Document
.-.
‘g;
Aalz4ud/t%uA&
. -,, .“ .,. .
TECHNICAL MEMORANDUMS NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS XO. 938 - L THE SHOCK-ABSORBING SY6TEM OF THE AIRPL417E LANDING GEAR By Pletro Callerio LfAeroteenica Vol. XIX, Ho. 6, June 1939 . .
, ...,,,. . .... . . .
Washington March 1940 . ..-— —.-— —
‘lllpplliliJ1’i#’@ll
-——- .-— .— _ ______
—- —___
llATIONAL ADVISORY COMMITTEE FOR AE30NAIJTICS - —---— TECHNICAL MEMoWLHDUM NO. 938 ,..
. . . ...
. *# L-.
,.., . . .-.
THE SHOCK-ABSORBING SySTEM OF THE AIRPLANE LAITDIEG GEAR* By Pietro Callerio A discueslon ip given of the behavior of”the fihock- absorbin% system, coneifltln% of elastic struts and tiret3, under landing, take-off, and tax~lng conditions, and a general formula derived for obtaining the minimum stroke required to eatisfy the condition impoeed on the landing Sear. Finally, the Operation of some typical shock- absorbing system is examined and the necessity brought out for taklny into account, in dynamic lmndlng-gear te~ts, the effect of the wing lift at the instant of contact with the ground.
1. In numeroue exa~yleg of airplane landing <ear, the 4ear consists of a ri%ld structure to which i~ attached a deformable member to which in turn is attached the wheel, clearly Indicating the modern practice of hqvlng the en- tire shock-absorbing gystem Within thQ landing gear. The Importance of such a system 1S evident: It is only nec- essary to consider the constantly Increasing landing epeede, a consequence of the high wing loads assumed by modern airplanes, and the steep flight-path inclinations permitted by preeent high-lift devices (reference 1).
The tendency toward glide landlnqs without leveling off near the ground - a tendency who~e principaL reaeon is found In the greater difficulty which is experienced in leveling off on landlng with high-lift devices knd which assumes particular importance for aircraft deai<ned for blind flyin4 - brings into prominence axnin the problem of the determination of the shock-iqbeorber characteris- tics. It is sufficient to congider the fact that an hir~ plane which lands nt a speed Of 120 kilometers per hour with a fliqht-path inclination of 1:9, If not properly leveled off by the pilot before the wheele touch ground, develops the same etre~s~~ me If it fell from a heiqht of 70 centimeters.
2. The principal qurqos~ of a shock-absorbing system is that, by means of the Considerable deformation of the —— -.
—— -—.— ———--—-—------.--———
l “SU1 eistema ammortizsatore dei carrelli d’aeroplano.n
L’Aerotecnica, vol. XIX, no. 6, June 1939, pg. 625-640.
2 R, A, O.A, Technioal l#emorandum. No. 938 elastic member embodied in the struotur”d, to permit the ver~ioal velooity of the airplane to be reduced cradun~~y to zero on landing, in such a manner that ”the forces pro- duced on the etructureO ehould not exceed the etreee val~ ues designed for those structures.
After the veloclty has been reduced to %ero, if the shock-absorbing system con- sisted of a perfectly elaBtic member the mtored-up energy would be retatored more or leem muddenly qivlng rice to a rebound which, if not controlled, miqht be not -only dle- agreeable but even dangerous.
In order to avoid this dif- ficulty, the shock-absorbing syetem should be capable of dissipating, with the aid o.f suitable arrangements, a large part of the”energy posseseed by Iihe aircraft in land- ing and of damping the return motion due tQ the stored-up potential ene-rqy c)f deformation of the system - permitting, however, the shock absdrber to aasume Its initial ~osition suffieie.ntly rapidly that it may be ready to operate in case of an immediately subsequent shock.
