;.-'L-iM i^ NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED Koyember 19^44 as Advance Eestricted Eeport IAI21 FEEQUEMCY OF 0CCURKE2JCE OF AIMOSPBERIC GUSTS AND OF EELATED LOADS ON AIRPLME STRUCTURES By Richard V . Rhode and Philip Donely Langley Memorial Aeronautical Lc'^oratory Langley Field, Va. I I- "424- UNIVERSITY OF FLORIDA DOCUMENTS DEPARTMENT 120 MARSTON SCIENCE LIBRARY RO. BOX 11 7011 GAINESVILLE, FL 32611-7011 USA NACA WASHINGTON NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were pre- viously held under a security status but are now unclassified. Some of these reports were not tech- nically edited. All have been reproduced without change in order to expedite general distribution. * L - 121 Digitized by tine Internet Archive in 2011 witln funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/frequencyofoccurOOIang l^^^/s'l ?fy i^crr^ r*s^ NIC A ARR No. 1)4X21 NATIONAL ADVISORY GOMYITTES '^OR AERONAUTICS ' ADVANCE RESTRICTED REPORT PREQITliNCY CP OCCURRENCE Or^ ATMOSPHERIC GUSTS AND OP RELATED LOADS OH AIRPLANE STRUCTURES By Richard V. Rhode and Philip Donely STO1MARY A number of samples of flight acceleration data taken hy the National Advisory Ccirimittee for Aeronautics under a variety of operating conditions were evaluated to determine the total frequencies and the frequency dls- tribittion of atmospheric ^usts. The sa'nples include ljl\B hours of operation by several airplanes of the domestic airlines of tbe United States, a f.'artin M-IJO air- plane of the Pacific Division of Pan American Airways System, and the Boeing B-I5 airrslane of the Army Air Forces. These data are svipplemented by V-G records, so that more than 9»000»000 miles of operation are represented. Samples taken on an Aerf^nca C-2 airplane at lovi? altitude in the turbulent air of the earth's boundary layer are compared with similar samples ta''cen on the Lockheed XC-35 airplane at high altitude withjn cumulus-congestus and cumulo- nimbus clouds. Similar data of German origin have been reanalyzed and included for comparison. It WHS concluded that the distribution of gusts within turbulent regions of the earth's atmosphere follows a substantially fixed pattern regardless of the source of the turbulence. The total frequencies are therefore governed by the total length of flight path in rough air, and operating conditions determine the total frequencies only by affecting the ratio of the length of flight path in rough air to total length of the path. Gust-load frequencies were foui'ad to be inversely'- proportional to airplane size. It v;as further concluded that the gust frequencies can be applied with small error to- the estimation of stress frequencies in the primary structures of airplanes. The results of the analysis are applicable to the fatigue NACA ARR No. Lli.121 testing of the primary strucUire of the airframe and to the estimation of the probability of encountering gusts of excessive intensity within any stated period of operation. INTRODUCTION The trend in airplane design tov/ard higher vtfing loading, higher soeed, ctnd larger size - and consequently toward higher mean stresses and greater severity of loads on the structure - has resulted in a growing ap-^reclation h-'T designers of the potential Importance of fatigue in the prlm^ary structure and of the necessity for designing on the hasis of fatigue strength for limited "life expectancy." Reference 1, for exarnple, displays a great deal of concern about the fatigue life of airplane structures , Life exnectancy is governed not only by fatigue but also by the ■probability of occurrence of single quasi- static loads of such high m.agnitude as might endanger the structure directly. This rjroblem has been made more acute by the overloading of airplanes due to wartime traffic demands. An obvious prerequisite for control of fatigue strength and for the determination of the probability of single large loads is flight data that show the frequency of occurrence of loads or stresses in the structure correlated with the many factors that Influence the frequencies. In the flight operations of transport- type airp].anss the principal source of structural loads and stresses is atmospheric turbulence, and most of the required flight data annli cable to transport airr^lanes may be obtained by measurements of the loads or stresses during cruising flight in rough air. Kaul (reference 2) and Fr-eise (reference J) have presented data on the wing-load histories experienced by a n-umber of airnlanes both under special test condi- tions in rough air and in some 600 hours of cruising flight on several branches of the Deutsche Lufthansa. Kaul obtained results b'' means of an accelerometer located near the center of gravity of the airplane and Freise, by means of a strain gage mounted on a chord member of a wing spar near the wing root. The results were expressed in references 2 and 5 i^ terms of applied wing load. NAGA ARR No. LL.I21 The UACA has from time to ti-fie collected data slnuMar to these presented by Kaal and Freise . These data include acceleration ineasureinents fron 1520 nours of the early operations of the domestic airlines of the United otates, 515 hours of miscellaneous cross-country flyinn- oy the Boeing B-lp airplane, a ll^-hour round- trip flight between Alaneda, Gslif.^and Hong Kong, China, by a Kartin M-IJO airplane of Pan American Airways Sj^stem, and two special gust investigations in the vicinity of Langlsy Field, Va. Data taken with the KACA V-G recorder (reference I4.) during some 8,300,000 miles of airline operations are also included to take into consideration the rare gusts of great intensity that are not normally encoLintered during the taking of samples of limited scope. In the precsent paper these data are analyzed and compared with the Germ.an data of references 2 and 5 to establish a broader basis for the determination of the frequency of loads resulting from atmospheric gusts. SYI;:B0L3 AIID i-I0IVl2ITCLATUI^ An acceleration Increment normal to chord of v/ing, g units vif weight of airplane S wing area a slope of lift curve p mass density of air at sea level 1/2 V0 ' equivalent airspeed U.. effective gu.st velocity K relative alleviation factor c* mean wing chord F total frequency, total nuinbor of occurrences of a phenomenon in a sample f frequency, number of occurrences of a phenomenon within a class interval ll NACA ARR No. iJ+IZl fj, relative frequency (f/p) ^g^^- average gust inter\'al, average distance along flight path in turbulent air between significant gusts L path of operation, total length of flight path for any considered scope of operation R path ratio, ratio of length of flight nath in turbulent a;ir to r-ath of operation The class interval Is the range between two values of a measured quantity within which measurements of like value are grouped (or classed) for the purpose of tabula- tion of frequencies . The class mark is the definitive value, or nid value, of a class. EPJTECTIin^ GUST VELOCITY AS BASIC ATTRIBUTE In most investigations of atmospheric turbulence conducted by the NACA, the acceleration response of airplanes to the gusts has been utilized in the measure- ment of atmospheric turbulence. Although much of the