MEASUREMENT OF THE EFFECT OF ACCELERATIONS ON THE LONGITUDINAL AND LATERAL MOTION OF AN AIRSHIP MODEL.

121 MEASUREMENT OF THE EFFECT OF ACCELERATIONS ON THE LONGITUDINAL AND LATERAL MOTION OF AN AIRSHIP MODEL. By E. F. R~LF, A.R.C.Sc., and R. JOULES, 3I.A. Reports and Memoranda No. 613. June, 1918. SUM ARY.--(a) Introductory. (Reasons for inquiry.)--the effect of accelerations was introduced in R. & M. 257 by an all-round allowance of 15 per cent. for the" virtual mass" of the airinvolved. Itwas desired to obtain direct experimental evidence, particularly with respect to the effects on the laterm motion, which are most important in the discussion of stability. For other experiments on virtual mass see R. & M. 59 and 612. (b) Range of the inves~gation.--various small airship models (1 in. in diameter) have been tested by causing them to oscillate in air and water, and deducing the desh-ed results from the periods of oscillation. Tests have also been made upon a large model towed in the William Froude National Tank. (c) Results.--The final tests in the Tank indicate a longitudinal " virtual mass" effect equal to about 1 per cert. of the mass of displaced fluid, and a lateral effect of the order of 1 per cent. The tests in the small water channel on one-inch models give a curve very similar to that predicted in I~. & M. 612 for the relation between acceleration effect and fineness ratio. (d) Applications and further developments.--the results are directly useful in applying the stability criterion for airships, the chief effect being approximately to halve the value of the derivative Y~. Further tests on models may be advisable as time goes on ; and it may also be possible to tind the effect of the gas enclosed in an airship envelope by a similar method. A theoretical account of the effect of accelerations upon the motion of a body in a fluid has been given in R. & ivi. 612, in which it is shown that the effect in question can only be treated as the addition of a certain " virtual mass " of fluid to the body when the accelerations are small. In the case of small oscillations of an airship involved in the discussion of stability, the accelerations will be in general very small, and hence a method of determining the " virtual mass " effect based upon the above assumption will provide valuable information with regard to stability. The experiments described in the present report are an attempt to

122 measure this effect in the case of airship models, not only when the acceleration involved is along the axis of the airship, but also when transverse accelerations are involved. The present method was first used in 1917, with the object of estimating the " virtual mass " effect in the case of a sphere. The sphere was suspended by a fine wire, and caused to oscillate as a pendulum, both in air and in water. If it is assumed that the effect of accelerations can be expressed by the addition of a mass of fluid (my) to the mass of the sphere (m), and that the damping is not great enough to affect the period seriously, then it can easily be shown that :- where Ta and T~ are the periods in air and water respectively, and wa and w~ are the weights of the body in air and water respectively. This assumes that the " virtual mass " effect in air is negligible compared with that in water. Two spheres, a and b, of equal diameter were employed, but were weighted so that their respective densities were 7.7 and 2.6. The periods in water were therefore widely different in the two cases, and gave an opportunity of a partial check on the method. It is possible that vital errors may be introduced by the fact that the sphere, in oscillating, is always moving through fluid which it has previously disturbed. If such errors are present, values obtained from tests in which the period was varied would hardly be expected to give consistent results. In the above tests the values obtained for my expressed as a percentage of the mass of the displaced water were 83.5 and 83 respectively, and seem to indicate that the experiments are not greatly affected by the fact that the sphere is not entering undisturbed water. This value of 83 per cent. will be seen to be considerably in excess of the theoretical value of 5 per cent. for a sphere in a perfect fluid,. and this is consistent with the physical idea that in a viscous fluid a greater mass of the fluid would be involved in the acceleration effect than in a non-viscous fluid. The success of the above experiments with spheres led to an attempt to measure the " virtual mass " effect on an airship model by a similar method. Still water in a large tank was first used, but subsequently experiments were conducted in a moving stream in the small water channel at the Laboratory. The model was suspended by two long parallel wires attached near the nose and tail. It could therefore oscillate either along or perpendicular to its axis, and it was at once realised that the lateral acceleration effect could be estimated as well as the longitudinal. By employing the above supporting device as a bifilar suspension, the model could be made to oscillate in yaw about an axis somewhere near its centre of length, and this fact was made use of in an attempt to estimate the effect of the fluid upon the transverse moment