In addition to this most important and essential function of the shock- ab.sobbing system, it is necessary to consider its qpera- tion during taxying and take-off. When the airplane tax- $es at low speed the chock nbsorber should simply permit the wheele to follow .the.irregularities of the ground and to damp *he chocks produced by them. Since, on tbe other..
hand, these shocks ”are not generally of a character ‘to give rice to dangerous stresses on the structure, too qreat n travel would be not only useless but unfavorable because it would hinder the maneuverability during taxying: The en- ergy dissipation provlde& b~ the tires may be aasumed suf- ficient in this caee, particularly If they are of the low- pressure type.
When the airpl~ne runs on the giound to take off, nfter ‘a firnt interval durin~ which it %s under conditions similar to those of taxying,” a ceTteiin verlocity is reaohed, beyond which aerodynnmi~ forces on”the ~inqs come increasi- ngly into play.
The load on the wheels gradually de-” creases.until finally, having attained the velocity of take-off, the load aecreases to zero. Even though the shock absorber (Ijeoause of its mechanical nature or char- acteristics) cannot be successfully deei$ned to accommo- date both high and low vertical velocities.a.nd is there- fore designed to accommodate the high vertical velocities, the low ones being chiefly damped by the aerodynamic forces: nevertheless, It.is necessary that there be a certain amount of travel of the shock absorber between the position that cor.respond.s to static lend and the poeltion of zero load In order that the wheels follow the profile of the.ground, . .
.
lf. A. C.A. “Techntcal Memorandum .Ho. ,939 thus preventing the reaction on the whe~le from being sub- jected-to abrupt variations In &ntenslty. “ ,.., ,.
.
. . .
Too small a ehook. absorber”travel (between &tatic and seto load paeitioug) would In puch a cage lead to the phen- omenon schematically illustrated fn figure 1. While in position A the weight is eupported”by the elastic re~c- tion on the shosk absorber, at position B - due to the unevenness of the 3round - there would be a further defor- mation of the shock-absorber elaetic e~etem. The mass m, which tends to remain in ite position, is thrust upvard ae a result of the compression of the spring and, If the chock absorber does not permit a sufficient distention, the wheel at a certain point may loee contact with the qround, with a consequent succeeding shock.
From what has been said above, it Is seen therefore that the shock absorber should possess the following re- quirements I 1) It should permit l~nding with s sufficiently large (landing gqar) trqvel.
?) It should dissipate n large Dart of the energy possessed by the oirplane due to the vertical velocity, and damp the return travel due to the energy ~bsorbed elss- ticEllly.
%) It g~ould Dermit q limitpd travel above qnd b~- low the position of etwtic lend during taxying at low qnd high velocity.
Although the above considerations refer particu- 3.
“Iarly to the landing <ear (so called), they apply to a 11 shock-absorbing s~stem” which term was meant in general - to include also the part referring to the tail wheel.
Since the behavior of both (units) is entirely similar, however, we may limit our considerations to the ehock- absorbing eystem of the landing #ear (main wheels), In which the greatest stre~ges occur ~nd which, in a particularly important case - namely, that of n two-wheel landing - takee all the load.
.
Let us therefore consider this landing condition and assume that outside of the shock-absorbing system, the other parts of the airplane have no elasticity. This ~S- sumptlon ie equivalent to the statement that all the points of the airplane undergo the same acceleration In landing.
.
.... . . -— . .. . . - ----- --—.-—.——— - - -
T I
N.A.C..A. Teehnioal Memorandum Ho. 9~8 Actually, with Increasing distance away from the landing gear, the acceleration qz%dually deerea~es due-to the work of deformation of the Interposed structures, but this de- AcoordinS to come Amer- crease is .sbsolutely negligible.
ican investigations, the elastio work of deformation may be considered to vary from 0.0115 to 0.q2Z0 kg m for each kilogram of the structure, and this corresponds to a tauf- flciently small pereent of the ener~y to be absorbed that it is not” worth while to consider it.
4. From the theoretical point of view the damping syetem is studied, in general, by neglecting the elastio- i.ty of the wheel (fig. 2), assuming all the mass m oon- oentrate& at the center of gravity and possessing the ver- tiaal voloclty V. aP*; and apparent woiqht assumln%, .
moreover, that the reaotion of the shook absorber is given . .
by. t-he simple expression cs + Kv R= (1) Kv Is a dissi- .
where cs is the elastle reaction, and pative term proportional to tho velocity.