philosophy underlying the concepts involved in the use of acceleration response in the iiieasurement of turbulence has not been published, some basic considerations are discussed in references l\. to 6. These considerations lead to the relatively simi-nle concept of an "effective gust velocity," which has been selected as the basic attribute or independent variable to which the statistical analysis best ai^piies. The ef f'ective gust velocity is defined by the relation PoaKU_VcV23 An = — ^_ (1) The relative alleviation factor K allows for the velocity of the airplane normal to the flight oath caused t>y application of accelerstion during the finite time of action of the gust. The factor X is given as a function of the wing loading in figure 1. The derivation of this curve, which takes into consideration f-r.e lag in transient development of lift and the gust gradient, is attributable NACA ARR No. lLiI21 to the authors tub has not 'bssn published. The curve in figure 1 is -cart of the A^iierlcan design require:nent3 and has been published as figure 11(a) in reference 7« Although derived at a relatively early date when little information on gust gradients v/as available, the rela- tionship described by the curve has remained in excellent agreement with suDsequently obtained flight data and with advances in the theory of ujisteady lift. SGCPE 0? IIE^SI^EMSNTS Extent of Operations Domestic airlines .- Acceleration records for 1320 hours, or abo-.it ll^5»0G0 miles, of flight were obtained during the early da^s of transport orerations on the domestic airlines of the united States. The data were taken during routine scheduled operations over a neriod of about 2 years. The average operating altitude was atout LOOO feet above sea level. The airplanes on which the measurements were made included the following tyoes: Pord 5~AT, Fokker P-IO-A, Boeing IxO-E, and Boeing 80-A. The routes flov;n covered most sections of tJ'-e United States and represent all types of cli?nate and toncgraohy in this country. The data from these early domestic-airline operations are referred to subsequently as "sample 1." The charac- teristics of the airplanes and a sum-mary of the operating conditions for all the samples are given in tables I and II, respectively. A large number of acceleration records were obtained later on the domestic airlines. These records represent i|2,105 hours, or about 7>'-0C)»000 miles, of routine transport operations by Boeing B-2l|.7, Douglas DC-2, and Douglas DC-5 airplaiies on several airlines covering most sections of the United States. The data fro:Ti these later domestic operations are called samples 2, 3, s-^d l\. for the B-2i4.7, DC-2, and DC-3 airplanes, respectively. (See tables I and II.) Alam.eda to Hong Kong .- Records were taken with number of instr-oments during a round-trip flight in Jione 193ci from Alameda, Calif, to Kong Kong, China by a Martin M-I30 airnlane of Fan American Airways System. The average altitude vras atout 10,000 feet MCA ARR !To. rJ.}.l21 and the flying time \vas II5 hoiirs, oorre spending to 17,000 miles of flight. The data from this flight are called sample 5' Records of acceleration covering 12^232 hours, or about 1,520,000 miles, of routine operations with Martin M-I30 and Boeing B-31I4- airplanes are included in the analysis for the route from Alameda to Hon^ Kong. The data from these operations are called saraple o. Boeing P-I3 airplane .- Records of acceleration v/ere taken on the E-1'3 aTrplane during 315 hours, or about 14.8,000 miles, of miscellaneous flying including a number of cross-country flights over various sections of the United States and one round trip to the Panama Canal Zone. These flights were made betv/een November 1953 and June 19^0. Tre average altitude of the operations was aboijit ^QOO feet. The data are subsequently called sample 7« XC-33 airplane .- Tre Army Locldised XG-55 alrrlase was flown in the vTcinity of Langley Field, Ya . during an investigation of atmospheric turbulence in the sur;imers of I9I4-I and 1914-2. vleasurements of acceleration and airspeed were taken only during flight through rough air, mostly within cumulus-congestus and cumulo-nimbus clouds. The surveys were made at various altitudes up to 3li»000 feet. Only two samples from these surveys are included in the analysis. One of these samples (sample 8) v;as selected at random from the several sets of data; the other sample (sample 9) represents the roughe s t f li ght . Aeronca C-2 airplane .- An Aeronca C-2 airrlane was flown auring an investigation in 1957 of turbulence at very low altitudes in the earth's boundary layer. A sam.ple (sample 10) was selected at random from the complete data and is included here for anal^^sis. Apparatus and Limitations Domestic airlines (earlv. operations) .- In the early transport operations only acceleracion records were obtained. The records were made v/ith commercial vibra- tion recorders that had been rebuilt into accolerometers by the NACA. Thiese accelerometers recorded against time on a waxed-paper disk about I4. inches in diameter. The instruments were arranged to make one revolution of the NAG A ARR 'So. Llil21 y disk in several hours. The time scale was therefore cramped and only the moderate and the large values of acceleration could be counted. As the airspeed was not recorded, effective gust velocities were evaluated on the basis of the known cruising speeds of the airplanes. Although the slopes of the lift curves were known from available data, the wing loadings of the airplanes as flown vi'ere not usually known. Effective gust velocities were, therefore, evaluated on the basis of the assixmption that the airplanes were flown at normal gross weight. This assumption leads to somewhat conservative values, as the airplanes were usually flown at less than normal gross weight. Domestic airlines (re ce nt operations) .- In the more recent domestic transrort o'oe rations" both acceleration and airspeed were recorded by means of MACA V-G recorders, which are described in reference l\.. These instrujnents do not record against time; the accelerations are registered vertically on a small smoked-glass plate while the values of airspeed are recorded horizontally. The record is an envelope of the maximum, and mdnimaira values of accelera- tion against a scale of airspeed. The sm.all accelerations are illegible within the envelope and only the larger values of acceleration that project beyond the envelope of the small values can be counted. No assumrtion as to airspeed is required with the KAGA V-G recorder, as the instantaneous value of airspeed associated with any observed acceleration is given by the record. As in the case of the early transports, the wing loadings of the more recent transport airplanes as flown were not Imown exactly. It was determined, however, that a reasonable aDproximation of the average operation weight was 85 percent of the normal gross weight; this value was used in the evaluation of effective gust velocities. Alam eda to Hong K ong . - During the round- trip flight between Alameda and Eon^ Kong of the M-IJO, the airplane was equipped with an NAGA. V-G recorder, an NAGA recording accelerometer, an NAGA airspeed recorder, and several 8 MCA ARR No. 1)4.121 NACA scratch-roccrding strain gages. Both the accel- erometer and the airspeed recorder recorded the measiired quantities against time with a scale sufficiently open to permit detailed evaluation of the records. The strain gages also recorded against tliue, .but the riiotion was of an intermittent character so that all the strain peaks could not he counted. Only one strain gage operated satisfactorily throughout the flight. Many of the strain values could, hovifever, he correlated v/ith the accelera- t i on me a 3 ur eme n t s . During the flight an observer operated the instru- ments and a comclete log of time spent in rough air, . total time, airplane weight, and other pertinent detail was kept. The records therefore permit a complete and accurate evaluation of the frequencies of effective gust velocities. Except for the records taken on this round-trip flight, all records of acceleration and airspeed taken on the Alameda-Hong Kong route were made with NACA V-G recorders , B-l~; airplane .