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Aviation History
1912
1912 - 0154.PDF
FEBRUARY 17, 1912. Conducted by V. The Foot-Pounds of Energy Storable In a Pound'Weigbt of Rubber. WE have much pleasure in publishing the following communication received from Mr. G. T. R. Hill relative to the above :— A motor of four strands, 6 ins. long, of Clarke's broad strip rubber, well lubricated with Twining's lubricant, was used, and its torque was measured at intervals when winding up to the breaking- point. The elastic broke at 328 turns. Curve I in the diagram was plotted showing the torque, which is correct to within about 3 per cent, in inch-ounces for any number of turns up to the breaking- 500^1 FT UBS PETR La 4 OOO S^OO 2666 1000 /V r—<cis—* ir-*** J--""^' ""IP A 3 '" 40 5,0 &F T° >* <5v <5f / A GTRH,L^ 100 50 IOO 150 point. Since the work done by a couple or torque when turning through « revs, is 2TT«C, where C is the value of the torque or couple, we see that the work is proportional to the average torque and the number of revolutions ; which is represented on the graph by the area under Curve I. Curve II is the sum curve of Curve I, and has this property, that its ordinate at any point is proportional to the area under I up to that point, and consequently is proportional to the energy stored in the elastic when winding it up to that point. Thus from II we can read off the energy stored, if the elastic is twisted up to its breaking-point or for any percentage of this number of turns. Curve II is nearly a parabola, as it will be seen that its ordinates do not differ very much from those of III, which is actually the parabola x2 = S'8y. Thus the energy stored increases nearly as the square of the number of turns, in fact towards the breaking point it increases faster than this. Twisting the elastic to 75 per cent, of its maximum turns, which is a reasonable limit, as we do not want to strain the elastic, we see that 1 lb. can store some 2,600 ft. lbs. of energy, a figure considerably above that given by other ex perimenters. It is not possible to find the amount of energy that can be stored in elastic by an experiment in which a weight is wound up. This method would do quite well if the torque were constant, but from the diagram it can be seen that it is very irregular, so that the elastic would wind up a very much bigger weight at the start than it could, say, when half run out, so what is wanted is a gradually decreasing weight ; in fact, the weight should decrease as the ordinates of the torque curve decrease from right to left in the diagram. Referring to the curves, we see that if the weight were adjusted so that it could be wound up till only ten turns more of the elastic were to go, about ten times that weight could have been hung on at the beginning. The two crosses on the torque curve show when the knots began to form and when one set had all formed. This forming of the knots probably accounts for the irregularity of the curve, and thus bars an experiment with winding weights. On receiving Mr. Hill's communication we forwarded it to Mr. T. W. K. Clarke, as being the original authority for stating E. JOHNSON, M.A. that some 300 ft. pounds of energy could be stored up in a pound weight of rubber. Mr. Clarke in his reply quite agrees with Mr. Hill's conclusions as correct ; he points out, however, that all the results were in favour of obtaining a high value. His own (and in fact all previous) experiments were carried out with un- lubricated rubber, and were of a rough-and-ready nature in the open some three-and-a-quarter years ago. The number of strands was also very large, about 40; whereas Mr. Hill Was using only 4 strands,iwell lubricated and (probably) so arranged that each took its full share, [which is quite impossible of attainment when the number of strands is large. The method in which Mr. Clarke's experiments were carried out was (briefly put) as follows:—"A spring balance was attached at a marked distance along the propeller ; after a certain number of windings the torque was read in each case. Friction was leliminate.. by taking the mean between the two scale readings when the balance was pulled so that the propeller was about to wind up, and when it was slacked off so that the pro peller was about to unwind ; being unlubricated and the strands many, the windings could not be taken to anything like the extent of Mr. Hill's experiments." Mr. Clarke also refers to another important point which appears to have been quite generally overlooked with respect to rubber. Most people think it curious that the load-extension graph is not a straight line—as, indeed, they say it should be. This, however, is not the case ; for the load in Hooke's Law, which does cause a proportionate "extension," is the load per unit of section. Of course, in ordinary springs this cross-section remains constant, but with such extensible stuff as rubber the cross-section is approximately inversely proportional to the total length, so that the graph, instead of being of the form y = mx (i) y being the actual load and x the extension, is of the form— (1 + x)y = mx (ii) Now those who have had the pleasure (?) of making the acquaintance of co-ordinate geometry will at once recognise what these two equations represent, viz., the first a straight line, the second a rectangular hyperbola, with its axis parallel to those of x and y, thus : A curve, as Mr. Clarke says, which is far more like the real thing (so long as the elastic limit is not passed). The asymptotes show (i) that you can never compress it to nothing ; (ii) that there is a certain load, P (never reached), such that (P - load) x corresponding total length = a constant. 500 TURNS \ 1 1 ^ORlGlINif\u ; LE:NGTH 1 / 1 1 / 1 1 / 1 / 1 / 1 / 1 / 1 ' 1 1 IP ____ ^^\ s * x There is also another point of considerable importance, viz., with respect to the resilience of rubber which is not without its bearing on Mr. Hill's most interesting and valuable experiments. Referring to some experiments made by us (" Model Aero- planing," page 25) with square rubber, the fact that the rubber was square is not, however, expressly stated. Mr. Clarke says : " As the load carried in the three cases shown in Fig. 14 for a given extension is not proportional to the cross section of the rubber in these cases, it made me think, perhaps, the rubber was not square. One would expect the load for a given extension proportional to ad'2- '54
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