;.-'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 
 
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 Fig. 1 
 
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NACA ARR No. L4I21 
 
 Fig. 2 
 
 -50 -40 
 
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 NATIONAL ADVISORY 
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NACA ARR No. L4I21 
 
 Fig. 7 
 
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NACA ARR NOo L4I21 
 
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