From the above assumptions there mm easlly”be de- rived the equation of motion, considering the equilibrium “between the applied forces and the foroes of inertia.
This study, however, would not present any %reat praotloal interest because the eonolusions arrived at by this math- em”atioal treatment are considerably modified because of thb fact that the dissipative term is taken proportional to the velocity instead of the square of the velocity as .
it normally aotual17 is, and because other elements are de~leoted (friotion, etc-), vlscoslty of the damping liquid, an~ particularly, because the shook absorber operates . .
jointly with the tires.
It may merely be pointed out that, according to whet%- er the damping is large or small, there is obtained ~ ape- riodic motion or an oscillatory damped motion, and-that in the case in which the coefficient m is equal to zero, the motion is the same as that of.a horizontally oscillat- ing mass whose damping is proportional-to the velocity.
In the ca,se of strong &-mmping there are obtained curves of tho type ofm those of f~qure 3, which show qualitatively -- .— ——-—--——- .——.—-—.— *The a.oparent wei.~ht @ is the difference between the weight P = mq and the lift (a. = 1 for low voloaity, zero aerodynnmio foroes; CL = O at the velocity of take- off).
.
19. A. C.A. Technical Memorandum No. 938 the variation of the force R“” as a function of the dis- placement sad>.the ~lqem. - ..,- . . . : . - . “.
5, The problem becomes considerably more complicated If the shock qbsor%er 3s .consldered as consisting bf two distinct elastic systems operating simultaneously - an as- sumption which corresponds to the actual conditions since the wheel tires must be considered in addition to the shock absorber: In this case, illustrated by the sketch of figure 4, calling RI the reactton of the wheel, and Ra the corresponding force on the shock absorber,. we have: R= =aR1 where a Is a coefficient which depends on the-geotietric characteristics of the landing gear under consideration.
The value of a may be constant or variable for the diff- erent positions assumed b~ the landing-gear struts during deformation. In this case, since the variations are al- ways rather small, a mean constant value may be asnumed for a. Making, in addition, the simplifying assumptions: Ra = Ca Sa + Rva the mathematical treatment leade to differential equations (reference 2) which are much more complicated than those obtained for the case of the shock absorber alone, re- ferred to above.
These equations, on account of false ass- umptions made in deriving them, cannot correspond to the actual conditions.” Oq account of the uncertainties of the mathematical procedure, we shall leave the theory aside and consider instead the practical problem that presents itself to the designer, namely, what displacement is necessary in order that the stresses on the structure should not exceed safe values. The regulations prevailing in various countries prescribe in general that thb shock-absorbing system should he capable of absorbing the kinetic energy due to a cer- tain vertical landing velocity PO, or that due to a drop of the airplane from a certain heiqht without any forces arising on the structure that exceed n times the weight.
Although, instead of the veloc~ty PO, the corresponding H = Voa/2g drop height may be used interchangeably, we shall refer to thb drop velocity PO”.
I
6 N.A.C. A. Technical Memo.randum. Ho.. 938 We many observe here that the initially presc$ribad load faator n permits the computation of the structure on the basis of a simple study of the landing gear as a whdle before any special- study of the shock absorber is “It is nbc.- carried out, whioh may be done subsequently essary, however, even for a preliminary study, to know the stroke of the shock absorber. in order to. define the extreme positions assumed by the wheels and by the land-” Inq-qear struts In take-off and in landing.. These Posi- tions must be oonsidaied both for strength calculations “and for the determination of the minimum distance of the propeller blades from the ground durtnq taxying - whioh distanoe must not be below a oertain value.
The advantage of reducing the travel of the shock absorber to a minimum is evident not only for weight econ- omy but alm in certain types of landing gear for prevent- ing the wheels from assuming too great a deviation between the positions ot maximum and %ero deformations.
Having, by some method, chosen a ~alue of the” ooeffl- cient n that should not disagree with that prescribed by the regulations, it 1S necessary that the travel be de- termined so as to guarantee that under the most unfavor- able landing conditions, this value is not exceeded?
