C.P. No. 733

MINISTRY OF AVIATION

AERONAUT/CAL RESEARCH COUNCL!

CURRENT PAPERS

Power Spectra of Low Level Atmospheric Turbulence

Measured from an Aircraft

by A. Burns, B.A.

LONDON. HER MAJESTY’S STATIONERY OFFICE

1964

TWELVE SHILLINGS NET

U.D.C. No. 551.551 : 539.431

C.P. No.733 April, 1963

A. burns, LA.

The note presents j0 power spectra 01' the vertxal component cf atmos- pherlc turbulence and 12 power spectra of the horu.onts.1 component measured on a Canberra aircraft while flymg at low altitude. The spectra relate to various types cf terrain m U.K. an6 X. Africa. Coqaratlve spectra are given for dd'ferent helgnts above ground vslthln the heqht band 200 to 1000 ft. Seine lnfcrmatlon is given on the associated ueteorolo&xal condltuzns.

The results are dlscusbed brIefly with a view to generallsug the basx shape of the spectra for the purpose of predlctmg fatigue lcack. Comparison I.S made with proposed analytIca expressIons clefmu@ tne basic shape,

RCP~~CFX R.A.E. TLch. Note NO. structures 329 - A.R.c. 24991

LIST o‘r' COWENTS

I I?!!RODUCTION 2 CvrLINE Ol? IrETHOD

3 FLiGIIT CONDITIONS

3.1 Topo&raphy 3.2 Meteorological condltlons

4 DATA PJWXTION 4.1 Accuracy of method

5 PJwJL!rs 5.1 Presentation of results 5.2 Normsl1sed s~ctra

5.2.1 Varlatlon of basx shape with heqht 5.2.2 Comparison ol' basrc &ape cf U.K. and N. African

spectra 5.2.3 Comprlson with analytical espresslons

5.3 Unnormallsed spectra 5.3.1 ComFarlson of vertlcsl uld horxontal twbulence 5.3.2 Effect of environmental parameters

6 coNCLuSIoNs 6.1 Normalised spectra 6.2 unnormal~set! sivctra

LIST OF SYMSOLS LIST SF RZ?QE?'CES

Al?%NDI~ES l-3

TABLES l-3

I-LLUSTRX!IONS - Fqs. 1-32

DETACHAl3LE ABSTRACT CARDS

LIST OF APPEXDICXS

Appendix

1 - Instrumentation and method cl' measurement 2 - Flqht condltlons

3 - Accuracy of method

Page

4

4

4

: 5

6 6

6 7 7

7 7

9

; 10

IO 11

12

13

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LIST @F TABLXS u

1 - Flight condltlons 2 - Ketecrological observations

3 - Power spectra characteristics

LIST OF 1LU;STRAUCXS

Nose-probe and boom momted on Canberra aircraft

Detaxls of nose-probe Power spectra - vertical and fore-and-aft turbulence velcclty

Comparative power spectra at different uxghts Comparatws power spectra over flat and hilly desert Comparative power spectra up- and down wind

Comparative power spectra up-,davn- and crosswind Comparative pcwer spectra of vertuxl and fcre-and-aft turlxlence at

different heights Comparative power spectra of vertical and fcre-and-aft turbulence fcr

drfferent ~2nd dlrectlons relative tc fl@it. patn Comparative power spctra hsxds cn snd stick free Comparative power spectra at various airspeeds

Composites of ncrmallsed paver spectra of vertx&t turbulence at different heights

Composlxes cf ncrmallsed power spectra cf fcre-and-aft turbulence at dtifercnt heqhts

Heasured and fitted ncrmallsed pcwer spectra at 200 ft

Measwed and fltted normalised power spectra at 500 ft Measured and fitted noxmallsed power spectra at IOCO ft Ratio of intensity of vertical to fore-and-aft turbulence at different

heights

Scale length of vertxal turbulence at different heq&ts

w 19 xl 21

ra I 2

3-11 12-16

37 18

19

2042

23

u, 25

26

27

28

29

30

31

32

-3-

I IRTRODUCTION

The ncte presents power spectra cL ' the vertical component of atmospheric turbulence obtained from measurements made on an aircraft while flying on the loirest 1000 ft of the ntmosphere*. In some casts power spectra of the horizcntal component of turbulence yl the direction of flight are included. The range of wavelength covered exterds from 50 to 8000 ft.

The spectra, which were obtained during an experimental investigation into power spectral methcdn of daterminmg gust loads in aircraft, were not intended to form a comprehensive set of data on their own, but rather to supplement more extensive work going on in this field.2~3. They do, however, indicate some interesting trends - particu;arly ldith regar?i to the variation of spectral shape with height, They are also of interest in a s much as they provide a direct comparison of atmospheric turbutence in ttmpcrate and sub-tropical conditions in U.K. and N. b,frioa respectively.

In or&r to use pcwer spectral methcds for determmmg gust loads it is first necessary to specify the power spectrum of atnlospheric turbulence in general terms, preferably in as sirqle a fcrm as possible. With this purpose 111 mind consideration is given to the reduction of the experimental power spectra to a common form and an exsmination is ,natle of the fit of curves derived from analytical expressions, some of which are in current use4.

