C.P. No. 324 (18.870)

A.R.C. Technical Repon

. 1,_ , . . b 7) C.P. ,No. 324 : n I: ’ 1, > (18.870)

*I .\ .ip=,c*;: ’ A.R.C. Tech&l Report

MINISTRY OF SUPPLY

AERONAUTICAL RESEARCH COUNCIL

CURRENT PAPERS

The Variation of Gust Frequency with Gust Velocity and Altitude

‘BY

N. I. Bullen, 5.Sc.

LONDON: HER MAJESTY’S STATIONERY OFFICE

1957

THREE SHILLINGS NET

C.P. No.326

U.D.C. NO. 551.551 : 533.6.093.8

Report No. Structures 216

October, 1956

ROYAL AIRCRAm ESTABLISHMENT

The variation of Gust Frequency wsth Gust Velocity and Altitude

N. I. Bullen, B.Sc.

Infonlatzon on atnospherrc turbulence obtamed from counting

accelerometer records I.S exuuned and relatxons g~nng the variation of

gust frequency vnth gust velocity and altitude are obtamed. The

results are amnanzed in a form convenient for use in estmting the

fatigue life of an aircraft.

LIST OF CONTENTS

1 Introductzon

2 The variation of gust frequency with gust veloolty

3 Tine variation of gust frequency with altitude

4 Conclusions

References

LIST OF ILLUS'LIIIITIONS

Turbulence encountered by Yeses aircraft

Total numbers of psts recorded on Herxes, Comet, Viking and Bristol Freighter

Nmber of gusts exceeding different mgmtudes per 1000 exceeding 10 ft/sec. E.A.S.

10 ft/sec E.A.S. gusts encountered by Comet

10 ft/sec E.A.S. gusts encountered by Comet and Viking

10 ft/sec E.A.S. gusts enoountered by Comet and?iemes

Frequency of occurrence of gust: of ma&nitude greater than 10 ft/sec E.A.S. at &fferent he@ts

+Jg

3

3

5

6

6

Figure

1

2

7

-2-

1 Introduction

The gust loads on an aircraft are important from the standpoint of both static strength and fatigue Records of aircraft acceleration in flight are obtained from counting accelerometers w

f ich record the number

of tunes various acceleration levels are reached'> - The ObJectivo is to record accelerations of the centre of gravity and it is i.mportant to be certain how faithfully tnis 1:; done in reality. The accelerometer is mounted in the fuselage and records the response to a gust with unde-flned space and time gradients. The record, moreover, relates to the local structure on which the accelerometer is mounted so that even when the position coincides with the centre of gravity of the undistorted aircraft, the records may be rrJluenced by structural deflections under lOXI.

The accelerometer counts are directly applicable only to the particular aircraft and operating conditions under which they are recorded. In order to give the results more general application, it is necessary to estimate the appropriate atmospheric conditions. For this purpose the height and speed of the azrcraft are required and these are recorded photo@aphically, together with the counts, at intervals of ten minutes. In the subsequent analysis, the cffact of the flexibility of the aircraft is ignored and the recorded acceleration is assumed to be that of the centre of gravity of the aircraft:.

In order to convert the recorded acceleration to gust velocity the method given by Zbrozek3, 49 is used. To simplify the aerodynamic analysis he assumes a rigid aircraft and ignores the pitchin: response induced by the gust. The gust velocity is assumed to incrLitse linearly to its maximum value. After conversion of the recorded accelerations to gust velocities by tiizs method, the member of gusts exceeding each magnitude in the required series is calculated.

2 The variation of gust frequency with &ust velocity

A typical set of records is given in Ref 5 relating to Hermes aircraft. The original data from which this report has been prepared were obtained from about 2000 hours flymg on B.O.A.C. routes. The flying is grouped in altitude bands of 5000 ft and Pig I shows xllles per gust plotted on a logarithmic scale against gust velocity. The ordinate corresponding to a given gust velocity IS the logarithm of the total number of miles flown in the altitude band, dlvidod by the number Of times the given gust velocity is equalled or exceeded. Itwill be seen that the variation of frequency with gust velocity is substantially the same at all altitudes, with perhaps the exception of the highest band which consists of only a small sawle. This band is more turbulent than Would be eqectcd and shows a slight increase in frequency of the higher velocity gusts. However, in order to estimate the relative gust frequenclcs it seems reasonable to total the gusts recorded at all altitudes. Tills has been done for ea b of the four aircraft for which records are at present available53 8, 7, 8. also includedv.

