NATIONAL ADVISORY COMMITTEEFOR AERONAUTICS

TECHNICAL NOTE 1976

SUMMARY OF INFORMATION RELATING TO GUST

LOADS ON AIRPLANES

By Philip Donely

,* Langley Aeronautical LaboratoryLangley Air Force Base, Va.

": CC'E

0 Washington Reproduced From

SNovemoer 1949.... Best Available Copy

aS0000803 196

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TABLE OF CONEWS

Page

SUMMARY ....... .............................. 1

INTR ODUCT I ON .... ............... ............. 1

BACKGROUND AND BASIC EQUATIONSOF GUST -LOADS RESEARCH ..... ........... 2

SHARP-EDGE-GUST FORMULA ....................

EXTENDED GUST EQUATIONS ......................... 5

GUST ALLEVIATION FACTOR . ... ........ ................ 8

THE STRUCTURE OF ATMOSPHERICGUSTS . ............... ....................... 9

METHODS OF GUST-STRUCTURE MEASUREMENTS ...... ............ 9

APPARATUS AND TESTS .l................... 10

RESULTS . ... ....... ......................... .11

Gust intensity ...... ........................ 11Gust spacing ........ ..................... ... 12Gust-gradient distance ....................... .. 12Spanwise gust distribution ....... .............. 13Longitudinal gusts .......................... .. 15

ACCURACY OF RESULTS ....... ..................... 15

DISCUSSION ....... ..................... ......... .16

Gust intensity .......... .................... 16Gust-gradient distance ....................... .. 17Spanwise gust distribution ...... ....... ..... 18

Gust spacing ........ ..................... ... 19Longitudinal gusts ......................... •.20

CONCLUDING REMARKS ................. .......... .... 21

AIRPLANE REACTIONS ............................ ... 21

THODS ............ ........................... 22

nmal sis ......... ........................ ... 22Gust-Tunnel Testing ........ ............ ...... .. 23Flight Investigations .......................... 24

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TRANSIENT AERODYNAMICS ................ . 24

Unsteady-Lift Functions .................. 25Infinite aspect ratio ........ .................. 25Finite aspect ratio ....... ................... .26

Slope of Lift Curve ........ .................... .30Section characteristics ...... ................ .. 30Aspect-ratio corrections ....... ................ .. 31Swept wings ......... ....................... .32Scale effects .......... ...................... 32Effect of power ......... .................... .33Multiplanes ......... ....................... .33Compressibility ........ ..................... .33

Downwash ......... ........................... 3 3

Maximum Lift Coefficient ...... ................. ... 34

RIGID-BODY REACTIONS ........ ..................... .34

Analytical and Experimental Studies .... ............ .35Analytical studies ....... ................... .. 35Experimental studies .................... 38

Discussion .......... ........................ .39Wing area .......... ........................ .39Mass parameter ........ ..................... .. 39Phase lag .......... ........................ .40Static margin ......... ...................... .40Center-of-gravity position ..... ............... ... 40Tail volume ......... ....................... .41Piloting and continuous rough air .... ............ .42Unsymmetrical gusts and airplane response .......... .42Horizontal tail loads ....... .................. .42Vertical tail loads ....... ................... .44Steady lift in contrast to unsteady lift ........... .44Gust shape . . . . . . . . . . . . . . . . . . . . . . 45Calculated and experimental results ... ........... .. 45

ELASTIC-AIRPLA REACTIONS ... ................. .... .46

Methods .......... ........................... .47Analytical Study ........ ..................... .. 48Discussion .......... ........................ .48Concluding Remarks Concerning Elastic-Airplane

Reactions ......... ....................... .. 50

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OPERATING STATISTICS ..... .............. .. 51

MTHOD ............. ............................ 51SCOPE OF DATA ........................ 51STATISTICAL METHODS ........ ...................... .52RESULTS ........... ............... .... ....... 53

V-G data .......... ........................ .53Time-history data ......... .................... 54Disturbed motions ......... .................... 54Path ratio ......... ....................... .. 54

DISCUSSION.................. ....... 55

Applied acceleration increments ....... ....... 55Atmospheric gustiness ....... .................. .55Frequency of encountering gusts .... ............. .. 56Probable speed Vp ............................... 56Maximum speeds ........ ..................... .. 57Speed-time distributions .... . ..... ........... 57Disturbed motions ........ .................... .57

RESUME ................... .................... .. 58

Gust Structure ....... ......... ............... 58Airplane Reactions ........ .................... .59

Aerodynamics ....... ......................... 59Rigid-body reactions ....... .................. .59Elastic-airplane reactions ..... ............... ... 60

Operating Statistics ....... ................... .. 60

C 0 N C L UD I N G REMARKS ................ ........ 61

A P P E N D I X A - COOPERATING AIRLINES AND AGENCIES ... ...... 64,

A P P E N D I X B - SYMBOLS ....... ................... .. 65

REFERENCES ........ ........................ 70

TABLES .......... ............................ 74

FIGURES ... .................... .............. .. 97

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NATIONAL ADVISORY COMMTTEE FOR AERONAUTICS

TECHNICAL NOTE 1976

SUMARY OF INFORMATION RELATING TO GUST

LOADS ON AIRPLANES

By Philip Donely

SUMMARY

Available information on gust structure, airplane reactions, andpertinent operating statistics has been examined. This paper attemptsto coordinate this information with reference to the prediction of gustloads on airplanes. The material covered represents research up toOctober 1947.

INTRODUCTION

The fact that all airplanes fly in rough air at some time poses anumber of problems relative to safe flight. One of the most importantof these problems is that of designing the airplane structure to with-stand the loads imposed by gusts. The three principal phases .of-thegust-load problem are: .(1) the determination of the gust structure"(that is, the size, shape, intensity, and frequency of occurrence),(2) the reaction of any airplane to gusts of known structure, and(3) the determination of the operating statistics.

No order of importance can be given to the three phases of theproblem since the final loads are a function of the gust, the airplane,and how the airplane is flown. The characteristics of gusts, where theyoccur, and the variation in their characteristics are of fundamentalimportunce because the gust is the source of the problem. Analyticaland_ experimental work on what happens to. an airplane when it strikes -,akno wn gust is of importance since a knowledge of .irplane reactionspermits the load calculation for any airplane. Finally, operatingstatistics are of importance in setting the level of loading for operatingairplanes since they define the gusts encountered under actual operatingconditions and the speeds at which the gusts are encountered.

Although research on gust loads has been carried on for many yearsand many of the results have been incorporpted in design rules (refer-ence i), these results have either been issued piecemeal or not publishedat all. Under these conditions, a compilation of available information

2 NACA TN 1976

within a logical framework is needed and, for this purpose, the presentpaper has been prepared. The scope includes all NACA material availableup to about October 1947 arranged according to the three principal phasespreviously mentioned.

Because airplanes are used to obtain gust data and the variousphases of research are interdependent, the first section of the paper isa presentation and discussion of the basic equations of the reactions ofan airplane as used in gust-load calculations. This first section isfollowed by sections covering gust characteristics, airplane reactions,and operating statistics and by a short concluding section on the coordi-nation of information and the calculation of applied loads. The materialcontained in this paper is based mainly on past work of the NACA, muchof which has been accomplished through the cooperation of the agenciesand airlines listed in appendix A.

BACKGROUND AND BASIC EQUATIONS OF

GUST -LOADS RESEARCH

In the earliest stages of research on gust loads, an immediatepractical answer to the question of appropriate design loads was needed.The problem was approached by recourse to the obvious and necessaryexpedient of measuring the accelerations under actual operating condi-tions so that some data could be made available to designers pending amore complete understanding of gust-load phenomena.

Accelerometers were used in this work although it was evident thataccelerations measured on one type of airplane would not be applicableto other types, or even to the same type operated at a different speed.The main effects of airplane characteristics and airspeed were takeninto consideration in overcoming this difficulty by utilizing a formulabased on the most elementary concepts of the nature and action of gusts.This formula, called the "sharp-edge-gust formula, was applied in sucha way that the accelerometer data were reduced to effective gustvelocities, the term effective being employed to indicate the fictitiousnature of these gust velocities.

Since that time, several advances have been made so that at presentthree concepts of evaluating airplane reactions are being utilized:(1) the very simple sharp-edge-gust formula, (2) extended equationstaking into account the gust shape and additional airplane characteristics,and, finally, (3) the sharp-edge-gust formula modified by an alleviationfactor. These relations and concepts are presented subsequently and formthe basis of NACA research on gust loads.

NACA TN 1976 3

SHARP-EDGE-GUST FORMULA

The simple sharp-edge-gust formula was derived on the basis ofnumerous simplifying assumptions which include the following:

1. The gust is sharp-edged in the direction of flight and representsan instantaneous change in wind direction or speed.

2. The gust velocity is uniform across the span of the airplane at

any instant of time or position of the airplane in space.

3. The gust direction is normal to the lateral axis of the airplane.

4. The airplane is in steadv level flight prior to entry into thegust, and the airplane flight path, attitude, and ground speed are notaffected by the action of the gust on the airplane. (This assumptionmight be visualized by imagining the airplane to be driven along a fixedtrack through the gust so that the airplane has no resulting motions dueto the action"of the gust.)

5. The primary effect of encountering a gust is to change the lifton the airplane.

6. The lift increment of the horizontal tail due to the action ofthe gust is negligible as compared to the wing lift increment.

7. The lift coefficient of a wing is a unique function of angle ofattack and independent of time.

For the assumptions noted, the expression for lift ?r load factorfor a gust of any angle is: , . . .

L_ j 2U dC S 132 -Sn = + Ln = + + cos / + _T P2- l tanC- W K-V) V U

<'"'' / C, 1 + - Cos

(See appendix B for definitions of symbols.) The term in bracketsrepresents the effect of the increased resultant speed and the term inparentheses, the lift in steady level flight plus the lift increment

4 NACA TN 1976

due to the change in angle of attack. If the particular gust anglesof 900, 0 , and 1800 are considered, then the expression reduces to

L dAn 1+CL S2

Sd W 2

for =90 0 and

/

L 2U- =1 + An =1 + -W - - V

for 3 =00 and 1800.

The so-called sharp-edge-gust formula is the equation for 0 = 900 forsea-level density and is generally written

dCLPoUeVe d -

An W

The effect of gust direction on the acceleration increment isshown in figure 1 for airplanes with wing loadings from 15 to 60 poundsper square foot flying at 200 miles per hour through a gust velocityof 15 feet per second. The ratio of the acceleration increment forgiven values of wing loading to the maximum value for each wing loadingis plotted against the gust angle P. Figure 1 indicates, as do refer-ences 2 and 3, that the acceleration is a maximum for angles close to 900.figure 1 also indicates that the vertical or near-vertical gust is 4to 15 times as effective in producing acceleration as the horizontalgust. Therefore, in reducing acceleration data, the assumption isusually made that the significant accelerations caused by gusts resultfrom vertical gusts, that is, P = 900.

The sharp-edge-gust formula, sometimes used with a correctionfactor, requires fairly rigid definition of the quantities to be substi-tuted. The equation is used for general research studies where massesof acceleration data are to be reduced and compared for evaluation ofpast airplane gust-load experience and for the prediction of load exper-ience. For research studies, the actual weight of the airplane is usedto determine the wing loading since the data from different sources

NACA TN 1976 5

are to be compared. For load-evaluation studies of operating conditions,the gross weight is used because it yields conservative values of theeffective gust velocity. In all cases, the acceleration increment isdefined as the acceleration minus one. The other quantities have beenstandardized as the result of instrumental limitations so that sea-leveldensity is used with indicated airspeed (assumed to be equal to Ve) andgross wing area. The slope of the lift curve is generally obtained fromthe formula

d% 6KZ '

)airplane wing A+ 2

For preliminary evaluation of acceleration data, sometimes a lift-curveslope must be assumed since the wing configuration is not known. Inthese cases, a value of 4.5 per radian has usually been selected.

In the case where loads are to be calculated by utilizing effectivegust velocities in the sharp-edge-gust formula, the quantities used mustbe consistent with those described. If different procedures are followedthe answers obtained obviously are incorrect in proportion to the devia-tion. The simple formula with its simplifying assumptions limits theoperations that can be performed on derived data.

ErDED GUST EQUATIONS

The restrictive assumptions of the sharp-edge-gust formula causedlittle concern until it was to be used for design calculations of glidersand airplanes whose wing loading and other characteristics differedwidely from those of the airplanes that were initially used to establishthe effective design gust velocities. The assumptions of infinite gustgradient, steady lift, and no vertical motion had to be eliminated inthe derivation of the equations for airplane response to a gust. Thebasis for the final solutions was the work of Kissner reported in refer-ence 2, which resulted in the analytical study presented in reference 4.

For the application of Kussner's work to the problem of gust loads,the assumptions already cited in the derivation of the sharp-edge-gustformula have been continued with the following exceptions: (1) The gustvelocity has been assumed to be uniform across the span of the airplaneat any instant and to increase linearly with distance in the directionof flight until the maximum gust vel6city U is attained; (2) the air-plane can rise but does not pitch under the action of the gust and is insteady level flight; (3) the unsteady-lift functions of Kussner and

6 NACA TN 1976

Wagner (reference 2), which were derived for the two-dimensional wing,are assumed to be made applicable to the finite wing by substituting theslope of the lift curve for the finite wing in place of the slope of thelift curve for the infinite-aspect-ratio or two-dimensional wing; and(4) except for the shorter gust-gradient distances, the accelerationpeak was assumed to coincide in space with the position of the point offirst attainment of maximum gust velocity.

The symbols used in the equation for the gradient gust are shownin figure 2, and the unsteady-lift functions used are shown in figure 3,taken from reference 5. It is indicated that, while a sudden angle-of-attack change, such as is obtained by rotating or pitching a wing, yieldsone variation of lift CL I the gradual immersion of the wing into a gust

yields a different curve CLg.

The equation of vertical motion can be written .as

g ) CL (t -t) dt9 t1 0c d

tipSV2 dC L d~z dt

J 2 dm M dt 2 V

where the first integral is the force due to the gust and the secondintegral results from the vertical motion of the airplane. Since theunsteady-lift functions CL. and CL depend on chord lengths from the

start of a disturbance, the equation is generally transformed so that the

Vdistance traveled s = --t rather than t is the independent variable.

The equation becomes

S g s)ds - s1 a) ds1-Lr La Ans0J 0

NACA TN 1976 7

from which the acceleration ratio An is seen to be a function of

the rate of development of transient lift, the mass parameter, and theshape of the acceleration curve.

The preceding equation has been solved by Fredholm's method (refer-ence 6) and the solutions obtained are of the form

/ -,

where C and B are constants representing solution of the integralsin the equation and whose values depend only on the distance penetratedinto the gust. Figure 4 gives the solution for a range of gradientdistance and mass parameter. Since the unsteady-lift functions CLg

and CLQ given in figure 3 were approximated for distances above

about 8 chords, the curves for the larger gradient distances in figure 4are also approximate. The dash line in the figure represents a roughlimit of applicability of the gradient-gust solution obtained by thismethod. Above the dash line, the solutions for finite gradients arenot valid, and the curve for H = 0 is to be used. The dash line wasdetermined on the assumption that no gradient gust has a peak accelera-tion occurring earlier than a gust with zero gradient distance.

Figure 4, together with the sharp-edge-gust formula, can be usedto evaluate flight records to obtain the true" gust intensity. Thegradient distance H = Vt 1 and airplane mass parameter Iig permit the

determination of the acceleration ratio from figure 4. The substitutionof pertinent values in the sharp-edge-gust formula yields an effectivegust velocity which, when divided by the acceleration ratio, gives thetrue gust velocity. In this case, true airspeed and the actual airdensity are to be used in the sharp-edge-gust equation.

In the evaluation of time-history data of airspeed, altitude, andacceleration to obtain gust-gradient distance and true gust intensity,the following methods have been used: The acceleration increment is.taken as the acceleration increment at the peak minus the steady value

prior to the start of the gust. In the determination of the gradientdistance, the time from zero to peak acceleration and the true airspeedis used. In expressing the gradient distance in chords, the meangeometric chord is generally used.

8 NACA TN 1976

GUST ALLEVIATION FACTOR

Much of the data obtained from commercial operations with the NACAV-G recorder and some gust data from special investigations are notamenable to analysis by the extended equations of the previous sectionbecause of limited information or insufficiently defined accelerationpeaks, and so means to account for the main effects of alleviation hadto be established. Since, for much of the work, the level of gustintensity has been set by the airline data and special investigations,the results of the extended equations have been used mainly to adjustmeasurements of effective gust velocity for the effects of unsteady liftand vertical motion. The gust alleviation or correction factors soobtained, were consequently based on a knowledge of the average gustcharacteristics and the response of the conventional airplanes on whichconsiderable data had been accumulated.

The gust alleviation factor is defined as the relative response oftwo airplanes encountering the same gust with the gradient distancedefined in chords. If a representative gust size is determined and aparticular airplane selected as being representative of the airplanesused for gust measurements, then the effective gust velocities arerelated by the acceleration ratios. Thus, if all gust measurements weremade on airplane 1 and the size of the average gust were known, theneffective gust velocities from the accelerations experienced byairplane 2 are related to those for airplane 1 by the expression

Ue 1 Ue2

The effective gust velocity representing the conditions is U or, ifmeasured with airplane 2, is

( )2 Ue2

NACA TN 1976 9

The ratio of acceleration ratios is the gust alleviation factor and maybe determined by calculation or by experiment.

For load calculations, a specific alleviation factor K was derivedand is shown in figure 5, as reproduced from reference 1. The factor Kis calculated with the Boeing B-247 airplane as a reference and theassumptions were made that wing loading is proportional to mass parameterand that the effect of pitch on the gust load increment is the same forall airplanes. The curve is calculated as the acceleration ratio for any

airplane to the acceleration ratio for the Boeing B-247 airplane = 16,N(S

= 11) when both airplanes traverse a gust with a gradient distanceof 10 chords. The resulting curve is based.on the assumption that allairplanes are similar to the Boeing B-247 airplane but have differentwing loadings.

THE STRUCTURE OF ATMOSPHERIC GUSTS

The determination of the characteristics of atmospheric gustspertinent to the airplane, their variations, and their frequency ofoccurrence in the atmosphere is of fundamental importance. Considerableresearch has been undertaken, therefore, to cover various aspects of thegust-structure problem. The research performed includes flight tests inthe neighborhood of Langley Air Force Base over a period of about 10 yearsand special investigations made in conjunction with comercial airlines,the military services, and the Civil Aeronautics Administration.

METHODS OF GST-STRUCTURE MEASRIEM TS

The general method followed in the investigation of gust structurehas been to fly airplanes in rough air and to deduce the gust charac-teristics from the reactions of the airplane. Whenever possible, theairplane which was the primary instrument, as indicated in reference 7,has been calibrated by testing dynamically similar scaled models in theLangley gust tunnel in order to obtain the actual relation betweenacceleration and gust intensity for various gust shapes. Most of thedata on over-all gust structure have been obtained from records of accel-eration and airspeed as a function of time. These records have providedinformation on the gust velocities, the gradient distance, and the gustspacing. In the evaluation of the records, the pitching motion of theairplane is neglected except in those cases where it can be includedthrough calibrations made in the gust tunnel.

10 NACA TN 1976

In addition to measurements of over-all gust structure, somemeasurements have been made of the distribution of gust velocity alongthe airplane span by recording the local wing pressures at variousstations along the span and the airspeed. From thin-airfoil theory, thechange in pressure at any location on an airfoil divided by the dynamicpressure q is a function of the angle-of-attack change and that, inturn, is equal to the effective gust velocity divided by the equivalentairspeed of the airplane. Local values of true gust velocity cannot bemeasured because the motions of the airplane are somewhat involved andcannot be taken into account.

The intensity of horizontal gusts has been obtained from airspeedrecords on the assumption that the absolute velocity of the airplaneremains constant in spite of rapid changes in wind speed which the air-plane may experience. The apparent changes in airspeed are taken as thehorizontal gust velocities when not associated with large normalaccelerations.

APPARATUS AND TESTS

Five airplanes having the characteristics shown in table I andfigure 6 have been used to obtain gust-structure data. As may be notedfrom figure 6, all airplanes except the XBM-1 were monoplanes, and theF-61C airplane had twin tail booms instead of the usual fuselage. Table Ishows that the weight of the airplanes varied from about 700 poundsto 55,000 pounds, and the wing mean geometric chord varied from about4 feet for the Aeronca C-2 airplane to about 19 feet for the XB-15 air-plane. The "sea-level" mass parameters of the various airplanes variedfrom about 6 to 23. In the case of the Aeronca C-2 and the XBM-1 air-planes, the response to known gusts had been obtained by tests in theLangley gust tunnel (references 7 and 8, respectively).

For the determination of the gust intensity, gradient distance, andgust spacing, all airplanes carried a standard set of instrumentsconsisting of:

(1) Recording accelerometer located at the center of gravity

(2) Airspeed altitude recorder

(3) Synchronizing timer

NACA TN 1976 11

The instrument ranges were adjusted to suit the particular airplane.All instruments were equipped to give sufficient record time and wereoperated at film speeds to give adequate time resolution. A switchconvenient to either the pilot or the observer enabled the instrumentsto be turned on or off at will.

All airplanes carried, in addition to the instruments mentioned,special instruments suited to the particular project. The XB-15 air-plane, for example, was equipped with strain gages on wing beams, andoptigraphs were provided to measure both wing and tail deflections.The XC-35 airplane carried four pressure recording units that wereconnected to orifices located-on the wing of the airplane (see fig. 7)to measure the differential pressure between the upper and lower sur-faces. Radiosonde data, as well as temperature measurements, were alsoobtained during the tests of the XC-35, XBM-1, Aeronca C-2, and F-61Cairplanes. Table II gives the scope of the flight tests. With theexception of the flight investigations with the XB-15 airplane, all testshad objectives associated with research on gust structure, and the flighttests were under the control of the test engineer as to the performanceand the type of flying done. The stability of the various airplanes wasadjusted whenever possible so that the airplanes showed stick-fixedstability.