The ncto is confined to infor~~~ticn on atmcspheric turbulence. Information was also obtained on the resulting response of the aircraft III terms both of acceleration power spectre and cf counts of acceleration levels exceeded. It is thus possible to ct,udy the relation bctwcen the turbulence input and the aircraft response expressed in varicus fonts. It is Rrcposcd to treat this matter III a separate note.

2 OUTLI;\~ OF .ETIIOD

The aircraft used was a standard Ca&erra B6. The velocities of the at.l?ospheric airflow were measured in flig!lt by the "direct method" in which the velocity is dctcrmined from dtiferenccs between the airflow past the aircraft and the aircraft motions relative to thL [jround. Yhe velocity of a~-flow along the normal, fore-and-aft and lateral flight axes of the aircraft was measured by means of a nose-probe with pressure sonsing or.Lfices at its head (see Figs.1 ana 2). Lateral. measurements were not, houever, ~analysed owng to suspected inaccuracies in the corrections associated with the ktch roll, The motxons of the aircraft were neasured by free and rate gyros and by accelerometers, the szqnals fromwhlch were integrated numerIcally to give velocity. Further details of the mstrumentation and methcd of measurement are given in Appendix I.

3 FLIGHT CONWl!IONS

The duration of sample chcstn was 2-k minutes (in a few cases it was cut to 2 minutes) which corresponded to a run of I& statute miles for flight at

*A physical description of the power spectrum of atmcspheric turbulence and definitions cf terms rciating to its propertics mill be found in Ref.1.

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300 kts E.A.S., the basx speed used for the tr?als. The 'xasurements :vere made over set tracks m U.K. and N. Afrxa, the awcrsft bung flown at approxunately constant height above grcuxd. Fcr ccnparatlve purpcses the heights chosen were elther 200, 400 and 600 ft above grcwd to ccrrezpcnd to "Operai~.cn Sv-ilfter" helghts5, or ZOO, 500 and 1000 ft ccrrespcndlng to ti-lo helghbs of the turbulence

6 measurements on trio Cardmgtcnballccn cable . In one flight the height was reduced to 100 ft ever the flat desert. Further &tails of the method of measurement are given 111 Appendix 2. Details of t!le flqht ccndltlcns are lxted 111 Table 1.

3.1 T opw,raph,y

The runs 111 U.K. were mostly made m the v:cmlty of Cardlngtcn over moderately flat agricultural land; the track avcldcd towns and villages but passed over cccas~onal farms and trees. Ram made m Sussex ccvered the ssme type of agricultural terraln but the ground was ccnslderably more rclllng and hzlly. Runs in E. Anglia were over flat feiiisnd and farming country.

In N. Africa runs were made frcm 3.1 Adem either over flat desert or over hilly desert near the ccast at Derna; the hilly desert was of rather an unusual fOTTMtlCl1 COLISlStlIlg Of 3. PlateaLl Sll2rplji CFXMi by VcdlSi thCSS WdlS WfTe mostly too narrcw for the ax-craft to fcllcx tlrelr cc:itcur.

Runs were also made from Idrls over flat cultivated desert. The N. Af'rlcan runs were over selected parts of the routes used m "Opcratlcn S\znfter".

3.2 Meteorolciilcnl condltlons

Obsellratlcns of surface hmnd-speed and dlrectun, cloud type and amount, vlslblllty, screen temperature and ~elatlve hun~d~ty, as made on an hourly basis for syncptlc charts, were cbtalned f'cr the hoas closest to the time of flight from the nearest metccrclcgxal statlens. These cbservattlcns are luted in Table 2. Besides these obxwatlons, cutsldc a7r te.xperature w.5 recorded on the axcraft m ccntmnuc~s trace fcrm throughout the rws. An extra "tempzrature run" at 1000 f't was u~cluded when not already part of the prograiwe, so that an average la-,-se rate could be determined from the dlffcrences m temperature between EdJaCWlt i’uns at 200 ft and 1000 ft. The averages obtaInedwe lIsted u1 Table 2.

4 DATA ?XiX.JCTION

It 1s not prcpcscd to dxcuss this matter m dctnll. The crlglnal recordings, whxh were in continucus trace form, iiiere dlgltlsed at discrete 1nterwJs of l/20 sec. Af'ter ccmblnug and lntegratln& tne dlgltlsed lnfcrmatlcn to gave the required velccltles of au-flow, the pcwer spectra were cbtalned as the Fcurxr trsnsfcxns of the auto-correlatlcn functions, the computation being carried cut on DXJCZ and uicrcury. A nuinbcr of processes were included to refine the accuracy of the spectral estlmatcs; "hannmg"7.

these included "pre-whltenmg" and Forty estunates were obtalned v!lth a resolution cf 0.25 c,p.s. The

anslysls was then repeated with the dltltlsrd rtadtigs added 111 non-cverlappmg groups of four to cbtaln more refined data at the longer wavelongt1ls. The resolution was then 0.0625 c.p.s.