- The 3-15 airplane was equipred with an ITACA recording accelero-^eter and an NACA airspeed recorder having t'^e time scales sufficiently open to permit detailed evaluation of the records. A number of NACA and. L'VL t^-pe scratch- recording strain gages were installed on shear and chord members of a wing spar at two stations along the span. The DITL type gages recorded continiTOUsly against time, and a count of the strain peaks is rjossible although such a count has not been made. As in the case of the round-trip flight to Eong Kong by the ^^.-IJO airplane, the strain records are used herein only to show the relationship between a number of meas^ared strains and accelerations. During the flights of the 3-15 airplane, an observer operated the instruments and kept a ccmrlete log of time spent in rough air, total time, airplane weight, and other pertinent quantities. The records from these flights t'lerefore rermit a conrlete and accurate evaluation of the frequencies of effective gust velocities. XC-35 airr'lane .- The XC-55 airplane was equipped with an "iTAGA recording accelerom.eter and an NACA air- speed recorder set to give an open time scale. The records obtained are amenable to detailed evaluation. The NAG A ARR ;-'o. l1xI21 CDeratlng weights for all flights are laiown, and effec- tive giast velocities can be cor.noletely and accurately evaluated. Aeronca C-2 air^^lane.- The Aeronca C-2 airplane v/as also fitted with an KACA recording acceleroneter and an NACA airspeed recorder, and the operating weiglits are accurately kno^n. Detailed evaluation of effective gust velocities is possible from the records. e\7^lt;ation cf frsou^ncy distributions AND TOTAL FHS^riENCIES Method of Count The r.iethod of counting frequencies used herein was dictated largely by the type of record available for analysis and by the quality of the records. Only the records from the KACA acceleroineter permitted detailed examination, but even v/ith those records it was necessarj' for 'Dractical reasons to confine the count to single maxim-urns and rainimums, or peaks, between any two consecutive intersections of the record line with the Ig reference level. This m.ethod of count neglects the m.inor oscillations suoeri/aposed on those counted. Kaul (reference 2) emoloj^ed a similar method of count, and in this respect the German and the American data are comparable . From the records for sample 1, in which the time scales were cramped, and from the records taken with NACA V-G recorders it was not possible to determine whether the acceleration returned to or crossed the Ig reference level after the attainment of a maxim.um or minimum value. In tiiese cases, therefore, the evaluation was made by counting the acceleration peaks standing out from the envelopes of the small accelerations, Since, excent for the V-G data, it v;as considerably more convenient to count accelerations directly than to convert accelerations to effective gxist velocities prior to the co^jnt, the conversion was made for relatively short sections of each sample on the basis of mean air- speeds for these sections. In this way large errors in airspeed were avoided and the small- deviations of the airspeed from the selected means v/ere of no great significance . 10 MCA ARR 1:0. l4l21 Class intervals The intervals for the classification of frequencies were chosen at about the sriallest values consistent with the accuracy of the several acceleration measurements - namely, about O.lg. For a number of reasons the intervals v/ere not always quite the same. This fact is of no consequence for, in any event, since the accel- eration values were conveniently converted to effective gust velocities after the count was made, the class intervals expressed in terms of effective gust velocity would not rem.ain equal for the various samples because of differences in air'-'lane characteristics and airspeed. The class intervals, expressed in terms of gust velocity, corresponding to the actual evaluation are given in table III. Threshold Values of Acceleration and "^'ffective 'just v'elocity In co'jr.ting the frequencies in the lowest class ('-hat is, the class containing the s^nallest values of acceleration), t^e result depends upon the m.inimum values that can be observed. Cn the records from the NACA accel- erometer, variations in acceleration attributable to gusts as small as O.C2g can be ccnvenientl'^ observed, and all greater values can therefore be counted. This limit of acceleration for which, the count can be made is termed herein the "threshold value" of the acceleration. On the V-j records and the records from the con- verted cormnercial recorders used in obtaining samiole 1, the threshold values of acceleration were rather high because of the lim.itations of the instruments oreviously described. The threshold values for the sai?iples are given in terms of effective gust velocitv in table III. Relati ve-:^equency Distribution 7t:e frequencies f and tne total frequencies F of the gusts for the 10 samoles are given in table III as counted within the selected class Intervals and to the threshold values of effective gust velocity. MCA ARR Fo. lJil21 11 In order to arrive at the broadest and most rational view of gust-frequency dis bribution, all daba were plotted in the form of relative-frequency polygons (reference 8). The polygon of relative gust frequencies is a graph of the ratios f/P = f^ for the different classes plotted at the respective class marks on a scale of effective gust velocity. Since the shape of such a polygorx is dependent upon bhe sl.?:e of the class interval andi upon the class mark of the lowest class within v^hich the coimt is made, polygons for the different samples can be compared only wlien nlotted for a common class Interval and for a common lowest class. In order to place all the data on a comnarable basis, a common class interval of I4..5 feet ^er second, the largest of the class intervals for wh.l ch cou.nt was made, was chosen. Since sam"ole 5 ^'"ic. samples 7 to 10 have about the same small threshold value falling within class 1, relatj ve-frequency polygons for these samples can be plotted ii.imediately after conversion to the coiamon