Let us now consider the airplane in landing. we as- sume that we have already carried out the preliminary in- vestigation of the landing gear sketched in figure 5: Makinq use of the previously given notation, we indicate by El the force on the wheel, by Ra that on the chock absorber, and by aP the apparent weight of the airplane at the Instant of landing, which weight may be considered constant for the brief period of the landing shockP The following relations may be written: Ea.= a Rx (force on the shock absorber is a times that on the wheel) * aas -Rl+.c@.
O (equilibrium between applied forces ~s and force of inertia); from these we have: Considering a time dt in which the center of gravi- ty i? lowered by ds while the tire is deformed by as= and the chock abeorbpr.by we have< dsa, l?. A..C.A.. Technical Memorandum .Ho. 938 ~vd~+apdm Ezdsz+R8dsa=-Mdt ..-. ,~- ., .-.
.’ and since ds = v dt : [ +aPds E1dsl+Radsa=-Md ~a
r)
After the time t required for the vertical velocity to be reduced to zero (ths center of gravity will be low- and ered by the amount s = h, the tire deformed by s>, the shock absorber by Sa). we have: (1)
h’s.+.f’ads~’~+aph
a relation which states that the shock absorhor should ab- sorb an amount of energy corresponding to the sum of the kinetic energies possessed by the airplane due to the ver- tical component of the velocity and the potential enerqy due to the displacement h of the center of gravity of the airplane after contact with the %round.
and We assume now that we know the curves Rx = f(sl) Ra = obtained simultaneously (fig. 6). In order 9(s2) that the forces on the structure should not exceed n times the weight, should be equal the maximum value of RI anP.
to nP, and hence the maximum of Ra should be Denotinq by Kz and Ka the ratios relation (1) becomes”: p Voa +aPh (la) KzSznP+aKa SanP =~~ from which, dividlnq by P and remembering that the total displacement h of the center of gravity is = S1 + a Sa h 8 I?. A. C.. A. Technical Memorandum IJo. 938 there is obtained “ To a nKISz+an KaSa= ~ +ah Hence , knowing-the deformation S1 of the tire at the co- efficient n, the shock absorber travel is gi~en by Sa = (2) If, the corresponding instead of the velocit? PO, drop height is considered, H = Voa /2<, there is obtained H- Si (n Kr - a) —--.— Sa = (2a) a (n K8 - a) This relation, in the case in which the shock absorber alone Is considered to operate, may be written: H Sa =h=—— (%b) a n Ka- CL .
which is “the formuln u5u?.llY given for the shock-absorber travel and is seen to be Independent of the weight of the airplane .
7. Let us consider what are the possible values that may be assumed by the coefficierlts K1 and Ka of for- mula (2).
As.regards the tire, although there are not many data on which to base a judgment, it may be assumed on the basis of recent tests (reference 3) that the defor- mations and the loads are connected by a relation of the .
type (3) ‘A~ml(m>l) If. instead of static loads, dynamic loads are considered - whioh, for example, are ohtalned by measuring the forces due to the accelerations determined from the drop of mass- es resting on the tire - similar ”diagrams are obtained, except for qreater curvature, in the sense that the tire behaves for low dynamic loads as If it were less rigid, and for the other dynamic loade as if 1$ were more rigid :.
.——--— ---- .- — -. . _ .-. -- ..-— --- —- -.. - . . ..- . . . - . . .
N. A. C.A. Tech~lcal Memorandum ”l!fd. 938 than if static loads “were hpplledl “ The relatiofi (3) is .- stlll .valld,.but the exponent m inoreaaoe to an appreoi- ---- .
r..-. . .. ~. - * . . ,., , ., able extent.
8.50 X Figure 7.
obtained with a low-pressure tire 10 (640 x 20$~ for two different tire pressures, E!lors clearly - In addition to what we.have said - that the di- vergence between static nnd dynnmi~ lends is more marked the less the inflation pressure of the tire.
