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Aviation History
1955
1955 - 0364.PDF
364 FLIGHT STRUCTURAL SAFETY . . . portance in aeronautical structures. Such rapid changes mayarise in a number of ways; with manned aircraft, for example, descent at high speed after prolonged cruising at high altitude willgive rise to rapid surface heating; the descent of long-range bal- listic rockets, such as the V.2, from great altitudes into the earth'satmosphere provides an extreme, almost meteoric, example. But more common, once aeroplane speeds approach Mach numbersof 2 or 3, will be the temperature change as the vehicle gains speed and altitude from the ground. In fact, for the ordinary rangesprovided by the earth's airways, steady temperature conditions will be the rarity, and the problem will be to ensure, during theshort time of flight, that temperature conditions at various parts of the vehicle, although continuously rising, do not reach certaincritical values. The aircraft will, in effect, be judged for its safety in terms of its temperature endurance (in hours or distance) com-pared with the duration of flight or range required of it. Rendel and Hancock, of Farnborough, have discussed this matter recentlyin a very interesting way; the critical temperature, from our pre- sent point of view, is that governing the performance of the struc-ture, and safety margins can be introduced—or ranges extended— by the introduction of refrigeration or of insulating coverings. Itcan be shown that, without such amelioration, a skin temperature rise of 100 to 150° C would occur for an aeroplane flying at M=2for only 10 min. This short endurance could, however, be transformed to a few hours by an insulating covering an inch orso thick. A lot has clearly yet to be learnt about temperature limits, forthe most damaging effects will be due to temperature gradients within the structure. The stresses due to these are both difficultto estimate and difficult to assess in effect, particularly when superposition of manoeuvring or gust loads is envisaged, and forsome time to come relatively arbitrarily specified critical tem- peratures—such as a wing surface temperature—may have tosuffice for the control of safety. No doubt an increased use of unmanned vehicles, for which safety is a less vital consideration,will help to build up empirical information ahead of experience with manned vehicles. The temperature cycles thus arising in flight will, in the case ofmanned aeroplanes, tend to occur on every flight, corresponding to a condition of repeated thermal loading. For very high speeds,the peak temperatures in each cycle, and the internal stress dis- tribution associated therewith, may be such that local plasticityand creep may occur, and the thermal cycle thus lead to progres- sive changes in the structure. Effects of this sort have been studied theoretically both inAmerica and this country. The maximum stress occurring in a wing of given material when the surface air temperature changesby T° is given approximately by EaT, where E is Young's Modulus and a the linear coefficient of thermal expansion. Foran all-aluminium alloy wing, this stress, which occurs in the wing webs, is about 10 tons/sq in for T= 100s C, and for an all-steelwing, about 15 tons/sq in. The response of the wing to repeated exposure to such temperature changes clearly depends on therelation of £ a T to the margin (p y —p) between the yield stress pyand the peak stress p due to ordinary flight loads. Parkes, of Cam- bridge, has studied the results of such repeated thermal cycles,assuming that full plasticity occurs wherever the total stress exceeds py. He finds that, if the thermal stresses EaT exceedthe margin (py —p) but do not exceed p y itself, the structure will"shake down" to a state of elasticity; on the other hand, if the thermal stress EaT exceeds py, a condition of alternate plasticityleading to failure after a number of cycles, or a condition of in- creasing permanent deformation arises. Freudenthal, however, has pointed out that the Theologicalbehaviour—of which creep is an essential component—of real materials produces significant changes in the effects of a thermalcycle. When the effects of external forces alone are concerned, creep has little effect on the magnitude of the internal stressesproduced by the external forces; but when we are dealing with a self-equilibrating system of stresses such as that due to a ther-mal change, creep and time play a major pan in determining what internal stresses actually arise. [The lecturer here illustratedFreudenthal's method of demonstrating these phenomena.] Concepts of Safety.