class interval. The polygons for samnles 5 and 7 s.re shown in figure 2; the polygons for samples 8 and 10, in figure 5; and the polygon for sample 9? i^ figure []_. A reference polygon, "relative distribution A," is shown in these figures to facilitate cornparisons . In constructing polygons from the remaining data, samples representing generally similar operations were combined. The combination of these samples, which include the V-G data, was rerforraed in such manner as to bring the relative frequencies of the rarer large gusts into a proT^er relationship with the other data. The basic assumption involved in the process was that, for data covering a large scope of operations, the relative- frequency distribution follows a single pattern. The validity of this assixraption is discussed in a later section. In the case of sam.ples 1 to []., all of which represent dom.estic transport operations, none of the data extended to low values of effective gust velocity for reasons previously given. The total frequencies for these samples are, therefore, relatively smaller than the total frequencies for the more refined samples because of th? omission of the I'requent low- value gusts. In order to brir^g the relative-frequency nolygon for the combined sairiples 1 to Ij. into T:iroi-)er relationship v\?lth the polygons for the m.ore complete samrles, it was 12 KACA ARR IIo. LliI21 necessary fi.rst to estimate the frequencies of the missing low-value gusts and the corresponding total frequencies. For this purpose a mean relative-frequency distribution from samples 5> 7> 8, and 10 was assumed to represent the missing low-value gusts of samnle 1, which, of the combined samples 1 to l^., had the lov/est threshold value. iVith this assiimptlon, the total frequency of sample 1, including the frequencies of the lower classes, was estimated to be 1,6C0,000 gusts for the 1520 hours of operation. The frequencies of samnle 2 were then reduced bv the ratio of the path of operations of sample 1 to the path of operations of samnle 2 (table IV), Similarly, the frequencies of samples 3 -^nd l\. were reduced to correspond to tlie path of operations of s,arrn?le 1, The s'om of the reduced frequencies within each class of samples 2, 5, and ).|. was then added to sample^ 1 to obtain the polygon for the combined samples 1 to 14., In combining samples 1 to Ix a pi-e caution was necessary in regard to class 6 because of the following considerations. After conversion of sample 1 to class interval k»5f the highest class in which data fell was class 6. This class is the lowest in which data from the V-G records fell. Thus, frequencies were available from all samples of the combination only in this class. In arriving at a combined frequency for class 6, two nossible methods could have been used; namely, either the reduced freqviencies from samples 2, y, and l\. could have been averaged with the frequency of sample 1, or the most reliable sample could have been used without inclusion of the les^"5 reliable samples. The second method was actually used and the frequency for class 6 was taken from sample 1 since the obscuration of some class 6 acceleration peaks within the V-G envelopes of samples 2, 3, and l\. made these data less reliable for this class. The freq^.iarcies for samples '5 and 6 were combined in a manner similar to that in which samples 1 to 4 were combined. In this case, however, it was unnecessary* to estimate a total frequency for sample 5f as the threshold value was comparable to the threshold values of the other comnlete samples. Also, inasmuch as the highest gust-induced acceleration for both samples was recorded within the rather limited scope of sample 5i this one value j^as assigned a frequencjr of unity for the combined samples. FAG A ARR No. lij-Kl I3 Polygons for the ccnbined camples 1, 2, 3> and l\. and for the combined samples 5 S-^d 6 are shown in figure 2. DISCUSSION Relati ve-Frequency Distribution Significance of various samples .- Tlie relative- frequency distribution for any sample of data does not necessarily represent general average conditions. ?or instance, the frequency distribution of sample 5 is not representative of average conditions because of the occurrence in sample 5 '^^ '^'^^ of the most severe gusts ever experienced on the Pacific Division of the Pan American Airways System. Even without other sam.ples for comparison, this fact mi _2,ht have been suspected from the form of the relative-frequency polygon for sample 5 in figure 2, which shows a sudden break to large values of Ue . Sample 9 -i-S anotlier case tl:at is not repre- sentative of average con-litions, because this sample was obtained during the roughest of a considerable number of flights made during a soecial investigation of turbulence within cumulus-conge stus and cumulo-nimbus clouds. For sample 9> ^^ can be observed from a com- TDarison of tbe polvgon in figure I4. v;ith the other nolygons in figures 2 and 5, the frequency distribution indicates relative!"" high proportion of gusts of high intensity. In contrast to the "fullness" of the frequency distributions for samples 5 ^ind 9» the frequency distri- bution for sample 7 shows relatively low proportion of gusts of high intensity. Tiriis result is in line with the conditions of ODeration, according to v/hich regions of high turbulence were avoided as far as possible so that greater weight v;as given the frequencies of the smaller gusts . Since the conditions governing samples 5> 7> ^^'^ 9 are Imown to give rise to more or less extreme frequency distributions, a sample representative of average condi- tions a-oplicable to large scoDe of operations would be expected to lie soinewhere between the extremes. Probably the most representative of the samples containing detailed data an the lowest classes are sam.-oles d and 10, ll^ KACA ARR No. ri;l21 v/^ich v/ere selected at random from a considerable mass of data. The relative-frequency polygons for these sainples (fig. 3) may be observed by comparison with figures 2 and it to lie between the polygons for samples "^ and 9 ^-^d inside the end point of the polygon for sample 5- The combination of samples 1 to L. and of samples 5 and 6 in the manner described greatly extends the scope of the data ap-oli cable to the respective operating con- ditions represented. The combined sajiiples are thus more true than any single small sample in the sense that the influence of accidental occurrences, such as the sncouin- tering of an unusually strong gust in sample 5> is sub- merged In the mass of data; that is, accidental occur- rences of this oort occur in sufficientlv large number v;ithln a sam.ple of large scope that they become more truly representative of the average conditions. Fig- ure 2 shov/s this effect clearly; the combined sample 5 and 6 and the combined samole 1 to k have relatively uniform distribiitions Iving betvveen the extreme distri- butions of samriles 7 and 9' For comnarison with the samples presented herein, distribution polygons of JJq have been constructed from Eaul's data wit^- a clasa interval of 1+-5' It may be seen from figure 2, v;hich shows the envelopes of the nol-v'gons for Kaul • s data, t'-at the German and the American results are in very good agi'eem.ent. Influence of airDlan e characteristics and source of turbulence.