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Aviation History
1928
1928 - 0670.PDF
TO FLIGHT 58 THE AIRCRAFT ENGINEER JULY 19, 1928 To determine the water-borne weight at each speed, we assume the V'2 law and when W« = air lift. Wic = water lift. W = total weight. V] = getting-off speed, we have (1) Wa + Ww= W Then Wa at any velocity V will be given by = Wa .substituting this in (1) we have WV2 M W W •y g + WW = W V2 W - Ww But W — Ww = Wa from (1) V2 Wa Wa _ W^ •••"v7 ^"w or T2 ~ V!2 Values of Wa are obtained from the above for the various speeds, and are deducted from W to get the required water- borne weight, Ww. Also the floats are run in test at the angle which will hold good for the full-size floats when in position on the machine, and the load on the floats is applied at a point which represents the centre of gravity of the machine. The carrier to which the model float system is attached during test can rock about a horizontal transverse axis, " the axis being situated relative to the model at the same height and longitudinal position to scale as the centre of gravity of the complete machine to its floats. Weights are so arranged on the float carrier that the centre of gravity of the whole is on this axis." This carrier is supported by a light transverse vertical frame which in turn is attached (with an arrangement •securing minimum friction) to the towing carriage of the tank. " A towing eye can be attached to the float carrier at any height, corresponding to scale to the height of the propeller axis on the machine. The float and frame is towed from this eye by a horizontal gate, the fore end of which is carried •on a transverse vertical frame. " A balanced towing rod connects this forward vertical frame to the lower end of the carriage dynamometer or by the spring attached to it, at its upper end. " The extension of this spring (as the towing carriage is moved down the tank) required to balance the float resistance is recorded on the drum."* The trim of the float is also mechanically registered and noted at the various speeds of the tests. The resistance at each particular speed of the model is then noted and tabulated. (fc) Resistance. If the linear dimensions of a vessel be L times the •dimension of the model, and the resistances of the latter at speeds Vx, V2, V3, etc., are R1; R2, R3, etc., then at the corresponding speeds of the vessel, the resistance of the vessel will be RXL3, R,L9, RSL3, etc. As our model speeds are " corresponding speeds" and we have obtained values of resistance of the model at these speeds, we can now determine the resistance of the full-size float system at each corresponding speed by multiplying each of the model resistances bv L3, which, in the case /20\3supposed, would be ( — The correction for frictional or skin resistance is, however, yet to he considered, since it is understood that Froude's Law of Comparison deals only with resistances other than frictional. Correction for Frictional Resistance. This correction as already mentioned is considered necessary in ship-work when dealing with a comparison between model and full-size ship. The frictional resistance of the ship's model is arrived at from the formula :—»-'(£)«-<sr The difference between this curve and the curve of total resistances plotted from the tank tests, gives at any speed the residuary resistances of the model—that, is to say, the resistances other than frictional. These " differences " are multiplied by V (which is the ratio of linear dimensions) and the results are the residuary resistances of the full-size ship at corresponding speeds. It is now only necessary to add to each of these results the frictional resistance of the full-size ship at each speed to construct the required corrected curve of total water resistance for the ship. To obtain this we use the same formula :— /•W\ /Tv1"83 R=/(w 0) x s x(| The value / is taken from the following table to suit, in the first case, the model length and in the second case the ship length- FROUDE'S RESISTANCES PER SQ. FT. IN LBS. OF VARIOUS SURFACES AT 600 FT. PER MIN. LENGTH OF SURFACE IN FEET. Nature of Surface. Varnish ... Tinfoil ... Calico Fine Sand 2 Feet. ed t o tanc e ionai . r o f sp e ch resi s propor t i o 2 2 1 2 is •00 •16 •93 •00 at g s.2 1 0- 0- 0- 0- i pe r 41 30 87 81 8 feet. ed t o tanc e lonal . - o f sp e ch resi s propor t I12 I 1 1 2 85 99 •92 •00 i lbs . •+3 g- %1%l 0-325 0-278 0-626 0-583 20 Feet. © cu r o f sp e ch resi s roport i o 1-85 1-90 1-89 2-00 i li & 0-278 0-262 0-531 0-480 ed t o 50 1 II • o f sp e ch resi s roport i 1o ft 1 1 1 2 •83 •83 •87 •06 Feet. m ;ane e i sq. ft . Eesi s per 0-25 0-246 0-474 0-405 / is the resistance in lbs. per sq. ft. given in table. It will be apparent, however, that with a seaplane we cannot directly apply the methods of naval architecture. In the first place, we are dealing with two floats, and it has been shown that the sum of the individual resistances of the floats differs from the total resistance of the system, f Further, the wetted surface area of the floats varies at each speed, diminishing to zero at " taking-ofi " speed, and consequently (even assuming a perfect float on which the decrease is steady), the calculation of the skin resistance at each speed presents more than a little difficulty. The fact of no skin resistance correction being made on float model tests accounts for some of the minor discrepancies which occur between the behaviour of full-size seaplanes and that predicted from model tests. The following table given by Mr. G. S. Baker, O.B.E., of the National Physical Laboratory, in a paper read before the Royal Aeronautical Society indicates in what respects model conditions differ from those found in the flying of an actual machine, and shows that even tank-tests have their limita- tions. Differences between Machine and Model Tests. Full Size Screw Thrust- equals water re- sistance plus air structure resistance plus acceleration force. Speed is increasing all the time. Model Corresponding thrust equals water resistance plus air re- sistance of hull and model structure. Speed is steady. • See " Ten Years' Testing of Model-Seaplanes," by G. S. Baker, O.B.E., t See "Effect of Divergent Wa\es on Resistance of Floats," by B. 6.Barillon (Ing. Paris), Nov. 4, 1926. 614/
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