—Under this heading, also, the work ofFreudenthal was instanced by the lecturer. Working mainly in the field of civil engineering structures [said Professor Pugsley], hehas since 1947 published a number of major contributions, and now, in his "Safety and the Probability of Structural Failure,"produced a pocket treatise on the whole subject. Those who have at one time or another struggled with the application of probabilitytheory to the problem will envy his facility. A standard problem of the past, for example, and one still of real interest, is the choiceof load factor for a given probability of failure due to over-load- ing, assuming relevant statistics of wing loads and wing strengthsare known. If these statistics are distributed normally, the whole problem is now reduced to the delightfully simple quadratic relation «a 1- where n is the load factor, Ro and 50 are the means and OR and as the standard deviations of strengths and loads respectively and f is a non-dimensional "radius" given by f = 2-15 V - logw2np0 - - - (2) Here p0 is the probability of equality of the parameters R and S,where 5 will commonly involve a time element. For example, S may be the maximum load recorded on the structure per week,in which case p 0 will be the chance of equality of R and 5 in anyone week. This probability p 0 bounds the area of the normalfrequency curve defining the probability of failure P, and for the small probabilities concerned P is of the order of 0-2p0 (see stand-ard tables of normal distribution and frequency functions). It is interesting to use these equations (1) and (2) to plot curves forload factor n against probability of failure P for various values of the variances ORIR0 and oslS0. Some such curves are shown inFig. 2 and show how rapidly the risk of structural failure can be cut down by an increase of load factor. This is, of course, notnew, but what is not generally realized is the great change of risk that must occur before it becomes noticeable to the users of aero-planes. Structural accidents occur seldom and form only a small proportion of the total accidents to a given aeroplane type; underService conditions, even in peace, the structural accident rate has to be doubled or trebled before the change is sensed by Servicecrews. Equations (1) and (2) refer to cases of normal distribution, andcan be depicted graphically. Similar, but not quite so simple, solutions exist for the important practical cases of normal-logar-ithmic and of extreme value distributions. For many practical problems, the three methods give roughly comparable results. The linking of safety standards with economic efficiency hasbeen considerably advanced, particularly in Sweden by A. I. Johnson. The general approach of all this work is to ignorehuman risks (or to assume we are dealing with structures that do not involve them) and aim to design the structure in the mosteconomical way, allowing for its finite life and the need for its replacement on failure. Thus the structure provided on this basisis the one that makes the total cost of its maintenance (by periodic replacement or repair) for its given purpose a minimum. Quiteincidentally, such a structure will have a definite failure rate, determined by costs alone. It is clear that the risks thus admittedmay be considerably greater than allowed in general practice, but the whole approach is obviously relevant to unmanned vehiclessuch as guided weapons. If we continue to think in terms of probability of failure, it isconvenient to cast the economic theory directly in terms thereof, as has been done by Freudenthal. If A is the initial cost of a struc-ture, C the capitalized cost of its failure, and P the probability of failure during its life, then the economic approach aims to makethe total A+PC a minimum. In other words, the design is ruled by the equation ; dA dC C_Q _ _ _ Q. Now both A and C will depend somewhat on P, and if we express this thus • • ; / A=A0(i-cioglop), ';: V •";•-' m v : ? ; C=C0+mA0(l-clogwP)Q, - - f® where m denotes the ratio between cost of reconstruction er replacement and initial cost, and Q is the factor of capitalization appropriate to an interest rate i, then it is easy to show that, to a good approximation 1 ^ C0+mA0 . Q _ . P cAa log10 e - (6) For a civil engineering structure, c may have a value of about 002 and the factor Q, for a life of 100 years and interest rate of 4 per cent, is about 25 (from tabulated values in Johnson's paper); hence from (6) i = 3,000 (^ + m\- - - (7) Thus I IP tends to vary linearly with C0IA0. Since Co includes allthe direct and indirect losses due to failure, C 0IA0 will often exceedm, which will commonly have a value in the region of 1 or 2. Taking CJA0=2 and m=l, (7) gives P=l in 9,000; in otherwords, it would be economic to design the structure so that, if 9,000 such were built, one would fail in the course of its life. The economic approach has, I believe, partly developed sorapidly because none of us working in this field have yet seen an acceptable and rational way of handling the human aspect of thesafety problem. Recent large-scale accidents, however, have
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