- it is evident from che -orecedina; dls- cussion x;ha^the major discrepancies between the fre- quency distributions for the various samtiles can be accounted for largely by accidental occurrences during the operations. 'A'iien the scope of the samples is sufficiently increased to be representative of average operating conditions, these accidental influences are not so strong and the frequency distrioutions tend to fall into the same pattern regardless of the source of the data. The results therefore indicate that individual gusts in turbulent regions of the atmosphere are distributed on the whole in a fixed manner irrespec- tive of the location of the turbulent regions and of the source of the turbulence. Figure 3 further illustrates the similarity of different samples. Sample 3 was NAG A ARR No. 11^121 I5 obtained at high altitude within cujriulo-nirabus and ciomulus-congestus clouds and represents turbulence having its origin in thermal convective processes. Sample 10, on the contz'sry, was obtained at very low altitude in the absence of thermal effects and the turbulence arose fro~n the shearing of the wind in the earth's boijindary layer. Notwithstanding these con- siderable differences in the aerological conditions, the frequency distributions are nearly the same and they are also in close agreement with those from other sources, Another point, most clearly evident from samples 3 and 10 but also evident fron the other data, is that the distribution of turbulence as measured is largely independent of airplane size and other airolane charac- teristics. The close similarit-'- of the distributions for saruple 8 (obtained with the Lockheed XC-55 airplane), sample 10 (obtained with the Aeronca C-2 airplane), and the samples from the airline operations indicates that the basic assum.ptions and concents underl^/ing the gust- load formula (equation (1)) are correct. Influence of disturbed motion of airplane in continued s^,vere turbulence.- Although the foregoi n g remarks aoout the influence of the airplane character- istics apply on the average, in continiied sovera tiarbulence the frequency distribution may ampear to contain abnormal frequencies in che higher classes unless precautions are taken to eliminate the effect of disturbed and controlled motions of the airplane. In the flight from, which sample 9 ^^^^ derived, which was the roughest of a large number of flights through curaulo -nimbus clouds, the airplane motion was con- siderably disturbed from, the desired straight path, so that the gyroscope of one of the flight instrum.ents was at times put out o.f action (referer^ce 9). Under these circumstances the airplane was subject to moderate acceleration fluctuations of long period upon which the short-period accelerations due to the turbulence weri superimposed. .Iilien the count was made in the described marjier chosen for the general analysis, abnormally high values of effective gust velocity v/ere ascribed to the various frequencies and the polygon appeared full (fig. Ij.) . '^hen bhe count v/as made with respect to the variable datum caused by the disturbed r.:otion rather than with respect to the 1 g datum, the frequency distri- bution confom:ed more nearly to the distributions of the other samples. The co:^i>ected nolygon retained a certain l6 MCA ARR No. li|l21 degree of fullness, however, which may he ascrihed to actual greater frequence of the riiore severe gusts. rifferences hetv/een two polygons li]<:e those shown in figure I|. provide 'Tieans of evaluating the effect of the disturbed motion on the freqtiency of applied loads. The data given here apoly specifically to the char- acteristics of the XC-35 airolane and cannot oe safely applied to other cases. This fact is of small concern, because large disturbed 'notions are rarelv encountered in normal operations, so that such effects as are shov/n in figure I4. would hardly be noticeable in a sample representing large scope of operations. Factors Governing Estimation of Total Frequencies Average and standard gust inte r vals . - The fa c t that the frequ-fncy distribution follov;s a fixed oattern for samples of large scope indicates that the total fre- quency is proportional to the distance flown within tur- bulent regions. Conversely, the average spacing betv;een gusts is inversely proportional to the distance flown. In order to -provide a use'f'ul basis for estimating the total frequencies of significant gusts (n;:^iely, those causing measurable acceleration of an airplane), the term "average gust interval" K^^ is introduced. This tern is defined as tl-'e average distance along a flight rath in tu.rbulent air between significant gusts. Nwaer- ical values of Xg^y have been derived from the total frequencies of sam.Dles 5> "> 3, 9, and 10 and are given in table IV. ■ In evaluating X.^^^. the actual path -lengths in rough air, which are also given in table TV, were divided by the total frequencies. The average gust interval \^y is plotted against mean wing chord in figure 5- The dependence of Xr^y on airplane size is evident, although the exact nature of the relationship is not entirely clear from the figure, Ttie average gust interval for the four samples shown in figure 5 i^ 11 chord lengths. This value may be used to estimate total frequency v/hen the path length in turbulent air and the airplane size are knovm . Although the joints on figure 5 do not fall on a straight line, they could probably be made to do so by suitable correction. Figure 6 of refarence 10, for example, MCA ARR No. 1J4.12I I7 shovi'3 a marked t'Sndency for average gu3t interval to increase with gust intensity; corrections for this efi^ect woi\ld raise the point for sample 7 and Tower the point for samples 8 and 9* Pat h ratio.- In order to estimate the total fre- qnencies~fc5r ac trial operating conditions over a long period of operations, it is necessary to know something about the percentage of the total flight path that falls within regions of turbnlence or about the actual total frequencies that occur within total paths of operation of large scope. Information on the relative period of operation within turbulent regions is given in table IV for samples 5 and 7 in terms of the path ratio R. The total frequencies are ? = 5230 rSI:- ' av or F s; 5.PJO -^ (2) lie when L is in miles, ^^-^ is in feet, and "c is in feet. Although the path I'atio is not knovm for the other samples to which such a ratio Is applicable, the total frequency of sample 1 is estimated at 1,600,000 gusts to a threshold value of Ug =0.3 foot per second in the manner previou.sly explained. Because this total frequency applies to a nath of operations of l[;S,000 miles and because the mean choi-d was about 10. S feet, R is approximatelv G.2I1 from equation (2). Operating conditions .