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Aviation History
1958
1958 - 0019.PDF
FLIGHT, 3 January 1958 19 The Rolls-Royce Soar, of rather more than 1JS00 Ib thrust, set entirely new standards of thrust/weight ratio when it appeared in 1953. Dangers of Applying the "Square- Cube Law" in Forward Planning ••• ; - By J. M. STEPHENSON BIGGER AND BETTER TURBOJETS IN the year 1873 the famous physicist, Hermann von Helm-holtz, published an article on aerodynamics, entitled ATheorem of Geometrically Similar Movements of Fluid Bodies, and its Application to the Problem of Steering Ballo^ms.In it he pointed out that aerodynamic forces vary with surface area, and weight (or buoyancy) with volume. The control problemof geometrically similar balloons thus becomes steadily more difficult with size, since forces increase more slowly than weight,according to the "square-cube" relation: (Force)3 * (Weight)2Helmholtz used similar reasoning to prove to his students that men would never be able to fly merely by flapping canvas wingswith their arms; and he thus exploded an ambition older than mythology. This point relating the size and flying ability of birds (alongwith many other applications of engineering to biology), was amplified by Professor W. D'A. Thompson of Cambridge in aclassic treatise On Growth and Form (1917). The discussion therein of dynamic similarity is of remarkable interest to present-day engineers, whose only serious difficulty may be that many of the humorous asides are intended for gentlemen, i.e., arequoted in Latin or Greek. The Ultra-light Gas Turbine. In the past few years the so-called square-cube law of the aforementioned scholars has been seized upon by many aeronautical engineers, and distorted toguarantee the pedigree of all manner of hobby-horses. It has been used to show that the Brabazon was too big, the Gnat toosmall and the Gyron too powerful. Perhaps the most novel deduction has been that future aircraft will use dozens anddozens of tiny jet engines, some pointing down for lift, some backwards for thrust—and presumably some sideways for con-trol, and inwards for pressurizing. The latest entry in this class is from the Air League of the British Empire, whose proposed1,500-knot Transatlantic Express has 70 engines and 44 passengers. At about the same time, a large aero-engine manufacturer onthe other side of the Atlantic displayed a wonderful confusion between dry engine weight (to which alone the square-cube rulecan be claimed to apply) and fuel consumption, in an advertise- ment for small turboprops: "The 3/2 power principle . . . resultsin the well-known fact [sic] that propulsive efficiency increases with decreasing power-plant size, whether one studies insects,birds, or aircraft gas turbines."* The vogue for the very small aircraft gas turbine was startedabout ten years ago, when Dr. Griffith of Rolls-Royce correctly pointed out that, so long as most parts of a turbojet engine couldbe exactly scaled down in dimensions, the ratio of thrust to *"Aviation Week," September 9, 1957, p.161. weight would automatically improve. A cluster of small engineswould thus be lighter than an original single engine. For example, if a 10,0001b-thrust turbojet weighs 3,000 lb,exact scaling to 5,000 lb thrust by halving all the cross-sectional areas would yield an engine weighing only 1,060 lb. Two suchengines would be nearly 900 lb lighter than the original, for the same thrust. The argument can be continued indefinitely: aneven more shrunken engine yielding only 1,000 lb thrust would in theory weigh only 95 lb, so that ten little engines arranged inthe wings of an aircraft like the Pipes of Pan (or clustered around the tail) would give the required 10,000 1b thrust with a weightsaving of more than 2,000 lb (or ten passengers). The general effect is shown graphically in Fig. 1. The apparent attraction of such arrangements has led somepeople to elevate the cluster principle almost to the status of that more famous square-cube law which is so much in the newsnow—Kepler's Third Law of Satellites, published in 1619: (Period)2 » (Distance)1(Or, for engineers, Period = 84 (l + /i/4,000)8'2 minutes, where h is the average altitude in miles.) The Limits. There are two physical reasons why the "square-cube law" of jet engines does not apply as simply as this. First, no complex piece of machinery can be scaled down indefinitelyand still work. There is always an absolute minimum to the practicable thickness of sheet and strip, to the clearances thatcan be maintained between moving parts and to the accuracy of machining. As the dimensions of more and more parts fall tothese limit values, an engine departs further and further from similarity as its size is reduced. The second limit of the "law" isthat it does not apply directly to propeller gears, or to acces- sories. Many of the latter (for example, governors, igniters,thermocouples) are functional in nature, and already as small as they can be made. For both these reasons, the similarity law departs from thesquare-cube line at the small sizes. The first attempt to breach these limits was made by Rolls-Royce with the series of engineswhich led up to the l,8601b-thrust R.B. 82 Soar of 1953 (photo). In these engines, much use was made of welded sheet, and the bareminimum of accessories was fitted. The Best Size. As a simplification it may be assumed thatthere is a minimum absolute weight (say, 200 lb) below which a reasonably efficient and controlled turbojet cannot be made,however small the thrust required. The data of Fig. 1 is replotted in Fig. 2 to show the ratio of weight to thrust; and when the lowerweight limit is added, it appears that there is a best size for a light jet engine. In this example the minimum occurs at 2,000 lb thrust. While Rolls-Royce were developing the Soar, many anxiouscalculations were made by the other manufacturers, and at Farn- tpoo- Fig. 1 (left). Theoretical weight-saying by using clusters. fcAVIKG, Fig. 2 (right). "Best" size by arbitrary weight limitation. WOO THMSrOb) WpOC
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