RESULTS

The time histories of acceleration and airspeed obtained duringthese flight investigations were evaluated to obtain the effectivegust velocity, the gradient distance, and the corresponding true velocity.As noted previously, every acceleration peak can be evaluated to obtainthe effective gust velocity corresponding to the acceleration incrementas measured from the 1 g datum, but only those acceleration peaks thatare preceded by a smooth part of record can be evaluated to obtain thegust-gradient distance and the true gust velocity.

Gust intensity.- The available data on gust intensity, as measuredby the effective gust velocities, have been examined in considerabledetail in reference 9, and the frequency distributions given in figure 8were derived therein. The results given in figure 8 are based on earlyGerman work, NACA flight tests, and V-G records from commercial transportoperations. Curves A and B are the approximate limits of the frequencydistributions of effective gust velocities for over-all operating con-ditions and show the probability that a gust will exceed any selectedvalue of intensity.

In addition, a more detailed investigation of limited scope hasbeen made (reference 10) of the XC-35 data to compare the frequency

12 NACA TN 1976

distributions of effective gust velocity in thunderstorms and linesqualls for various altitude ranges. Table III sunmarizes the dataobtained to a threshold of 4 feet per second for several ranges of alti-tude from the surface to 35,000 feet. Table III also lists the recordtime and the average spacing between gusts for each altitude range.Figure 9 shows the probability distributions of effective gust velocityfor the several altitude ranges that are obtained by curves fitted tothe data of table III. In this investigation, the data for altitudesbelow 5000 feet were not used because the conditions investigated repre-sented random record taking in both clear air and clouds at the end ofthe flights.

From the tests performed with the XC-35 and the F-61C airplanes,the variation of expected maximum effective gust velocity with altitudewithin convective clouds has been determined. These results are sum-marized in figure 10, in which the data for the XC-35 airplane corre-spond to 100 miles of rough-air flying, while those for the F-61C air-plane correspond to 1000 miles. The latter data were obtained duringthe 1946 operations of the U.S. Weather Bureau thunderstorm project atOrlando, Fla., and are based on the maximum values of effective gustvelocity for each 3000-foot interval; however, the XC-35 data utilizeda complete count of all gusts,

Gust spacing.- Some information on gust spacing, that is, thedistance from peak to peak, has also been obtained. In reference 11,an analysis was made of the XC-35 data to determine the average spacingbetween the large gusts (defined as Ue greater than 5 to 8 fps)in areas of continuous rough air. Continuous rough air was definedas a sequence of large gusts in which the spacing between gustswas less than 2.2 -tconds. Table IV, reproduced from reference 11,sumarizes some of the pertinent characteristics of the large isolatedand repeated gusts. The table presents a comparison of the average andthe range of intensities and the average and range of spacings forisolated single gusts and sets of two and three repeated gusts occurringwith equal frequency.

More general information on gust spacing, contained in reference 9,indicates that the average spacing between gusts that were counted to anestimated threshold of 0.3 foot per second was a function of the airplanemean geometric chord. This count indicated an average spacing betweensuccessive peaks of U- chords so that the number of gusts per mile ofrough air is roughly equal to 500/E. The definition of the number ofgusts per mile of rough air led to the concept of "path ratio" whichprovides a measure of the percent of rough air encountered under oper-ating conditions.

Gust-gradient distance.- Figure 11 presents a typical plot ofmeasurements of gradient distance and gust velocity. Inspection of the

NACA TN 1976 13

figure indicates that the scattered pattern of data is not amenable todetailed analysis and, for such purposes, the data on gust-gradientdistance were sorted according to the variable under consideration.Figures 12(a), 12(b), and 12(c) present the data on the average gust-gradient distance as a function of the gust velocity (width of bracket,4 fps). Figure 12(a) is a sunmary of the data for all airplaneswith Hay expressed as multiples of the mean geometric chord;

figure 12(b) presents the same data with Hay expressed in multiplesof the airplane wing span; and figure 12(c), in feet. For comparisonwith other figures and for subsequent use, a faired curve was drawnthrough the data in figure 12(a) to agree best with the data fromthe XC-35 airplane.

The results presented in figures 12(a), 12(b), and 12(c) do notinclude the complete data for every airplane since some brackets, parti-cularly below about 8 feet per second, are not complete. The magnitudeof the acceleration increments for values of U less than 8 feet persecond was about the same order as the resolution of the accelerometer.For the larger gust velocities, some iaverage values were not plottedsince the number of points represented was less than three.

In some cases, sufficient data were available to obtain the probablevalues of the gust-gradient distance. The probable value was determinedby fitting a theoretical frequency distribution to the data and deter-mining the point with the highest frequency. The results are plottedagainst the corresponding average gust-gradient distance Hav infigure 13. Figure 13 includes two solid lines, a 450 line representingthe equality of the quantities and a line through the data offset by2 chords.

Data for the gust-gradient distance for the XC-35 and F-61C air-planes have been utilized to determine the variations of the averagegradient distance expressed in chords as a functi6n of altitude. (Seefig. 14.) In the case of the XC-35 airplane where no fixed altitudeswere flown, altitude brackets were selected, and the average gradientdistance was plotted against the center value for the pertinent bracket.The F-61C airplane tests were made at fixed altitudes, and the data havebeen plotted at the appropriate altitude level.

Spanwise gust distribution.- Records of local wing pressures andairspeeds obtained during the flight investigation with the XC-35 air-plane (reference 12) were evaluated to obtain the local values ofeffective gust velocity at each of four spanwise stations. The generalmethod followed was to plot the data for each gust as a function of thespanwise location and connect the points by straight lines. The indivi-dual spanwise distributions were later identified with the correspondingvalues of the gust velocity U and the effective gust velocity Ueobtained from the other flight records.

14 NACA TN 1976

Data on the spanwise distribution were sorted according to the shapeof the distribution as indicated in figure 15. Six shapes ranging fromthe uniform or rectangular distribution to the double triangular distri-bution are shown, and under each shape is noted the total number of gustsclassified in that category. Figure 15 also indicates possible variationsincluded under each heading.

The spanwise gust distributions represented in figure 15 were, inturn, evaluated graphically to obtain values of the lateral gust-gradientdistance H. The results are shown in figure 16 where the average valuesof the gradient distance in chords are given for a range of values ofgust velocity. The associated gust velocity U was obtained from thesynchronized acceleration data, and the faired curve shown in figure 16corresponds to that given in figure 12(a).

The significance of the values of Ue obtained from pressuremeasurements as compared to those determined from acceleration measure-ments has been examined in reference 12. Figure 17, reproduced fromthat reference, shows the average value of the local effective gustvelocity as a function of the effective gust velocity for a given gustas determined from acceleration records. The average value of Ue fromthe pressure measurements is the average value weighted according to theamount of wing area represented by the particular orifice or measuringstation. Also .shown in the figure is the line for equality of the twomeasures of Ue and the error band.

Since, in some cases, it is convenient to divide the lateral gustdistribution into symmetrical and unsymmetrical components, the gustshapes listed in figure 15 were classified according to whether they weresymmetrical or unsymmetrical and then represented as having a linearvariation of gust velocity across the span of the airplane. The resultsare shown in figure 18. The inset in figure 18 indicates the type ofvariation assumed and the two quantities obtained from the evaluation.The average gust velocity Ueav and the increment in gust velocity at

each wing tip AUe were taken as the symmetrical and unsymmetricalcomponents, respectively. Many small values have been omitted fromthe figure.

As in the case of the gust-gradient distance, the data have beenfurther analyzed to find an average unsymetrical gust increment.Figure 19 has been prepared from the summary of data for the differentgust shapes to show the average gust velocity for a gust of the unsym-metrical shape as a function of the average gust velocity of a triangulargust for equal frequencies of occurrence.

In addition to the determination of spanwise gust distribution fromlocal pressure distributions, synchronized records from accelerometerslocated at the center of gravity of the airplane and in the wing wereevaluated to obtain the angular acceleration in roll, which is related

NACA TN 1976 15

to the spanwise gust distribution. The results of the evaluation ofaccelerometer records for 17 flights are shown in table V, which indi-cates the frequency of occurrence of given values of angular accelera-tion with the associated values of normal acceleration increment.

Longitudinal gusts.- Rapid airspeed fluctuations have been used toevaluate the magnitude of longitudinal gusts. Figure 20, prepared froman analysis of the XC-35 airplane data, compares the maximum values ofthe horizontal gust velocities obtained from the rapid airspeed fluctua-tions with the maximum vertical gust velocities. Each point representsa separate traverse or run. The results of a detailed analysis of air-speed and acceleration records in gusty air from the XBM-l and Aeronca C-2airplane investigations are shown in figure 21 and indicate, for bothairplanes, the relation of the horizontal gust velocities to the verticalgust velocities for equal frequencies of occurrence.

ACCURACY OF RESULTS

Consideration of instrumental and reading errors in evaluating thedata from the several airplanes, together with a knowledge of the problemsinvolved in the reactions of an airplane, indicates that the possibleerrors in the derived quantities that are of interest are approximatelyas follows:

Gust velocity based on acceleration, percent .... ...... ..... . ±10Gust velocity from pressure measurements, feet

per second ........ ............................. ±4Gust velocity from airspeed measurements, feet

per second ............. .......................... ±10Gust-gradient distance, chords ....... ................ ±1 to ±2Lateral gust-gradient distance, percent .... ............. . +.±20

Spacing, chords ............. ......................... ±1

The accuracy of the gust-velocity measurements, whether true gustvelocity or effective gust velocity, from acceleration records dependson the quality of the records obtained, the availability of a gust-tunnel calibration of the airplane, and experience in reading andinterpreting the records.

The local gust velocities obtained from wing-pressure measurementswere tested for accuracy by comparing the average value of the localgust velocities with the effective gust velocity from acceleration data.The results indicate that the two quantities are equivalent but that thedata scatter over a range of about 4 feet per second.

16 NACA TN 1976

The gradient distances determined from accelerometer records are afunction of both the time resolution and the response characteristics ofan airplane due to known gusts. Examination of gust-tunnel test resultsindicates that, under average conditions, the airplane response placestwo limits on the gust-gradient distance determined from accelerationrecords. The first limit, for the shorter gradient distances, is speci-fied by the lag in lift. The gradient distances lying above the dashline in figure 4 are not generally recognizable on an accelerometerrecord. Thus, this limit is from 2 chords to about 4 chords for theaverage airplane. The second limit, for the longer gradient distances,arises from the fact that, as the airplane penetrates farther and fartherinto a long gradient gust, the effect of the pitching and vertical motionof the airplane, under the action of the gust, tends to counteract thecontribution of lift due to each increment of gust as it is encountered.

The lateral gust-gradient distance is a more questionable quantitythan the gust-gradient distance determined from accelerometer recordssince no single concept as to shape has been obtained. The lack ofdetailed data and the erratic character of the gust distributions in aspanwise direction (fig. 15) require the use of considerable Judgmentin arriving at any numerical values. Comparison of the actual values ofthe gust-gradient distance from accelerometer records and the corre-sponding values of the lateral distance from pressure records indicatesthat the data are reasonable and in agreement with the actual conditions.From the preceding remarks it is obvious that the error is significantand the value of 20 percent previously mentioned is only a crude estimate.

DISCUSSION

Gust intensity.- Because only a small number of all the accelerationpeaks in rough air can be evaluated for true gust velocities, the effectivegust velocity has been used as the measure of intensity and frequency ofatmospheric gusts. Although the effective gust velocity Ue is afictitious quantity, it bears a fixed relation to the gust velocity fora given airplane and given conditions of air density, gust shape, andgust size. The effective gust velocity is generally about 50 percont to70 percent of the gust velocity.

The largest effective gust velocity recorded to date was about55 feet per second and corresponds to a gust velocity of 100 feet persecond for typical conditions. Fortunately, gust velocities this largeare not frequently encountered. The distributions of effective gustvelocity in figure 8 show that the limiting distributions for a widerange of airplane sizes and weather conditions are reasonably close.Reference 9 concluded, on the basis of these results, that the distri-bution of gust intensities was essentially independent of airplane size

NACA TN 1976 17

and source of turbulence. Figure 9, in contrast, shows that the XC-35data for different altitude brackets result in distributions with slopesthat vary and, when checked against figure 8, differ from those curves.This discrepancy indicates that the distributions of effective gust

velocity may not be independent of the source of turbulence. Independ-ency is a reasonable assumption at this time for general use.

Figures 9 and 10 show that, for altitudes above 9000 feet, themaximum gust intensity in rough air associated with convective clouds isessentially a constant. Below 9000 feet, the XC-35 data indicate adecrease in intensity, due in part, according to reference 10, to thefact that the records were taken in clear air and clouds. Considerationof figure 10 indicates that little difference exists in the expectedmaximum gust velocities for all altitude ranges.

Gust-gradient distance.- Figure U and similar plots for otherairplanes show that gust-gradient-distance data are of a random character.Comparisons of such plots indicate that airplane size might be a signifi-cant parameter, as in the case of boats where waves of small wave lengththat are of no concern to a large boat cause the small boat considerabledifficulty. In a similar manner, gusts that cause a rough ride on asmall airplane, such as the Aeronca C-2, would be expected to be of suchsmall size as to have little effect on a large airplane, such as the XB-15.

Comparison of figures 12(a), 12(b), and 12(c) indicates that thegradient-distance data show much less scatter on the basis of the meangeometric chord than on the basis of span or feet. The scatter of points

1when the gust-gradient distance is defined in chords is about lf to 1

for a given value of U, while for the gust-gradient distance plotted interms of airplane span, the scatter is greater. The data of figure 12(c)show that when the gust-gradient distance is expressed in feet, theaverage values of the distance vary from 40 feet to 200 feet for a givengust intensity. Inasmuch as the agreement for the different sets ofdata is best when the gradient distance is expressed in chords, the gust-gradient distance appears to be roughly independent of the airplane whenexpressed in wing mean geometric chords.

The adequacy of the average value of the gust-gradient distance forthe representation of gradient-distance data deserves some consideration.The relation between the average value and the most probable value 'shownin figure 13 indicates that the probable gradient distance is about 1 chordto 2 chords less than the average gradient distance. Since the offsetappears to be constant, the use of the average gust-gradient distance,which is generally easier to determine, is believed to be satisfactoryfor analysis.

18 NACA TN 1976

As indicated in table II, a variety of weather conditions, from line

squalls to gustiness in the ground boundary layer, is included in thepresent data. If the data of figure 12(a) are assumed to be comparable,regardless of airplane, the type of weather appears to have no effect onthe gust-gradient distance.

Figure 14 indicates that the average gust-gradient distance is inde-pendent of altitude in convective clouds. The data scatter somewhat butthe over-all agreement appears to be good.

General considerations would indicate that the gradient distance

might increase with gust velocity. Previous study and figure 12(a) haveindicated such a relation, although the evidence is not conclusive.When the faired curves of figures 12(a) and 16 are considered, such avariation appears to be a reasonable estimate. The evidence available(fig. 12(a)) is believed to indicate that for large gusts the averagegradient distance is essentially constant but decreases rapidly at the

smaller gust velocities.

Spanwise gust distribution.- The shapes of the lateral gust distri-butions, as indicated by figure 13, take many irregular forms. Fromconsideration of the frequency of occurrence, the triangular, double-triangle, and unsymmetrical gust shapes predominate. Inasmuch as thedouble triangle can lead to wing bending moments along the span equalto those due to a uniform gust distribution, while the triangular gustshape would lead to reduced wing bending moments, the selection fordesign of a uniform gust velocity across the span for the symmetricalload condition is conservative. The relative percentages of the sym-metrical (triangle, and so forth) and unsymmetrical gust shapes indicatethat the unsymmetrical gust varying uniformly across the span appearsquite frequently.

Comparison of the data for the average lateral gust-gradient dis-tance as a function of gust velocity U (fig. 16) with correspondingresults for longitudinal gust-gradient distances (fig. 12(a)) indicatesthat the gradient distances are essentially the same in both directions.This agreement is indicated by the fact that the same empirical curvefits both sets of data and the results show the same trend of increasinggust-gradient distance with increasing gust velocity. Because data fromonly one airplane have been presented and the precision of measurementof lateral values is poor, as previously cited, the excellent agreementbetween figures 16 and 12(a) is to some degree fictitious, the degreebeing unknown. Within the limitations of results the lateral and longi-tudinal gust dimensions are concluded to be essentially the same.

Inspection of figure 18, relating the unsymmetrical components ofthe effective gust velocity to the average uniform gust velocity acrossthe span, indicates that no clear relations between the unsymmetrical

NACA TN 1976 19

components and the average gust velocity exists but that two boundariesappear to exist. A fairly definite boundary rising from the lower left-hand corner of the figure and corresponding to equality of the unsym-

metrical component of gust velocity and the average gust velocity isindicated. As higher values of the average gust velocity are considered,the results scatter considerably, but an upper boundary is found atfrom 9 to 10 feet per second. The boundary holds for gust velocitiesup to 40 to 48 feet per second. On the basis of this upper limit, theunsymmetrical component of gust velocity above 10 feet per second can beconsidered rare. Therefore, the unsymmetrical gust can be considered tobe composed of two components, an unsymmetrical component amounting toa maximum of about .l0 feet per second with opposite signs imposed at each

wing tip and a linear gradient across the span, and an average uniformgust velocity of any pertinent value.

A question of some importance is the determination of the magnitude

of the unsymmetrical components for other aircraft of entirely differentspans. For example, if the span of the airplane were doubled, would theunsymmetrical component amount to twice the value obtained from the datashown herein? In order to obtain information on this question, themaximum value of the unsymmetrical gust components computed in refer-ence 13 from angular-acceleration data was compared with the valuesobtained herein. It was found that for the XB-15 airplane, which has aspan of about 150 feet, the unsymmetrical components of gust velocityat the wing tip would be about 13.7 feet per second. 'This value isslightly greater than indicated by figure 18 but is not, by any means,proportional to the span of the airplane. Similar data of a statisticalnature obtained for the XC-35 airplane (table V) indicate that the maxi-mum value of the angular acceleration on that airplane varied from about1.95 to about 2.25 radians per second per second. Computations utilizingthe formula given in reference 13 yield a maximum gust-velocity component

of about 121 feet per second. This value is in fair agreement with the

one obtained for the XB-15 airplane and indicates that the tip valuesare independent of span. Since the values based on angular accelera-tion are somewhat more conservative than those based on wing pressures,more reliance should be placed on these values.

When the information on unsymmetrical gusts is utilized, the averageeffective gust velocity that should be used in conjunction with the maxi-mum unsymmetrical component of 14 feet per second must be determined.The data of figure 19 indicate that for an effective gust velocity in theneighborhood of 30 feet per second, the average gust velocity for theunsymmetrical gust would be about 22 feet per second.

Gust spacing.- Inspection of table IV indicates that the spacing ofrepeated gusts for two or three gusts in sequence is about 22 chords

with a spread in actual values of some 20 chords for all sequences.

20 NACA TN 1976

The spacing is approximately twice the average gust-gradient distance of10 to 14 chords. These data indicate that the gust shape in the direc-tion of flight is either triangular or sinusoidal in character ascontrasted to the "flat-top" gust assumed in past years.

From time to time, comparisons are made of the gust spacing inreference 11 of 22 chords with the gust spacing that was derived fromstatistical gust data in reference 9 of 11 chords. The discrepancy be-tween the two figures arises from the fact that the data on gust spacingpresented in reference U1 were obtained for the larger gusts and representdata on gust intensities ranging from 5 feet per second up to the maxi-mum value recorded, whereas the gust spacing listed i-n reference 9is based on the average spacing of all gusts from a gust velocity of0.3 foot per second to the maximum value experienced by any of the air-planes considered.

The sequences of gusts found in reference U were such that inabout two-thirds of the cases of sets of two the gusts were of oppositesign while the remaining sets of two were composed of gusts of like sign.The larger gust intensity could be found at any point in the sequenceunder consideration.

Longitudinal gusts.- Inspection of the data for the maximum valuesof the horizontal and vertical gust velocities in the same traverse(fig. 20) indicates equality of the gust intensities in the two direc-tions. Figure 21 for the XBM-1 and Aeronca C-2 airplanes gives essen-tially the same indication, but the agreement is not exact and thediscrepancy between the values of the gust velocities is an offset ofroughly 1 foot per second. The data obtained from the Aeronca C-2 air-plane show the larger discrepancy. Some of this discrepancy may be dueto the fact that the amount of horizontal-gust data was larger than theamount of vertical-gust data for the Aeronca C-2 airplane and smallerthan the amount for the XBM-l airplane.

Since the maximum gust intensity in the horizontal direction isequal to the vertical gust intensity for the same region of turbulenceand a preliminary investigation of frequency distributions indicatesthat the frequency distributions are essentially the same, the atmos-pheric turbulence seems to be isotropic. Previous indications as tostructure of vertical gusts, that is, gust spacing, gust-gradientdistance, and lateral distributions of gust velocity, would be assumedto apply to horizontal gusts.

The preceding results indicate equal gradient distances for thelongitudinal and lateral faces of the gust velocity distribution, andthis equality suggests that the gust is symmetrical about a verticalaxis. In keeping with this concept, the findings suggest that thedistribution might be visualized as a four-sided pyramid with a base

NACA TN 1976 21

length of 20 to 28 chords. While such a velocity distribution mayrepresent the average gust, because of the wide variations in shape, awedge-shaped velocity distribution such that the velocity distributionalong the span is uniform and the longitudinal shape is either triangularor sinusoidal is recommended for load calculations.