On examining some tire depression curves obtained for with dynamio loads., it Is found that the value of Kl the usual pressures mnd.deform~tions permitted in practice, fluctuates between 0.32 nnd 0.35 for .1ow- and medium- pressure tires, and between 0.40 and 0.43 for high-pressure tires. In any case, since the dynamic behavior is marked- ly different from the static-behavior, It Is necessary to carry out a systematic series of dynamic compression tests on tires of uniform size, so that it may be possible to deduce , with sufficient approximation, the values of the exponent m, Kz required and hence, of the coefficient for the determination of the energy effectively absorbed by the tires.
As regards the coefficient KS, it ne.turally varieO greatl~ from one type to another. While it has a value approxlmmtely equal to 0.5 in the case”in which the shock absorber consists simply of a spring without initial ten- sion (a very rare case, of course), it has a value betreen 0.80 nnd !3.85 for the oleopneumatic and oleoelastic typee that have received much study.
Theoretically, n value of Ka might.be obtained eqwl to 1, but on account of the large number of not ensily determinable factors that enter into the phenomenon (drop height, velocity of deformation, vlecoslty of the llquld, etc.), it is best not to assume for the shock absorber - ~t least, for the preliminary study - n value exceeding 0.85~ We may observe that while it ie wise to aseume rather low values for the coefficients KI and K8, it Is of no advantage if they be too con- servative, In the ease in which the chock-absorber stroke has been computed on the baeis of too lore.values of K1 and K8, the work that the deformabl~ system cnn perform ie qreater than the work necessary to reduce the” vertical velocit~ to zero, and therefore either the shock absorber does not reach the end of its stroke or, having reached it, determines forces on the structure that are lese than those for which they have been designed.
In either case, the utilization of the shock absorber iEI not logically the best.” - .
10 H.4.C.A. Teohnioal Memorandum No. 938 Naturally, the opposite occurs and with consequences that may be very serious if the values of K are chosen too high (i.e., if travel IS insufficient). . In this case, even in landings that do not correspond to the maximum velocity assumed for the computation, stresses may he pro- duced greater than any provided for, and these may cause failure of some pnrt of the landing gear or fuselage.
The appreciable difference between the energy-absorp- tion characteristics of the tire and shock absorber shows that for equal total trnvel h of the center of gravity, the amount of energy absorbed is greater, the greater the shock-absorber travel in comparison with that of the tire.
8. In this connection’; the fact should be brought out that , according to the regulations at present in force, it would not be possible to assign the shock-absorbing func- tion to the tires alone, even when restricted to the low- pressure type, without introducing inadmissible landing loads.
In the case of the tires alone, equation (la) lecomes P vo~ Kx S2 n P =- —+(ZPS %2 the corre- and dividing by P, substituting for T0812% sponding height H, and remembering that for the drop test a= 1: nKS =H+S H ——— = s .nK-l Even assuming that tires are available that can de- flect by an amount s~ = 0.75 H*, by taking for Kl a value of 0.35, there is obtained H 0.75 H = ———— n x 0.35 - 1 from which n = 6.7! Aside from the prescribed regulations, moreover, it is not logical to expect qood results from a shock absorber that has such a low work characteristic and which therefore can be emploFed only for very low vertical velocities.
—— -— —-— ————— ------- . .-—— *The minimum value for H, permitted by the R.I..N.A. , is 30 centimeters.
-..
—.. - .- .
H. A. C.A. Technical Memorandum No. 938 9. Let us consider a typical example of shook ab- sorber, oonaisting. ofv,a .sprinq without initial tension vhi ch , .on campressinq, “foroeg-’th& o-il’”66ntatned in-the chamber A to flow through a constant orifice, and let us neglect for the moment, consideration of the tire (fig. 8).
Relation (1) in this case may be written: a m To +uPh= Rd.s r ‘-.
where R, neqleotlnq the friction, may be expressed by the relation In the above formula the first term represents the the work performed by the spring of elastic constant c1 s second is the dissi~ative term, v being the resistance coefficient of the liquid flow through the orifice. We assume that R may be considered constant during the en- ttre stroke h and equal to the maximum allowable value Since the force is constant, the acceleration is anP.
also constant, so that the velocity varies linearly from To to zero. We thus have the relations: v= Vo”a t
s = V. t -+ “
.