-5-

4.1 Accuracy of method

The accuracy of the methcd 1s dilxussed in Appendx 3. For wavelengths less t!mn 2500 ft the 90," confidence llmzts determined on the lines suggested by Tukey7 he 26$ tc 299 either s~dc of the estimated pcwer spectra. At longer wavelengths the accuracy deterlcrates.

Check comparisons at du'ferent aircraft airspeeds shwcd that the power spectra did not vary slgnlfuxntly wztil alrcraft speed; this udxatcs that the motions of the axcraft, whxh have different characterlsltxs at different speeds, had been successf&ly elxuliated. Checks were also :nade that the response of the axeraft to the movement of the controls by the pilot was not affectIn& the spectra. A check comparxcn made between spectra obtaIned from concurrent measurements on the aircraft and on a captive ballocn cable showed reasonable agreement6. These checks arc ~XQXI ssed more fully m Appendu 3.

5 FEGULTS

5.1 Presentation of results

Estmmtes for the u&vldual power spectra of the vertrcal and horlzontsl components of turbulence are plotted in 1)lgs.j to 11. Log-log paper 1s used 3.~3 conformity w1t.h usual aeronautical practice. T!le estunates show a certain amount of scatter and falred curves have been drawn fcr comparative purpsses. Compsi-a- tlve spectra for different hslghts, ten-am and wmd du-ectlon are shown m Flgs.12 to 19. Vertxal snd horizontal ccm:~or.ents of turbulence are compared m Flg3.20 to 23. Spectra for the ;>lrcraft flown "hsnds on" snci "stick free" are compared 3.n Ylg.24 and spectra for dlffcrent nwspeeds 1n Flg.25.

Characterlstlcs cf the turbulence obtalnablc frcm the power sy;ectra such as the root mean square velcclty, ' tne scale parzmeter of the turbulence and the index of the frequency r!ltn uih~h the power spectra1 density decreases at short wavelengths are llsted in Table 3. The r.m.s, values are obtauled by integrating the power spectra over the wavcband 10,000 to 10 ft. Scme extrapolation has been necessary lo cover this mavebwd, ,&lch has been proposed as a standard for the evaluation of r.ln.s. velocltles of turbulence. 'The ertrapolatlon has lnvclved only s!nall addxtlons of the orJcr of 7,; to the r.x.s. values for the waveband covvcred by the i.ieaswements. 'l'he scale para;neter cf the turbulence & is determmed from the formula 8 = ;/2x nm, ?,herc ; 1s the mean alrspecd and nm IS the frequency at whxh the prcduct of the frequency and the power spectrsl dcnslty IS a rna~~mum~~. In physuzl terms the scale parameter as defined here is the most conanon wavelength or eddy sxe &vlded by 2x. Falred curves were used both in the determlnatlon of 8 and of the frequency Index p wzth whxh the spectral density decreases at short wavelengtns; orlglnal spectral density estunates were used m the dctcrmmnet~on of the r.m.s. values.

*In a number of cases , particularly when the spectra refer to norlzontsl turbulence, no max~xxun occurs w1thx.n the waveband covered by the spectrum, mplymg that the scale parameter exceeds 8000/2x f 1300 ft.

-E-

In the discussion which follcws it IS sometimes convenient tc treat the ordinate of the power spectra as defmmg the energy content of the turbulence. The reason underlying this usage is that the crdinate is proportxonal to the square of the velocity and hence to the enerw if the density is fixed.

5.2 Normalisecl spectra

5.2.1 Variation of basic shape with height

In order to study the basic shape of the spectra with a view to generalisation, the spectra have been normalised by reducing them to a conmcn r.m.s. value of 1 ft/sec. The spectra are classified in 3 classes of height:- 200 ft, 500 ft (this includes spectra obtained at 400 and 600 ft) and. 1000 ft. Considering first the vertical component (Fig.26) it is imnediately apparent that there is a change in basic shape between 200 ft and 1000 ft, the spectra relating to 500 ft lying in between and to some extent overlapping the other two classes. At long wavelen&ths the spectral density decreases with decreasing height and at short wavelengths it increases, the crosscver occurring at a wavelength of about 1500 ft. In general the effect of such a shift of energy from long to short wavelength would be to increase the nunioer of gust loads predicted by the power spectral method, the exact amount depending on the frequency characteristics of the aircraft. Rough calculations indicate that the amount is likely to be significant and that a generalised form of power spectrum which varies with height is desirable.

The effect of height on the horizontal component of turbulence in the direction of flight is similar to that on the vertical component but much less marked (Fig.27). The need here for a generalised form of spectrum which takes account of height is less apparent.

5.2.2 Ccmpariscn of basic shape of U.K. end N. African spectra

At any one height the normalised spectra of the vertical ccmpcnent of turbulence are remarkably alike despite the variation in tcpcgraphical and meteorological conditlcns under which they were cbtalned (see I?1

? .26). The

agreement is particularly close for the U.K. spectra at 1000 ft cbtalned at 1000 ft in N. Africa).

spectra were not At 5CO ft slight differences can be detected

between U.K. and N. African spectra: the latter are Just startme, tc flatten at long wavelengths xn a mxncr similar to spectra at 200 ft. (The cnly N. African spectra of this class which dces not shcw this flattening relates to 600 ft.) At 200 ft the effect of terrain end its interacticn iiith the metecrological environment is becoming evident and the spectra are mere variable in shape particularly at long wavelengths. 'Within this variaticn it is impcssible to distinguish between U.K. and N. African spectra.