CONCLUDING REMARKS

Although much of the information on gust structure can be ration-alized to obtain a "standard" gust, this material should be used withcaution for unconventional types of aircraft. The gust structure ofinterest is, of course, dependent to some degree on the airplane charac-teristics. Many other sizes of gusts exist and those that affect theairplane may be only a small part of the random variations that exist in

the atmosphere.

- Available information on the structure of atmospheric gusts has/shown that, when the gust size and the gust-gradient distance are expressed \in mean geometric chords, the gust size is independent of airplane,weather, topography, and altitude. The probable size of the gust is20 chords, and the probable gust-gradient distance for the standard gustis about 10 chords. A wedge-shaped gust with the gust velocity uniformacross the span and either triangular or sinusoidal in shape with a baseof 20 chords is believed to be the proper type for most load calculations)

For a sequence of gusts, the gusts may be of either like or unlikesign and will be continuous, with the gust peaks spaced 20 chords apart.

Since the maximum horizontal and vertical gust intensities andfrequency distributions are essentially the same within any region ofrough air, the gust structure obtained for vertical gusts should applyequally well for horizontal gusts. Such information is pertinent wheregust loads are under consideration for diving airplanes or missiles.

Since the data are influenced by the reactions of the airplane, theapplication to unconventional configurations should be investigated bya detailed analysis of several possible combinations of gust shape andsize.

AIRPLANE REACT IONS

The second phase of the gust-load problem is that of determiningthe reaction or forces imposed on an airplane due to a known gust. Thefactors considered are the aerodynamic coefficients and the possible

22 NACA TN 1976

effects of stability and elasticity. The purpose of this section is toindicate what is known about these factors by coordinating the availableinformation. In most cases, specific procedures or numbers to be usedin load calculations are not obtained. In regard to some factors, thestate of available information is unsatisfactory but the factor isconsidered and its status is indicated.

METHODS

The three methods utilized in the study of airplane reactions were ananalysis and two experimental methods. The experimental methods consistof tests of models in the Langley gust tunnel and flight tests with full-scale airplanes.

Analysis

Inspection of the equations given in references 14 and 15 indicatesthat the inclusion of unsteady lift leads to variable coefficients, whichresult in integral equations when the unknown appears under the integralsign. In all cases the integrals that appear are of the same form andrepresent the application of the principle of superposition to unit-Jumpsolutions to obtain the response to arbitrary or known disturbances.

The principle cited is illustrated in figure 22 for a linear varia-tion in angle of attack for which the lift on an airfoil after sl chords

of penetration is desired. In figure 22(a) the angle of attack is assumedto vary directly with s and the development of lift per unit change inangle of attack is assumed similar to that shown in figure 3. The angle-of-attack variation is assumed to be approximated by a series of unitchanges in angle of attack superimposed in the s direction. For steadylift, the corresponding variations of lift with s are indicated by thestraight line and steps in figure 22(b). The unsteady lift develops foreach step in angle of attack according to the dash curves and the approxi-mate lift at sl is the sum of the contributions of each step at s1 .The result at s I can be written as

d CL _

i

CCL s)- dd CLA(sl - s) As0 0

NACA TN 1976 23

or for an analytic expression of differential increments

SdCL s CL ds

This expression is comonly known as Duhamel's integral and is illus-trated by Berg in reference 16. The integral can be evaluated analy-tically step by step as indicated in figure 22 or graphically by Carson'stheorem (reference 17).

As previously mentioned, the type of equation obtained is of the

form

dl Si dC LC A CL(Sl s) ds-B CL (Sl -S) ds

L w 1 L . T h e d

where C is the local value of CL at l* The difficulty inW1 W

solving the equation arises from the fact that the relation between CLw

and s must be known before the second integral on the right side canbe evaluated. The equation shown is a simple case and the more completeequations of motion consist of additional integrals and, in some cases,derivatives of integrals.

Solutions of equations of the type shown have been obtained bymethods of successive approximation, Fredholm's solution (reference 6),Laplace transforms (reference 14), or by assuming, as in reference 18,that the function is known. The need for solutions for arbitrary dis-turbances and the complicated nature of solutions generally lead tographical or approximate methods in all but a few cases.

Gust-Tunnel Testing

The Langley gust tunnel (fig. 23) was built to permit the determina-tion of airplane reactions and other pertinent quantities under controlledand known conditions. It consists of a catapult to launch a dynamicallyscaled airplane model into steady level flight through a vertical jet ofair having characteristics that are under control, a means of catchingthe model, and, finally, suitable equipment to record the required

24 NACA TN 1976

information. The old NACA gust tunnel described in reference 19 wascapable of handling 3-foot-span models of airplanes at speeds up toabout 50 miles per hour but in 1945 was replaced by a tunnel that isable to handle 6-foot-span models at speeds up to 100 miles per hour.

The accuracy of measurement at present is about 0.05g for accelera-tion, 0.3 foot per second for speed, and 0.01 inch for deflection of thewing or flap. Angular motions are determined within 0.10 of pitch-angleincrement and about 0.20 for the position of any flap. All measurementsexcept that of speed are incremental values from steady conditions and,as such, depend upon the steadiness of flight prior to entry into thegust. At peak acceleration for sharp-edge gusts, the acceleration incre-ment is considered accurate to within 0.lg and the pitch-angle incrementto about 0.10, but the accuracy is questionable for the longest gust-gradient distance of about 16 chords.

In fundamental studies such as the determination of unsteady-liftfunctions, the solution obtained from gust-tunnel tests is an indirectone since the acceleration increment due to a gust is dependent on thedifference between two terms. Thus, it is not possible to determinewhether the correct values of the unsteady-lift functions are used, butonly whether the use of unsteady-lift functions for a given shape isadequate. If sufficient data are collected utilizing different modelsof many sizes and shapes in different gusts, the various unsteady-liftfunctions can be evaluated to a limited degree.

Flight Investigations

Two approaches have been utilized for flight investigations of air-plane reactions, one consisting simply of detailed analysis of flightrecords to obtain the relations desired, for example, between the pitchof an airplane and the acceleration imposed on the airplane, and theother consisting of flying an airplane in rough air to obtain statisticaldata for different conditions and then statistically comparing the reac-tions of the airplane. The first approach was used in a rather crudemanner in reference 3, in which a determination was made of the effectof airplane wing loading and speed on the gust load factor. The statis-tical approach may permit checks to be made of both theoretical and gust-tunnel results, but the procedures and techniques have not been developedto the point where precise results can be obtained.

TRANSIENT AERODYNAMICS

The material presented in this section covers the development of thelift force and downwash but does not cover the variation in moment

NACA TN 1976 25

coefficient. The development of lift following a sudden change in angleof attack is assumed to be independent of the slope of the lift curveand can be treated as a separate subject. The neglect of possible varia-tions in moment coefficient appears justified at this time on the basisthat theory indicates that the zero-lift moment coefficient is unaffected.

Unsteady-Lift Functions

In the present paper, the variation of lift coefficient for a unitchange in angle of attack has been referred to as CL or as the

Wagner function, and the corresponding variation in lift coefficientfollowing a change in angle of attack due to penetrating a unit gust hasbeen called CL or the Klissner function. The Ktissner function is

grelated to the Wagner function in that it has been derived from it byconsidering the airfoil penetrating a gust to be replaced by a deformingairfoil where the deformations correspond to the chordwise angle-of-attack distribution due to gust penetration. Unless otherwise stated,the lift at any time after the start of the angle-of-attack change isexpressed as a fraction of the final lift coefficient.

Infinite aspect ratio.- Both the Wagner function and the Kiissnerfunction for unsteady lift have been derived a number of times. Theformer was originally given by Wagner in reference 20 and has beenchecked experimentally by Walker in reference 21 by measuring the circula-tion about a wing following a sudden change in forward speed. Figure 24summarizes the computed and observed circulations obtained by Walker.Although the amount of direct experimental verification is limited,several analytical studies agree and indicate that the Wagner functionshould be close to correct.

The Kissner fuhction has also been computed a number of times anddifferent results have been obtained. Figure 25, which Is based on datataken from references 2, 5, and 22 to 25, presents the results of sixseparate computations of the lift ratio CL as a function of the

gdistance penetrated into a sharp-edge gust and shows considerablescatter. The derivation given by ICssner in reference 5 is probably thebest. No direct experimental verification of this factor is available,but Kiissner has made several attempts at verification by dropping air-foils equipped with end plates through the boundary of a wind-tunnel jet.The tests made by Kiissner have been described in reference 5 and thecompal-isons of the computed and experimental flight-path curvaturesindicate good agreement, at least for penetrations up to 3 to 4 chords.

26 NACA TN 1976

The values of CLa and CLg for the infinite-aspect-ratio wing are

presented in figure 26. If the pitching motion of the airplane is notconsidered, the exact shapes of the unsteady-lift functions are unimportantand the discrepancies noted in figure 25 do not appear to be significant.

Finite aspect ratio.- The effect of finite aspect ratio on theunsteady-lift functions has been investigated by Jones in reference 14and these results are shown in figure 26. This figure indicates that,as the aspect ratio decreases, the lift develops more rapidly, parti-cularly at the start, until for the limiting case of zero aspect ratiothe variation in lift might be expected to correspond to that for steadyflow conditions. The estimation of the unsteady-lift functions forlower aspect ratios than those shown in figure 26 has been made by extra-polating the data by assuming that at zero aspect ratio, the unsteady-lift function disappears. Unpublished tests made with a flying winghaving an aspect ratio of about 1.27 showed that this method led toreasonable values. The calculated value of the acceleration ratiowas 0.92 as compared to an average experimental value of 0.93. Theseresults indicate, therefore, that for flying wings finite theory applies.Other results, shown in figure 27 and given by Keuthe in reference 17and by Sears and Keuthe in reference 26, indicate that the unsteady liftdeveloped on a low-aspect-ratio wing subjected to a gust more closelyapproximates the unsteady-lift function for the two-dimensional casethan that for aspect ratio 3.

An indirect verification of unsteady-lift functions has been obtainedby comparing the calculated and actual response of airplane models to asharp gust. The curves in figure 28 show the calculated accelerationratio sn/,n s as a function of the mass parameter [1g* The calculation

for aspect ratio 6 is based on the unsteady-lift function given infigure 26 and that for infinite aspect ratio is based on the unsteady-lift functions given by Rhode in reference 4. The test points shown infigure 28 represent experimental values of the acceleration ratio deter-mined from tests in both the old and the new gust tunnels. The resultsare for all types of airplanes from tailless high-speed configurationswith wings swept back 350 to transports. As can be seen from figure 28,the experimental data scatter about the curve based on the unsteady-liftfunctions for aspect ratio o and below the curve for aspect ratio 6.The results indicate that, for airplanes that include a fuselage, theuse of the unsteady functions for infinite aspect ratio have givenadequate and in mdst cases more accurate predictions of the accelerationratio than the computations based on the finite-aspect-ratio theory ofJones.

The discrepancy between experiment and theory was considered as tothe effect of interference on the experimental results. If the fuselageis considered as an elongated wing having a chord three times that

NACA TN 1976 27

of the wing, then at peak acceleration in a sharp gust, the wing hastraveled about 4 chords while the fuselage has traveled 1. On this basis,the lift on the fuselage might be considered zero or at most about halfof its steady-flow value. If this hypothesis is compared with the mater-ial given in reference 19 (some of the values were in error and have beenrecomputed), the results shown in table VI are obtained. The results intable VI indicate that, although Jones' unsteady functions are much toohigh on the basis of gross area and the functions from reference 4 aresomewhat high, the use of a net wing area plus one-half the fuselageintercept brings all calculations into closer agreement. In fact, forthe infinite-aspect-ratio functions, the discrepancies are less than theprecision of the data. If the net wing area is assumed, then both finite-and infinite-aspect-ratio functions differ from experiment by about thesame amount, the results based on reference 14 being high and thosebased on reference 4 being low. Similar corrections may apply to Keuthe'sresults (fig. 27). Although the evidence indicates that the unsteady-lift functions for infinite aspect ratio should be used for conventionalairplanes in conjunction with the net wing area plus half the fuselageintercept, the use of net area is recommended and is discussedsubsequently.

Unpublished tests of a skeleton airplane equipped with a wing sweptback 45 shoved that the installation of the fuselage had no appreciableeffect on the maximum acceleration increment. In this particular case,however, the length of the wing from the leading edge of the root sectionto the trailing edge of the tip section was almost equal to the lengthof the fuselage. Since one effect of sweep would be to modify the rateof development of lift on the wing, the difference between the liftdeveloped on the wing and that on the fuselage for a given gust pene-tration may have been too small to be noted during the test. Althoughthe evidence is still scant and conflicting in some respects, the use ofnet wing area appears to be better than the use of gross wing area forthe sharp-edge gust except when the side projections of the wing and the.fuselage are about the same length.

The determination of the proper wing area for the gradient- gust iscomplicated by the introduction of the pitching motion of the airplane,and comparisons must be made between the detailed calculations and experi-ment. In the investigations that have been made (reference 15) theresults have indicated that the use of the net wing area yields the bestover-all agreement between calculations and experiment for gradientdistances between 0 and 16 chords.

The use of tapered and swept wings for modern aircraft leads toproblems in the computation of the gust load factor. Relatively littleinformation is available on either problem, but the data of reference 19indicated that moderate amounts of taper (up to 2:1) have little or noeffect and can be neglected at least until experimental evidence of a

28 NACA TN 1976

more accurate nature is available. Large values of taper (for example,of about 3:1) and large sweep angles (300 to 400) lead to considerableconcern as to the adequacy of the unsteady-lift functions, particularlythe Ki ssner function CL The concern arises from the fact that for

wings of high taper, the root section with the larger chord will have arate of development of lift for a given distance penetrated into a gustconsiderably less than that of the narrower tip chord. In the case ofsweep, the root of a sweptback wing penetrates the gust first and thelift may develop an appreciable value before the tip sections ever enterthe gust.

With regard to the effect of wing taper on the unsteady-liftfunction, no theoretical developments are available to permit accuratecomputation, and calculations have been made by utilizing strip theoryto develop the unsteady-lift functions for the finite wing from the two-dimensional functions of Kissner and Wagner. Experimental data availableto check the effect of taper on the unsteady-lift functions are indirectand are the result of tests of two specific airplanes. In both cases,calculations based on the results presented in reference 4 were in agree-ment with the experimental data for the sharp-edge gust in which pitch

can be neglected. In the case of the large flying boat with 32:1 taper

ratio, the discrepancy amounted to about 2 percent. The maximum dis-crepancy was well within the experimental error. On the basis of these

limited results, the effect of taper, at least up to 31:1, appears to be

negligible insofar as the calculation of total loads is concerned.

No theoretical studies are available for the sweptback wing, butrecent test results for a straight and a 450 sweptback wing are available.Tests were made on a straight wing with a 2:1 taper and on the equivalentof the straight wing where each half-wing was rotated about the midchordpoint at the root so that the span changed with the angle of sweep. Thesweep was such that the midchord line was at an angle of 450 to itsoriginal position. Flights were made through a sharp-edge gust, and anaverage time history of acceleration increments as a fraction of themaximum value is shown in figure 29. For comparison with the experi-mental results, two curves are shown, one based on the theory presentedin reference 4 which disregards the effect of sweep on the unsteady-liftfunctions and the other represents the calculated time history of accele-ration based on the assumption that strip theory could be applied to derivethe Kissner function for the swept wing.

Figure 29 shows that strip theory is in good agreement with experi-ment throughout the entire history, but the neglect of the effect ofsweep on the lag in lift is in error at the start of the motion, althoughgood agreement is obtained for distances greater than 4 chords. Both

NACA TN 1976 29

calculations should yield essentially the same values for the largerdistances since the conditions tend to approach the steady state. Thediscrepancy between experiment and strip theory appears to be due in partto positive pitch of the model during the traverse of the gust. Therefore,the effect of sweep on the unsteady-lift functions cannot be neglectedif the shape of the curve is considered important.

The unsteady-lift theory as developed by Wagner, Jones, and othershas been evolved for monoplanes only but the unsteady-lift functions forbiplanes may be needed in connection with gust-load calculations. Notheory is available on this problem, but consideration of the vortexsheets associated with the biplane indicates that, for -the first fewchords after a sudden change in angle of attack, the tip vortices of thewings are short and have a negligible effect on the mutually inducedangle of attack of one wing upon the other. Since the equivalent mono-plane theory assumes campletely developed vortex systems with the shedvortex at infinity, it might be expected that for a biplane in a sharpgust the two wings would act independently, and, therefore, the unsteady-lift functions and other associated aerodynamic parameters for the bi-plane should be based on the characteristics for each individual wing.Figure 30, which has been reproduced from reference 8, shows the resultsof tests of a biplane. The results in the figure are the accelerationsobtained as a result of experiment in the Langley gust tunnel, the curvepredicted by assuming that the two wings act independently, and the curvepredicted by assuming that the equivalent-monoplane theory holds.Infinite-aspect-ratio unsteady-lift functions were used. For the shortergust-gradient distances where the tip vortices might be expected to havelittle effect, theory and- experiment are in excellent agreement if thetwo wings are assumed to act independently. The computed curve foracceleration increment, based on reference 4, is considerably below theexperimental data; thus the tip vortices have little effect, at leastup to 8 or 10 wing chords. As the gradient distance is increased to20 chords, the experimental data fall below both calculated curves becauseof the pitching action of the airplane.

The effect of compressibility on the unsteady-lift functions is ofinterest because it may change the shape of the curves, but little orno information on this problem is available. Jones has indicated thatfor subsonic speeds the effect of compressibility would be to reduce the

aspect ratio of the wing according to the relation 1i - M2 . The Ecorrection of reference 27 is changed at the same time to correspond.For the transonic range where mixed flows occur the variation in theunsteady-lift functions is unknown. At supersonic speeds the effectof unsteady lift would be expected to disappear since the effect requiresthe transmission of pressures forward. It would be expected that theunsteady-lift functions would change only slightly up to high subsonicspeeds and that at supersonic speeds, the functions would disappear.

30 NACA TN 1976

Slope of Lift Curve

Investigations to determine the proper slope of the lift curve tobe used in gust-load calculations have been made mainly in the Langleygust tunnel. The information available for presentation is indirectand in many instances inconclusive because of interrelations of manyfactors. The factors involved in the computation of the proper slope ofthe lift curve include the determination of the airfoil section character-istics, aspect-ratio corrections, interference effects, the effects ofconfiguration with reference to sweep and multiplanes and the effects ofcompressibility and power.

Section characteristics.- As indicated by the results presented infigure 28, the conventional estimates of the lift-curve slope togetherwith the unsteady-lift functions for infinite aspect ratio gave the bestresults in predicting the acceleration increment due to a sharp-edgegust for ordinary airfoils. The use of the laminar-flow section intro-duced airfoils having higher slopes of the lift curve. The increasewas of considerable concern since it amounted to an increase of 10percent in the load-factor increment. Brief consideration indicatedthat the slope of the lift curve depends on the steady-flow relationbetween the boundary-layer thickness and angle of attack. It was

believed that under unsteady flow conditions the relation for steadyflow would not apply and, therefore, the boundary layer would not havetime to adjust itself during a sudden change in angle of attack. Sinceno experimental or theoretical information was available in connectionwith the probable slope of the lift curve, experimental evidence wasneeded.

For this purpose a skeleton model with a laminer-flow wing wastested in the Langley gust tunnel. The characteristics of the test

model are given in table VII and figure 31. For the first tests thewing had a smooth surface. For the second tests, carborundum grainswere glued over the leading edge of the wing back to 7.8 percent of thechord on both the upper and lower surfaces. The slopes of the liftcurve for the smooth and rough wings have been included in table VII andare based on experimental data presented in reference 28 corrected tofinite aspect ratio according to reference 27. In addition to the lift-curve slopes obtained from low-turbulence wind-tunnel tests, the theore-tical lift-curve slope, based on the theory presented in reference 29, isalso included in the table.

The average values of the acceleration increments for the smoothand rough wings and the probable errors are given in table VIII. Theacceleration increments computed on the basis of the characteristics in

table VII have also been included. Table VIII shows that the maximumacceleration increments for the two test conditions are essentially the

same. Comparison of the 0.02g experimental difference with the calculated

NACA TN 1976 31

difference of 0.26g shows that roughening an airfoil to produce aturbulent boundary layer has no effect on the slope of the lift curvethat is applicable in the unsteady flow conditions of a sharp-edge gust.If these results are extended by the assumption that the flow conditionsfor a conventional airfoil in the steady state are simulated by thosefor the roughened low-drag wing, airfoil section characteristics areconcluded to have no significant effect on the acceleration incrementobtained in unsteady flow conditions of a sharp-edge gust.

Since the most probable gust is one with a gradient distance of10 chords, the averages of the maximum acceleration increments for thetwo test conditions were calculated for gusts with gradient distanceup to 12 chords by applying the principle of superposition to the testresults for the sharp-edge gust. The results of these calculations

showed only 2 -percent difference between the average values. On the

basis of this simple analysis, airfoil section characteristics have nosignificant effect on the acceleration increments for gusts with grad-ient distances from 0 to 12 chords. From the present data, however, it

'is not possible to specify the gradient distance at which the differencewould become noticeable as the result of attaining quasi-steadyconditions.

For the laminar-flow type of airfoil, tests in low-turbulence windtunnels together with the aspect-ratio corrections of reference 27should yield an adequate prediction of the acceleration increment due toa sharp-edge gust. The use of the corrections and the determination ofsection characteristics for an arbitrary airfoil are, however, stillopen to question since tests in low-turbulence tunnels on the arbitraryairfoil sections tend to show low slopes of the lift curve. In view ofthe many interrelated factors, some of which are discussed in subsequentparagraphs, it appears that the selection of an arbitrary section lift-curve slope of about 6 per radian will be adequate for gust-loadcalculations.

