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Aviation History
1919
1919 - 0672.PDF
CORRESPONDENCE LANDING GEARS [1974] [THE article on "Stresses in Landing Gear," by Mr. H. H. Thomas, published in our issue of April ro, has called forth some comments, printed below. Unfortunately it will not be possible to have a discussion on the article, since, we regret to say, its author has succumbed to an attack of influenza.—ED.] To the Editor of FLIGHT. SIR,—IN the article on " Stresses in Landing Gear," by Mr- H. H. Thomas, in your issue April 10, he states in effect that if W is weight of an aeroplane in lbs., and V its vertical velocity of descent in feet per second at the instant of landing, WV2 and d the deflection of rubber absorber in feet, then — " average intensity of impact." I have noticed a similar treatment of this question in " Design of Aeroplanes " by A. W. Judge (Second Edition), and I beg to point out a fallacy in the result. WV2 The kinetic energy at mstant of impact is ft. lbs., and in the process of absorption the wings and body of the machine (that is, practically W lbs.) descend d feet (the specified deflection), thereby losing potential energy approxi mately Wd ft. lbs. Hence, as both K.E. and P.E. are stored in the absorbers—at maximum deflection we have approxi- /WV2 \ ~zz + Wi ) ft. lbs. of stored energy (neglecting mately heat losses). Since stored energy = work done /WV2 ( - 4- Wd ) /WV2 • I 2-gd + w) We have Vd approx. Where P = average intensity of impact. F = maximum intensity of impact = 2P (assuming a linear law for rubber force — deflection) or F = /WV 2 + 2W approx. Comparing this with equation (1) in article in question, we have a result greater by 2W approx. Actually the term 2W should be replaced by 2W] where W, is the weight of all parts of machine which lose potential energy whilst the rubber extends owing to the pull of gravity W, lbs. Equation (2) in the article is also in error. If h is the height of " free fall " in feet (that is, from point of release until wheels first touch the ground), then K.E. at latter instant equals work done by gravity = Wh ft. lbs. During extension of rubber, W, the pull of gravity, still acts on the rubber over a distance d ft. (the deflection). Hence stored energy (neglecting losses) = Wft -f- W^. If P - mean force, Fd = W h + W, d »•-¥ + *. W, being of previous value. /2WA \ Then F = 2P = ( J~ + 2Wi) = max- force. Equation (5), being deduced from (1), is, of course, equally in error. Mr. Thomas states that "as the machine is necessarily moving forward however at the moment of a'ighting some portion of the weight would be borne by the wings." There seems an ambiguity here. The effect of the forward move ment of the aeroplane is taken into account in the above solution, because V has been taken as the vertical component of the gliding velocity, and had there been no forward motion the machine would be "pancaking." The effect of forward motion has played its part in keeping V the vertical velocity ,. WV2 small—or the same thing -~ small. In the concluding portion of the article the author says in effect that owing to the frictional force F. tan 0 parallel to the ground coming in, " the vertical load will be increased in the ratio of sec 0 to 1." This is clearly wrong, since a force " at right angles to the force of impact " cannot pro duce any effect in the vertical load. The total force of impact will be obviously */J* + F*tsn 2/8 = F sec fi and will act in a direction 0° to the vertical, where £ is the angle of friction. J. R. PIKE, Wh.Ex. The Stresses in the Landing Gear of an Aeroplane SIR,—The recent article by Mr. H. H. Thomas on the above subject is somewhat misleading. He states rightly that the WV2- kinetic energy of a moving body is —— , but since the kinetic energy of a body depends on the mass of the whole body, W being used as a measure of the mass must be the weight of the whole body (an aeroplane in the case under considera tion) and not that part only which " is not air borne." In a normal landing the velocity of the machine at the moment of impact with the ground will be such that the lift force on the planes is still equal to the weight of the whole machine. Since the horizontal component of this velocity will not be reduced greatly during the first impact and rebound, it may be assumed without much error that the rate of loss of potential energy at any instant is equal to the rate of work done against the aerodynamic lift forces. The work done on the machine by gravity need not therefore be considered. It remains to consider how the kinetic energy due to any downward component (V) of the velocity is converted into strain and heat-energy, and what proportion can reappear as kinetic energy on rebound. Mr. Thomas assumes that all the kinetic energy is ex pended in stretching the rubber " shock absorbers." This is only correct when the tyres, axle, and other parts of the undercarriage are rigid and do not deform. Even if this were the case in practice, the extension of the shock absorber does not usually follow a straight line law starting from zero, as the rubber is in most cases wound on with an initial tension, so that no extension is caused by the weight of the machine when at rest. Had Mr. Thomas's calculations referred to the energy absorbed by the combination of tyres, axle and rubber, the assumption of the straight line law, starting from zero, would be roughly correct for some types of undercarriage. Using this latter assumption, and the notation of the previous article, the maximum force which the undercarriage exerts on the machine will be approximately F - WV" d'g ' d' in this case being, not the extension of the rubber, but the total downward movement of the centre of gravity of the machine from the instant of impact till the vertical component V of the velocity becomes zero. The force F will, of course, increase from zero to the maxi mum value during impact, and doubtless Mr. Thomas makes an unintentional slip in stating the reverse. For any accurate determination of the stresses arising in an undercarriage from a landing under assumed conditions, or for the estimation of the most suitable proportions for the rubber shock absorber, data is required of the stress strain characteristics of the various component parts of the par ticular type of undercarriage under consideration. Informa tion of this nature may be obtained with sufficient accuracy by subjecting the undercarriage to static load, and measuring the total vertical displacement of the load, and also the part of the vertical displacement -which is due to the extension of the rubber. By taking a series of these measurements for increasing and decreasing loads, strain energy diagrams may be plotted for the absorbed and restored energy between any desired limits. For any given maximum force " F " let the total energy absorbed by the undercarriage be E, and the total energy dissipated be — • WV2 WV2/a —1\ Then E = and the energy restored will be I 1 • 2g sy zg \ a J Since this is in the form of kinetic energy the velocity (V1) of rebound will be Vl=\/Vf-^)' This can only be zero when a — 1, i.e., when all the energy absorbed by the undercarriage parts is dissipated. It is evident that this cannot be the case with rubber, and still less with the axle and tyres. In the case of an abnormal landing with reduced hori zontal component of velocity (" pancake " in the extreme case), the vertical component " L " of the aerodynamic forces on the planes may be less than the weight " W." In this case an additional amount of energy (W—L)^1 must be absorbed by the undercarriage, before V is reduced to zero. 672
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