>-v from which, eliminating the time t = ~, there is readily obtained .
Voa ~a .
-2as The above equation states that Va variee linearly with Voa the deformation s, from the maximum value to zero.
The variation of Va with S is Indicated in figure 8.
Since the values of the elastic reaction increase at the same time from O to the final value anP, it is suf- ficient that w Voa =clh =a”nP .— .- 12 N. A. C.A. Technical Memorandum Ho. .938 in order that the resultant E remain constant during the stroke. In this case, therefore, the above-defined coeffi- cient Ka woula come out e ual to”l and” the. shock-absorber stroke giyen lIy formula (2b Y would be the minimum, namely~ h-= *= (4) In a manner analogous to this simple case, it may readily be seen that by suitably varying the size of the orifice of the escaping oil, there may theoretically be obtained a constant internal force also for other types of Such a shock absorber, as oleoelastic and oleopneumatlc.
condition can practically be obtained by making the oil flow through an annular opening determined by a hollow cYl- inder, in which Is situated a calibrated rod or piston of suitably varying cross section so that at each instant uVa=anP-f(s) where f(s) is the reaction of the elastic part of the apparatus.
The conditions are entirely different when the tires are also taken into account.
In this case “the reaction of the shock absorber cannot be constant during the entire duration of the landing becauae at each instant we must have Ra = a Rl, and RI naturally varies from zero to the final load nP. Only in the case in which the load is above that for which the tire is completely compressed does the shock-absorbing system function as if the tire were absent: hence, for the stroke in which the shock ab- sorber acts alone, it can operate with constant internal force.
We may point out, in order to complete our observa- tions on the operation of the shock absorber, that In the case in which the latter has an initial load Rao during the first Interval of the shock, there occurs only the de- formation of the tire until the load lla~a is RIO= reached, after which the two systems work simultaneously.
In any case, It appears evident that when the shock ab- “sorber and tire operate together, the coefficient K can never attain the value 1, which is possible with the shock absorber working alone?
10. A fact that should be particularly brought out is H. A. C.A. Teohnioal Memorandum, No, 938 that the addition of the tire, .by producinq variations in rn-ay have con- t“he’velocity ‘In the ‘dieel-pati.veterm .p V,a, siderable effeot on the behavior of the two acting to- gether. For this reason, the teets which are usually car- ried out on the shook absorber alone, should he oarried If the out instead on the tire shock-absorhirg system.
shook absorber is mounted on the landing gear In such a manner that the foroe on it is equal to that acting on the wheel (landing gear with forked shock a“bsorber, for exam- ple), the tests do not require any particular attention.
In the case, however, that the value of a in the rela- tion Ra = a El is different from 1, It is necessary to bear” in mind the following considerations.
.
The subscript p will refer to the test conditions.
For the set-up indicated in flqure 10, we have for equilibrium: daSp - Rz+ aP = O ‘P –~p while for the actual conditions, we have : Since R1 = Ra/a, we obtain, by keepinq the value of Ra the same in the two cases: M= (s”R+ a g) a Ra —.
‘P = S~+ag . .
from which a (S1l + a=g) <5) =M -p ‘P +ag “Moreover, for-the qctual case, we have: .: .
Sl + a Sa (6) while for the test, . .. --— .
lT.AiU.A. Technical Memorandum Ho. 938 (7)
‘R “= ‘1P + ‘s
Setting S1 %p = -&- which can be obtained with sufficient approximation by varying the tire pressure, there is obtained: With the aid of (5) and (7), we also have: Equation (5) then becomes: In the case where a is sufficiently small to be neglect- ed, we have : a =Ma ‘P that is, the test can be carried out by employing a mass = aa M. In this case, teat since the velocity of the MP and the true velocity are connected by the relation s!
=as~ P It is necessary to consider for the drop test, Instead of the velocity PO, a vilocity V. la; or, instead of the drop H, a drop H/aa .