5.2.3 Ccmpariscn with analytical expressions

Figs. 28 to 30 show spectra of the vertical component of turbulenoe derived from two analytical expressions compared with the experimental results. The band covered by the normalised experimental spectra is shown hatched. The first analytical expression which is in current use is9

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C2L (1 + 3 02L2) G(R) = !'

n(1 + rl* L”)2

where L the scale length IS takeu equal to the height above ground, R IS the an@ar wave n~~xbcr (= 2x/A where h 1s the wavel.ength), and the expresswn is normalx5ed to p.ve a r.m.0. value of 1 ft/sec over tne same waveband as the expermental re.;ults.

The second analytz.cal expresszon

G(n) = 2.32 c; L tanh QL

(QL)5/3 (2)

1s rewritten here x.n a fcrm slightly different from the crlguu.l suggested by Yenryqo. Scale lengths of 620, g,O and 160 ft have been chosen to give a good fit at hexghts of 1000, ijO0 and 200 ft respectxvely, and the expressx~n is nonnallsed as above.

It 1s ap?arcnt that the sharply defzned “knee” of exp’“SS10” (1) 3.3 not 2.n general Justtiled by e”erlmcntal results although It can provldc a good fit 111 a few cases; nor 1s there any justlfxatlon for tlx frequency Index of -2 with which the expressIon decreases at short wavelengths. Avera&;e values of the slopes deflnlng the frequexy index of the experunental spectra are:-

Ht above Average s t andard ground slope Range devratlon

1000 ft -1.65 -1.53 to -1.80 0.16 500 ft -1.68 -1.27

/ t0 -1.72 I O.Lj

200 ft -1.58 ; -1.23 to -2.oj / 0.32

These values are much ncarcr to the mdcr. of -5/5 of Kolmogoroff ‘:, sun~la.r~ty theory than to an index of -2.

Expression (2) gives a much better fit than expressxon (1) both because the curvature 1s more gradual and because It conforms wt.11 a frequency index of -5/3. 5%~ expressxon may net prove altogether satlsfactcry though, suxe It gzves mcrcasulgly large values of spectral dtnclty at long wavelengths contrary to expectatuxl. Further experlmentr~ cbservatlons of spectral density at longer wavelengths are requlred to resolve this matter.

Houbolt Steiner and. Pratt 11

expression (I) have suggested a mcdlf’led version of

such that the,specLral density varxs with a frequency index of -5/3 at short wavelengths. At long wavelengths the expressun 1s) however, still very like exoresslon (1) with the same ratlier pronounced “knee”, which does not m general fit the experimental results.

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It as not considered worthwhile to discuss the fitting of analytrcal curves to the porrer spectra of the horizontal component of turbulence, since these spectra obey a simple frequency law throughout the waveband observed. The resultisthat any analytical Curve, which decreases with an appropriate fre- quency mdex at short wavelengths, can be made to fit if the scale of turbulence is chosen long encugh.

5.3 Unncrmal~sed spectra

So far only ncrmalised spectra nave been considered; a more complete picture is obtained if the qectra are considered in their unnormalised form which contains information on the intensaty or r.m.s. velocity of the turbulence as well as on the basic shape.

5.3.1 Comparison of vertical and horizontal turbulence

The relation between the power spectra cf the vertical and of the horizon- tal component of turbulence is strongly dependent on neight above ground. Figs.20 to 22 show a remarkably similar pattern in the effect of herght on this relation. At a height of 1000 ft the vertlcel spectra lie above the horlsontsl; at 5CO ft they tend to come together at long wavelengths, and at 2.00 ft and below they cross over. Smce the r.m.s. velocities are determined mainly by the long wavelength energy this effect i s reflected in a decrease in the ratio of s, to su with decreasing height, where sw and su are respectively the r.m+s.

velocitres of the vertical end norizontal components of turbulence. This ratio changes frcen a value greater than 1 at 1000 ft to less than 1 at 200 ft (see Fig. 31).

In general, the scale parsmeter of the horazontal component of turbulence is greater than that of the ertical component. This is in agreement with earlier experimental results 8 . Quantitative comparison of the scale parameters is not possible since that of the horlsontal component is too large to be determined from the experimental observations. For turbulence over flat and slightly hilly terrain the scale parameter of the vertical. component approxi- mates to the height above ground, except for some one-third of the spectra when it is too large to be deter-ate (see Fig.32). There is no apparent explana- ticn for these large scales in terms cf the environmental parameters: the influence of convective activity on the scale cf turbulence is, however, suspected to be complexq2. Over hilly desert the scale of the vertical compcnent is somewhat larger than over flat or slightly hilly tern-am (see IYg.32).

5.3.2 Wfcct of environmentat parameters -

The emphasis so far has been on the similarity of spectra at any one height. At 200 ft, however, some variation due to environmental parameters is becoming apparent and the effect at this height of certain parameters on the unnormalised spectra is now discussed. It should be noted that the oases considered are few in number and results are therefore only indicative.