123 of inertia. This latter effect does not modify the expression for the stability criterion of an airship, viz. :-- N~ N~ i > since both N~ and N~ are equally affected. The transverse acceleration effect, however, is very important, since it will affect Y~ and ~ -- U differently. Experiments were made with the model shown in Plate 2, R. & t~. 55, Technical Report for 1911-12. This model was 1 inch in diameter and had pointed ends, both ends being of the same form. By inserting a parallel portion at the centre the fineness ratio was varied. With a fineness ratio of 6 : 1 the values of ~ expressed as a percentage ratio of the mass of the displaced fluid were 1.7 per cent. for the longitudinal motion and 16 per cent. for the lateral At a fineness ratio of 8 : 1 these values increased to 18.5 and 128. per cent. respectively, while a fineness ratio of 1 : 1 gave values of 26.5 per cent. and 132 per cent. The longitudinal effect increases with fineness ratio, as predicted by the curve deduced from general considerations in R. & M. 612, and has nearly reached its maximum value at a fineness ratio of l : 1. The lateral acceleration effect is large, as might have been expected from the theoretical value of 1 per cent. for an infinite cylinder in a perfect fluid. It therefore becomes important from the airship stability standpoint to investigate the lateral effect in a moving fluid, and an attempt was made to do this in the small water channel. It was realised that such results would be very rough, since the model was 1 inch in diameter and the channel only 3 ins. wide. With a view to estimating the wall effect in the channel the 8 : 1 model was swung both in a large tank and in the water channel with the water at rest. Values were found of 18.5 per cent. and 27 per cent. for the longitudinal motion and 128. per cent. and 14 per cent. for the lateral differences of 8.5 per cent. and 11.5 per cent. respectively. It thus appears that the wall effect will not prevent a rough estimation from being made. Tests on the 8 : 1 model in a moving stream are given in Table 2, and it will be seen that the longitudinal effect is roughly independent of forward speed, while the lateral effect is reduced as the speed increases. With a view to a more complete investigation of the effects of speed and fineness ratio, a series of models were tested in which a cylindrical centre portion of varying length was fitted with hemispherical ends. The " fineness ratio " extended from 1 : 1 (a sphere in this case) to 8 : 1, and the results obtained are given in Table 3. It will be seen that the longitudinal effect decreases up to a fineness ratio of 3 : 1 or ~ : 1, but afterwards increases. This is also shown by the curve of Fig. 2, which bears a striking resemblance in general form to that predicted in R. & M. 612. In those tests in which the forward speed was varied, it will be noticed that the previous conclusion was substantiated, viz., that forward

124 speed has little effect upon the longitudinal acceleration effect. In the case of the lateral effect, increase of speed causes a decrease of the effect in the cases of fineness ratio 1 : 1 and 2 : 1, but with a fineness ratio of 3 : 1 no change could be observed. It was not possible to extend the-experiments to higher fineness ratios, as the longer models could not be made to swing sufficiently steadily to enable readings to be taken. Determinations of the effect of accelerations on the yawing motion were only made in still water, as with the bifilar suspension the model could not execute a pure oscillation in yaw when in a moving stream. The effect measured has been expressed by giving the " virtual moment of inertia " of the fluid involved as a fraction of the moment of inertia of the displaced water. For the pointed models of 6 : 1, 8 : 1 and 1 : 1 fineness ratio, values of 78 per cent., 12 per cent. and 123 per cent. were obtained, so that this quantity would appear to be of the same order as the lateral acceleration effect, when defined in the above way. As a result of the above rough experiments, it was considered well worth while to attempt similar measurements on a large airship model, towed in still water on the carriage of the William Froude National Tank. A model about 3 ft. in length was chosen (see Fig. l) and heavily weighted with lead. This was supported on a ½-in. rod attached to a cross piece which rested upon two points, as shown in the figure, so that the model could swing as a pendulum. By rotating the model through 9 relatively to the cross piece, it could be made to swing either longitudinally or transversely, as desired. This apparatus was placed upon the carriage of the Tank so that the model was about 18 ins. below the surface of the water. Tests similar to those described in the small water channel were made, at various speeds of the carriage, and the results are given in Table 4. It will be seen from that table that the longitudinal acceleration effect is again not greatly dependent on forward speed; the value of the period for 3 ft/min, is quite possibly in error, as it was extremely difficult to observe at so high a speed. Taking a mean of all observations, the effect is 6 per cent. of the mass of fluid displaced, while if the reading at 3 ft/min, is neglected the value would be 12 per cent. The lateral effect also appears to be very nearly independent of speed. The second set of observations are the better, as they were made in perfectly still water, the carriage not having previously made a run that morning. Under these conditions, it was much easier to observe the swings of the model. The value of the lateral effect found was 11 per cent., so that for a rough estimate of the acceleration effects in the stability formuhe, values of 1 per cent. and 1 per cent. for the longitudinal and lateral motion should give results not far from the truth. The range of vl/'j covered in the experiments is considerable, as may be seen from the fact that it is equivalent to ~ range of speed from zero to about 6 ft/sec, in the wind tunnel on the same size of model.

