NASA NACA-TN-4332-1958 An approach to the problem of estimating severe and repeated gust loads for missile operations《估计导弹运行的严峻和反复骤风荷载的方法》.pdf

1、J /;!ij:l!i-.NACA TN 4332 .?where, as indicated earlier (eq. (9),V i I- and10560N o 1D 20for the airplanes used in the gust measurements.approximation2 2A “2-_e?_,.Cc). _u_o/_._fO _(aW) e do“w = P1 eThe solution of equation (15) is given byThus, to thiswhere15-Ude/5-3k 2+ P2e (zs)bl = 2.2 C_-kIA(z6)

2、b 2 = 5.3 C_k2_A1 e- w2/2bl 2_ 2 (_) : _ I_ _ . _2/2_22Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-16 ? N_CA TN 4332The determination of the values of bI and b2 thus depends upon _-iwhich is the ratio of the acceleration response to unit discrete

3、 gustsof the standard fom (cosine shape) and the root-mean-square accelerationresponse to a random gust input _w = i. This ratio must be establishedfor the airplane involved in the gust-data collection program.For the single-degree-of-freedom case, vertical motion only (whichappears adequate for pre

4、sent purposes as indicated in ref. 2)_i = pVSm s)2W (z7)I-_- is a gust-response factor depending on K, thewhere the term _airplane mass ratio, and on s, the ratio of wing chord to scale of tur-bulence L. (See refs. 2 and i0.) Thus, from equations (12) and (17),(18)For present purposes, this ratio wa

5、s evaluated on the basis of a char-acteristic transport configuration as given in table V of reference 2in order to determine values of bI and of the Northrop P-61C airplane(the airplane actually used in the Thunderstorm Project gust survey) forthe determination of b 2. The same form of gust power s

6、pectrum as thatin reference 2 was used as well as a value of the scale of turbulence Lof 1,000 feet. The ratio - varies with altitude and the actual valuesXobtained are given in table I. The values of b I and b2 for the var-ious altitude brackets are also given in the table. The associatedprobabilit

7、y density and cumulative probability distributions f (_w) and(_w) for the various altitude brackets are given in figure 7. The dis-tributions of _w forthe nonstorm turbulence _l(qw) and _l(ew) andthe storm turbulence f2 (_w) and _2 (Cw) are also given separately infigure 8 for each of the altitude b

8、rackets.iIProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-3G NACA TN 4332 17APPLICATION TO GUST-LOAD CALCULATIONSIn the preceding section_ a simplified description of the turbulenceat the various altitudes was derived in terms of the probability dens

9、itydistributions of the root-mean-square gust velocity. This distributionis given by-%2/2b12I !in which the parameters PI and P2 represent the proportion of flighttime (or distance) in nonstorm and storm turbulence, respectively, andbI and b 2 represent scale-parameter values for the individual prob

10、-ability distributions of Cw for the two types of turbulence. Thevalues of PI_ P2, bl_ and b2 varied with altitude. In this section_the foregoing specification of the turbulence environment is applied tothe problems of missile gust-load-history calculations.Estimation of Severe Gust LoadsAs indicate

11、d in equation (3), the gust response history for a givenairplane under given conditions, exposed to a gust history consisting ofa series of locally stationary Gaussian processes of common spectral form(as, for example, defined by eq. (19), may in general be expressed as= o/o (2o)whereY responsequant

12、ity of concern (load_ bending moment, stress_and so forth)S o number of response peaks per mile of flight in rough airfor the specified spectral form of the gust input and_ asindicated in reference 2, need not be restricted to single-degree-of-freedom systemsProvided by IHSNot for ResaleNo reproduct

13、ion or networking permitted without license from IHS-,-,-18Substituting equation (19) into equation (20) and integrating yields-Y/bl -y/b#a(y)= Plooe + P20oe (21)The res_Its given by equation (21) may be viewed as a description ofthe statistics of the peak values of y and represent averages forexten

14、ded operations under the specified conditions. As such 3 they donot apply directly to a single missile flight but must be viewed as theoverall response histories of a large number of missiles for the specifiedconditions.Equation (21) must be applied separately to each significant segmentof the fligh

15、t plan since the turbulence parsmeters PI_ P2_ bl_ and b2vary with altitude and the missile parameters Go and _ may also beexpected to vary widely with the flight segment. If several flight seg-ments are significant, either the overall load history G(y) must bedetermined as a weighted average (weigh