-Y-

(4 TaTam ro&qhness

P1g.17 shows ccmparative spectra of the vertical ccmponent of turbulence for hilly desert end flat desert. As m&t be expected the hally desert spectrum is the more severe xiitn a T.:~Ls. velcc1ty of 3.8 f%/sec compared with 2.2 ft/sec for the flat desert, The mcrcase in spectral density occurs at all wavelcngthc but IS xost marked at long wavelengths. Other spectra cbtalned over the hilly desert also show high values cf spectral density at long wave- lengths (set Fig.1 3).

(II.) h'md directicn relative to flight path

Comparative spectra from runs made up- anddownwxld in 2. An&la, surface wmcl 17 kts, and m Sussex, suri'acc wind 11 kts, show little difference due to did. dlrectlcn (~lgs.18 and 19). The vertical spectra would have lain even closer together if ground speed instead of azspeed had been used in converting from tune to space media. This suggests that the frequency characteristics of the vertical compenent of turbulence are mfluenced by the spacing of topo- graphical features. Dtiferenoec are too small and data too few, however, for this result to be conclusive.

Crosswind spectra on the otiie i^ hand she% a marked difference from up- and dcwn*Jmd spectra (see Plg.lg - results fcr L. Anglia only xnce low flying restrictrcns prevented crossw~~3 runs 111 Sussex). The energy at long wave- lengths 1s considerably less for the crossvGnd spectra. It would be unwrse, however, to attribute this to the effect cf wind direction wathout further evidence; the runs were of necessity made ever different tracks and, although the terrain lias chosen to be as l~cmcgeneous as possible, thin could have xnYue:med the results.

6 coWi?JSIox3

Power spectra of atmcspherlc turbulence have been obtained from aircraft measurements in the height band 200 to IOCO 3 abcve grcund, crier varrcus types of terrain III li.K. and K. Lfrica, aad in ccnditions of neutral to moderate atmospheric mstabillty; a study of these spectra leads to the following conclusions:-

6.1 Nomllsed spectra

(1) The basic shape cf the po:ier spectra cf the vertical component of turbulence varies with height abcve grcund, the prcportion of long wave (> 1500 ft.) to shcrt wave energy decreasing with decreasing hGight. The horizontal compcnent shcrt#s the same trend but tc a much loss marked degree.

(ii) At any one height there is considerable slmllarity r.n the basso shape of the spectra despite the varaatlon of topographical and meteorological condrtions. Generalisation of the shape of the spectru;n in a form which takes account of height appears practical. Variation in the basrc shape of the spectrum of the vertical component, due to the effect cf environmental parameters, 1s becoming more apparent, however, as the height decreases to 200 ft.

- IO -

Appendix 3

two methods was well within the confxlence lltilits. This 1s not a conclusive check, however, since some differences, especzJly at long wavelengths, nught have been expected; small differences were ui fact mdlcated such as have been observed by earlier ex?eruenters ahen comparmg fixed pcrnt spectra with spectra obtained travelling tl;rcugh the medlum13.

IiWl'RKE~hL AND STATISTIC& ACCURACY

The above exercises provide a rough cvcrnll cilock of the iccuracy of the method. Particular sources of rnaccuracy are now ducussed in rather more detail.

Inaccuracies of two kinds are likely to occur: waccuracles m the measure- ments due to transducer, recorder and trace-reader lurutaticns and statlstxal lnaccuracles due to the finite duration cf the sample. Both kinds of lnaccuraoy tend to be greatest at the lcw frequency end of the spectra. If wavelengths longer than 2500 ft are excluded then the accuracy of measurement 1s probably well within I@$, while the VW,6 confidence lunts dctcrmmed on the lines suggest&d by Tukey lie 2676 to 29% either sxde cf the estlrnatcd power spectra.

At longer wavelengths It 1s dlfflcult to assess the accuracy. Instrument errors arxe through gyro drift and small varlatlons in the lg datum level of the accelerometer which accumulate when mtcgrated. Another source of error 1s that the sanplc length us somewhat short to Justify the extcnslon of the analysis to such long wavelengths. Nevertheless the results at long wavelengths appear to mdlcate trends in a region whlc!l 1s becommg of increasing lntcrest as aircraft speeds momase, and they have tcereforc been mcluded although quantitatively they should be treated wth reserve.

- 18 -

G( )

L

e

n

"m

B

UP J-J

;

s

n

A

o-

ft

ft

c.p. S.

0.p. S.

f t/xc

f%/seo

I-ad/f t

ft

f t/xc

Ref. No. Author

LIST OF SYMESOLS

generalised functicn for expressing power spectra cf turbulence

scal.e cf turbulence used in analytical representation

scale parameter derived from spectral estunates, = G/Z% n m frequency

frequency at whicn the product of the frequency and the power spectral density is a maxamum

frequency index witn whJch power spectral density decreases 111 sub-inertial range

suffices denotmg fore-and-aft and vertical components of turbulence

mean airspeed of aircraft

root mean squsre velocity of turbulence obtolned from spectral estamates for w&veband 10,KlO ft to IO ft

angular wave number = 2x/K

wavelength

root mean square velcoity of turbulence over waveband DJ to 0, used in snslytxal representation.