and since we find that :-- 125 It was observed that in the case of the lateral motion, which was of course the more heavily damped, the amplitude was roughly halved at each swing. This fact was used to give an idea of the effect of the damping upon the period of oscillation. Thus, if the damping term is supposed proportional to the transverse velocity (a likely assumption) the equation of motion is b'+~6+ke =o Whence ----Ae'~tcos (~(K--~ ~).t +~). If the amplitude is halved in time T (the period) ½ A ----- Ae -~T and 2 = -- ~ log~ ½ The period was roughly 4 seconds, giving :-- =.35 K=2.5 2 The value of 7 is.3 and the period is therefore overestimated.3 by ½- ~ 2r~ 1 per cent. or.6 per cent., so that for the present experiments the effect of damping may be neglected. Experiments such as those above described are very easily and quickly made, one run of the Tank carriage sufficing to obtain several values for the period of oscillation. It is therefore probable that a repetition of the experiment upon several types of airship model would be worth the time spent upon it. While it is fully realised that there are certain objections to the method, it does not seem at all likely that they can introduce errors as great as 1 per cent. of the " virtual mass " to be measured, and if this is so, the method is competent to give exceedingly valuable information concerning quantities which have hitherto been almost entirely neglected in the discussion of airship stability. These tests can be made without disturbing the normal work done upon the Tank carriage, as the model can be lifted from the water on the forward journey of the carriage, and the measurements made upon the return journey, only low speeds being required. It is possible that some information as to the effect of accelerations of the enclosed gas in an airship upon the stability might be obtained by some method similar to the above, but this has not been yet attempted.

126 TABLE I, EXPERIMENTS IN STILL WATER. Sphere. Pointed Airship Model. 8:1 8:1 1: 1:1 Weight in air (lbs.),, in water,, M.I. of model (lbs. ins. 2)... M.I. of displaced water (lbs. ins. s )... Period of swing {sees.)-- Longi- ~. air... tudinal f_water Lateral ~ ~;;; Yawin~ ~alr... ].water Virtual mass as % of mass of displaced fluid-- Longitudinal Lateral " Virtual M.I." as % of M.I. of displaced fluid... i. 286.249 1 "34 2 "64.59 1.7 2.23 1.57 3-66 -- 2.26 4.64 2.41 4.54 ~3. 1.7 16. -- 78..237.312~ [}.3, 15 O. 395.42.139 [}.IX :.159 -- 1. 94 -- --.55 2.2 -- ~.2~ 5.64 -- t.{ 2.21 -- 12.1~ 7.52 4.9{ --.29 18.5-26.1 1128.5 132 12. ~ 2.35 1.19 1.945 3.86 ~4 123 TABLE 2. MODEL OF 8:1 FINENESS RATIO WITH POINTED ENDS IN WATER CHANNEL. V~locity of Flow (ins/sec.). Longitudinal. " Virtual Mass " Effect. Lateral.77 1-4 1.5 27 % 21 26 2O 156% 118 11 79

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127 TABLE 3. CYLINDRICAL MODELS WITH HEMISPHERICAL ENDS, IN WATER CHANNEL. Fineness Ratio. 1 : 1 sphere 2:1 3:1 4:1 5:1 6:1 7:1 8:1 Velocity (ins,/see.)..37.86 1.48 "29.91 1.4 "VirtuatMa~"Effeet. Longitudinal. 82 % Unstable Jp J, 46 % 41 36 36 32 "5 I~t~ral. 6s % 64 39 18 IO 92 73 61 118 "44 25 2 118 1.8 25 2 I18 1.58 3 6 118 27 5 131 29 "7 2 5 16 31 5 136 28 5 186 TESTS ON AIRSHIP TABLE 4. MODEL IN WILLIAM FROUDE TANK. Weight in air.. 4.2 lbs.,, water.. 15.2,, ]Forward Speed (ft/rain.). Longitudinal. Period of Oscillation, Lateral. 55 1 15 2 25 3 3 "26 3 "29 3.35 3 "276 3.1 4.2 4" 4.7, 3.88 4 "33 4.3 4-4.2 4.5 Means 3.25 4.I2 4 "3 The " virtual mass " effects are 6 per cent. for the longitudinal motion and 115 per "cent. and 11 per cent. for the two sets of lateral periods. As pointed out in the report the latter set is probably the best, and values of the period above 2 ft/rain. axe very uncertain and difficult to estimate. Neglecting the value at 3 ft/min., the longitudinal value is 12 per cent. instead of 6 per cent.