16、ted, perhaps best, by the flightdistances in each segment) or the load histories for individual flightsegments must be considered separately. In many practical cases_ oneor two flight segments only are gust critical. This condition simplifiesmatters appreciably and is considered in a subsequent sect

17、ion.If the load history, as specified by equation (21), is exsmined,it is clear that a small but finite probability of exceeding large valuesof y exists no matter what values of y are chosen. In any case_ itis therefore impossible ta select a value which will never be exceeded.Instead_ it is necessa

18、ry to accept some tolerable risk level or somefinite probability of exceeding a chosen value. The actual probabilityvalue chosen would presumably depend upon the particular missile_ theconsequences of a structural failure_ and economic and military tacticalconsiderations. The question of the choice

19、of the probability value isbeyond the scope of this paper_ and consideration herein is restrictedto the problem of determining the load value once the probability ofexceedance is chosen.Consider the case of a single missile flight involving a flightdistance Dr . This flight may be viewed as yielding

20、 a sample of therandom process y(t) of distance Dr . The random process y(t) hasan average of one exceedance of a specified value YL in D(YL) flightmiles where1i,iI,Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-i . _ACA _ 4332 19and where G(y) spec

21、ifies the average load history of the missiles forextended flights. If it is assumed that the exceedances of YL are“ distributed at random, then the probability of exceeding YL in a givenflight distance Dr is approximately given byPe (ys) (23)provided that D(YL) Dr which is assumed to be the case of

22、 interest.(The assumption of random distributions of YL on y(t) does not applyin a strict sense to the random process y(t) as specified by the non-stationary input of equation (19). This assumption and the approximationof equation (23) are adequate for present purposes and are conservativeto the ext

23、ent that the cases of multiple values of YL separated by aflight distance less than Dr are excluded.)For given values of D r and Pex(YL) equations (22) and (23)specify the value of G(YL)“ The result of the load calculation givenby equation (21) may then be used to determine the required value of YLt

24、o achieve the desired Pex(YL). If several flight segments are beingevaluated separately; the value of YL may be determined in such a man-ner that the desired exceedance rate Pex(YL) is given by1IP _ is the exceedance probability for the individualwhere ex(YL iflight segments .and the probabilities i

25、n the various segments areassumed independent.A Simple Formula for Estimating Severe Gust LoadsIn many cases of interest only a portion of the flight path or asingle flight segment may be gust critical. If only a single flightsegment is gust critical_ it appears possible to derive a relativelysimple

26、 formula for YL in terms of a few significant quantities. For: :_ii !_! : : : i y _ :17 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-2O _CA _ 4332this purpose, it is of interest to examine the relative contributionsto G(y) of the two te_ns on the

27、right-hand side of equation (21). Let(Y)=_z(y)+a2(y) (2_)Gowhereal(y)-Pzea2(y)“P2eThe gust data presented earlier indicate that for the significant alti-tude bracketsPI _ 20P2 (26)b2 _ 3bIFor these conditions_ the relative contributions of the two te_s areschematically illustrated by the following s

28、ketch (a logarithmic scaleapplies to the ordinate):.i.01001.000iGoz ili il-IiProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4352 21As can be seen from the sketch_ the principal contribution to G(y)arises from GI(y) (the nonstorm-turbulence c

29、ontribution) at low valuesof Z_ and from G2(Y) (the storm-turbulence contribution) at high valuesAY- Which of these two cases is of concern would appear to depend_of _ .in large part_ on the particular m/ssile and the desired exceedancerate. It is believed that the region of high values of _- is of

30、prin-Acipal concern although, in some applications where operational consid-erations permit planning for the avoidance of storm turbulencej theGl(Y) case may alone be applicable.In either case, equation (21) yieldsYL = biA ge Pi + lge Go - lge _(YL=biA Pi+log ao+loge(i= 1,2) (27)Substituting for D(Y

31、L) from equation (23) into equations (27) yieldsYL = biA ge Pi + lge Go + lge Pe YL(28)which is a simple and useful result. Equation (28) specifies a valueof YL in terms of the following groups of parameters:(a) Gust input parameters bi and Pi(b) Missile response dynamics _ and GO(c) Operational par

32、ameter Dr(d) Desired exceedance rate PexFrom figure 4 and table Ij representative values of P and b forthe altitude brackets of 0 to 40_000 feet are for the nonstorm-turbulencecasePL= 0.06 bI = 3.5 i: !j : /: :Provided by IHSNot for ResaleNo reproduction or networking permitted without license from

