical conclusions are borne out in fact. The motion of the water at the back of the ® ® FLYING AT HENDON. IT was not so very long ago that the writer would look out of his window at some poplar trees to ascertain whether* or not there would be any flying at Hendon, but now it seems that these trees can bend nearly double and still someone or other is almost sure to go up at the aerodrome. Such was the case last Saturday. The wind was blowing at between 30 and 50 miles per hour during the afternoon, yet in spite of this Pierre Verrier had the 70 h.p. Maurice Farman biplane brought out and put up a brilliant display. Further interest is attached to this flight in that a passenger, in the person of E. "Vitry"—none the worse lor his nasty spill at Farnborough recently—was carried. Two circuits of the aerodrome were made, the biplane making but little headway when going against the wind. Some anxiety was felt, when it came to making a landing, for this is admittedly the trickiest part of a flight. The machine, however, was brought to rest with perfect safety, but no more flights were attempted that day. Sunday, the next day, was, perhaps, a little better as regards the wind, although rather more gusty. Several pilots went up, therefore, including one of some note—M. Chevillard, the chief instructor of the Henry F'arman School at Etampes. This pilot Bade several flights in the 80-h.p. Henry Farman biplane, executing some astonishing banked turns and dives. We can promise those of our readers who go to the Easter meetings some flying worth seeing, tot M. Chevillard has decided to take part in the races. Louis Nod also went up several times on the same machine, and the Maurice Farman biplane was again out, piloted by P. Verrier. M. Marty, who flew the 80-h.p. Gnome-Caudron biplane, recently acquired by the Admiralty, over from France, with Mr. A. Ramsay as passenger, was out testing the same machine. MARCH 22, 1913. square plate inclined to a current of water is rendered visible by coating it with Nestle's milk, and the photograph shows a contin uous cork-screw sheath in the wake of the plate. Imagine the speed to be gradually raised. For some time nothing remarkable happens, but eventually the flow changes its character to that represented in Fig. 3. Instead of a continuous spiral streak, the eddies now come off in definite loops, and there is no resemblance between the new and the old flows. Imagine the small plate now to be removed and one twice its size substituted, and the experiment again repeated to find the velocity at which the flow changes. This has been done at the N.P.L., and it is shown that as nearly as it can be measured the change occurs in accordance with the friction law, i.e., doubling the size of the plate and halving the velocity always produces the same type of flow. This observation definitely proves that these eddies are produced by friction, and do not obey Froude's law as they are often supposed to do. Now carry the experiment further, and change the fluid from water to air. A channel was made to take a model twice as big as that in the water channel, and the flow was made visible by smoke. Exactly the same changes were observed (Figs. 4 and 5) but the speed at which the flow changed was very much higher in the air than in the water. The mathematics says between six and seven times. We have not yet been able to do the experiment so accurately as to get a better number than that deduced from the laws of similitude. I will conclude by referring to the two other experimental illustrations of the friction law of corresponding speeds. One refers to skin friction and has a bearing on the calculation of the resistance of dirigibles and aeroplane bodies, and the other refers to the resistance of stay wires. In each case the same results have been plotted in two ways, one of which compares the observations at the same speed and the other at corresponding speeds. The simplicity of the latter is strikingly illustrated by the difference in the curves. For the pipes we see that the curves have no apparent connection (Fig. 6) when plotted at the same speed for air and water flowing through the same pipe. At corresponding speeds (Fig. 7) they could not be separated without the help of distinguishing points. For wires the lines at the same speed basis (Fig. 8) have different inclinations and do not always pass through the origin. On a corresponding speed basis (Fig. 9), however, all the observations fall on a single curve without exception. In either case we could use the corresponding speed curves for all sorts of diameters, all sorts of speeds, and all sorts of fluids. The question which we set ourselves to answer at the beginning of this paper is solved when we know any one of these curves from the model to the full scale machine. To do this is a somewhat difficult task in some cases, and all accurate full scale experiments will be useful in order to establish model testing in a firm and unshakeable position. Until then it appears to be impossible to do anything better than to make predictions from model tests, using such discretion as may be suggested by experience on actual flying machines. ® ® Last, but by no means least, mention must be made of Marcus D. Manton's flying on the old 50-h. p. Grahame-White school 'bus. He handled this biplane with great skill, for a machine of this type and power has little or no chance in a wind like that blowing on Sunday—it was, in fact, to our way of thinking, rather risky for the machine to be out at all. ® ® ® ® EASTER MONDAY AT BROOKLANDS. THE following are the entries received for the Aeroplane Handicap, which will be held at Brooklands on Easter Monday. The course will be an out-and-home cross-country one of about ten miles. First prize will be Fifty Guineas, presented by the British Petroleum Co. ; second prize of £25 ; and a third prize of/io. The event is timed to start at 5.20 p.m. :— Entrant. H. Spencer T.O. M. Sopwith Maurice Ducrocq C. H. Gresswell (Aircraft Co.) Do R.H. Barnwell... R.H. Barnwell. . F. W. Merriam... Pilot. H. Spencer H. G. Hawker J. Alcock Pierre Verrier ... M. I. Cheviliard A. Knight R. H. Barnwell F. W. Merriam Engine. Machine. h.p. 50 Gnome Spencer B. 40 A.B.C. Sopwith B. (Burgess-Wright type.) 50 Gnome H. Farman B. 70 Renault M. Farman B. \ 80 Gnome H. Farman B. I 50 Gnome Farman type B. 60 R.E.P. Vickers M. 50 Gnome Bristol B. B. = biplane. M. = monoplane. 332
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