Aspect-ratio corrections.- As previously noted, the data in fig-ure 28 were obtained for conventional airplanes, but the data in table VIIIapply to a skeleton airplane with little or no fuselage. The combinedeffects of fuselage interference, aspect-ratio corrections, unsteady-lift functions, and section characteristics are all involved and at thepresent time cannot be entirely segregated. For the time being, simple

6Aaspect-ratio correction factors appear to be adequate. The factor A + 2

has been used with satisfactory results in connection with gust-loadstudies.

32 NACA TN 1976

Swept wings.- Table JI (from reference 30) shows the results ofgust-tunnel tests on a wing swept back 450. The tests were made in asharp-edge gust and the acceleration increments for a gradient distanceof 9 chords were obtained by superposition. All results are correctedto zero pitch of the model. Calculated values are also included. Oneset of values is based on the results of wind-tunnel tests of the air-plane model, tail off, and the other set differs from the first in thatthe slope of the lift curve for the swept wing was taken as that for thestraight wing multiplied by the cosine of the sweep angle. In both cal-culations, the unsteady-lift function for the wing CT was obtained bymeans of strip theory. g

Inspection of the results given in table IX shows that the use ofthe cosine law for predicting the slope of the lift curve for the sweptwing gives excellent results, the differences between experiment andcalculation being within the experimental error. The use of lift-curveslopes from steady-flow tests to calculate the acceleration incrementsfor the swept wing yields values some 20 percent below experimentalresults. Similar tests on a 450 sweptforward wing verify this result.

The low value of acceleration increments calculated from the resultsof wind-tunnel tests has been of concern. At present, no definiteevidence is available to explain this discrepancy, but it is believedthat the difference can be ascribed to the behavior of the boundarylayer in the unsteady flow condition that exists during traverse of agust. The discrepancy emphasizes the importance in the prediction ofgust load factors of using the proper lift-curve slope. On the basisof limited data better results seem to be obtained if the cosine law ofvariation is used rather than wind-tunnel results.

The results obtained to date apply to a definite method of sweepingthe wing (rotating the wing panel) to obtain the equivalent straightwing. Other systems lead to other combinations of aspect ratio and sweepand may yield different results. In such calculations, the same procedureas that described in the present paper should be utilized.

Scale effects.- Tests in the old and new gust tunnels of models ofthe Boeing B-247 airplane (table X) were made to obtain a measure of anyscale effects. A 3-foot-span model was tested in the old gust tunnel as areference for design requirements. When the new gust tunnel was builtthis model and one dynamically similar but twice as large were tested.The results of all three tests are shown in figure 32 as a plot of theacceleration ratio as a function of gradient distance in chords.

Inspection of figure 32 shows excellent agreement between theresults for the two models; this fact indicates that for the conditionstested no scale effect was present. The largest discrepancy is for asharp-edge gust and is no greater than differences in results for tests

NACA TN 1976 33

of the same model in two tunnels. Some of the discrepancy may be due tothe fact that the gust shape was the same in absolute dimension butdiffered slightly on the basis of chords of the two models.

Effect of power.- When the slipstream covers the entire span of theairplane, the steady-flow slope of the lift curve has been shown toincrease about 100 percent for the slipstream corresponding to the climbcondition. Since the working velocity has been increased by the intro-duction of power, a real increase in the lift-curve slope has probablybeen obtained. Under these circumstances, the angle-of-attack change dueto the gust would be utilized in connection with the increased slope ofthe lift curve. In actual practice, the suggestion that the power-onslope of the lift curve should be used where the slipstream covers most

*of the airplane span is not as serious as it appears at first sight.The highest lift-curve slope is obtained at relatively low forward speed,a condition at which the load factor due to the gust is small. For

conventional airplanes, the power-off lift-curve slope appears correct.

Multiplanes.- For steady flow conditions the biplane is usuallyrepresented by an equivalent monoplane. This assumption no longerapplies for the transient lift conditions that exist in a gust. The

question of the proper slope of the lift curve to use for the transientconditions is in part answered by the results presented in figure 30.On the basis of the agreement shown in figure 30, the wings should beconsidered as acting independently and the slope of the wing lift curveas being computed on the basis of the average geometric aspect ratio of

the two wings.

Compressibility.- The effect of compressibility on the slope of thelift curve under unsteady flow conditions is a subject of much interestand one for which no experimental evidence is available. It is thoughtthat the lift-curve slope should follow the Glauert factor in thesubsonic range, but in the region near the critical Mach number andthrough the transonic region the mixed flows combined with transientconditions might delay or cancel the effect of compressibility on thelift-curve slope. For the time being the usual canpressibility factorscould be applied up to the critical Mach number and above that, the

.results of wind-tunnel tests should be utilized.

Downwash

Figure 33 (fig. 9 of reference 31) shows the change in verticalvelocity at the tail following a sudden increase in wing circulation forseveral values of the distance from the trailing edge of the wing to theleading edge of the tail. The change in vertical velocity is plotted asa function of the distance of the tail surface from the vortex shed bythe wing.

34 NACA TN 1976

Figure 33 indicates that the tail surface first encounters a grad-ual increase in upwash until the leading edge crosses the center of theshed vortex, when, following a violent change in direction, the downwashapproaches its steady-state value. The curves for different tail lengthsindicate quite clearly that the effect of increasing the tail length isto increase the time delay of the velocity change in proportion to thetail length. The violence of the direction change as the tail penetratesthe vortex depends on the vertical location of the tail relative to thevortex, and, until more accurate predictions can be made of the locationof the vortex, such changes might be disregarded. Figure 33 indicatesthat the assumption proposed in references 31 and 32 of a space lagbetween the change in lift on the wing and the change in angle of attackat the tail is reasonable and should be taken into account in anydetailed calculations.

The indications to date are that the results obtained by utilizinga space lag of downwash have been in fair agreement with experiment, butthe corresponding calculations neglecting the space lag of downwash havenot been made to determine the seriousness of the error of neglectingthis quantity.

Maximum Lift Coefficient

Reference 19 shows that for an airplane model traversing a sharp-edge gust at its steady-flow maximum lift coefficient, the maximum liftcoefficient during the action of the gust was not limited to the steady-flow value. Farren in reference 33 made tests of two-dimensional air-foils at constant angular velocities through maximum lift and return.

Angle-of-attack variations range as high as 12 er chord of travel and

the results indicated that the maximum lift coefficient could range from30 to 50 percent above the steady-flow value.

No concise estimates of maximum lift coefficient during suddenchanges in angle of attack can be made, but the sketchy information thatis available indicates that a conservative estimate for incompressible-flow conditions is an increase of about 25 percent over the steady-flowvalue. In the transonic region, the effects of compressibility maylimit the maximum lift coefficient, and in this range the investigationsmade in the various wind tunnels would be pertinent.

RIGID-BODY REACTIONS

The available data op gust structure and aerodynamics have beenanalyzed and the next problem is the determination of the behavior of

NACA TN 1976 35

the airplane as a whole since the motions of the airplane have animportant bearing on gust-load calculation. The significant parametersof airplane behavior as determined from analytical and experimentalinvestigations are subsequently sumiarized and possible simplificationsinvestigated.

Analytical and Experimental Studies

The material presented is the result of analytical and experimentalstudy of arbitrary and special configurations. The analytical studieshave been of a general nature and about two-thirds of the experimentalstudies can be so classed. The rest of the experimental research hasbeen done in connection with specific problems or airplane designs. Thescope and results of the analytical studies are presented first, followedby the experimental studies. In addition to the behavior of and theloads on airplanes caused by vertical gusts uniform across the span,limited research and studies on unsymmetrical and lateral gusts aredescribed and reported in appropriate sections.

Analytical studies.- The analytical studies of the loads on andbehavior of an airplane traversing a gust have been performed for auniform upward-acting vertical gust. Current theory indicates that theincremental loadings for a downward-acting gust are equal in magnitudebut opposite in sign. Further assumptions are that:

(1) The airplane maintains a constant forward speed during the

traverse of the gust

(2) The airplane is in equilibrium prior to entry into the gust

(3) The aerodynamic center of an aerodynamic surface is at thequarter-chord point

(4) The moment coefficient at zero lift is a constant for transientconditions and has the same value as for steady flow conditions

(5) The control surfaces of the airplane are locked

Extended analyses in which the airplane is considered free to pitchas well as to rise under the action of a gust have been made by the NACAfor conventional, canard, and tailless airplanes. In the case of theconventional airplane, the analysis was rather wide in scope; whereasfor the other two types of aircraft, the analyses were-limited to specificcases. The procedure used was an iteration process.

The calculations were aimed at covering all configurations and valuesof stability which would be reasonable for conventional airplanes and

36 NACA TN 1976

such values of the mass parameter and moment of inertia which would fallwithin the capacity of the gust tunnel. The pertinent airplane charac-teristics assumed in the analysis are given in table XI for all the com-binations considered. As can be seen from the table, the static marginsrange from 0.009 to -0.503 and the mass parameter ranged from 10.25 to30.75. The calculations were made for three gust-gradlent distances -0, 8, and 16 chords. The flight conditions assumed were a gust velocityof 6 feet per second and a forward speed of about 40 miles per hour. Thecalculations were not made for all combinations of variables noted intable XI, but some intermediate values were interpolated.

The results of the calculations are shown in tables XII(a), XII(b),and XII(c) as the acceleration increments at maximum acceleration forthe airplane with the center of gravity at 15, 25, and 35 percent of themean aerodynamic chord, respectively. Each table shows the results forthe three gust-gradient distances and for various combinations of tailarea and tail length. The incremental values of acceleration which arecontributed by each motion or source are tabulated and then totaled toobtain the wing acceleration, the acceleration increment resulting fromthe lift on the tail, and finally the total acceleration incrementimpressed on the airplane.

In addition to the results of the analysis being presented intabular form, figures 34 and 35 indicate the effect of pitch on the totalwing load. In figure 34, the ratio of the total wing load increment,including the effect of pitch, divided by the total wing load increment,assuming the pitch equal to zero, is shown. A value of 1 indicates thatthe effect of pitch was negligible and values greater than 1 indicatethat the effect of pitch increased the total wing load. The results areshown as a function of the static margin for three gust-gradient dis-tances. The individual curves shown in the figure represent given con-figurations but different center-of-gravity positions. Figure 35 is asimilar plot of data from tables XII(a), XII(b), and XII(c) of thetotal acceleration increment as a function of the static margin forcomparison with the experimental data from the gust tunnel.

Figure 36 shows the wing lift increment resulting from pitch of theairplane in terms of the total wing lift as a function of mass parameter.The three solid curves represent the three center-of-gravity positions.The curves represent the "average" airplane with medium tail length andmedium tail area traversing a flat-top gust with a gradient distance of8 chords. The dash lines included in the figure represent the pitch-

increment ratio U--. This ratio has been used to correct for pitch

U/V

effects on the basis that the change in acceleration due to pitch is

NACA TN 1976 37

proportional to the ratio of the pitch increment to the gust angle. The

distance between the dash and solid lines is a measure of the error of

this assumption.

The data in tables XII(a), XII(b), and XII(c) were also utilized toobtain the total tall load increment divided by the tail load if thedownwash, the vertical motion, and the pitch are assumed to be zero.The results are shown in figure 37 as a function of the static mar-gin dCmcg/dC L for the three gust-gradient distances. The total tail

load shown is that at the time of maximum total airplane load. The linesconnecting the points represent the same configuration and the movementalong the line to the right indicates increasing static stability.

Detailed calculations have also been made for a flying wing withabout 250 of sweepback and for a canard airplane. The characteristicsof the airplanes are shown in table XI. The calculations for the flyingwing were-made for two center-of-gravity positions and for three gradientdistances - 0, 8, and 17.5 chords. Table XIII shows the results of thecalculations and includes the contributions from the different sourcesfor the two center-of-gravity positions. The total wing load incrementsare shown for each center-of-gravity position. Calculations were madeby using finite-aspect-ratio unsteady-lift functions on the basis thatno fuselage was present. The total acceleration increment has beenplotted in figure 38(a) for each center-of-gravity position. The canardairplane had the same general characteristics as the conventional

Boeing B-247 transport airplane. The calculations for the canard air-plane for net wing area and for the two unsteady-lift functions have beenobtained from reference 15 and are presented in table XIV. The calculatedtotal acceleration increments for the canard are shown in figure 38(b)as a function of gradient distance.

Figure 39 indicates the effect on the calculated loads of substitut-ing the wing loading for the mass parameter. This figure is a plot ofthe acceleration based on wing loading divided by that based on the massparameter as a function of wing loading. The calculations were made for

three classes of airplanes - transports, personal airplanes, and flyingboats. The results are shown as a function of the wing loading. Pointslying above the line indicate overestimation of the acceleration incre-

ment, and points below the line represent underestimation of the accele-ration increment.

As mentioned in the section about gust structure, the suggestion

was made of either a triangular or sinusoidal gust shape in the directionof flight. As a check on the interchangeability of the two gust shapes,figure 40 shows the ratio of the acceleration due to a sinusoidal gustto that for a triangular gust as a function of the mass parameter whenthe unsteady-lift functions for infinite aspect ratio and aspect ratio 6

38 NACA TN 1976

are used. The calculations were performed by a step-by-step procedurethat took into account the possible lack of coincidence in the gust peaks.Other calculations indicated that for gusts with a distance of 10 chords,the maximum lag in the acceleration peak would be about 2 chords whenthe wing had an infinite mass parameter.

Experimental studies.- Most of the experimental data available arefrom general tests in the Langley gust tunnel with upward-acting gustsperpendicular to the flight path. Most of the research can be classedas general and includes the material presented in reference 19. Theresults of tests of specific models that are applicable to generalstudies are included.

A general study was made of the effect of the stability of airplaneson the gust load factor; the stability characteristics were varied overa wide range within which conventional airplanes would be expected tofall. The tests were performed on an arbitrary "stability" airplanemodel for correlation with the extended analysis previously described.The characteristics of this model are given in table XI and the totalacceleration increments obtained from the tests are shown in figure 35.The tests were made for three gust-gradient distances and with the center-of-gravity positions at 17.5, 25, and 30 percent of the mean geometricchord. The combinations of tail area and tail length used on the testmodel are listed in figure 35.

The unconventional airplane models listed in table XI include aflying wing and a canard airplane. Tests of the flying wing were madewith the center of gravity at 20 percent of the mean geometric chord.The acceleration increment, forward speed, gust velocity, and pitch ofthe model were measured during each test flight. The tests consistedof a series of five or more flights of the airplane at a forward speedof 40 miles per hour through vertical gusts with gradient distances of 0,8, and 16 chords. The test results have been included in table XIII andare shown in figure 38(a). The test conditions for the canard airplanehave previously been reported in reference 15. The pertinent charac-teristics of the model have been included in table XI and the results ofthe experiments are given in table XIV and in figure 38(b).

A few flight tests have been made to obtain data on the behavior ofan airplane subjected to unsymetrical gusts and on the gust loads onthe vertical and horizontal tail surfaces. The results for the unsym-metrical gusts have been discussed previously in the section entitledIT,"The Structure of Atmospheric Gusts and indicate reasonable agreementbetween calculation and experiment. The results of investigations ofgust tail loads on the 0-2H and XB-15 airplanes are given in table XV asratios of the effective gust velocity on a tail surface to that deter-mined for the wing. The XB-15 airplane is shown in figure 6 and des-cribed in the section on gust structure and the general characteristics

NACA TN 1976 39

of the 0-2H airplane can be found in reference 34. Because of the useof improved instruments, the results from work with the XB-15 airplaneare considered better than those obtained on the 0-2H airplane.

Discussion

Wing area.- The results presented in figures 35 and 38(b) show goodagreement between experiment and the detailed calculation based on netwing area. If gross area were used, the calculated values would behigher than the experimental values for a sharp gust. For a gradientgust the reverse would be true since the amount of alleviation due topitch would be increased. A similar result applies to the canard air-plane of figure 38(b) as indicated by table II of reference 15, whichshows a decrease in acceleration of 30 percent for a gradient distanceof 16 chords (A=o).

Mass parameter.- Analytical studie.s that are based on extensiveequations indicate that the mass parameter is the significant variablein that it affects the amount of alleviation due to vertical motion.The mass-parameter term has a negligible effect for a sharp-edge gustbut is important for long gradient distances. This result is due to thefact that for a sharp gust, the airplane does not acquire much verticalvelocity, but in a long gust the vertical velocity approaches the gustvelocity.

In addition to its effect on the vertical motion of the airplane,an increase in the mass parameter for a given airplawe, by increasingthe gross weight, unexpectedly increases the alleviation of the totalwing load due to pitch. (See fig. 36.) As the mass parameter increases,the resistance of the airplane to rotation would be expected to increaseand therefore the amount of pitch and the alleviation due to the pitchingmotion would be decreased. The result just noted arises from the factthat the pitching moments on the airplane arise not only from the actionof the gust but also from the vertical motion of the airplane. Byreducing the vertical motion of the airplane, the adverse pitching momentis decreased, and thus the favorable effect predominates and providesmore alleviation.

In some cases, such as in computing the factor K, wing loadinginstead of mass parameter has been taken as the significant variable.Such a substitution presumes a fixed relation between wing loading andmass parameter. Figure 39 indicates that this substitution may resultin either underestimation or overestimation of imposed accelerationincrements. The answer in any case depends on the relation between wingloading and mass parameter. Figure 39 shows that the substitution ofwing loading appears satisfactory for transports but results in too-lowacceleration increments for personal airplanes and too-high values forflying boats.

40 NACA TN 1976

Phase lan.- The data from the general analysis were utilized toobtain the lag in chords of the acceleration peak behind the flat-top-gust peak. Figure 41 shows that the lag is primarily a function of thegradient distance for a given mass parameter although some variationsdue to the tail area and tail length are noted. No effect due to avariation in the center-of-gravity position from 15 to 35 percent of thechord is noted. The results indicate that for a mass parameter of approxi-mately 10, the lag in the gust peak could be as much as 2 chords for an8- to 10-chord gust. Computations indicate that this lag increases to3 chords for a gradient distance of 8 chords when the mass parameter isabout 30.

In the calculations for the triangular and sinusoidal gusts, thelag of the acceleration peak behind the gust peak for infinite massparameter, the most adverse case, does not exceed 2 chords. The effectof the phase lag of the acceleration behind the gust can probably beneglected since, for many calculations of acceleration increments andload factors, a change of 1 chord in 8 has a negligible effect on theacceleration ratio.

Static margin.- Figure 34 indicates that the total wing load on aconventional airplane decreases with increasing stability and increasinggradient distance because of the resulting increase in pitch. Thefigure also shows that the method of obtaining a given static marginis more important than the actual value of the static margin. Theresults for tailless airplanes are discussed in the following section.

Although no data are available for canard airplanes, a comparisonof figures 38(b) and 32 (both airplanes have the same static margin) showa marked effect on the acceleration increment due to the radical changein configuration. From the results obtained, it is concluded that theeffect of airplane pitch on the wing load cannot be specified by staticmargin alone.

Center-of-aravity position.- Inspection of figure 34 indicates that,for a given configuration, the alleviation due to pitch varies almostdirectly with the center-of-gravity position. The rate of change ofpitch effect with center-of-gravity position is roughly independent ofthe configuration for the conditions analyzed and depends mainly on thegust-gradient distance. For a gust with a gradient distance of 8 chords,figure 34 indicates that a 1-percent change in center-of-gravity posi-tion gives a 1-percent change in load factor. The change in load isdoubled for the gust with a gradient distance of 16 chords and abouthalved for a sharp-edge gust.

The results shown in figure 34, which are for a single value of themass parameter, and those presented in figure 36 indicate that the effectof pitch on the gust load factor will increase as the mass parameter is

NACA TN 1976 41

increased. Figure 36 shows that for a mass parameter of 10, a 1-percentchange in center-of-gravity position represents about a 1-percent changein load factor, whereas tripling the mass parameter to a value of about30 increases the rate of change in the total wing-load increment 2 percentfor each 1-percent shift in center-of-gravity position.

The tailless airplane for which calculations were made had a mass1parameter of about 26, and a 1iF -percent increase in load for a 1-percent

rearward movement of the center of gravity for 8 chords was indicated(fig. 38 (a)), which is in fair agreement with the curves shown in fig-ure 34 for the conventional airplane. Although the analysis is crude,the results indicate that, for both the conventional and tailless air-planes, the effect of the center-of-gravity position is about the same.Consideration of figure 34 indicates that, although the center of gravityis significant in determining the changes in load on the airplane, thecenter-of-gravity position is not significant in setting the absolutelevel of the total load for any particular airplane.

Tail volume.- The two middle lines of figure 34 for approximatelyequal tail volume indicate that this quantity by itself is not of primeimportance. Inspection of the results for a gradient distance of8 chords shows that for equal tail volumes but different tail lengths a

- variation of 10 percent in the effect of pitch on the applied wing loadincrement can be obtained for a given static margin. For similar con-ditions and a gust with a gradient distance of 16 chords, the change inload increment is about 20 percent. A change in tail volume obtainedby increasing the tail length and reducing the tail area results inhigher loads on the airplane.

The results shown in figure 34 for the same static margin indicatethat the change in tail area does not yield significant variations inload, whereas the change in tail length results in a significant modi-fication of the amount of wing load imposed on the airplane. The datathus indicate that for the maximum alleviation of load by means of pitchof the airplane, a short tail length and large tail area appear to bemost beneficial, although the combination will probably lead to anuncomfortable ride due to the violent pitching motion of the airplane.The use of a small area with a short tail length will yield results nottoo different, although the reduction of damping in pitch may emphasizethe pitching oscillation to the detriment of passenger comfort andcontrol of the airplane in continuous rough air.