11. From the preceding considerations, an apparently curious fact is derived which we shall illustrate by a nu- merical example: To fix our ideas, assume we have an air- plane of 1,800 kilograms, provided with wheels having tires 8.50 x 10 (640 x 105 mm) inflated to 1.75 kg/cma, for which the regulations fix a maximum load factor of n = 3 for a drop of 40 cm.
The maximum permiselble load on a wheel is 900 x 3 = 2,700 kg, to which corresponds a static .
.- .
I?. A. C.A. !Cechnlcal Memo&ndum Ha. 938 deformation of. 138 mm and a dynamic deformation of 128. mm, “‘a’fid--a ‘co”effi-c~ent-‘Kl.=-0.33..
Not oon?ide-ring.,the ooq- tributlon of the tirei and assumlri$ the shock-a~aor%br force to be ~onst~nt, for whloh Ka = 1; and aesuming fur- ther, for” slmpl.ioity, *ha% the coefficient a of the land- ing gear is equal to 1 (that is, that there ex~sts the same load on the wheel as on the shookmnbsorber), the “stroke re- quired in order.not to exceed th~”.faoto~ n = 3 from equa- tion (4), in which .a = 1, ‘ sincd.the effect of the lift is not oonsldered in’ the test, is H = 40 “ = -— s = 20 om” an-1 3-1 The shock absorber can therefore dissipate an amount of work L = 3 x 9“00 x.20 = 54,000 kg cm ,. .
corresponding to the energy” due t.o the drop of 990 kg from a height of 40 cm, and of the work due to the travel of 20 cm permitted @y the shock=ebsorber stroke, and is therefore suitable for the required drop test.
We now coneider the tires al SO to be taken into ac- count .
Aseuminq for the moment that the shock abeorber, even when working with the tire, still operates with the coefficient Ka = 1, and that it is permlttod to attain, as before, a value of n = 3, tho travel of.the shock nbsor”oer from (2,%), In which CL equal 1, is found and m to be (nK, - 1) = 40 - 12.8 (3x0.33 - 1) = PO ~m sa=H-sl ———..
nKa - 1 3X1-1 that is, prnctlc.nlly the same as before. “ Since, however, the value of KS cannot be equal to unity, the stroke of 20 cm, which was sufficient with the tire not mounted, becomes insufflclent,. .
TIIis means thnt tho tire, in addi- “. tion to impairiug the operating conditions of the shock nbaor-oer, is not sufficient to nbsorb the energy due to the greater travel “it permite the center of gravity cf the airplnne.
In the case considered, for example, the defor- mation of 12.8 cm corresponds to mn amount of work L“ = 990 X 12.8 = 11,520 kq”cm ——— . ..—. — .. .. .. .. .—. - ..
16 I?. A. O,A. Technlcml Memorandum Ho. 938 # while the energy absorbed by the tire is . .
= K1. nPs = 0.~3 x 3 x 900 x 12.8 = 11.480 kg cm The 40-centimeter drop test with the addition qf the tire would therefore give rise to accelerations greater than those obtainable with the shock absorber alone.
12. On the basis of the. besults obtained in the above example, it might be concluded that a landing on wheels without tires should be more gentle, or at least, less ab- rupt, for equal vertical velocity, than a landing on wheels provided with tires. Evidently there is some fun- damental divergence between the conditions of the tests conducted according to present-day procedure and the true conditions.
As a matter of fact, it is the aerodynamic forces, which are not taken into account in the tests, that ac- count for the above divergent results.
The value of the coefficient a in formula (2), in other words, is not to be considered equal to 1 as is usually assumed, but should be correctly evaluated and taken into account in carrying out the tests.
Acoount must thus be taken of the fact that on landing of a mass m the with velocity Vo, weiqht Is not P but only a fraotion - normally small - of P, and hence that the work which the shock-absorbing system must perform is that defined by the second member of (1)s L= ++aPn and not
‘<+ph
Li=-2 The difference is riot at all negligible, especially for long-travel shock absorbers.
The value of a may be com- puted from the formula ~=—- (8) l+r$ where ~ is a coefficient defined by Verduzlo (reference 4) as the IIlanding charaoteristlcH . ..— . . . — N. A.~. A. Tech&ieal Memorandum .l?q.. ,93.8 B being the lift -draq ratio of $he a~rplane in the land- ,--- -.~ng htt~tute-, . .