- Tiae path ratio and therefore the total gust frequency for any path of operations manifestly will depend on the operating conditions. A feeder-line transport operating overland at low altitude, for example, vvould be expected to enco'unter a greater percentage of tu.rbulent air than an airplane operating at high altitude above the mechanical turbulence near the ground and above most of the conveotive clouds. Although the operating conditions are important in defining total frequencies, the data available at this time are too sketch^^r to permit correlations between l3 NACA ARR No. l4l21 total frequencies and the factors ccmposing the operating conditions . In order to "~'ermit estiinations of total frequencies, all available pertinent data including those from German sources have been asseinhled in table V. The first four sets of Gernan data in table V have been based on the data of reference 5. Owing to the fact that Freise presented frequexiclea for noncontiguous classes, the total frequencies given v/ere obtained by multiplication of the frequencies co^'onted bv Freise by 2,5, which is the ratio of the interval between class marks to the interval within which the original count was made. The path ratios from the German data were estimated by application of equation (2). In applying the data of table V to the estimation of total frequencies, some nida;m.ont will have to be used to ensure that values of path ratio most nearly repre- senting the operating conditions are used. It will be noted that path ratios range from about 0.006 to O.2I4., with an average value of aoout C.l. APPLICATION 0? GUST FHEQU.^NCIES TO ESTIVATION OF STRESS FREQUENCIES Choice of Gust-Frequency Distribution The relative-frequency polygons representing the available data permit some latitude in the selection of a frequency distribTition to be applied in a design nroblem. Choice o^ a conservative gust-frequency dis- tribution for use in estimations of stress frequency depends i;pon the relative significance of the small and. large stresses in tlie oroblem r'-nder analysis. If the problem is to determine the probability of occur- rence of large stresses in excess of the strength of the structure at the design limit load, a more con- servative estimate will result from the selection of a frequency distribution having relatively high frequencies at the higher values of effective gi^st velocity. For other purposes, the selection of a distribution having the higher frequencies at the low effective gust velocities may give a more conservative estimate. Two limiting relative-frequency polygons, A and B, representing MCA ARR No. l1|I21 I9 the approximate limits of the data are shov/n in figure 6. Polygon A has previo^isly been used as "relative distri- bution A" to facilitate comparison of the data shown in figures 2 to J4,. Per some purposes 3i.iiiimation curx'es, or ogives (reference 3), are ^.lore convenient representations of frequenc-'-'- distributions than fi'equency nolygons . Unit svormatlon curves ccrresnondr'ng to polvgcns A and B of figure 6 are therefore given in figure 7. Relation betvi/een Effective Gust Velocity and Stress in the Structure Direct ap-oll cation of the gust-frequency distribu- tion and the total frequency by means of equation (1) with the usual design assujiiption of static load will yield ap'oroximately correct values of stress frequency. There are, however, several phenomena that modify'- the actual stress frequencies fro'-i the stress frequencies esti^nated in this simple manner. These nhenomena include ; (1) Superposition of uncounted small gusts on the larger gusts counted (2) Distribution of gust velocity across the span (5) D^mamic response of the structure Uncoun ted surfer imposed gusts.- As loreviously m.en- tionecirj the minor peaks in the acceleration records were not ordinarilv counted unless they occurred as single phenomena between tvto consecuta x^e Irtersections with the Ig datum. A special total count of these neg- lected peaks was made in one case fr'om a clean-cut record without reference to the exa-ct m.agnitudes of the acceleration increments or to the acceleration level at which they occurred. It was foimd t':at the number of these s;nall superimposed ■neaks was about twice the "cotal frequenc:/ counted in the manner adapted for the general analysis. These superimposed peaks were irregular in shape, sequence, and time or place of occurrence. The magnitudes of" th© -superimposed, acceleration peaks with respect to the ad.iacent acceleration levels were small and did not in any case exceed a value corresponding to AUg = I4..5 feet per second. The great majority of these peaks were -near, the threshold value of O.3 foot per second. 20 MCA ARR No. ri|T21 Discussion of the reason for the consistently small magnitude of the su^oerimpossd peaks is beyond the scope of this paper, as the question of the rela- tionship between gu.-^t intensity and gust dimensions and the question of the probability of superposition of randomly distributed gusts are involved. Kaul (reference 2) reports a similar count of suTDerlmposed peaks from a record of vifing-tip deflection. Kaul implied that the acceleration records did not contain such -neaks and that the extra peaks counted v/ere due to damped vibration of the wing structure after disturbance h'T the individual gusts. The ratio of bhe number of extra -oeaks to the nujnber co^onted with respect to the Ig datum, was, however, about 2 - a result that Is in agreement with the authors' count of the extra acceleration peaks. It seams probable, therefore, that some additional acceleration peaks due to 3^^perimposed gusts an-:' some acceleration peaks due to vibration response of the wing-fuselage system, were acttially coLinted in both cases. So far as the mere question of gust frequency is concerned, without regard to superposition, these additional small -neaks may be placed in class 1. The inclusion of such s 'lall peaks in a fatigue test, however, cannot properly be effected on the basis of this simple classification. If the superposition of the additional small peaks is felt to influence the fatigue strength to an important degree, the phenomenon of superposition must be taken into account. The superposition may perhaps be pictured suff Icientlj^^ well for application to fatigue tests by imagining the periods of the x'arious stress cycles to be proportional to the amplitude. Farther, assume the cycles corresponding to the basic gust frequency distribution to be applied without super-cosltion. Finallj?-, superim.-cose the additional small cycles on the basic cycles of class 2 and of the higher classes, distributing the additional small -oeaks uniformly along the time scale to determine the numbers to be superimposed on each basic cycle. The actual anollcatlon of surerlmposed cycles in fatigue testing is a difficult matter and requires either the constr't.iction and use of a familv of summation curves with mean stress as a parameter or the construc- tion of a comnlex fatigue m.achlne with which the small MCA ARR No. lM-121 21 cycles can be superimposed on the lar:3er cycles. The derivation of the surrmiation curves would require that the basic stress cycles be considered as square waves .for the purpose of establishing a finite number of mean stress values, and the actual testing would involve the difficu.lty of occasionally holding the mean stress levels at very high values while the small cycles were being applied. Dist r ibution of gust velocity along span . - The distributrbn of gust ve 1 oc ' tj al ong the s -oan o f a wing is not always uniform, so that the usual assumption of uniform distribution leads to som_e error in estimation of stress frequencies from the gust frequencies. The results of the gust investigation with the XC-35 ai^:"- Dlane indicate the various typical spanwise distribu- tions that actually occur and the frequency of each type. If desired, further refinement of the stress frequencies can be made from these data, which are reported in reference 11. D^Tiamic re spo nse of the structure .