Bata from test flying on the Comet are The graphs of log (number of occurrences) against gust

velocity are of approrznately the same slooe for all the aircraft. The small varmtlon may be attributed to the differences in flexibility of the aircraft, for which no allowance is ma&.

* If allowance is made for flexibility xn stressing, its effect on both acceleration and stress should be included.

-3-

-4; -4; -35 8 -30 15 -25 -20 -10 64 259 1192 -15 6665 98:;

up to a gist vcloclty of 30 ft/sec up gusts arte more frequent than flaw @usts in the ratm of about 3 to 2. Thm my be partly due to manccuvr~ng accelerations whrch are supcrmrpossd on those produced by gusts, although It 1s doubtful-whether the effect of' this can account for all the dlspaarlty. At h&m gust velocltles the down gusts appear to predonrnatc although the mmbers ar,: too mall for this to be very slgrilf1car.t. A possible explanation 1s that no allowanci 1s made for any changes Nh%ch m&t occur zri the slope of the lift curve at the lx& posltlve mcldences mvolved; when the arrcraft 1s in level flight at a posltlve xc~dence, a stallmg up-gust 1s of' a lower velocity than a stallmg dmm-gust, and thus errors mtroduced by assurmng a constant slope to the lift cui-VC fiear the stall have a &t-eater influence on the estmzttes of the up-gusts.

In the estmatlon of fatigue damage from gust data It 1s usual to assume that an up gust 1s associated with a doti, Last, of equal ma&-etude, and to take the mnean of the numbers of up and dov,n ~U,US'GS as the number of fatxyc loadmg cycles. For this purpose the numbers of up and down gusts given above are added and an empzrical curve fitted. L2mndardum3 to gave 1000 gusts of 10 ft/sec or greater tx foImula 1s:-

;?’ = 27,800 e -o.3~~v+ 878.2 e-o.20816~

where v is the g&ist velocrty in feet per secor,d and F 1s tne nu-ibex- of guste equal to or exci,aJlg v f$/sec. The above :orm of thi mpress~on 1s of tire when calculatn-,~ damage IO0 Sor calculating frequutncltzs a more conmxnent fern is:-

F = ,04.444~-0.~4945v + ,02.9436-0.0904~

The relation 1s shcwn graphxally 13 Fig 5. In most cases, the lowest meaxred acceleration corre ends to a gust vcloclty well helm IO ft/sec and usually approaches 5 7 ft sec. In this range time frcqucncy dlstrzbutlon ~IICJNS no abmpt change am3 accordingly It 1s thought Juctlflable to extrapolate the curve to 5 ft/sec. For any cjlven velocity a conf'ldence rangs can be e&mated and that for 95< confidence 1s shown lr? the f~~~re. The estmnted racge makes a llowance fo~,the tendsncy of the gusts to occur near together m rcglons of turbulexe . The frequencxs ezven by the formula for velocltles above 35 ft/sec., snculd be used mth caution as tne total nwnber of gusts recorded above thl s valm 1s only 13 and the salTlmg errors artz large. Tie rmgcd pomts on the f'lE;Ure correspond to eYper1rrenta1 values. It 1s nsleadm-,, homver, to compare thclr denatlons from the fitted curve with tre gz.ver~ confidecce bard as the expirimentdl pomts are not mdependefit. Apart from t& fact t!:st cuii~latlve frequencies are plotted, hl& or lcm nmbtrs of gusts tend to occur to&eei;her for all gust velocitxs and the expenr;rxr;tal pomts are hl&hly correlated.

A numerical coIi-panson between the observed end calculated freqmncx?s is made III the followw?g table, the enpirxal formula beme factored to fit the observed frcqucixy at ',O ft/sec.