LIST CIi REl%xENCES

Title. etc.

1 Zbrcsek, J.K. The relationship between the discrete gust and power spectra presentations of atmospheric turbulence, with a suggested model of low alti- tude turbulence.

A.R.C. K.&x. 3216. narch, 1960. 2 Dressel, T.L. B-66 B low level gust study.

WADD Tech. Rep. 60-505 Vol.11 Fewer spectra. March, 1961.

3 Smith, F.B. An analysis of vertlcnl wind-fluotuatlons at heights between 500 and 5000 ft. Quart. Jour. Roy. ivict. Sot. Vo1.87, No.372.

April, 1961.

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LIST OF REFEX33NCES (CONI?))

Author Title, etc

U.S.A.??. I:'Lilitary Specification MIL-A-8866. Aircraft strength end riyidlty, reliability rcquire- rents, repeated leads and fatigue. I&Y, 9960.

Eullen, N.I. Gusts at low altltudc in N. Africa. A.R.C. Current Paper No.581. Septcmbcr, 1961.

Burns, A. Power spectra of the vertical component of atmos- phenc turbulence obtained from concurrent measure- ments on .3.n alrcraft and at Tuted points. A.R.c. C.P. 689. January, 1963.

Blackaul, R.B. Tukey, J.W.

The measurement of power spectra. Dover Publlcatlons, 1958.

Pasqtill, F. The statxtxx of turbulence in the lower part of the atmosphere. Symposium on Atmospherx Turbulence and its relation to Aircraft. Novcnbcr, 1961.

Press, H. Meadows, X.!i'.

A rc-evaluatxn of gust-load statistics for applica- tlon 1I1 spectral calculatlans. N.A.C.A. TN.3540. August, 1955.

Henry, R.M. A study of the effects of wind. speed, lapse rate, and altitude on the spectrum of atmospheric turbulence at low altitude. Prcscnted at the I.A.S. 27th Annual bkcting, New York. January, 1959. I.&S. Report No. 59-43.

Houbolt, J.C. Steiner, R. Pratt, K.G.

Flight data end conolderatxnn of the dynsmx response of airplanes to atmospheric turbulence. N.A.S.A. pnpor prcsen'ced to Struct. and Mat. Panel and to Flight Mcch. Panel. A-, Paris, July, 1962.

Webb, E.K. Tech. Paper No.5 Melbourne C.S.I.B.O. Div. Met. Physics 1955.

Lappe, U.O. Analysis of atmcsphcrlc turbulence spectra DavIdson, B. obtained from concurrent auplsne and tower Notess, C.B. measurements.

IAS. Report No.59-44. January, 1959.

Ref. No.

4

5

6

7

8

9

IO

11

12

13

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INSTRI.RWJTATION AND METHOD Ol? MEASU~WNT INSTRK;ZXI'ATION

The velocity of the airflow relative to tine aircraft was measured by means of a nose-probe mounted on a 10 ft boom. The head cf the prcbe consisted of a steel hemisphere with five pressure sensing orifices, the pressures from which, together with the pressure from a static rmg, activated inductive differential pressure transducers, S.E. Laboratory type 70, fitted behind the orifices (see Fig.2). The pressure transducers were kept as close as pcssible to the orifices in oriler to minimise organ pipe rcsonanccs in the connecting tubes.

The accelerations of the aircraft at a point near the aircraft c.g. were measured with a Structures type 4 accelerometer sensitive to normal acceleraticn, and r<ith a specially designed combined accelerometer sensitive to lateral snd fore-and-aft accelerations. Lateral and fcre-and-aft acceleraticns were, however, found to be small and were not included in the analysis; nor were they recorded exe t during the early stages of the experiment.

?I A standard type

IT 3-7-15, IO /set rate gyro was used tc measure rate of pitch and yaw and a type IT l-5-6 Pitch andRoll Indicator (free gyro) to measure angle of pitch. This gyro was modified so that the gravity erection could be sxitched off prior to recording since it was thought that the erection device might feed in spurxcus signals in turbulent conditions. Initially a second gyro of special design, with no pendulum erection, was used to check the IT l-5-8 gyro.

Standard methods cf emplificaticn and recording were used. Initially the pressure transducers were used in ConJunction with S.&:. Laboratory mOdUlatOrS but later they were used with Films and Quipment amplifiers. Signals were rccordcd in ccntmuous trace fcria on a i'ilms and Equipment recorder and on a Beau&urn Al3 reccrder.

Ficasuremcnt cf vertical turbulence

In deducing the vertical velocity of the turbulent airflow account was taken of the vertical translation of the aircraft and of the angle of pitch end its rate of change. Means wore provided for cerrectmg bcth for deflection of the probe boom under 'g' and for oscillatory fle&xure of the boom; in practice these corrections were found tc be unnecessary, tne prcbe proving very stiff in flexure, (natural still air frequency 36 c.p.s. ). Rate of pitch was neglected in the final anelysis since excluding this quantity made no significant difference.