On the basis of these analytical results, it is concluded that thetail volume is a secondary factor in establishing the level of wing load.The results indicate that the larger the tail length for a given staticmargin the greater the load imposed on the wing. For a gradient distanceof 8 chords the effect on the total wing load due to the various elementsof configuration can vary from 10 to -20 percent.

42 NACA TN 1976

Piloting and continuous rough air.-, Previous analytical and experi-mental studies were made for a single gust isolated in space and withelevator fixed, whereas airplane flights are in continuous rough air witha pilot modifying the reactions of the airplane. Although there are fewavailable data covering this condition, on the basis of statisticalanalysis, significant differences have been found to exist between pilotsand between airplanes of the same type. The effect of different pilotswas as much as 20 percent and differences between airplanes were 5 to10 percent. It appears frcm these results that the pilot is more import-ant than the variation between airplanes of the same type in determiningthe loads applied to the airplane. The variation due to both factors isestimated to average 15 percent.

Little or no correlation between the maximum angular motions of anairplane and the maximin loads in the same traverse has been found. Itwas found in another flight test that one pilot moved the controls fivetimes as often as another pilot and no significant difference in the loadsimposed w&s found. These results led to the conclusion that the effectof the pilot on the imposed load is due to his past actions and is notdirectly related to the effect of any single gust.

At the present time the question of the effect of piloting and air-plane motion in continuous rough air on the prediction of gust loadfactors is only being approached. The redeeming feature at present isthe fact that the evaluation of flight load experience under actualoperating conditions will include piloting effects for the airplanestested. The question still to be answered is whether data on pilotingeffects taken in the past on older types of airplanes are valid formodern high-speed airplanes flown by pilots with different training andwith airplanes designed for different requirements of flying qualitiesand stability.

Unsrmmetrical gusts and airplane response.- Little is known concern-ing the response of airplanes under the action of a gust which strikesonly one wing. The only material available is empirical in characterand has been previously presented in this paper in connection with thestudies of gust structure. In that material it was indicated that cal-culation by a simplified method, neglecting the alleviation effects ofmotion, would have to be adequate until more information concerning thesignificant parameters and the motions of the airplane is obtained.

Horizontal tail loads.- The results given in figure 37 indicate thatthe static margin and the tail volume are not of primary importance inthe determination of tail load. The data indicate a reasonably orderedvariation of tail load with center-of-gravity position. The magnitudeof the tail load varies rapidly with gradient distance, the variationranging from about 50 percent for a gradient distance of 0 chordsto 0 percent for a gradient distance of 16 chords. Inspection of

NACA TN 1976 43

tables XII(a), XII(b), and XII(c) indicates that the decrease is duemainly to the increasing importance of the effect of pitch-angle incre-ment as the gradient distance is increased and due to the fact that thetotal tail load is composed of one large term due to the gust, to whichis added many small contributions from various sources which may be ofeither sign. The net result is that the tail load is, in many cases,small and equal to some of the small components. The calculation of thetail load thus requires an extremely high degree of accuracy in order toobtain an accurate answer.

As previously noted, the material presented in figure 37 and table XIIshows the tail load at the time of maximum airplane acceleration. Itis thought that the maximum tail load may result from a differentsized gust than that which is critical for the wing or it may occur at adifferent time that at maximum acceleration. In view of the many uncer-tainties in the calculation of tail loads due to gusts, it has beensuggested from time to time that the tail load be calculated as the

increase in lift due to the gust alone multiplied by the factor 1 - d.dm

A slightly different concept would be to assume the gust velocity equalto about half that on the wing.

What few experimental data from flight tests are available appearto be in essential agreement with the preceding suggestion. Table XVindicates that the ratio of the effective gust velocity on the tail asdetermined from tail-load measurements to the effective gust velocityfor the wing is equal to 0.53 and 0.64 for the XB-15 and 0-2H airplanes,respectively. The results compare favorably with an estimated value

for 1 - dc of 0.5.dM

In the case of the canard airplane, inspection of the data intable XIV indicates that for a gust with a gradient distance of 8 chordsthe effects of pitch and vertical motion cancel so that the totalstabilizer load is approximately equal to the load that would be imposedon the tail surface due t6 the gust alone. For the longer gradientdistance of 17.5 chords, the cancellation is not complete, and the totaltail load amounts to about two-thirds of the tail load resulting fromthe action of the gust. For the practical case, calculations of thehorizontal tail load for canard airplanes might be based on the lift dueto the change in angle of attack resulting from the gust if both thevertical motion and pitching motion of the airplane are neglected.

In summary, the available results indicate that it is not possibleby means of detailed calculations to obtain an accurate estimate of thehorizontal tail load due to the action of the gust. The tail load on

44 NACA TN 1976

the horizontal surfaces can be best estimated as the tail load due to the

gust alone multiplied by the factor 1 - " For the canard airplane,dm

the downwash factor would be assumed to be zero.

Vertical tail loads.- The suggestion has been made that alleviatingeffects be neglected in the calculation of vertical tail loads due tothe action of side gusts. On this basis, the effective gust velocityfor the vertical tail would be related to the vertical velocity for thewing by the relation

Uewn

Uevert. tail U wing

6 airplane

The experimental data in table XV show excellent agreement between theratio of effective gust velocities and the reciprocal of the accelera-tion ratio. The relation given is equivalent to the calculation of thevertical tail load for a true gust velocity with no alleviation due tounsteady-lift effects or airplane motion. The suggestion appears satis-factory and it would presumably also apply to the vertical tail on thecanard airplane.

Steady lift in contrast to unsteady lift.- Consideration of theequations of motion for steady and unsteady flow indicates that the useof steady-flow lift functions for generalized studies of gust-loadproblems is not warranted. The ratio of the "steady-flow accelerationto the "unsteady-flow" acceleration in the same gust is

1 1 s l n(s) ds

Ansteady 0

Alnunsteady - s

I %s - s)An(s) ds

NACA TN 1976 45

where C is the unsteady lift coefficient for a gradient gust. Forinfinite mass parameter, the ratio of accelerations varies from infinityfor zero gradient distance (C = 0 at H = 0) to 1.0 for infinitegradient distance (steady flow, C = 1.0). The variation with massparameter would not be so drastic because it affects only the allevia-"tion term, but, since the integral in the denominator contains anunsteady-lift function, considerable deviation would be expected at smallvalues of mass parameter. Therefore, the trends indicated by steady-flow calculations are not necessarily expected to be those for unsteady-lift calculations.

The calculated results shown in figure 38(b), in which the unsteady-lift functions for A = 6 and w were utilized, indicate the importanceof unsteady-lift-curve shape at large gust-gradient distances. As indi-cated in the figure, for gradient distance of about 18 chords, thesubstitution of unsteady-lift functions of aspect ratio 6 for those ofaspect ratio o changed the calculated acceleration increment by 50 per-cent. It is apparent that in the case in which the pitching motion ofthe airplane is significant and the detailed response of the airplane isto be calculated, minor changes in the unsteady-lift functions themselvescan lead to serious discrepancies. The neglect of unsteady-lift relationsshould involve more radical deviations than the substitution of oneunsteady-lift function for another and does not appear to be valid.

Gust shape.- Figure 40 shows that the sinusoidal gust can be sub-stituted for the triangular gust with a small relative error. The curvesindicate that the relative error is about 2 percent for a range of massparameter from 5 to 80, with the absolute error varying from 5 toabout 8 percent high. The results indicate, therefore, that the trendspredicted for the one gust shape should apply equally well to the othergust shape.

Calculated and experimental results.- Inspection of figure 28indicates that, for the case in which the pitch effects are negligible,the scatter in computing the acceleration ratio appears to be randomand the experimental results fall on each side of the calculated curve.Some of the scatter noted is caused by pitching of the model and someis undoubtedly caused by difficulties in making the experimental measure-ments. On the whole, the calculated results appear to agree in a satis-factory manner with experiment. Similar agreement is indicated infigures 35, 38 (a), 38(b), and 32 for H = 0 where pitch is considerednegligible. It is believed, therefore, on the basis of these results,that the unsteady-lift functions, the slope of the lift curve, andsimilar items involved in the calculations are known with an accuracycomparable to that for other elements of gust-load calculations.

46 NACA TN 1976

For gradient distances other than zero or for those cases in whichthe pitch is a factor, the discrepancies between calculation and experi-ment become larger as the gradient distance increases until, as indicatedby figure 35, the errors are serious for gradient distances of 16 to2O chords. In the case of both the conventional airplanes (fig. 35) andthe canard airplane (fig. 38(b)), the calculations for the longer gust-gradient distance are unconservative and lead to smaller predicted loadfactors. In the case of the tailless airplane (fig. 38(a)) the calculatedvalues are in good agreement. Consideration of the data presented infigure 32, in which the effect of pitch has been neglected in the cal-culations, indicates that the neglect of pitch for the longer gust-gradient distances will be conservative. The good agreement for thetailless airplane (fig. 38(a)) at all gradient distances compared to thevariation in agreement between calculation and experiment for the othercases indicates that the introduction of the tail surface and possiblythe fuselage has much to do with the adequacy of the detailed calcula-tions of airplane response to a gust. The errors indicated for thelonger gust-gradient distances as compared to the sharper gust indicatethat the pitch effect is probably the least accurately predicted quan-tity and, therefore, leads to the errors noted.

From the results obtained it appears that the wing load due to agust can be calculated within 10 percent for gradient distances up to10 chords. The accuracy in any individual case or for large gradientdistances cannot be estimated because of pitch and secondary effectsthat may be significant but are not recognized until test results areavailable. Minor changes in variables such as downwash can lead toserious variation of numerical results, and the estimation of loads bydetailed or extensive calculations is not of sufficient accuracy towarrant much confidence in the results.

ELASTIC-AIRPLANE REACTIONS

Since the loads imposed when airplanes encounter gusts are appliedsuddenly, the dynamic response of the airplane structure has been ofconcern since the initiation of gust-load studies. A number of studies(references 2 and 35 to 40) have been made at various times to evaluatethe importance of dynamic response and of the various parameters involved.In 1939, projected airplane designs indicated that dynamic response mightbe of concern and an analytical and experimental study was undertaken.The results of this investigation are presented in reference 38.

In this section the results obtained in reference 38 are summarizedas well as some results from unpublished studies. The significance ofdynamic response and the importance of the various parameters in producingdynamic responses in airplane structures are of chief concern.

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Methods

The analytical method developed in reference 38 was to reduce theairplane structure to an "equivalent" biplane whose upper wing had thesame motion as the original wing tip and, by using an effective dampingfactor .instead of unsteady-lift functions, to obtain two simultaneous

linear differential equations. The equivalent biplane, in which theupper wing is connected by springs to the lower wing-fuselage combina-tion, is adjusted so that the components have the same motions as thewing tip and fuselage of the airplane under study. The equivalentsystem must include the proper distribution of aerodynamic forces aswell as inertia and elastic forces. The deflection of the upper wingof the biplane is taken as a measure of dynamic stress. The dynamic-

stress. ratio is defined as the ratio of dynamic to static wing-tipdeflections. The static deflection is computed in the same manner asfor normal design by including inertia effects but neglecting aerodynamicdamping due to vibration of the upper wing.

The spring constant, equivalent masses, and aerodynamic damping forthe equivalent system are calculated so that the static and vibrationcharacteristics of the original wing are represented. In general, thefollowing conditions are to be satisfied:

1. The total mass of and the total load on the equivalent biplaneshould be identical with those of the original airplane.

2. The upper wing should deflect under the equivalent static loadthe same amount as the original wing tip under its corresponding static-load distribution.

3. The natural frequency of the equivalent system should be thesame as that of the original wing.

4. The kinetic energy of vibration of the upper wing should closelyapproximate that of the original wing for the same tip amplitude of

vibration.

5. The damping coefficient of the upper wing should represent, atleast up to peak load, the damping of the motion of the original wing.

The shape of the forcing function used in the calculations ofreference 38 was obtained from accelerometer records of gust-tunnel testsof different models by subtracting the computed acceleration incrementdue to vertical motion. This procedure was followed since the predictionof airplane reactions as affected by stability and other factors is ofdoubtful accuracy, as previously noted. For representative gust sizes(H = 0 to H = 20 chords) it was found in reference 38 that a curve of

the form Ate -bt was a good representation. The forcing function for

48 NACA TN 1976

the complete airplane was then divided so that the upper wing of theequivalent biplane would have the same static deflection as the originalwing tip.

In addition to and as a check on the method of calculation, testswere made in the Langley gust tunnel with a model having two wings ofdifferent frequencies. The wing deflection and fuselage accelerationwere the primary quantities measured. The model used is shown diagram-matically in figure 42 and its characteristics together with the test

conditions are given in table XVI.

For each of the two wing frequencies tests were made at one forwardspeed and three gust sizes. Time histories of pitch, acceleration incre-ment of the fuselage, and wing deflection were obtained. Some resultsof the tests are shown in figure 43, in which the maximum wing-tip deflec-tion per unit acceleration increment is plotted for one wing as a func-tion of gradient distance.

The analytical procedure described in reference 38 was utilized to

compute the response of the system when damping of the motion is includedand when aerodynamic damping is neglected. The results have been includedin figure 43 for comparison with experiment.

Analytical Study

In order to determine the effect of the various parameters ondynamic response, a series of calculations was made at three gust-gradient distances for four airplanes. The characteristics of the air-

planes, which were designated as A, B, C, and D, are given in table XVII.

The parameters studied were the wing stiffness, airplane weight, andforward speed, with all damping neglected. The gust velocity was notvaried since ratios of dynamic to static conditions were utilized and itwas not a factor for linear equations. The conditions used in the cal-

culations are given in table XVII.

The calculated results for each airplane of the maximum deflectionratio, wing-tip acceleration ratio, and fuselage acceleration ratio are

shown in figure 44.

Discussion

Inspection of the results of figure 43 indicateB, in general, that

dynamic response is overestimated when damping is neglected; whereas the

inclusion of damping leads to fair agreement with experimental results.

The results obtained were not sufficiently accurate to provide an absolute

NACA TN 1976 49

check of the calculation. The results do indicate, however, that thecalculations give a fair prediction of the ratio of maximum wing deflec-tion to maximum fuselage acceleration.

Time histories given in reference 38 but not shown herein indicatethat the method of calculation did not predict correctly the amplitudeof the wing oscillations after passing the peak load. The result isdue in part to the fact that the damping coefficient was adjusted togive a good estimate for the first wing motion and would be overestimatedfor the subsequent vibratory motion. Putnam (reference 39) attemptedto resolve this difficulty when he extended the method of reference 38.Another possible factor is that the simplifications used are still toodrastic. Other results (reference 38) indicate that the use of a constantdamping factor is reasonable if its magnitude is adjusted for the averageeffect of unsteady lift.

Inspection of figure 44 indicates that the dynamic-stressratios dmax/bst and wing-tip acceleration ratios I2SwmAnrmax

increase as the gradient distance decreases. Recent calculations formore modern aircraft bear out this result and indicate that elasticresponse is becoming increasingly important. The fuselage accelerationratio l2 5f JZmA did not appear to differ greatly from 1.0 and

does not appear to be seriously affected by gust size.

The calculations shown in figure 45 for the effect of wing stiffnesson the dynamic-stress ratios indicate that at the "critical" gradientdistance of 10 chords, the high-frequency wing shows a dynamic-stressratio of 14 percent below the low-frequency wing. Further analysis isneeded before a definite conclusion can be reached that a reduction ofwing frequency by changing wing stiffness tends to increase the dynamic-stress ratio at any gradient distance.

The results given in figure 46 illustrate the variations of thethree ratios due to increasing the forward velocity of model C from200 to 400 miles per hour. The increase in velocity together with thecorresponding increase in the rate of application of the gust load wouldappear to result in an increase in the dynamic-stress ratio. Figure 46,however, shows that the dynamic-stress ratio does not vary much as thespeed increases and this lack of variation is thought to be caused partlyby the increase in aerodynamic damping with speed. Although the resultsfor the fuselage acceleration ratio show little effect of speed, thewing-tip acceleration ratio increases from about 1.8 to 2.5 as the speedis doubled.

The 'calculations for model D were made to show the effect on thedynamic-stress ratio of a change in flight condition from normal gross

50 NACA TN 1976

weight to overload gross weight. Table XVII shows that the forwardvelocity is different in the two cases, but consideration of the fore-going discussion may justify the assumption that speed has a negligibleeffect on the findings. The results are given in figure 47 with dynamic-stress ratio plotted as a function of the gradient distance of the gust.A reduction in wing frequency brought about by the addition of mass isshown to result in an increase in the dynamic-stress ratio.

Av-ailable information on repeated gusts such as given in table IVhas been used (reference 38) to determine the dynamic effects on wingdeflection in repeated gusts. The following table (from reference 38)indicates the dynamic-deflection ratios for two gusts of given intensityspaced 25 chords apart. Also given in the table are the deflectionratios for the single gusts of greater intensity which have the sameprobability of occurrence as the sequence of two gusts used.

"Design" "Design"repeated single

Model Condition us usts

C 1 o.96 1.07D 1 1.08 .92D 2 1.10 1.09

The variation in the results indicates that the dynamic-stress ratiosfor a repeated gust should be investigated. The results also indicatethat these dynamic-stress ratios are probably not much greater thanthose determined for a single gust likely to be encountered in flight.

Concluding Remarks Concerning Elastic-Airplane Reactions

Study of available results and unpublished data indicates thatdynamic response is becoming of greater importance with modern advancesin airplane design. As mass tends to be distributed along the wing,more exact solutions are needed and, until the various factors such asunsteady-lift functions, inertia terms, elastic constants, and the span-wise gust distribution are known more exactly, such calculations shouldbe utilized on a relative basis. Although new and more elaborate methodsof calculation are available, serious problems still remain as to thebasic aerodynamic and elastic coefficients.

NACA TN 1976 51

OPERATING STATIST ICS

A knowledge of gust structure and methods for computing airplanereactions is insufficient for gust-load calculations without"knowing:the'conditions for which load calculations are required. Thus, in order tosolve the practical problem of load prediction, the gusts that airplanesencounter and the operating conditions (speed, weight, altitude, and,perhaps, center-of-gravity position) that are likely to exist at thetime the gust is encountered must be known. The fact that the source ofload, the atmospheric gust, is of a fairly random character and that theoperating conditions vary widely make it impractical to predict theexact loads and the associated conditions that are experienced by agiven airplane during its lifetime.

METHOD

The general method of obtaining the desired information has beento install instruments in aircraft and to record their experiences andoperating conditions without interfering with routine practices. Threeprocedures have been used: the installation of simple instruments suchas the NACA V-G recorder giving broad coverage as to route, airplanetype, and time but no detailed information, the installation of specialinstrumentation for a very limited period of time to obtain informationon a particular quantity in detail, and, finally, the installation offairly elaborate instrumentation controlled by an observer to obtainas much detailed data as possible on several quantities during one ormore flights.

The NACA V-G recorder (reference 4) records on a smoked glass platethe normal acceleration as a function of the airspeed at which it wasimposed. In use, a record plate is left in the instrument duringoperations and the resulting clear area on the glass represents anenvelope of accelerations and airspeeds experienced by the airplane.

Standard NACA photographically recording instruments or motionpictures of indicating instruments are used for more detailed measurements.

SCOPE OF DATA

The characteristics and pertinent dimensions of transport airplanesfor which gust statistics have been collected are given in table XVIII.The listed values of the limit load-factor increment due to gusts, the highspeed in level flight, and the placard do-not-exceed speed were obtained

52 NACA TN 1976

when possible from official sources. For the older airplanes where thedesign conditions differed from modern requirements, the pertinent speedsand load factors were recomputed according to reference 1 in order toplace all the characteristics on a comparable basis.

Table XIX is a sumary of the conditions investigated and includesthe routes, periods covered, and the amount of data obtained. The opera-tions have been subdivided into prewar, wartime, and postwar periods.For the prewar and wartime periods, information was obtained with the V-Grecorder, but for the postwar period sufficient V-G records are notavailable. Special studies of speed and Mach number variations areavailable and some of the results have been included. The materialcovered in table XIX does not include all the data obtained since scat-tered V-G data of insufficient scope for analysis have been disregarded.

STATISTICAL METHODS

The random character of gusts and the lack of control over flightconditions have resulted in the use of statistical methods of analysisto smooth data, to eliminate improper weighting, to extrapolate results,and to place data from different sources on a comparable basis. Thebasic data in most cases are a count of the values of a quantity accordingto magnitude. Since the application of statistical methods to gust loadsis fairly recent, the mass of data collected earlier offers some diffi-culties because the requirements of statistical analysis were notconsidered in their collection.

Pearson type III probability distribution curves (see references 41and 42) have been utilized in the analysis on the assumption that theyadequately represent the data on operating statistics. The curve is

determined by three parameters: the mean value, the standard deviation,and the coefficient of skewness. In general, the goodness of fit hasbeen based on engineering judgment rather than any test procedure.

An important problem in the study of the frequency of exceeding thelarger values of load or speed under operating conditions is the deter-mination of whether observed or estimated differences in frequenciesbetween samples are real or represent limitations of the data. Nosatisfactory test for this purpose has been found, but a 5:1 ratio offrequencies has been used in reference 43 as an engineering measure. Ifthe differences are less than this criterion, real differences may existbut are considered too small to be determined from the available data.