- Owing to the flexibilit" of wing structures, accelei-ations caused by gusts v;ill not be the same at all points along the span. The accelerations at the v.'ing tips will be somewhat greater than and out of phase with those at the .fuselage. Some calculations pertaining to two typical large airplanes (reference 12) and tests in the Langley gust tunnel indicatod that the maximum tip acceleration at about 200 miles per hour was about twice the acceleration at the fuselage and occurred earlier than the fuselage acceleration. The wing oscillation in these cases damped out in 1 to 2 cycles. The effect of such dynamic action is to cause, at the outer portions of the wing primary structure, super- im.posed stress cycles with a maximum amplitude about 10 percent of the static stress for the uniformly distributed gust. Because the natural rierlod of v\f3.ngs increases almost in direct proportion to the wing linear dim.ensions and becaiise the size of gusts to vdiich airplanes will respond also increases as the airplane size, the ratio of natural i^eriod to neriod of application of load remains about constant for constant flight soeed. The d:/namlc response of the structure would, therefore, aripear not to Increase with airolane size. 22 WACA ARR No. r4l21 If desired, the additional frequencies of the small dynainic stresses at the cuber portions of the wings can be Included in the same manner as the uncoijnted super- imposed gust frequencies. Exp er imental evid ence .- Sc;ne test results from the stress 'and acceTeration raeasurements on the 'J-IJO and the B-I5 airplanes are shovi/n in figures 3 to 10. Comparative stress frequencies cannot he shov/n, but the figures illustrate the degree of agreement between peak stresses as measured and as would be calculated by the usual assixmption of static load for the corresponding measured accelerations. For the Vi-lj>0 airrlane (fig. 8) a datum stress increment corresDonding to application of a load factor of 1 was determined by taking the difference between stress while in level flight in smooth air and stress while at rest on the water. Correction was made for wing weight. The olot therefore indicates the agree- ment between gust-induced stresses as measured and gust-induced stresses as determined by multiplication of the datujtn stress by the meastxred acceleration. The distribution of the points along a line of 1^5° slope indicates excellent agreement; this result and the lack of scatter beyond the limlbs of error denote lack of serious dyiriamic response of the structure. The results shown for the B-I5 airplane in fig- ures 9 ^^d 10 are given simply as plots of measured stress against measured acceleration because a datum stress increment was not measured. The stress-load relationships shown are, hov/ever, substantially linear; this fact, together with virtual absence of scatter bej-ond the limits of error, shows absence of serious d;;>Taamic response. These results indicate that, with the exception of the small uncounted superimposed stress peaks, the stress frequencies of the -orimary wing structure will be given with sufficient exactness, for all practical purposes, by application of the gust frequencies through equation. (1) and the usual assuinption of static load. Application to tail surface s.- Tlae gust-frequency data given herein are not directly applicable to tail surfaces. Som.e unpublished flight data on the relative magnitudes of effective gust velocities on wings and MCA ARR No. LLi.121 25 tail surfaces Indicate, however, that a rough approxi- mation of the tail-load frequencies might be obtained by utilizing the gust frequencies given here and by multiplying the values of effective gust velocity by 1.6 for the vertical tail surfaces and by O.5 for the horizontal tail surfaces. CONCLlTDINa REMARKS Available flight data are sufficient to indicate that the distribution of gusts vvithin turbulent regions of the atmosphere follows a substantially fixed pattern Vi/hich is independent of the source or cause of the turbulence. The average Interval betvi/een gusts causing measurable airplane response is about 11 chord lengths, and the total frequency of significant gusts in any stretch of rough air is therefore the length of the flight path in rough air divided, by 11 times the mean wing chord. The total gust frequency to be expected during the operating life of an airplane depends upon the operating conditions, v.'hich determine the ratio of path length in rough air to the total path of opera- tions. Information on the path ratio as a function of operating conditions is sketchy at this time and should be supplemented by fiirther measurements . From the available informatjon, the average path ratio for a variety of operating conditions is about 0.1, although Individual values vary between about O.OO6 and 0.2l|. . The available data on gust frequencies permit ar-proximate determination of stress frequencies in the orlmary structures of airrlanes due to gusts. These frequencies aroear to describe adequately, for many design purposes, the stress conditions for transport-type airplanes in flight. Supplementary information on stresses in secondary members of the structure and on the additional frequencies of small stresses in the primary structure resulting from dynamic structural response and nonlinear lateral gust distri- bution is desirable. This information vi/ill have to be 2l| NACA ARR No. ll'^^l o'bta^.ned by stress measurements correlated with airplane size, clead-v.'eight distribution, and other factors. Langley Memorial Aeronautical Laboratory National Advisory Coinmlttee for Aeronautic: Langley Field, Va. NAG A ARR No. l4l21 25 RSFERSNGSS 1. Bland, Reginald B., and Sandorff, Paul E.: The Control of Life Expectancy in Airplane Structures. Aero, Eng. Review, vol. Z, no. 6, Aug. 19^3 ^ T.^, 7-21. 2. Kaul, Hans ".V.: Statistical An.alysis of the Time and Fatigue Strength of Aircraft Wing Structures. NAG A Tr ::0. 992, 191^1. 5. Preise, Kelnrich: Spitzenv;erte und KMufigkeit von Boenbelastungen an Verkehrsflugzeugen. Jahrb. 1953 der deutschen Versuchsanstalt fur Luftfahrt, E. V. (Berlin-Adlershcf ), pp. 2IO-22I4.. \\. Rhode, Richard V.: Gust Loads on Airplanes. 3AE Jour., vol. Ii-O, no. 3, Iv'arch 1937, ?" • 3l-33. 5. Rhode, Richard V., and Lundquist, Eugene E.: Prelimi- nary Study of Apnlied Load Factors in Bumpy Air. NAG A TN No. 37!^, 1931. 6. Donely, Philip: Effective Gust Structure at Low Altitudes as Determined from the Reactions of an Airplane. NAGA Reo. No. 692, I9I4.O. 7. Anon.i Airplane Airworthiness. Pt . O'l of Civil Aero. Manual, CAA, U. S. Deot. Commerce, Feb. 1, 191^1, p. .2-2. 