IIeasurement of horizontal turbulence

Although it was originally intended to obtain the power spectra of the component of turbulence in the lateral direction, this undertaking was abandoned because of the prevalence of the Dutch roll. The yawing oscillations in this mode, which occurred at a frequency of about 1 cycle every 34 seconds at an airspeed of 300 kts Z.A.S., produced such large difftrcntial pressures

- 14 -

Appendix 1

at the prcbe tip that they dwarfed the required differentisl pressures from the lateral turbulence. Although 1x1 theory a correction could have been made for this effect, in practice it would have xnplled cbtalnlng the velcclty of the turbulent axflcw as a smdl difftirence of large quantltxs and the method was considered mvalid. Power spectra were obtnmcd, hcwever, for the hcrizontsl component of turbulence along the fore-snd-aft 3x1s of the azcraft by means of a sensitive pitot-static arrangement feeding rnto an lnductlvc pressure trens- ducer. The large signal due to the steady alrspced was balanced out clectrlcdly and only changes in airspeed recorded. It was assumed that all changes were due to variation xn the horxontal alrflow and tiiat the aircraft grcun& speed remained sensibly constant. Decause of the lnertla of ihe alrcrsft this assump- tlon 1s justified at all but very low frequencies such as that of the phugoid motion. At this frequency, which YLS of the order of 1 cycle every 50 seconds at 300 kts E.A.S., sea level, there 1s likely to be considerable error; the corresponding wavelength of 25,000 ft, however, lies well outsxle the waveband of 8000 ft to 50 ft ccnsxlered 111 this ncte. Special steps were taken in the analysis to minimxe the spurious dlffuslon of energy from very long wavelengths into the wavebad of interest.

- 15 -

l?LIGICC Cil:~wTIO,xS -

Measurements were taken during each run while the aircraf't was flown on a constant heading and at as near a constant awspeed as pcsslble. Height above grcund was maintained approxunately constant nlth the aid of the radio alto- meter: m cases cf hilly or undulating terraln this involved some manoewrlng m oiler to follow the contours of the ground. No special lnstructlons were g~vcn to the pilot as regards control movements except for a few runs over moderately flat terrain when he was ask& to remove hln hands and feet f'rcm the controls altogether. It was fcund that, provided the an-craft was carefuliy trlmrned beforehand, It could be flown hands and feet off qute successfully for the cntur run with only very occas~ornl tcuchc.s on the stick to steady any phugold motion whxh developed.

When comparative spectra were obtalned at different heights the runs were repeated m the same dxectlon over the shme track m quick successnxl to muumlse varlatlon m metcorologxal condltlcns. Three such runs could be made in about 20 rmnutes. Compnratlve runs upend, downwmd and crosswmd were lnade as far as possible over hc,nogencous terrain; these runs could be carried out ~1 somewhat quicker succession than those at different hr;@ts. The comparative runs for flat and lnlly desert wrt: made mlthln 30 mmutes of each other.

Although most runs wcro zfidc nt 300 kts E.A.S., on one occas=on MS were repeated at awspccds of 200, 300, 1,OO and 475 kts E.A.S. The duration m tune of the sample ius kept constani so that the run s at the higher speeds covcred mcro terrain than those at lower speeds. 'The ternam was flat desert and appesred to be homo~enecus so that ihe saw turbulence spectrum was expected from all runs.

- 16 -

ACCURXY OF 3iElXOD

Ciiecks were made that the spectra o f vcrtlcal turbulence did not vary significantly either with airspeed - to some extent this checks that the motions of the aircraft are being eliminated - or with the amount of control exercised by the pilot.

ELJFECT OF VARYING AIRSPEED

Fq.25 shows comparatwe pwer s?ectru of the vertical component of turbulence obtained at different airspeeds. ?!ie agreement between spectra is on the whole quite good and withIn the confidwcc limits for wavelengths of less

thnn 2500 ft. At larger wavelengths, where rather more discrepancy might be expected due to the finite lengths of the samples tht run at 400 kts has given ratner high values of spectral density compared 141th the other runs. ThlS does not appear tc be due to a systematic error with airspxxd SUKXZ the long wave- length values at 475 kts are in clos e agreement w1tn t11cse at 200 and joo kts. T&cm ds a whole these results indxatc that the mctzcns of the axcrsft are being successfully eliminated.

i%'FWT OF PILCT'S XUTROL I~UV~';IE!ITS --

In theory the rc~ponse cf the aircraft due to the pilot's movemtnts of the controls shculd not affect the turbulence spectra. Because of possible ms.ccurac2.os, however, m the measurement of the aircraft motions and its analytical treatment, It ~vas considered advisable tc check that the pilot was not feeding tinergy into the spectra. ~ovqwat~vc spectra, relating to flight m w:mch the aircraft was flown "hands on" and "stxk free" arc shown xn F1gs.a+(3) and (b). There 1s little evldcmx to suggest that the pilot 1s contributing in a positlvc sonse to the turbuloncc spectra; at 503 ft the "hands on" rind "hands off" spectra are cor+rable, while at 1000 ft the "stick free" spcctrm shcws a slightly greater mcrgy content at zitl mwclcngths than the "hands on' spectrum. This may be due to incomplete ellmz~notion of thd rather marked phugcid motion developed during tlw "stick free" run. hlthcugh the wavc- length of this motion lies well outside the range of interest, some energy from this wavelength cculd, despite preventative processes in the andysls, have diffused into the waveband of interest.