A serious limitation in the analysis of operating statistics existssince the results are used to predict future operating experience. Ifno extraneous factor enters, such as changes in design rules, operating

NACA TN 1976 53

regulations, or the introduction of newer airplanes, then the predictionmay be satisfactory. Such changes as, for example, the shift from pre-war to postwar operations may lead to some uncertainty as to the appli-cability of a prediction. Predictions assume that the trend in the datahas not been affected by new factors. (No method yet is available forevaluating or detecting the effect of changes in the data now used.)

Other questions that occur in statistical analyses arise in connec-tion with the existence or inclusion of data from two different regionsor populations as part of the same sample, the presence of absolute andphysical boundaries that cannot be exceeded, the effect of extraneousvariables, and the effect of gradual transitions from one region toanother. The presence of such limitations can have serious results asfar as the significance of the results is concerned and such effectscannot always be evaluated or separated. An example of the effect ofdifferent regions might be the combination of acceleration data involvingflight below maximum lift coefficient and flight above maximum liftcoefficient. The aerodynamic characteristics of the airplane and itsbehavior in the two regions are entirely different. Thus, a sample thatcombines such data does not offer an adequate means of predicting futureexpectations of a given acceleration except for the conditions of theoriginal data, since any derived curves are a composite of two independentsets and therefore the prediction can only apply to the same combination.

RESULTS

V-G data.- From the individual V-G records that are summarized intable XIX, frequency distributions of the maximum accelerationincrement An.., the maximum speed Vmax, and the speed Vo at which

maximum acceleration increment was experienced have been compiled forthe wartime and prewar periods. The statistical parameters: the mean,the standard deviation, and the skewness are given in table XX, whichalso includes the values of V0 max , Ln max and Vma x recorded during

the period under consideration.

The parameters of the Pearson type III curves given in table XKhave been used to obtain the flight miles to exceed the specified valuesof a selected quantity. The transformation from probability to flightmiles was performed through use of a nominal cruising speed and theaverage flight hours per V-G record. Table XXI gives the flight milesto exceed: (1) the limit load-factor increment, (2) the placard speed ofthe airplane, and (3) an acceleration increment corresponding toencountering a gust with an effective gust velocity of 37.5K feet persecond at the most probable value of Vo, Vp. The probable speed Vp

has been included in table XXI as a fraction of the high speed inlevel flight VL.

54 NACA TN 1976

Time-history data.- Time histories from the special investigationsof the postwar period have been evaluated to obtain the flight miles toexceed the placard speed, the probable speed of flight for each sample,and the distribution of airspeed. Because of the limited duration ofthe samples, each sample was read to obtain the maximum speed during afixed interval of time (6 to 10 minutes) and the resulting frequencydistributions were then used to obtain the flight miles to exceed theplacard speed. The results are included in table XXI and in figure 48.Figure 48 presents the percent of total flight time spent at speedsequal to or greater than any selected fraction of the high speed VL.

The probable speed noted in table XXI for airplanes E and F is theprobable speed of flight and is not, as in the case of other airplanes,the probable speed at which maximum acceleration will occur. A simpleanalysis in which the velocity-acceleration envelopes were synthesizedfrom the speed-frequency-distribution data and the gust-frequency dataof reference 9 indicated that the probable speed for maximum accelera-tion was about 0.03VL greater than the probable speed of flight.

The data obtained have also been evaluated according to flightcondition to obtain curves of the flight hours required in climb, cruise,and descent to exceed given values of speed. Figure 49 is typical of theresults obtained for airplane E.

Disturbed motions.- From the data obtained in the special investi-gations a statistical study has been made of other quantities of interestin gust-load studies, such as the effects of disturbances on the relativefrequency distribution and the fraction of the time spent in rough air.

Some question has arisen as to the effect of the selected datum onthe frequency distributions obtained in continuous rough air. Thisquestion is partly answered by the tests reported in reference 9 on oneof the roughest flights with the XC-35 airplane where the relative gust-frequency distribution was determined by using a disturbed datum and an-arbitrary 1 g datum. The results of the study are given in figure 50.

Camera records of the pilot's instrument panel in the XC-35 airplanehave been evaluated to obtain the relative frequency of occurrence of themaximum total variations in the angular displacements of the XC-35 air-plane during separate traverses through clouds. The results aresummarized in figure 51 as the relative frequency of exceeding selectedvalues of yawing, rolling, and the pitching displacements and the rateof turn. It should be noted in considering this figure that the quantityplotted is the sum of the maximum positive and the maximum negativevalues recorded during each cloud traverse.

Path ratio.- The available data for prewar transport operationgiven in reference 9 indicate that the path ratio (the miles of roughair divided by the total miles flown) varied from 0.24 to 0.006 for

NACA TN 1976 55

different routes in the U.S. and abroad and had an average value of 0.1.Since, on the average, 500/c gusts with an effective gust Velocity greaterthan 0.3 foot per second are encountered per mile of rough air (refer-ence 9), the number of gusts that will be encountered on the averageduring the lifetime of an airplane can be estimated. No path-ratiodata are available for postwar operations. Attempts to obtain such datafrom the indirect evidence of V-G records lead to erroneous results.

DISCUSSION

Applied acceleration increments.- For the prewar period, table XXIshows a wide scatter in the flight miles to exceed the limit accelera-tion increment. The values vary by a factor of about 300. A variationby a factor of 42 occurs for the same type of airplane operated ondifferent routes by different airlines. In four out of the six samples,the flight miles to exceed the limit acceleration increment would begreater than 13 million, or, if a cruising speed of 200 miles per houris assumed, it might be expected that the limit load factor would beexceeded about once on the average in every 60,000 hours of flight.

The data for the wartime period do not show as much variation offlight miles and the variations do not appear significant within thatgroup. In comparison with the prewar operations, however, the flightmiles to exceed limit acceleration have consistently decreased; thisfact indicates that the pressure of the emergency on wartime comnmercialoperations resulted in higher imposed loads on the airplane.

Atmospheric gustiness.- The flight miles to exceed the accelerationincrement corresponding to an effective gust velocity of 37.5K feet persecond at the probable speed (table XXI) indicate that the operationalexperience on the basis of a "gust intensity" have much less scatter.The spread in flight miles was 15:1 for the prewar operations andabout 7:1 for the wartime period. For prewar conditions, when thedata for airplane D on route V are neglected, the scatter is within thearbitrary 5:1 criterion and, in comparison with the spread in flightmiles for limit acceleration increment, indicates that the differencein the level of roughness encountered on various routes is not ofengineering concern. A similar observation is indicated for the wartimeperiod although the smaller average flight miles indicates that flightsduring that period were through more severe weather conditions than forthe prewar period.

In connection with prewar data for airplane D on route V oftable XXI, the low value of flight miles shown may be significant andindicates that early transpacific flights encountered more severeweather than was experienced along other routes. When the distances

56 NACA TN 1976

involved in transpacific operations and the lack of weather ships in thisperiod are considered, more frequent accidental encounters with severeweather might be expected than for the transcontinental routes oroperations in more populated regions.

On the basis of the information concerning the flight miles toequal or exceed the acceleration increment corresponding to 37.5K feetper second at the probable speed, the level of route roughness is con-cluded to be largely independent of the route, airplane, or operator.It is not possible at this time to state whether the maintenance of a

constant level of roughness is due to dispatching practices, meteorolo-gical forecasting abilities, or both.

Frequency of encountering gusts.- The available data on path ratiogiven in reference 9 indicate a wide spread in values obtained, and at

this time an average value of 0.1 seems to be the best estimate avail-able. Since the path ratio is the proportion of the total miles flownthat are spent in rough air and the number of gusts per mile of roughair has been found to be essentially constant at 500/8, the path ratiocan be defined as the actual number of gusts divided by the total numberexpected if the total flight path were rough. It should be noted thatthe path ratio defined by gust counts depends on the threshold (in thiscase, the threshold is 0.3 fps). When used with a gust count of500/c gusts per mile of rough air and the gust frequency distributions offigure 8, the recommended average value of path ratio can be used toestimate the probability of an airplane encountering a gust of anyspecified intensity.

Although no information is available as to the variation of thenumber of gusts or path ratio with altitude, terrain, or weather, thepath ratio would probably decrease with altitude.

Probable speed Vp.- The determination of the miles to exceed 37.5K

feet per second at the probable speed showed the flight miles to berelatively constant, and, therefore, the wide variations in the flightmiles for limit load factor might be ascribed to variations in theprobable speed. On this basis, the results indicate that the probablespeed is important in determining flight miles to limit accelerationincrement.

The data on the probable-speed ratio (table XXI) indicate ascatter in the speed ratios for any given period. The speed ratio formaximum acceleration increased from the prewar period to the postwarperiod for the same airplanes and routes from an average value of 0.75to about 0.86. It appears that the speed ratio might be a function ofthe route, airline policy, and the airplane characteristics, but no

conclusion can be drawn as to the significant parameters that determinethe speed ratio.

NACA TN 1976 57

Although no data have been analyzed with regard to the imposedgust loads for the postwar period, on the basis of the current designrequirements and if the level of roughness is assumed to remain thesame as for the prewar period, the imposed gust acceleration incrementfor a given number of flight hours will be about 12 percent higher onthe average for the postwar period than for the prewar period. Alter-natively, the increased probable speed for the postwar period wouldresult in an appreciable decrease in the flight miles to exceed a givenacceleration increment.

Maximum speeds.- Inspection of figure 49 indicates that theprobability of exceeding a given value of airspeed is a function of theflight condition. Figure 49 indicates that the descent is most import-ant, and for one postwar airplane the placard speed might be exceededon the average about once in 200 hours in descent. A simple sorting ofthe data with regard to the smooth air and rough air showed no apparenteffect of rough air on the speed tendencies.

For complete flight operations, the data given in table XXI showthat the flight miles to exceed the placard speed decreased from manymillions of miles during the prewar period to about a quarter of millionof miles during the postwar period. The reduction in the flight milesto exceed the placard speed for the postwar period is of considerablesignificance.

Speed-time distributions.- Figure 48 shows that a relatively higherpercentage of time is spent above high speed in level flight than wouldbe expected from estimates made by airline personnel, which estimateshave indicated a value of less than 1 percent. The high percentage maybe due in part to performance abilities of the airplanes in excess ofthat indicated by the regulated speeds or due to high-speed descents atthe end of flights. Until further information is obtained, the resultsin figure 48 might be assumed to be representative of postwar operations.

Disturbed motions.- Tolefson (reference 44) showed that the maximumangular displacements of an airplane do not correlate with the maximumintensity of gusts encountered during a given run. The correlationcoefficient between the angular motions and the maximum gust intensitywas about 0.3. The disturbed motions may depend more on the sequence ofthe gusts encountered than on the intensity cf any individual gustencountered. The data cannot be extended to other flight conditionsexcept by assuming dynamically similar conditions.

Inspection of figure 51(a) indicates that the amplitude of therolling motion is much greater than either pitch or yaw. Similar resultsare indicated in figure 51(b) for the angular velocities. The data offigure 51 can be utilized, if dynamically similar airplanes and a

58 NACA TN 1976

constant level of atmospheric turbulence are assumed, to estimate thefraction of the airplane life flown before displacements or angularvelocities of the airplane in excess of selected values are experienced.

Relatively little data have been obtained on angular accelerationsin rough air and the data for roll are discussed in the section aboutgust structure. Twenty-one values of angular acceleration in pitch wereavailable from flights of the XB-15 airplane and show that the linearacceleration increments at the tail were 0 to 40 percent greater thanthe acceleration increment at the center of gravity. The averageincrease was about 25 percent. If dynamically similar airplanes are

assumed, the results can be expressed as an average value of the angularacceleration in pitch for any airplane as

d-SL LO 20n

dt 33/2

At present exact estimations of the angular acceleration in pitch arenot possible.

The effect of disturbed motions on imposed loads is appreciableand may affect the frequency distribution by as much as 50 percent(fig. 50). A previously mentioned analysis of piloting effects thatcould be construed as disturbed motion indicated a variation of some20 percent in the imposed loads. Although such variations cannot bepredicted at this time, current methods of estimating loads considerthis factor in that the measured flight load experience includes sucheffects.

/ /

RESUME

A resume of the more important findings under gust structure, air-plane reactions, and operating statistics is included because of thevariety of subjects covered.

Gust Structure

The gust-gradient distance and gust size are largely independent ofweather, altitude, and airplane when expressed in terms of the meangeometric chord. The gradient distance for a vertical gust has aprobable value of 10 to 14 chords for the higher gust intensities and isthe same for both spanwise and flight directions.

NACA TN 1976 59

The gust shapes vary widely but triangular or sinusoidal profilesin the direction of flight seem good approximations.

An approximation to the spanwise gust profile for unsymetricalgusts would be a uniform distribution on which is superimposed a linearvariation of gust velocity with equal and opposite gust intensities ateach wing tip.

Gust spacing for use in estimating the number of gusts in roughair as a function of gust intensity is about 11 chords for velocitiesabove a threshold of 0.3 foot per second. The spacing is independentof other factors.

Lateral, longitudinal, and vertical gusts have essentially thesame characteristics.

The frequency distribution of gust intensities in rough air isindependent of altitude and airplane when the gust intensity is expressedin terms of indicated velocity.

Airplane Reactions

Aerodynamics.- Although the two-dimensional unsteady-lift functionsyield the most satisfactory estimates of the load increments due togusts for conventional airplanes with fuselages, finite-aspect-ratiounsteady-lift functions appear pertinent for flying wings. For unconven-tional configurations such as swept wings, strip theory with two-dimensional unsteady-lift functions appears adequate.

The slope of the lift curve for gust-load calculation can be bestestimated for engineering purposes by using an arbitrary section valueof 6 per radian and simple aspect-ratio corrections. For swept wings,the best estimate of lift-curve slope is obtained by correcting thevalue for the equivalent straight wing by the cosine of the sweep angle.

Available information on compressibility effects indicates thatthe unsteady-lift functions would.be only slightly affected below thecritical Mach number and would tend to disappear for supersonic speeds.At this time, the use of high-speed wind-tunnel data is suggested forestimating the slope of the lift curve.

Rigid-body reactions.- Analysis indicates that the mass parameteris a significant measure of airplane reactions and that the use of netwing area results in best agreement between calculation and experiment.Analyses neglecting unsteady-lift effects are not considered adequate.

60 NACA TN 1976

No one significant parameter of airplane stability for flight ingusty air has been found. The center-of-gravity position is an importantfactor for a given airplane and arrangement and tail volume have some-what less effect. Comparison of experiment and calculation shows thatminor differences in the constants used in calculation can vary the agree-ment from good to poor. Detailed calculations of airplane reactions forestimating loads are not warranted at this time because the accuracyrequired is beyond the scope of present information.

Available data on horizontal and vertical tail loads indicate thatdetailed calculations of tail load are not warranted. The lift oneither tail surface due to a gust can be estimated apparently byutilizing a true gust velocity and neglecting the alleviating effects ofunsteady lift and airplane motion but considering the downwash.

Elastic-airplane reactions.- Analytical and experimental studiesindicate that extensive simplifications lead to unrealistic answers andmore exact solutions are required as the wing mass becomes a greaterfraction of the total mass.

The effect of forward speed on elastic response was negligible,but the wing-tip accelerations increased with speed.

It does not appear feasible to obtain generalized solutions ofdynamic response.

Operating Statistics

The average miles to exceed limit load factor varies widely accord-ing to operator and period. A most important factor in setting the levelof load appears to be the probable speed, that is, the speed at whichmaximum acceleration is most likely to be experienced, since the gustexperience on all routes was about the same. The probable-speed ratio(ratio of probable speed to the high speed in level flight) is increasingas new airplanes are introduced with a consequent reduction in theaverage number of flight miles required to exceed limit accelerationincrement.

The flight miles to exceed the placard speed has decreased for thenewer types of airplanes.

The total number of gusts encountered by an airplane during itslife is a function of the amount of rough air flown. The amount ofrough air is on the average about 10 percent of the total mileage. Thenumber of gusts encountered in rough air depends on airplane size andan average figure would be 500/c gusts per mile greater than 0.'3 footper second.

NACA TN 1976 61

The disturbed motions of an airplane in gusty air do not correlatewith the maximum gust intensities experienced. Results indicate thatthe disturbed motions may change the loads in gusty air by 20 to50 percent.

CONCLUDING REMARKS

The available information on gust loads does not permit the deter-mination of applied loads under actual operating conditions on an absolutebasis. Lack of information on gust statistics, the behavior of airplanesin rough air, transient aerodynamics, and operating conditions make suchan estimation of doubtful accuracy. Consequently, the procedure hasbeen to transfer loads data from a reference airplane to new airplanesby using available knowledge of aircraft behavior. Statistical data onflight loads and gust experience under actual operating conditions arecollected in order to set the level of loading, and "transfer" coeffi-cients based on a knowledge of airplane reaction are then calculatedand applied to new airplanes. No radical change in operating conditionsor airplane characteristics are assumed to be introduced. In addition,it is implied that ail airplanes are of the same general character(conventional) and that the relative loads for single isolated gusts area measure of the relative loads in a sequence of gusts. The importantfeatures and implications in this procedure are that the same proceduresmust be used to evaluate loads data as are used in loads calculations.In addition, the procedure presupposes no drastic change in airplaneconfiguration. The use of the same procedures of calculation tendsto eliminate errors that are due to inability to predict airplanereactions on an absolute basis in that errors in the evaluation of loadsdata cancel those in the calculation of loads.

Extensive changes in configuration may be a serious limitationsince the procedure assumes in its general application that the effectof pitch on gust loads is the same for all aircraft and that all air-craft respond to the same gusts (as function of airplane size) to experi-ence significant loads. When new configurations such as taillessairplanes or canard airplanes are considered, the load transfer mustbe based on the relative motions of the reference airplane and the newairplane and not on the motions of the new airplane alone. A secondelement, gust selection, has not yet been resolved but it would appearthat tailless airplanes, because of small damping in pitch, and canardairplanes, because of the adverse initial pitching moment in a gust forswept-wing airplanes, might select some other ranges of gust sizes than

'those selected by conventional aircraft. So far, no information isavailable on this problem and it can only be assumed that availablegust-structure data are adequate.

62 NACA TN 1976

In some generalized solutions of load prediction, a further restric-tion has been introduced by the substitution of wing loading for massparameter as a significant variable. The use of an alleviation factorbased on such a substitution is still further restricted by the assump-tion that all airplanes have the same relation between wing loading andmass parameter. Information presented on the load transfer coefficientindicates that the load transfer coefficient has appreciable spreadwhen this substitution is made and the spread seems to be a function ofairplane type and use since the data can be grouped according to landtransports, flying boats, and personal airplanes. If wing loading isused, therefore, different relations should be considered according toairplane class and use.

In cases where the dynamic response may be a factor, it should beconsidered as an amplifying factor for the incremental loads whetherfor studies of large loads or repeated loads. Dynamic response shouldbe considered on a relative basis since the uncertainties in calcula-tions due to lack of knowledge and practical simplifications have notbeen resolved.

Of the many related problems, that of gust-alleviating systems isof great importance. Such systems are of particular interest in reducingloads and improving riding comfort for high-speed aircraft. The twoproblems may not have compatible solutions since load reduction impliesthe reduction of stresses in all critical members without impairingother qualities of the airplane while the improvement in riding comfortimplies the reduction of airplane motions and accelerations. Althoughthe basic problem of reducing the load due to a single gust is amenableto analysis, the related problems of maintaining other airplane qualitiesand of determining alleviation in rough air introduce difficulties.

Three fundamental systems of gust alleviation are available andconsist of changing airplane characteristics, aeroelastic systems, andaeromechanical systems. The first method consists of emphasizing thepertinent characteristics of the airplane, such as increasing the wingloading to reduce accelerations, decreasing the slope of the lift curve(by use of vents or sweep and by changing the aspect ratio), adjustingthe stability characteristics to obtain favorable response in rough air,or using free-floating flaps. Aeroelastic systems generally involvetorsional deflections of the wing due to imposed loads. Such systemscan be designed by incorporating slant hinges or flaps operated by wingdeflections or by the adjustment of the torsional and bending rigidity.Aeroelastic systems have the advantage of being inherent in the construc-tion of the airplane and the disadvantage that they form an additionalsource of elastic phenomena such as flutter or dynamic response due toa series of gusts. Aeromechanical systems cover combinations of servo-mechanisms, detectors, and aerodynamic controls. Some detector systems

NACA TN 1976 63

considered are the use of an accelerometer or strain gage to measureaccelerations or load and the use of a feeler vane or similar system todetect gust-velocity or angle-of-attack changes. The servo-systems areassumed to operate the conventional controls of the airplane or tooperate wing flaps or spoilers. The difficulties are those of possiblefailures of complicated mechanisms, the question of oscillation of thesystem, the response of repeated gusts, and, finally, the need as air-plane speed increases of obtaining a servo-system that has a high fre-quency response (imposed frequencies up to 10 cps). The advantagesare flexibility and utilization of many of the available mechanisms.

Langley Aeronautical LaboratoryNational Advisory Conmittee for Aeronautics

Langley Air Force Base, Va., August 5, 1949

64 NACA TN 1976

APPEND IX A

COOPERATING AIRLINES AND AGENCIES

The following airlines and agencies have cooperated extensivelywith the NACA in obtaining much of the data used in the preparation ofthis paper:

American Airlines, Inc.

Eastern Air Lines, Inc.

Pan American World Airways System

Trans World Airline, Inc.

United Air Lines, Inc.