8. Rietz, H. L. : Frequency Distrloutlons - Averages and Measures of Dispersion (Elementary Methods). Gh. II of Handbook of Mathematical Statistics, H. L. Rietz, ed,, Houghton Mifflin Co., 192i^, VV' 20-53. 9. 'flight Research Loads Section: XC-55 Gust Research Project Bulletin No. 5 - Operations near Gold Front on August 12, 194-1 - Maximum Gust Intensities. FACA RE, April I9I+2 . 10. Moskovitz, A. I.: XC-35 Gust Research Project Bulletin No. 8 - Analvsls of Gust Mi-asuroments . NAG A RB No. LkD22, \4i^. 26 MCA ARR No. 11^.121 11. Moskovitz, A. I.: XC-55 G'^i.st Research Project Bulletin No. 7 ~ Preliminary Analysis of the Lateral Distritution of Gust Velocity along the Span of an Airplane. NA.OA RB, March I94.3. 12. Pierce, Harold 3. : Dynamic-Stress Calculations for Two /^irolanes in Various Gusts. NACA ARR, Sept. 191^1. NACA ARR No. L4I21 27 01 W kJ eu s Q <: w CO w <: o H M Ctl JTJ o ■s w s a: o u cc ^ fe. <: M CO (- H < W S t:. ^4 < a: y^ >H <* CL, ri H 2: t. W o g CO 1 o H I-I M R & CO rl 1— cc u. W o F- o •a: K < a^ o Slope of lift curve, a • J- « J- N>1 O • • J- VD Ov • J- vD • VO vo vo • vo « Ov • Ifv ON • Relative alleviation factor, K o o o • OX CIN o o c:n o crs d irx OS • o o o • rH O • i-H o C\J o • o rvj O • r-l LTV CO o • r-l -t o » rH o o • r-l o o • r-l r- • o Mean chord (ft) • o ■H • O .-1 so • O • ON o » O • t-t O • o l-t o • vo I-I O • o • r-l vo • CO r-\ • ON CM • ov o • -J- 00 <— CO • r- • r-l • o CO 1^ CO ON o o ^^^ r-l r-l 5 i-\ irv irv LTV vo f o CQ 1 o K •O c c O 1 O X •a O O ►J 1 o oi o c o u < CO f-l OJ fOi -d- U^ vo t- CO o o rH 00 o I-I e-1 Cd o CO > < o o K Cd < CS e w M ^ I-I o 41 ir-l C s n 00 O tl C5 NACA ARR No. L4I21 28 to S ■■-' x- ^ -1 3 C (T, JZ •*-' s as « CO c »•. c » c c e E ci F I-c ^ « *^ tt -J ^ E «) 5 c^ o c •-.0) c •r. n 0) t. 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O 'Jl l-H t] E- Eh O NACA ARR No. L4I21 29 w < o tc o w < E- o E- 1 1 t 1 1 1 1 t 1 U-N i/> t 1 1 1 , 1 1 1 LTN 1 1 1 1 1 1 o 1 1 1 r-l o o o o o o rH i-H o o o o r~i o ' 1 1 1 1 1 ON ni rVN o o o o OJ ,~i o o ■M r\J o r-< 1 1 1 1 1 1 03 c~- ITN M r-H o o CM \£> o o r-i »H OJ O 1 1 1 1 rvj r\J 1 1 ITS u^ , 1 t 1 1 1 r- O lTn rOv f-H o o vO N-N O o 1 1 1 f\J ON .-t fH 1 f i-H pO 1 1 NO NO OJ o v£> ON CO r-4 r-H 1 1 1 1 \ n c 1 1 1 1 1 1 U^ LTN 1 1 0) o 1 1 1 t 1 1 • • 1 1 C3 Lr^ 3 fO, t- 1 1 1 t 1 t r^ t— 1 1 1 vO t^ f-t o t^^ lO -^ l/N r^ o- NO ON t 1 1 t 1 1 1 1 rH f-t rH o tVN r- 1 1 1 1 1 1 1 1 &. O ro 1 1 t 1 1 1 o o 1 1 r- f-l -d- o c^ r- CO NO -d- NO CO rH o t- 1 1 1 1 1 1 1 1 I 1 1 1 1 1 1 1 (-4 r-4 1 1 1 1 1 »-i ^^^ ^^^ •^ H-N r\i 1 1 , 1 1 1 , 1 l/^ ITN , 1 1 1 . 1 1 1 1 • • t KN 1 1 1 1 1 1 t CO no 1 1 ^ C^ K> NO U-^ IfN f\J t- 1 1 1 1 1 1 1 1 fM rM 1 1 ON OJ r-t f^ ^r^ NO O iH r^ i-t rH r-t 1 1 1 1 , , 1 1 ir\ ir\ 1 1 f\J CO rH CO CO CO lTs OJ t ( 1 1 1 1 1 1 (\J rg 1 1 O -d- OJ N-\ ft «-t N^ NO <\J 1 1 1 1 ' 1 ' t f~i w 1 1 O o- C\J f\J -d- -d- r- -rt 1 1 1 1 1 1 ) 1 ITN lTn t 1 U-N lTn 1 1 1 1 1 t 1 1 O o t 1 on _:t rH o ITN U^ o o 1 I 1 1 1 t 1 1 CO CO 1 1 NO ^^ fTN ro, CO CO -^ CO »H 1 > 1 1 1 1 1 1 t 1 1 1 1 1 CM r- 1 i-t t 1 1 1 CO f-t ON fH o rH O rH O r-* O rH rH o OJ c <^ o O -H 4J -K ceo b03 €> + 1 + 1 + 1 + 1 + 1 + 1 + t 4 1 + 1 + 1 ^ bO C< CO »^ •O ^ o 1 ITN vf> -d- ITN rH ■H C 1 a -d- NO O NO dj (D 1 CO O LT. ,-H- K> ■U P 1 « tt « a o zr 1 f\j NO OJ ^f^ LTN e- c f-i OS n >-- c D o o o 00 CO -li- o o O n t^ B • c 3 Lr^ tsy lTn CO CO ve lO to O 01 « (J. • • I-I -P ^H (N -d- -^ A OJ rg (M -^ -i rO o c — •H o iH a H f\J N^. -d- ir> NO r^ CO ON O E d (fl (d f-i a M o M E-f cc u O -s O M M W si: s £ o o Of 43 01 60 C c •d c NACA ARR No. L4I21 30 Cd CD < Eh < Q Q Cd < Cd cc <: CO (J Eh CO Pd <: Gusts per mile of path of operation, III I vo 1 -::^ 1 II III 1 ^ I -J- I II II) 1 rH 1 lTN t II 1 1 1 1 * 1 .III 1 t 1 1 O 1 III Average gust interval, ^v (ft) 1 I 1 1 O t O O as T) 1 1 1 1 CO 1 LfN K> TvJ _zf III 1 rH 1 r-^ r^ r->. 1 1 1 1 1 cd Path ratio, R 1 1 1 1 CO 1 U-s 1 1 1 1 1 1 1 lO » U-v 1 1 1 1 i I 1 O 1 rH 1 I 1 lit 1 O 1 O III ! 1 1 1 .1 • 1 p I 1 1 1 1 O 1 III Path in rough air (miles) 1 1 1 1 r-l 1 r-l O N^ C> 1 " 1 1 O 1 _z}- ^ C-- -^ III 1 rH 1 t-- Path of operation, (miles) O O O O O O O 1 1 1 O O O O O O O 1 1 1 o o o o _d- o no 1 1 1 «ha««««« a^^l 1 1 LTN o o o c^ o r— 1 1 1 _d- o o 00 i-i ltn _d- 1 1 1 iH GO O^ J- CX) III « « * at III iH rH h(A rH III Average true airspeed (mph) OI^OOrH rHfOvOOiO r-i_c}-cocoLnu>u> r-t^r- r-i r-4 f-^ t-{ r-^ i-{ l-i r-t r-i Flying time in rough air (hr) III 1 t^ 1 J- u^ f<> u^ 1 1 1 1 VXD 1 CO ^r\ _zl- vo III 1*1 » ••• III 1 O 1 J- Total flying time (hr) O t^ _rj- _^ iTN r\J ^f^ i i i r\J ^ ^<^ fM rH hO, rH 1 1 1 K\ r\l u^ N-N rH OJ rC\ 1 1 1 •t»A.K at 111 rH OJ O cr OJ 111 r-i f-\ r^ r-^ III 1 Sample rHf\jro,_z; LOvor- CO C^O r-t © c ■A rH C c o s n fO © o £1 M u ^ :3 >H t) ■p K <: TO o a iH 'O o X3 !r"^ > t3 >. Q < X3 < VC ■c 1-1 p © <- t- m •^ 3 o ai ct! t-( fd O tH fH E o u 4-, ^ c ps o o o © p. n C o © m cfl XI O rH ca > at NACA ARR No. L4I21 31 CO a o M F^ M M » O 01 O !3 O CI M f- M < Fh crt < M err 0- M o &< o 6- r-! ^ c < 00 1^ > •k < m c= Ir' c; Fh J h-l ra H B < <;^ <: t-> K ^ C5 DO o 2; W OS O >, 1 — 1 r-{ (D O ■P £1 >> C n t>» O -H a n rH n t, u >> c P m ■p 3 a *j rH C <71 o o 4J n -1 a •r< t. c -H !h C a t, X •p n *-» »H o SCO) n o u fr« a a Cl rA C & a) 1) *i e m a a a m e G t. L. *> C to 1-, s. t, C c o o O -3 C T3 o C O -H *:> a cr: ■y a 5=5 T3 -1 3 -H a P" a> -p t 3 O x> o t^ Ih p. t. t. > > O T) .■_( a t> r-t a 3 a C.iJ -P p. O a u o E- o -O « CO m tTN ro j:: o lTn lO. t^ O J- _^ ON »c\ c- -p ^^ -d- o f-i _^ J- t- CI a- r- o ot -P K 1X1 o O rH O r-* rH o o o o. a « • • • ■ • t. o o o o ° o CD o o o o ' «H -O . >% o n -p o c n "M .H c o o » 'X' a [--- IM Lf> rj CO -}■ t- J- -* *^ 3 ^ 4J Or-* ^0 (M O o OS ^/N OD r~ u^ rj O o" E « J) • • • • • • • E-i « t. f- II i-t O rH t- f~\ 00 CO J- r» o tr^ vO o o o o 1 o o ON J- o to r-^ o 1 r-l c o ao O CO ON o LO t C3 •^ C rH a > < C a 1 tw C — o O o O c o o O o 1 O -^ tn •H o o O a o a-- vo ^D 4J d- t. o J- 03 _d- rH o~ fM 1 S m •-< <0 « •. ^ (K •s * » 1 JJ t< -^ 1 ITN C-- t-^ « t^ r-K t~- O 1 aj c E D- C — ^ iH -d- rH -d- 1 1 O <« e c e t!0*l "O Br-t o o O o o o o o o o o o o o o o o t^ o VD t-- » • * * « •t 6 > rH -P O r-( --* o m r\J (\l t\J J- J <: > m m c a o a 3 ^ ^ d) • O ® a o rH c 1-4 O c o p. Ctn •H £ .'^ tn ^ «-. >> c c CO >> . C a rH »H •H c. u ■P t3 a ■p 00 a •C -P T r-< a a a bO c • a c c C ■rH *> 4J (C o rH C o ,-i t^ o a 3 a rn C c o c. o rH O c 3 o o < <: c S E s o 5 e- •rt o vJ O •P ^ E E • • d to a c M) • > to o c 1=> fH rH « o s o H » ,M e i< c o 4D U •e tl 4J •H t, a n t< a p 3 . 60 «-. c hO n a (h >^ O CO c m o c wH d: bC «1 t. . o 01 c c ID C t. rH » +J ^ cc J-J ^ o :o a c £ C' 3 n 3 t. t^ > fci C, *j B o 3 C o O P fc O »H -p t. rH O o o -p o o •rl « a *^ 4J -p t- 4J ■p L. a n c c 3 o a ffl 5 •d c c c b; a m > (D o o ■tH •H ^H HJ c a^ E •-< -o r-t rH r-* -p c t. a t. c o u !- U 3 d- c rH a a p <£. c; C3 cn cn cc > H» cc < O E5 :-■; o Mi > til o < ■t o w n B E-1 Eh •=C fH s o NACA ARR No. L4I21 Fig. 1 I NACA ARR No. L4I21 Fig. 2 -50 -40 -£0 -10 10 £0 30 Effectii/e gust lyelocity . fps Figure 2.- Polygons of relofive-frequency distribution of effect/ t^e gust yelocity NACA ARR No. L4I21 Figs. 3, 4 ■Si :s