-4-

action becores less effcctY*e as the altitude mcreases. If tii1s 1s the case the cvmge In slop i! shown by thu Comt cur-x at about 25,000 ft may not in fact bt &L to the pzlot's avoldmg action but may represent a real change in atnmpherlc trend. Further light on this questlonw~ll be obtamed as rwords from au-craft cmismg at greater aithdes become waxlab&.

Estmates of the average &ust frequency at varxous im[*lts based on all the relevant data are giver. in F~lg 7, whew a corf~dcncs ran& of 95:: LS shcwn about each expermental pout, allowance bemg mdt f’or tne tendency of the gusts to occur xn groups. The value shomi for t:x lmest altitude of 1050 ft 1s the mari of the Comet, Hermes and i'lklng, club, cruise and descent. '71th the exception of the Ccmet these show little sigmficant difference. the value for th; Comt 1s sormvlnat hlgl: but IS, however, based on a very mall smplc, (oriy 860 m&s). Apart from this altitude band, th; remmder of the mm curve follows values obtain4 from the Comet data.

The value for the cmlse of mch auxxraft has been obtamed by taking the aver-age of t?nc k@cst T;hree or four altitude ban?s. Tlzs 1s thou&t to give i more representative fisre tear: that for the Kornlal crulslng altztude only, which 1s obtaIned w&r selactlvslg eocd condLtioi%. Tne i~rovcmcnt achlcved ur,dercruising coixl~tlons by the pllot's avoiSln& action is mdwatcd by the dashed lue m Fxg 7.

4 Conclusions

The present mformatlon on 'cl- ,e variation of gust fre~.!uency mth gust velocity and altltudc is convml.,ntly mmarued m Figs 3 md 7. lhse flyres give a representation of atmospherxc turbulence vrh~ch may be used for the cstimtlon of axcraft f3tlgx da;sge resulting frm &ust loads.

E.

1

2

3

4

5

6

7

8

9

10

11

iluthor

J. Taylor

J. R. Sturgeon

J0 Zbroeek

J. Zbrozek

J. R. Eeath-Smith

J. R. Heath-3mth

J. R. Heath-Smtn

J. E. kplm

J. R. IiIeatii-Smth

J. Taylor

N.I. Eullen

Desqy and use of cour,tm& accelerxoneters R & M 2012. Jum 1950 Unpubll$,ed wo,-k on acceleration m3sUrements.

Gust allevztatmn factor Part of a & x 2970. ALLgust, 1953 Coqressibxllty effxt on gust loads pati of R&M 2970. Au@sf, 1953 Turbulence encountered by Hermes IV aircraft To bc publlshcd

Turbulence cxountered by Comet I au-craft C.P. No.ZL+%. May, 1955 Turbulence encountered by Vik1r.c au-craft over Europe. C.P.311. July, 1956

Unpbbllshed work

Unpublxshed work

The estxmtlor of fatigue lives To be p';bl?shcd

Tht. samplmg erronof turbulcrice nexs~u-einents. R.A.E. Report Struotllres 2C8, Xay 1956. A.R.C. 18,764

MILES PER GUST GREATER THAN IO VSEC E.A.S.

VIKING CRUISE

A VlKlNCj CLIMB 8, DESCENT

0 IO 2o ALTITUDE 30 40

FIGS. IO FT/SEC. GUSTS ENCOUNTERED BY COMET 8 VI KING.

MILE5 PER GUST GREATER THAN

IO FT/SEC E.A 5

I I / I

1’ I I I

/ I

HERMES 1

II I I I I I I I I IO 7.0 ALTITUDE 30 40 THOUSAND5

OF FEET

FIG. 6. IO FT/SEC. GUSTS ENCOUNTERED BY COMET & HERMES.

C.P. No. 324 (18 870)

A.R.C. Technkal Report

To be purchased from York House, Kmgsway, London w.c z

423 Oxford Street, London w I P 0 Box 569, London s E I

IJA Castle Street, Edmburgh 2 rag St Mary Street, Cardrff

39 King Street, Manchester 2 Tower Lane, Brwol I

z Edmund Street, Bxmmgham 3 80 Ch&ester Street, Belfast

or through any bookseller

S.O. Code No. 23-9010-24

C.P. No. 324