‘Vo- --the mlnlmum -tauppor.ti.pg vgloc-i-ty near the ground, Rnd V. the yertionl velocity of deaoent.
~OF the.usual values of p as appenrk~from figure 11, ...
vnr- which ~ives the plot of: equatl~h (8).,” the value of a Ies from 0.2 to 0.3.
. .
ConsMerln* in our numericnl exe.mple a mean value “ a= 0.25, . it is seen that a travel of 20 em permitted by the stroke of the shook a~sorber, and 12.8 om.permitted by.the compression of the tire, corresponds effectively to a “total amount of work 0.25 x 900 x 32.8 = 7;380 kg C% ‘equal to 20.5 percent of:the kinstlc energy possessed by th~ airplane In landing, instead of .
. .
.+ 900 x 32.8 = 29,52b kq om .
,..
equal to 82 percent of the total kinetia enerqy in a drop test where the lift iS not ta~gn into account..
When it is ~onsidered that the work of deformation of the tire is about 11,500 kg cm, It will be understood that the addition of the tire to the shock absorber im- proves appreciably the lmnding ~haracterietics instead of impairing them as would occur In a drop test carried out accordinq to the criteria actu~lly prevailing.
The method of conducting the drop test, if the latter is to represent effectively ~ possible l~nd~nq condition, must therefore be such that only the weight aP perform~ work. There might therefore be used a set-up such as that shown In figure 12, or a similar one.
Ws may noint out, finally, that Instead of the drop height, it WOUld bg more suitabls in the regulations to oonsidar the equivalent vertical velocity Vot and in de- termining the values to be Imposed In computing the land- inq gear, to take account of the elements that influence this velocity, particularly the wing ~~ading, and the pres- ence of hl%h lift devices.
Translation by S. Reiss, National Advisory Committee for Aeronautics.
.—-—- — —— . ..
.“. . “ 18 N. A. C.A. Techritcal Memorandum No”. 93”8.
RIC1’ERE19cEs 1, Panetti, Mti: Atterramen%o con ipersostentatori.
LIAerotecnlca, vol. 15, no. 5, May 1935, p. 483.
2, Michael, Franz: Theoretische und experimentelle ~rundlagen fir die Unterguchung und Entwickelung von Flugzeug - Federunqen.
Luftfahrtforschung, vol. 14, no. 8, August 20, 1937, p. 387.
3. Avlano : Sollecitazioni dlnamiche negli orqani de- forhahili, del carrello dlatterramento degli aeroplani .
Convegno di Aerotecnica, Milano, 1937. .
4, Verduzio, Rudolfo: Sulla determlnazione delle car- atteristiche elastiche del congegno di atterra- mento degli aeroplani. LIAerotecnica, vol. 13, no. 3, March 1933, p. 163.
l . .
N.A.C.A. Technical Memorandum No. Y38 l’igs,l,2,3,4,5,6 ctP v
I
TmmJ+m4m..-
A B R
‘t
Fi~gure 1.
Figure 2.
s,R - -~~ R ,/ \ s K ‘\ ‘ ..;?.
Iq .- lt ~ r,e3.
Figure 4.
,-- / S2 ‘1 Figure 6.
Figure 5.
,, , ..-.
N.A.C.A. Technical Memorandum No. Y3B . .
.
.. ,1 . , .
,-.
3% ,.-.
.. ---- .....
25(w R 20!X 15JC 100L 50( 0.6 I —- —.
+ 0.4 \ —- .— d 0.2 c1 40 60 80 p 100 Figure 11.
N.A.C.A. Technical Memorandum NO. 938 Figs.8,10,12 ,, =,.. ,,- .
.,.. –.. ,.- ‘., – . . . . .
.. . .
i
.-
.-
—
,, v t
a I
R2 =Rl ‘R2=-1 I s = S1+S2
&
I S =S1 + aS2
m tR Figure 10.
Figure 8.
Figure 12.