Department of Commerce

U. S. Weather Bureau

Civil Aeronautics Administration

U. S. Air Force

Air Materiel Command

Air Weather Service

U. S. Navy, Bureau of Aeronautics, Structures Unit

NACA TN 1976 65

APPENDIX B

SYMBOLS

A aspect ratio (b2/s)

B arbitrary constant

b wing span, feet

C arbitrary constant

c mean geometric chord of wing, feet

C mean aerodynamic chord, feet

CL lift coefficient

CL variation of lift coefficient when penetratingg a sharp-edge gust, expressed as a fraction

of final lift (Kitssner's function, refer-ence 2)

CLa variation of lift coefficient following a suddenchange in angle of attack, expressed as afunction of final lift (Wagner's function,reference 2)

C Mcg pitching-moment coefficient about center ofgravity

D differential operator (ddt

dCm cdC L static margin

f frequency of occurrence

fw wing frequency, cycles per second

g acceleration due to gravity, feet per second persecond

66 NACA TN 1976

H gust-gradient distance (distance in which thevertical velocity of a gust rises linearlyfrom zero to its maximum value), feet or chords

K gust alleviation factor

L lift, pounds

1distance from trailing edge of wing to leadingedge of tail, chords

M Mach number

n normal acceleration, g units

in acceleration increment due to a gust, g units(n - 1 for most cases)

An, acceleration increment, g units

pSUV

computed according to formula -

Anr acceleration increment on rigid airplane, g units

P probability

q dynamic pressure, pounds per square foot (pV2)

S wing area, square feet

s distance airplane has penetrated gust at time t,chords

t time from start of gust penetration, seconds( s/V)

U gust velocity at peak of gust, feet per second

Ue effective gust velocity, feet per second

computed from recorded acceleration increment

A n W Sas

d CLPoVeK d/

NACA TN 1976 67

u vertical gust velocity at any point, feet persecond

V true airspeed, feet per second

Ve equivalent airspeed, feet per second

V p probable speed, miles per hour

VL design level-flight speed, miles per hour

VMax maximum indicated airspeed, miles per hour

Vnev placard do-not-exceed speed, miles per hour

V o airspeed at maximum acceleration increment,

miles per hour

W weight of airplane, pounds

z vertical displacement of airplane, feet

dp/dt angular acceleration in roll, radians per secondper second

dq/dt angular acceleration in pitch, radians per secondper second

de/da, downwash factor

angle of attack, degrees

f3angle of gust to direction of flight of airplane,degrees

A incremental value

bf absolute displacement of equivalent fuselage, feet

bw absolute displacement of equivalent wing, feet

bst deflection of equivalent wing under conditionscorresponding to normal static design procedure,feet

bdmax maximum value of 8w - bf, feet

0 pitch angle, degrees

68 NACA TN 1976

x gust spacing (distance between gust peaks), chords

P9 mass parameter (p. is twice the relative density(reference 24) givided by the lift-curve slope)

p density of air, slugs per cubic foot

Po density of air at sea level, slugs per cubic foot

Subscripts:

av average

p probable; denotes the most probable value of aquantity as determined from experimental data

o denotes value computed from local measurements

cg center of gravity

w wing

1 for extended equations denotes point atwhich solution applies

max maximum

Subscripts used with An:

o acceleration increment due to a gust

m acceleration increment due to vertical motion ofairplane

o acceleration increment due to pitch of airplane

q acceleration increment due to angular velocity ofairplane

C acceleration increment due to downwash

w acceleration increment on wing

NACA TN 1976 69

s acceleration increment on stabilizing surface

T total acceleration increment

Examples:

nkow acceleration increment on wing due to gust

AOTs total acceleration increment due to tail

70 NACA TN 1976

REFERENCES

1. Anon.: Airplane Airworthiness. Civil Aero. Manual 04, CAA, U.S. Dept.Commerce, Feb. 1, 1941.

2. Kissner, Hans Georg: Stresses Produced in Airplane Wings by Gusts.NACA TM 654, 1932.

3. Rhode, Richard V., and Lundquist, Eugene E.: Preliminary Study ofApplied Load Factors in Bumpy Air. NACA TN 374, 1931.

4. Rhode, Richard V.: Gust Loads on Airplanes. SAE Trans., vol. 32,

1937, pp. 81-88.

5- Kiissner, H. G.: The Two-Dimensional Problem of an Aerofoil in Arbi-trary Motion Taking into Account the Partial Motions of the Fluid.R.T.P. Translation No. 1541, British Ministry of Aircraft Produc-tion. (From Luftfahrtforschung, vol. 17, no. 11/12, Dec. 10, 1940,pp. 355-362.)

6. Lovitt, William Vernon: Linear Integral Equations. First ed.,McGraw-Hill Book Co., Inc., 1924, pp. 23-72.

7. Donely, Philip: Effective Gust Structure at Low Altitudes as Deter-mined from the Reactions of an Airplane. NACA Rep. 692, 1940.

8. Donely, Philip, and Shufflebarger, C. C.: Tests in the Gust Tunnelof a Model of the XBM-l Airplane. NACA TN 731, 1939-

9. Rhode, Richard V., and Donely, Philip: Frequency of Occurrence ofAtmospheric Gusts and of Related Loads on Airplane Structures.NACA ARR L4121, 1944.

10. Tolefson, H. B.: An Analysis of the Variation with Altitude ofEffective Gust Velocity in Convective-Type Clouds. NACA TN 1628,1948.

11. Moskovitz, A. I., and Peiser, A. M.: Statistical Analysis of theCharacteristics of Repeated Gusts in Turbulent Air. NACA ARRL5H30, 1945.

12. Moskovitz, A. I.: XC-35 Gust Research Project - Preliminary Analysisof the Lateral Distribution of Gust Velocity along the Span of an-Airplane. NACA RB, March 1943.

13. Rhode, Richard V., and Pearson, Henry A.: A Semi-Rational Criterionfor Unsymmetrical Gust Loads. NACA ARR, Aug. 1941.

NACA TN 1976 71

14. Jones, Robert T.: The Unsteady Lift of a Finite Wing. NACA TN 682,1939.

15. Donely, Philip, Pierce, Harold B., and Pepoon, Philip W.: Measure-ments and Analysis of the Motion of a Canard Airplane Model inGusts. NACA TN 758, 1940.

16. Berg, Ernst Julius: Heaviside's Operational Calculus. Second ed.,McGraw-Hill Book Co., Inc., 1936.

17. Kuethe, Arnold M.: Circulation Measurements about the Tip of an Air-foil during Flight through a Gust. NACA TN 685, 1939.

18. Donely, Philip, and Shufflebarger, C. C.: Tests of a Gust-AlleviatingFlap in the Gust Tunnel. NACA TN 745, 1940.

19. Donely, Philip: An Experimental Investigation of the Normal Accele-ration of an Airplane Model in a Gust. NACA TN 706, 1939.

20. Wagner, Herbert: Uber die Entstehung des dynamischen Auftriebes vonTragfli1geln. Z.f.a.M.M., Bd. 5, Heft 1, Feb. 1925, pp. 17-35.

21. Walker, P. B.: Experiments on the Growth of Circulation about aWing with a Description of an Apparatus for Measuring Fluid Motion.R. & M. No. 1402, British A.R.C., 1932.

22. Klissner, H. G.: Zusammenfassender Bericht 11ber den instation renAuftrieb von Flugeln. Luftfahrtforschung, Bd. 13, Nr. 12,Dec. 20, 1936, pp. 410-424.

23. Garrick, I. E.: On Some Fourier Transforms in the Theory of Non-Stationary Flows. Proc. Fifth Int. Cong. Appl. Mech. (Cambridge,Mass., 1936), John Wiley &Sons, Inc., 1939, PP. 590-593.

24. Jones, Robert T.: The Unsteady Lift of a Wing of Finite AspectRatio. NACA Rep. 681, 1940.

25. Von Karman, Th., and Sears, W. R.: Airfoil Theory for Non-UniformMotion. Jour. Aero. Sci., vol. 5, no. 10, Aug. 1938, pp. 379-390.

26. Sears, W. R., and Kuethe, A. M.: The Growth of the Circulation ofan Airfoil Flying through a Gust. Jour. Aero. Sci., vol. 6, no. 9,July 1939, pp. 376-378.

27. Jones, Robert T.: Correction of the Lifting-Line Theory for theEffect of the Chord. NACA TN 817, 1941.

72 NACA TN 1976

Vi28. Quinn, John H., Jr.: Effects of Reynolds Number and Leading-EdgeRoughness on Lift and Drag Characteristics of the NACA 653-418,

a = 1.0 Airfoil Section. NACA CB L5J04, 1945.

29. Theodorsen, T., and Garrick, I. E.: General Potential Theory ofArbitrary Wing Sections. NACA Rep. 452, 1933.

30. Pierce, Harold B.: Tests of a 450 Sweptback-Wing Model in theLangley Gust Tunnel. NACA TN 1528, 1948.

31. Jones, Robert T., and Fehlner, Leo F.: Transient Effects of theWing Wake on the Horizontal Tail. NACA TN 771, 1940.

32. Cowley, W. L., and Glauert, H.: The Effect of the Lag of the Down-wash on the Longitudinal Stability of an Aeroplane and on theRotary Derivative Mq. R. & M. No. 718, British A.R.C., 1921.

33. Farren, W. S.: The Reaction of a Wing Whose Angle of Incidence IsChanging Rapidly. Wind Tunnel Experiments with a Short PeriodRecording Balance. R. & M. No. 1648, British A.R.C., 1935.

34. Pearson, H. A.: Pressure-Distribution Measurements on an 0-2H Air-plane in Flight. NACA Rep. 590, 1937.

35. Bryant, L. W., and Jones, I. M. W.: Stressing of Aeroplane WingsDue to Symmetrical Gusts. R. & M. No. 1690, British A.R.C., 1936.

36. Williams, D., and Hanson, J.: Gusts Loads on Tails and Wings.R. & M. No. 1823, British A.R.C., 1937.

37. Sears, William R., and Sparks, Brian 0.: On the Reaction of anElastic Wing to Vertical Gusts. Jour. Aero. Sci., vol. 9, no. 2,Dec. 1941, pp. 64-67.

38. Pierce, Harold B.: Investigation of the Dynamic Response of Airplane

Wings to Gusts. NACA TN 1320, 1947.

39. Putnam, Abbott A.: An Improved Method for Calculating the DynamicResponse of Flexible Airplanes to Gusts. NACA TN 1321, 1947.

40. Pierce, Harold B.: Dynamic Stress Calculations for Two Airplanes in

Various Gusts. NACA ARR, Sept. 1941.

41. Peiser, A. M., and Wilkerson, M.: A Method of Analysis of V-GRecords from Transport Operations. NACA Rep. 807, 1945.

NACA TN 1976 73

42. Kenney, John F.: Mathematics of Statistics. D. Van Nostrand Co.,Inc., 1939, Pt. I, pp. 60-75, and Pt. II, pp. 49-51.

43. Peiser, A. M.: An Analysis of the Airspeeds and Normal Accelerationsof Douglas DC-3 Airplanes in Commercial Transport Operation.NACA TN 1142, 1946.

44. Tolefson, H. B.: Airspeed Fluctuations as a Measure of AtmosphericTurbulence. NACA ARR L5F27, 1945.

74 NACA TN 1976

-P rH 0 0 m Cuj

a) -:1 0 0- 0C 0\mH r-q O\

LCU\ _:t fn _:tH

p rd(n' \QD 0 nC 04-* P, N \,D 0 \,D LC\(D 0Io *

o\.. F-~ cc)- cr c, $LH

0 0 _- 0 0

0 0 0 0 0 0r 0 0 0 -

0 C6 0 CuH \H CC) \10

E-1 _: -zt H E-- \.0m ~ Cu

00Cu 0 00 ~ 0 0 co00

LC\ Cuj t- 0~ -

S H 0 L\LCl\ O7\HLCl\ Cuj

0 l 0 0 0

00

00)

NACA TN 1976 75

*4

01 0

$1 0 c

0

0 1IW 4HOL 4' 0 0I

p4 ,-

00 0

00

01k00 0, 0 0 0

0 0 r43 ISW4 000~

Ea H P

4I 0 0

0 0* 0 0

* 0 00 0 0 0

0 H -4

0 0

00

0- 0 0 0 0

o 0 0 ;L 4

0 ccu

76 NACA TN 1976

0 0 n! H t-- -:-H10 0 CC t0 0 H' nr~0 00 N\J -*

0 n 0

01 0 0-tn: \

0 0 -th~ t- fiCr r40 00 .-- 0j c

0 0 _:t oa, \1 -4~ H H0- --- \DO

(.0 0C 0r )\0 HL

w0 00 (r rq r U H GO H1a'

0 0 0 H0 ~~~\~0 n , C n-- cc) a\0,~*" r 0 00 1--0G C. (Y) * 0

H: -%~ H

004-3H

0~0 0 ON w0LN\C\ICJ000 CM0 01 011H o 0 00 nMC~- '.u a\ *

-ml 0 Hn C

00

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0 4- -, r)0r 0 r0

NACA TN 1976 77

(n H5 C\j \

_:t c0 n '

f 0 0~ 0 0

w ~ ~ ~ \ cco w N

Id --J-0 0 0

0 0 u~ C~- COM

' 0Y) _Y)

0o 0

(D2 r- (1) PN P4\ tr\ n

+:) H- HH. .

m (D 0

H H Hj

0w4 0 0v 0

co4-) ' - .0 001

P4'

000 m f

0 0 0

78 NACA TN 1976

TABLE V

FREQUENCY OF OCCURRENCE OF GIVEN VALUES OF ANGULAR ACCELERATION

IN BOLL WTH ASSOCIATED VALUES OF NORMAL

ACCELEkRION INCRDENT

[XC-35 a&irplans datq

I 9 c C? 0 t 0 " -7 9 'Oc O )' cC; ~ 0 0 0 0 0 0 0 A -f H C4 (.00000 0 0 0 0d 0 0 0 0 0 0 0 0 00 4

. .. . . . .T 1°i cL- D v(raaa\ oH ('') 4 4 u'0,, - 0) 0'o 0 H o'. - ) .0 0. - 040 H (-'e 4 -

e 000 0 0 0 0 0 0 H I H H H. 4

1.9 to 2.0 11.8 to 1.9 - -

1.7 to 1.8 i

1.6to 1.7 1 1 I 1 - , ! 3

1.5 to 1.6 1 2

1.4

to 1.51.3 to 1.4 4 Fi .1.2 to 1.3 1 11.1to 1.2 2 1 1 - - i

1.0 to 1.1 3 3 2 1 1 10

0.9 to 1.0 3 1 4 1 2 1 1 12

0.8 to 0.9 I 5 3 6 3 1. 1 210.7 to 0.8 4 4 7 3 1 2 2 2 1 260.

6 to 0.7 1 9 8 16 2 1 2 1 40

0.5 to o.6

2 15 7 30 171 2 1 2 2 80.

4to 0.5 1 1 8 21 45 24 1 3 1 5 1 1 4 1 1 118

0.3 to 0.4 1 1 1 3 11 32 77 66 2 6 13 7 17 1 2 1 247

0.2 to 0.3 1 3 2 13 14 107 1291 8 12 6 11 30 1 4 2 353

0.1 to 0.2 1 44 20 36 136 153 5 13 20 21 2713 11 1 .W8o to 0.1 1 27101 147 12 161 23 40 42 15 6 1 1 1 455

0 to-0.1 2 6 13 23 80 17817 191 85 99 79 9 7 1 1 619-0.l-to-0.

2 1 33 10 9 9 151581 152 78171013 2 1 545

-0.2 to-0.3 1 10 9 5 5 5I 20 161 UI6 12030 3 1 11 617-o03to-o.4 111 4 8129 42 5122148264 1282817 85 1 712-o-4to -0.5 8 10 20 31 1 11 11 116 124 19 16 8 1 1 477

-o.Sto-o.6

1 1 7 9 15 2 10 35 8310026 710 2 308-o.6 to -07 1 8 1 5 3 24 52 5020 3 52 1 175-0,7 to -0.8 1 2 3 1 1 3 12 24 3624 8 53 122-0.

8 to -0.9 1 3 2 3-1 19 31 9 8 1 1, [ 86

-0.9 to -1.0 1 3 2 6 14 116 2 6 3 5

-1.0 to -1.1 2 1 8 13 2 9 1 1 1 38-1.1 to -1.2 1 2 3 1 3 1I 15

-1.2 to -1.3 2 1 1 3 1 9-1.3 to -1.4 1 3 5 1 10

-1.4 to -1.5 2 2 2 1 7

-1.5 to -1.6 1 11 3

-1.6 to -17 4 4-1.7 to -1.8 1 1 2-1.8 to -1.9 11 2

-1.9 to -2.0 1 12.0 to -2.1

-2.1 to -2.2-2.2 to -2.-3-. t2. 1 1

Total ii 61 35 149 235 792 952 16749 1042 914 5151105 30 9 61 15651

NAC IA TN 1976 79

*m 0

0~~2 -P -01cM O4 Z7H 2O

0r

HP0

00

0

E-4 ri -H

H

0 0

00

0 0o 0

o Ho0 0

00

0

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00000

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00430

H 0 00 Pi0

-p 0 -Hp4

00 C'1 \10 cO0. L-- 0 H .P, -0 1 Cm 1 __ __ _ __ _ r-4c

w~

80 NACA TN 1976

TABLE VII

CHARACTERISTICS OF AIRPLANE MODEL

[Laminar-flow wing]

Weight, lb . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

Wing area, sq ft . . . . . . . .. . . . . . . . . . . .. ... 5.44

Wing loading, lb/sq ft ........ ..................... ... 2.18

Span, ft . ............................. 7

Mean aerodynamic chord, ft ....... ................... .. 0.829

Aspect ratio . . . . . . . . . . . . . . . . . . . . . . . . .... 9

Taper ratio ............. ........................... 0.382

Center of gravity, percent M.A.C ...... ................ ... 30.5

Wing section ......... ................. ... 653-418, a = 1.0

Lift-curve slope, per radian

Smooth wing (steady flow) ...... .................. ... 5.01

Roughened wing (steady flow) ...... ................. ... 4.18

Theoretical ... ................... .............. 5.41

NACA TN 1976 81

q q 9o o 0

+1 +1 +1

o 0 4-:)o0 Hr 0 H

-P -0 0 -P

•~ .r--j, 01o

- O -j40 0.10 0 0 00~0

0H -P -H

0 0 oa) L

(D 0

P N -H Fo CH 0= ' o 0 ,0

0 U)0 Q 0 0-P a 0 mN0I 02N 0 -P ,10

0 0 ()-0, 0 q

0P 0 0- -%0

0A~ 0 riH0H 0 r- t) H

0'~ 0 0 0 0 43

C; 0 0

+1 +1 +1

00

0

000 -H 0

0 00O -

a) 0 0

0 1 01- 0 0

0 -0

0

0. 4

ca0 - H 0~ r-1 PF0

82 NACA TN 1576

zp

0y)

H

0. r0

E-1p

00

0 H 4-- 0 m0 0 ol

NACA TN 1976 83

t-- cc) cc) o n~ cj -:t t-- 0 co0 cm 0.- CH 0 nO 0

I H H- 0 r) 0 cu * * 4--

a,\ a 0 '. H) 0- n Hi Ct - CflU t- CO \,D 0 * *

mI 0 H6C

Crd H CU O

4- *r \1 * ~ n0 t

1r' co\CU-4 Q\ CI- *- *yl * ~ (Y

a * ** *

F- H

* * * *

0q

E-1 r0

OT,*

pqp

HD H

'P,

m 0 0

0- 0> P4 U

H) -H 0 H 0a) Cl) 0 0 r C C

aq 0-1 ) r

84 NACA TN 1976

II o

CM 0CI

1101 aE-f 0

0 rQ tr -iC

C.) HO H 'HOCr H'A 0

. . -;t(V . . 0 5cyj0H-j0

0 0 rLC\

C'J.

1~ ~ ~ 0 0- -. ,

H, 000

0 8 0 Cl) 0 co

H -H 0

H- 0 -;

CI\;

H.............................

P4 .

P4

4- IL

H 04

V -Hs

30 0HC2 ~ t

NACA TN 1976 85

TABLE XII

MAXIMM TOTAL ACCELERATION INCRMENTS ON CONVENTIONAL AIRPLANE

[All increments given in g units]

(a) Center of gravity, 15 percent M.A.C.

Tail length Tail area

EF=O

0.199 1.86 -0.21 -0.05 0 1.60 0.23 -0.03 -0.07 0 -0.01 -0.01 0.11 1.71

0.91 .283 1.72• 364 1.88 -.24 -.07 0 1.57 .40 -.o5 -.14 o -.01 -.03 .17 1.74

.199 1.681.37 .283 1.70

•364 1.72

.199 1.92 -.28 -.06 0 1.58 .19 -.o4 -.06 0 -.01 -.02 .o6 1.641.825 .283 1.66

.364 1.92 -.28 -.o5 o 1.59 .32 -. 07 -. 11 0 -.01 -- 03 .1o 1.69

E=8

r .199 1.90 -0.45 -0.27 -0.01 1.17 0.21 -0.06 -0.08 0.02 -0.03 -0.02 0.o4 1.21

0.91 .283 1.20L 364 1.90 -.45 -.30 -.01 1.14 .38 -.lo -.15 .02 -.07 -. .04 1.18

.199 1.241.37 .283 1.22

.364 1.21

,199 1.90 -.48 -.15 -.01 1.26 .16 -.06 -.06 .01 -.02 -.03 0 1.261.825 .283 1.25

.364 1.91 -.49 -.17 -.01 1.24 .30 -.11 -.11 .02 -.04 -.05 .01 1.25

ii = 16

0.199 1.93 -0.47 -0.75 -0.01 0.70 0.22 -0.06 -0.08 0.02 -0.09 -0.03 -0.02 0.680.91 .283 .62

.364 1.93 -. 39 -.90 -. 01 .63 .39 u.09 -- 15 .03 -.20 -.05 -.07 .56

r .199 .761.37 .283 .73

L 364 .70{ 199 1.93 --58 -.48 -.Ol .86 .19 -.07 -.07 .02 -.o6 -.03 -.02 .841.825 .283 .84

.3641.93 -. 60 -. 44 -. o .88 .34 -. 14 -- 13 .03 -. 10 -. 04 -. 04 .84

I ,-N C

86 NACA TN 1976

TABLE XII - Continued

MAXIMUM TOTAL ACCELERATION INCPEMENTS - Continued

(b) Center of gravity, 25 percent M.A.C.