33、IHS-,-,-22 NACA TN 4332and for the storm-turbulence caseP2 = 0.0025 b2 = i0.5Utilizing these values in equation (28) yields the following results:For the nonstorm-turbulence case,YL = 3.5A og e 0.06 + 10g e Go + log eYL = 3-5K(log e Go + El)(29)whereD rEl= loge Pex 2.81For the storm-turbulence case_

34、Dr_K_YL = 10.5_ o_ e 0.0025 + log e GO + log ePexOo+(30)whereD rE2 = loge 6.0PexThe values of E1 and E2 are shown in figure 9 for a range of valuesof Pex(YL) from 0.001 to 0.2 and for a range of values of Dr from I0to 5,000 miles. The charts of figure 9 can be used directly along withthe missile res

35、ponse parameters _ and Go to determine the load valuesin accordance with equations (29) and (30). The simple form of theseProvided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-NACA TN 4332?23results suggests that they could be used in preliminary design st

36、udiesand in the development of design specifications.In order to illustrate the applications of the foregoing results,an example is given. Consider a missile having a flight range in thelower atmosphere Dr of i00 miles and values for Go of i0 and forPex(YL) of 0.01. For this case, a value of E2 of 3

37、.2 is obtainedfrom figure 9(b). Using these values in equation (30) for the storm-turbulence case yieldsIt is of interest to note that doubling the rangeyieldsDr to 200 miles(31)YT,= 64Xor about a lO-percent increase in the value of YL“ (A lO-percentincrease is also obtained if Pex(YL) is reduced by

38、 one-half, that is,Pex(YL) = 0.005.)If the missile operations are restricted to the avoidance of stormareas and equation (29) for the nonstorm-turbulence case is consideredapplicable_ the value obtained for the initial example is as follows:YL = 30AIt is clear that a large reduction in the value of

39、YL (from 58_ to307) may be achieved by the avoidance of storm-turbulence areas. Thestructural penalty for all-weather missile operations thus appears large.Estimation of Repeated Gust LoadsThe problemof calculating the repeated loads and developing afatigue loading differs in a significant respect f

40、rom that of the limitlqad case. In the case of large loads, it is useful to consider the.overall his_ory of a fleet of missiles to insure that, on the average 3the critical load is exceeded with a given frequency. In the fatigueProvided by IHSNot for ResaleNo reproduction or networking permitted wit

41、hout license from IHS-,-,-24 NACA TN 4332case_ the fleet concept in this form cannot be used. Instead_ thecumulative load history of the individual missiles is of concern. Thedetermination of such cumulative load histories requires informationon the concurrent gust histories for the various flight s

42、egments of aparticular missile flight. No information of this type is available.In some practical cases_ significant simplifications my be feasible.One such possible simplification is considered herein.It is assumed that the missile gust history for the significantpart of the flight is statistically

43、 homogeneous and is specified bya given value of the root-mean-square gust velocity. This assumptionmay be expected to apply best to the case of missiles of short flightduration and appears, in general_ to be conservative. On this basis_the cumulative load history for a given missile may be obtained

44、 from thefollowing equation:t(y)= Di i(y) (32)whereGt(Y) expected number of response peaks exceeding given values of yDiGi(y)flight distance in ith flight segmentresponse history in ith segment which is obtained from=This procedure assumes that the root-mean-square gust velocity is con-Stant but tha

45、t G o and _ vary with flight segment. (It also assumesthat the flight distance is sufficiently_long to insure that the loadhistory is close to the expected value Gt(Y).) For a given missileoperation_ the losd history (and thus the fatigue damage) from equa-tion (32) depends only upon ow“ The distrib

46、ution of the load historiesfor a series of missiles_ in t_rn_ depends upon the probability distri-bution of ow. Thus_ the specification of a value of Ow which isexceeded with a given desired probability implies that the associatedload history, as given by equation (3_), is likewise exceeded with thi

47、ssame probability. For example_ for a probability level of 0.001_ fig-ure 7(b) indicates that the value of _w exceeded with this probabilityvaries between 6 and ii for the various altitude brackets (ignoring thelowest altitude level). The conservative choice of a value for ow ofProvided by IHSNot fo

48、r ResaleNo reproduction or networking permitted without license from IHS-,-,-NACATN 4332 ? 25ii feet per second for calculations of repeated loads in equation (32)would thus yield a load history which would be exceeded with a proba-bility of less than 0.001.COMMENTSONAPPLICATIONSANDLIMITATIONSThe applications of the results obtained in the previous sectionto load calculations pose a number of problems. The a_plications, ingeneral, require the determination of the quantities A, Go, Dr,and Pex“ The choice of values for the last quantity Pex depends up