T I

Tail length Tail area A-.,, A%" - 4,% A n .n% 6n. An. Ane, Lq A DT

H= 0

0.199 1.86 -0:22 -0.01 0 1.63 0.23 -0.03 -0-07 0 C 0 0.13 1.760.91 . 1.87 -.23 -.o2 o 1.62 .32 -.04 -.11 0 0 -.01 .16 1.78

364 1.88 -.25 -.03 C 1.60 .4o -.06 -.14 0 0 -.02 .18 1.78

r .199 1.74

1.37 .283 1.76

.364 1.79

.199 1.92 -.29 .01 0 1.64 .19 -.04 -.06 o 0 0 .09 1.73i .6 15. 2 1 7 6

•.354 1.92 -.30 .02 0 1.64 .32 -.07 -.11 0 0 0 .14 1.78

H=8

0.199 1.90 -0.51 -0.11 0 1.28 0.21 -0.07 -0.08 0.02 -0.01 -0.01 0.06 1.34

.364 1-9o -. 5o -.16 o 1.24 .38 -.12 -.15 .03 -.03 --03 .08 1.32

S.199 1.371.37 .283 1.90 -.51 -.10 0 1.29 .26 -.09 -.10 .02 -.02 -.02 .05 1.34

S.364 1.34

• 199 1.90 -.53 -.02 0 1-35 .16 -.07 -.o6 .o o -.01 .03 1.381.825 .283 1.37

.364 1.91 -.54 -.05 0 1.32 .30 -.12 -.11 .02 -.01 -.03 .05 1.37

H = 16

090.199 1.93 -0.66 -0.35 0 0.92 0.22 -0.08 -0-08 0.02 -0.04 -0.01 0.03 0.950. 91 [ .283 .88

.364 1-93 -.58 -.53 0 .82 .39 -.13 -.15 .04 -.12 -.03 0 .82

.199 .961.37 .283 .92

.364 .88

.199 1.93 -.68 -.280 .97 .19 -.08 -.07 .02 -.04 -.02 0 .971.825 .283 •95

S.364 1.93 -.66 -.32 0 -95 -34 -.15 -.13 .03 -.07 -.03 -.01 .94

NACA TN 1976 87

TABLE XII - Concluded

MAXIMUM TOTAL ACCELERATION INCPAMENTS - Concluded

(c) Center of gravity, 35 percent M.A.C.

Tail length Tail area] An, % Ln e n0 ,% 6n.. A,,% nn.. 6n. t ne. A.A.T(f't) (sq ft) { w -' w~

H= 0

0.199 1.86 -0.22 0-03 0 1.67 0.23 -0.03 -0.07 0 0.01 0 0.14 1.810.91 [ .283 1.84

L .364 1.88 -.25 -03 0 1.66 .4o -.06 -.14 0 .01 0 .21 1.87

• 199 1.821.37 .283 1.84

•364 1.86

.199 1.92 -. 30 .08 0 1.70 .19 -.04 -. 06 0 .01 .02 .12 1.821.825 .283 1.84

.364 1.92 -.32 .08 0 1.68 .32 -. 07 -. 11 0 .o2 .02 .18 1.86

H=8

0199 1.90 -0.54 0.04 0 1.40 0.21 -0.07 -0.08 o.o2 0.01 0 0.09 1.490.91 .283 1.48

L .364 1.9o -. 56 .o o 1.35 .38 -.13 -.15 .03 0 -.01 .12 1.47

F .199 1.501.37 .283 1.50

.364 1.50

•199 1.90 -.58 .12 0 1.44 .16 -. 07 -. 06 .Ol .02 .01 .07 1.511.825 .283 1.52

• 364 1.91 -.60 .12 0 1.43 .30 -. 14 -. 11 .02 .03 -. 01 .09 1.52

H = 16

F0.199 1.93 -0.85, 0.06 0 1.14 0.22 -0.11 -0.08 0.03 0.01 0 0.07 1.210.91 .283 1.93 -.79 -. 07 0 1.07 .31 -.14 -.12 .o4 -.01 -.01 .07 1.14

.364 1.93 -.75 -.18 o 1.00 .39 -.17 -.15 .05 -.o4 -.o .07 1.07

• 199 1.191.37 .283 1.14

• 364 1.o8

F .199 1.93 -. 82 .01 0 1.12 .19. -. 10 -. 07 .02 0 0 .o4 1.161.825 .283 1.13

S.364 1.93 -.77 -. 10 0 1.o6 .34 -.18 -.13 .04 -.02 -.02 .03 1.09

' NACA

88 NACA TN 1976

C\CJ

II0-- co' 0I \1

4, n' \0 0':

co ~ 01p0I 01 0

0 c00 00 t- coI

H m \1 TTH C

0 :5c00 0 000 0 0oco 004, c CQ c CQ' CMj C\j C 04

~0 4'

m 0

w P-l(4D

0 0 0

NACA TN 1976 89

O0 0 H.3 a I

C C'J He 4

0 0; 0,

II~ C)J CCII 0 00

ml~ 00

U6 Lrt- C0 1

o ~~~Cr) C?)CiCi r rqj0 0 0

HH HHj 0- - a

-p 0

liii I:- r)CJII I 00 I 0I I;

II cuc'0, 0'1

_:0

Ir\C\j C

CL~j

0 4:0

Hq H 4

90 NACA TN 1976

U3 H3 40HH

E-4H

0

CYCM

00

0

CH 0

CM

00

0 0

ra~U +1 4

*-i

ON 0 m\

0~ t,

00 0 - i

0

10

NACA TN 1976 91

Pv

TABLE XVI

TEST MODL CHAACTRISTICS

[Nonrigid airpl ane]

Weight, lb ............................. .. 1.832

Wing area, sq ft ........ ......... ............... .. 1.183

Mean geometric chord, ft ....... ........ .......... .0.394

Span, ft .............. ....... .................... 3.0

Slope of lift curve, per radian ...... ................. ... 4.73

Forward velocity, fps ......... ...................... ... 61.0

Gust velocity, fps ............. ........................ 6.0

Pitching moment of inertia, slug-ft2 . . . . . . . . . . . . .. . . . . . 0.00782

Radius of gyration of wing, ft ......... ............... .0.663

Weight of wing, lb .......... ...................... .. 0.293

4Z C

92 NACA TN 1976

m 'a

4)0,-0

0 000

0~~~ IC' u~CU I '

(1) 'H C0H" H

4-4 r4-

aD 0 0 0 0 0 0 00 \0 0 0 0 0C 0U('. 4-4 4-4 -* N c

0 0-~

H4 H

00

0~

0

H~-- Cu\ HONu ~ * H C

0 4r

100

NACA TN 1976 93

0 0 nr U-\ 0 mY~0\ ou cm L-- 0 t--0 CH H- C) Nu H t

t-- 0 \.O -t _:

Cuj Cu Cu Cu Cl Cu

H- 0 H o N~H CH- cn~C \ o Cuj

Cu Cu H H Cuj Cu

--t \0 co 0 n \0

H Y) Cu Cu Cu Cu Cu

CU md cm Cu t4-C - 0

HE'1,

0

"0\ t-

E-4 Hr or Cuj ty-) N-Co0 H H H H H

Ct) L\ 0 f C

S2 0\ 4- 0' H \O -

0 0 0 0 0 0

0 C\ 0l H 0 0 0~n Cvi 0= 0~ Lf\a\"

HM _t(1

<4 C.) P q F

94 NACA TN 1976

-P

4- 0+43

o

0 0 0 0 0C..0 0 c') -It Sn OD 0

0 't \- H* r0 H H1 -flm NCui

+' -' 4P 0 4P -P2 0 --P -P

o H \D~

o ~ 0r ' r 0 0 0rmbt- 0 a\ en LA 00 o e) \JD

cu cucm \0 U-\ m

0 Y

M~)HC C H H

0 (0i en4

t- o t 0 e0 t-

p- * * H H r

0 0 49CH- H H (

H v Hl H1 H. 0% H

~ t- - 0 \0 \0D CU Hen mn mn * (n mn 4 4 1Ch 0, 07\ 0\ (7\ 0% C\ a

HH 400

0~~ ~ ~ ~ 0 4 0Q4-110 o

H

.pFa P4~H H

NACA TN 1976 95

OOOLCU\o 0 nr C\LCn

000000 0003jw ______

0cu C - Hq14CUj N Od rH

0'000 - 00

'o U'\CU L-0 .tC\ 0

0 n 0

0 -t3.D 91 MO\ 0\ M

0 00 a\-* H~ m N

rdo

CO 0\ CD 0 C\;O Co

cm Ej 0 0\0 Cj 0M LI-

0 HH .-IHH

'dC4-') -H 0_:t u (7 0 t CC \ 0

02

96 NACA TN 1976

p ~ 0 0

I x

0

0 00H H H

0- x x x

0 0 I

LrI cm 0 0 Y o

0 0 00 O\ 0I 1C.m H.- \DI OW()

H- tH HH

HL

0U

NACA, TN 1976 97

/ AZ-t

00

-~ -:

o

- 0

,---

4-0

4

00

w0

JCI.

98 NACA TN 1976

4,

0

NACA TN 1976 99

~C .6

/ 24( ' 6 78

Figure 3.- Unisteady-lift functions for infinite aspect ratio. Fromreference 5.

H,/ cbord~s

0 65 /0 A5 20 2,5- 30 35 40

Figure J4.-~ Acceleration ratio as function of the mass parameter. Abovedash line, finite gradient solution is not valid.

100 NACA TN 1976

/6

/2/

- .6

.2

002 0 30 ,/0 501a/0 W///oad/7[; /S fl~ 33-

Figure 5.- Variation of alleviation factor with wing loading.From reference 1.

NACA TN 1976 101

XC-35 XBM-1

Aeronca 0-2 F-610

L-50539Figure 6.- Airplanes used in gust research.

NACA TN 1976 103

Figure 7.- Location of' orifices along spani of' XO-35 airplane.

lo4 NACA TN 1976

oHop

oe~ 00

-- P

S.0

o~o0

oll~ 0 0-

Pz4

1ID

4-'

C'D0 -

NACA TN 1976 105

35

30*30 71V/le Al, ola'4e

o /00 XC-35I 000 -1

25

~20

0

5 __ _

S0 30

Figure 10.- Expected effective gust velocity at various altitudeswithin convectiye clouds for 100 and 1000 miles of flight fromdata for XC-35 and F-61C airplanes, respectively.

106 NAcA TN 1976

00

0~~ 00Nj

0 0

0 0 00 0 0 0 H_ _

0 0 0

0 0 00 o

0

0 0 o o

0 ~000 ~ iZ -

0 00 0 0 12&b 0 0 0

0 0 0000 00 00 0 0 0

00 C90 4) 0 o0 0 000 00 . 4_____ 0 0 0- 0 d a

0 00010 0 0Z k10 0 00aD

0 0

00 0 01 &80 0 c0___ 0 t)

0 00 0% 0o %?0 0bol 0 OC08%

0 000

00

0 0 00 1

0- 0

OAM

cz 0 g D

fr~ ~/9O/9 /SY?

I

NACA TN 1976 107

50 _

o A eponci C -240 -- XC-35

X)BM -/v XB-15

f0,5 C

N20

/0 1 _

0 4 8 /2 15 20A vercge 9v/-grcidfe/ d!//ocefi/y, chord/s

(a) Gust-gradient distance in chords.

Figure 12.- Variation of average gust-gradient distance withgust velocity.

lo8 NACA TN 1976

z:z

P4.

qj

0 0 <>

C4-V)

NACA TN 1976 109

a

ID C

H 0

ElE N

0 03

110 NACA TN 1976

4.4

0

(30

IQ1

C.1-C

gp~o) cd H~u~ /p l u/po g 'oo42

NACA TN 1976 lll

35 x/o

30 o XC-35EJ F-&/C

25 EnI

EE

/0

E5

0 1 2 A6 1?o

Avercge gradein' d/lstolce, -o chord5

Figure i.- Variation of average gradient distance with altitude.

112 NACA TN 1976

Rcc fwngv/cir /syn eria

f 93/7p-sL troozoidci/ TrIanguv/ar

S'coc/trcpezo'a'/ Double ral)ucW

- Jt7Plc7/l/" C//3/P/-bul///017

--P/--ss1i/'/e dC//of?11 fron?7 Ihe wdw-o Pos/on W/0rC /ocoI geiSt I/e/OCI4/ e,4

/s meCOUfc/

Figure 15.- SpanvlIse gust distributions and frequency of occurrence ffor each type.

NACA TN 1976 1i3

4.

.H

°~

4,

0m

o,

S H

q)

114 NACA TN 1976

0

0'

0 0

0~ q)

- - 04 1140 0

0P

0 w0

0 ~ ~ 0 0, .

f43

NACA TN 1976 115

0 a,

0 0'

00

00

0- - 0

0 JP00 OD 0 0

00 0

0 (9 0 0 0 )

0000000 0 00C0

0~ 00 0

0 00 0 0 00_ 0 00p~ 000S a60

0 0_00__0 00

0 00

0c o- 6- 00 0 c0 0 0 0 G 0, Q S: C

0 00

0 0. 00H

0.0

-. H

EdY "0 g/ou 111V

116 NACA TN 1976

0

0

-H 0

10,

Qr(r:

NACA TN 1976 117

r-A

co a

4 w4' w

\ CH~

00

00

0 0 M

*H*

V3V

\0

o o4o

Q0)

0 0

0 0 o 0c 0 0P

o a N CHV0 N 0 aCO) V +:)

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00 -0 00 a) ~000 pc P, r

or 00C

0 4) 00\

-P 0 N

118 NACA TN 1976

(4~~ I

I

, I I

S

(a) Angle-of-attack change.

!7 feaqylflowf /

- -1;iKA C

...-h-S .. s -"

AL

S/ IA

(b) Lift-coefficient change.

Figure 22.- Diagrammatic illustration of the superposition (Duhamel)integral for evaluation of lift following arbitrary variation inangle of attack.

NACA TN 1976 119

Vt

cn

ITT

NACA TN 1976 121

.6-B/

[A Eoerimefnt

_---4Ca/culafed

.2

0 . 2 3 4 S 6Dis/ance, chordq

Figure 24..- Comparison of calculated and experimental circulation followingabrupt increase in speed. From reference 21.

iD

100 A0

e.

0

.8 .

ou Kis/ner) reference 2

0~ KvTT,?er, referen~ce ifEO- A KI'5ss/e/, referen9ce 224 6orrIck, eeene2

<>~ Jones, r~eferen;ce 24o Vo/n 7ffr/r~n- Secrso reference 25

.2

o 2 4- 6 a Io /2 /40,stance , c horZ5

Figulre 25.-Unsteady-lift function for 8an airfoil traversing a sharp gust.

122 NACA TN 1976

I I - -

I a

I

4-)

43

-D

N-N67S

/Ou4,

NACA TN 1976 123

- --- C7/c'/a-- 7 <ne

,"3

CoIculoibq Von k(&rm6n and Sears-- 6xp em'in ntc/ Nrde~hb

-I o' I 2 3 4 5 6 7

Figure 27.- Comparison of calculated and- experimental circulations foraspect ratios 3 and. co.

A

00

*0 0

*0 0

0 1 2 16 20 24 25 32

F 2 ori o alcuat. and. axsrmen eloi

fo hr-dg ut.Pthasmd eo

124 NACA TN 1976

4,

/

z

Il//I 0£5,04,__

I0IC'

9~jqj -~

K~Z~ £5

4,

'~ .~(I)&~K

~0

£5

'.40

('94,£5'-I0H000

0

4,mN.

N ONN

c'.JN 0ON~

r~4XL2UJ~7

NACA TN 1976 125

C6

0

10

CC\\

0

X'ACA TN 1976 127

rd

04

NACA TN 1976 129

0 2 -Scqle //00'/de!, 517o1lus/ /u1,el] z- 5 -cGae mode%, lhrge guvst Aloe/0 7 -scale rnode/4 lar/ e 90st /u qe

-- -Co//clateo referdwce 4

QJ

0 4 8 /2 /5

Figure 32.- Experimental acceleration ratio for Boeing B-247 airplane asa function of gust-gradient distance.

130 NACA TN 1976

Io Cd 0

-- 0

0

4-3

0

41

H0

I'DD

L -H0cn I

-, P.

c:m

NACA TN 1976 131

12

.8-- _ __

/0.

A-1C

3 .91 /331.099 81.- .73

A: 4 ., /. /..5" .8 363'

.b 8.264 1.37 I49

~j4

1fm n 4. GC.)

00

S/5

.2 1 2 _

A

* NACA '5

0 .2 4 0 -2 -4 0 2 -. 4

dCl

(a) =. (b) 1=8. (c) 1=6.

Figure 34.- The ratio of total wing load to the wing load with no pitch asa function of static margin for a conventional airplane.

n el aaea at T2 ercet lmeangeometcalc lat? ePI ft.l (f/) (cU /- )o0o 0.199 0.9/ O./* /% D I¢q 1.37 .273A A\ .I9 192.5 -3e3

SO\ .3,64 1-3 7 A4geV 3,, 64 8,2-' .665

0 17, 3 , - 40 -

C~c

(a) Hr=o0. (b) R=8. (c) H =16.

Figure 35--Comparison of calculated and experimental accelerationincrements for conventional airplane. All points except wherenoted have center of gravity at 25 percent mean geometric chord.

132 NACA TN 1976

{percent chor/)

k-30 - """ -5

0 4 8 12 A5 20 24 28 3Y2M1,55 . 00aln e te& rg

Figu~re 36. - Variation of relative lift due1 to pitch wit~h mass paetex %8

for a gust-radient distance of 8 chords.

1'q 'f) (fl) (CI/)- 0199 0.9/ o. I 1

,6 k. . .3 6 4 .9 1 .3 3 1- --199 12,-35

~4

15~

\S _- --._ _ .A 86_ _

~:30

[] 2 5\.

1I7 -2 -. 0 - - - -- -

N- --

AI~s~,oor,, e"e ji

Figure 3.- Vaiad nrmn safation of reltiv liat due to picgwtums prmteoyfor a convgadentdiotanl oai8pchod.

11 " __= -. 364 -. 5' 0 :2 -.4

.2 eq

(2--- =- . (_ =.(c =6

Figure 37.-- Tail load increment as a fraction of tail load due to gustonly for a conventional airplanle.

NACA TN 1976 133

3

(pelce/f AbC.)Ca/cula/ed e 0

_ _C_ O/cuced 8

0 &kpe~rfle/ 20I I!4 8 /2 /6 20rust- 9rad/er/ d/sfa,'?c&, Chocs

Q(a) Tailless airplane.

3

SCGcQl/ed, A = _ _

0\-_ Cac'iuedj A =6

0 4 8 12 20

(b) Canard airplane.

Figure 38.- Comparison of calculated and experimental accelerationincrements for unconventional airplanes.

134 NACA TN 1976

/4-o Transpor/s

_ 0 Pe IS 017Ta aP O S

A e~Prj~97s2 /2-

AA A 0

0 0/.05 0]" o----------------

o -- 1 170 01

.8 0on

.61

.6 , I , I i I , I , I0 /0 20 30 40 50 60 70

W19 /o0'//7, W/S

Figure 39.- Relative response of representative airplanes as a functionof wing loading. (Acceleration based on W/S divided by accelerationbased on mass parameter.)

,~~.SywJjdo/ T~ja

00 zo 30 40 50 60 7a9 80A,/ass a6¢ee.,U

Figure 40.- Relative response of an airplane encountering sinusoidal andtriangular gusts as a function of mass parameter.

NACA TN 1976 135

00

C*42

0

4 --

0

0,

42

rnp

00

cx~t

0

P40

136 NACA TN 1976

0to

P14

G~ca

H

0Q)

k0 -

KA

K c-H

rz4

NACA TN 1976 137

0 --

0o

0

-

mJ

138 NACA TN 1976

L Q)

S0-P4

_a~o _ ial.m y _ qo It

S 0 A

0 0 ,

4P

9clO (ILI/D '/0 0,o

uinulmu jool-tr

NACA TN 1976 139

I -3-

-

0

~? 0

- _ _ - -I

-~ 0

0q

qj4

(z 0

sol~~~lCA ulumu j l

140 NACA TN 1976

CU_ r,0

4421

rl H

0,8/IOA W!fW/X~e/ 10 0 /1

Cld)

E,1?_1 -17IXU JO04O

NACA TN 197611

000515o

- -H

I-JJ4- C - --6 CHn

- -- _ - - j *~0

-~~~~- 0 _ - - --

-$ rx H

Sr0

C'14zoz~ coqaC

IDS

142 NACA TN 1976

2.4

-o-- Cond//ion I, normal gross welgq/--- a-- Cornfion 2, over/o gross we/9/

2.0

C;--/.6

co /2 -"-_

0--.

K

0 .4 8 12 16 2O 24Gradcen! d/s tan ce, ftchord/ a

Figure 47.- Effect of change of wing frequency due to addition of massModel D, conditions 1 and 2.

NACA TN 1976 143

fr0

4,

0

ID 01 JO41,11,20,1

144 NACA TN 1976

0fr

00

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(a) Relative frequency of given values of angular displacement.

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(b) Relative frequency of given values of angular velocity.

Figure 51.- Relative frequency with which selected values of angularmotions will be exceeded in rough air.

NACA-Langley - 11-4-49 - 1200

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