In conclusion it appears that the pilot I. 9 not feeding ln any signlflcant energy to the power spectra of the turbulence; on the contrary by checking the phugoid motion it is probable that he is improving the accuracy of the turbulence measurements.

CWARIS9N OF AIRCRUT AND BALLOON CABI. UUSJREhIEiiS

When comparative measurements of atmcspneric turbulence were made on a captive balloon cable at Cardington and on the Canberra aircraft flymg past the cable, agreement between thr power spectra of vertical turbulence c:btained by the

- i7 -

Appendix 3

two methods was well within the confxlence lltilits. This 1s not a conclusive check, however, since some differences, especzJly at long wavelengths, nught have been expected; small differences were ui fact mdlcated such as have been observed by earlier ex?eruenters ahen comparmg fixed pcrnt spectra with spectra obtained travelling tl;rcugh the medlum13.

IiWl'RKE~hL AND STATISTIC& ACCURACY

The above exercises provide a rough cvcrnll cilock of the iccuracy of the method. Particular sources of rnaccuracy are now ducussed in rather more detail.

Inaccuracies of two kinds are likely to occur: waccuracles m the measure- ments due to transducer, recorder and trace-reader lurutaticns and statlstxal lnaccuracles due to the finite duration cf the sample. Both kinds of lnaccuraoy tend to be greatest at the lcw frequency end of the spectra. If wavelengths longer than 2500 ft are excluded then the accuracy of measurement 1s probably well within I@$, while the VW,6 confidence lunts dctcrmmed on the lines suggest&d by Tukey lie 2676 to 29% either sxde cf the estlrnatcd power spectra.

At longer wavelengths It 1s dlfflcult to assess the accuracy. Instrument errors arxe through gyro drift and small varlatlons in the lg datum level of the accelerometer which accumulate when mtcgrated. Another source of error 1s that the sanplc length us somewhat short to Justify the extcnslon of the analysis to such long wavelengths. Nevertheless the results at long wavelengths appear to mdlcate trends in a region whlc!l 1s becommg of increasing lntcrest as aircraft speeds momase, and they have tcereforc been mcluded although quantitatively they should be treated wth reserve.

- 18 -

TABLE 1 - Flight conditions

Date Flf&t &

Run No.

106 01 02 03 04 05 06

El ‘iden

El Aden

Flat desert

Flat desert

CardIngtOn

Cl AdErl t111ly desert I

I m

Zardlngton

Sussex Sollf’lg farmland

E. fir@lia FLS f enland

:lrspeed Direction kts of mn

E.kS. degrees

I I

I

246 l, H

246 0 n

93 270

Not ‘?corded

270 93

270 90

2ci3 la0 om

T Surface ~1 nd

DirectIon de@VeS --

310 360

350 N " n

m r n I! " ii

PIolOE recorded

- I

Speed ‘its

17 15 16

f, ” ”

Lapse

rate WlcOO It

1.2,%,=5 2.5

2.5 I,

n

n

3.75 R

3.10

Not

rcc?rded

Redarks

Up,iqd and donrwlnd runs, I:lnd I

S1iEt-a ly across 1

track. J

Runs at 3 heights ’ into ,,Ind and

cross,~fnd. Into s

Pf nd and cross- ” c

wind runs not g strIctlg comparable s b

Q ” Cmprative rms at ’ 2 f 3 heisnts i

) 2 2 I L c

ccmprar:fve runs 92

fhands on’ and z-i

r~tick freer OfI

T

>lrectlon of runs f * relative t3 Wind vwled

TABLE 2 - Meteorological observations ---

---

Flight NO.

-- 64.02

05

77

90

152

160

162

;pEtl kt s

15 13

16

5

)uection degrees

330 360

350

220

lsibdity n.m.

11 11

5%

10

330

320

320

20

11

8

Not Not recorded recorded

270 22

280 25

-

._.

1

f

I

SCl-fXZ

:e!npera- i;ure oc

24 28

30

18

28

13

II

sot resorded

63

16 63

r I

I

Iunndity %

62 56

30

73

73

72

54

Lapse rate

~c/1000 ft

1.25~6.25" 2.50

2.8

2.8

3.5

3.75

3.45

3.75 decreasing

to 3.1

Not recorded

Not recorded

-

i

Cloud smount type and. base

-.- j/G alto cu l/O alto cu

Ml1

3/0 cu increasing to 6/8 cu 2800' 7/8 21to stratus

25,000'

3/a strata cu

l/B cu 1800' 1/3 alto cu 18,000'

G3 ‘U lncreaslng to L/S al 3000 i/G strata cu 5000' L/8 alto cu 25,000'

Nil

6/8 cu 2500' U3 strata cu

22,000'

2/B cu 3000' 7/8 strata cu 4500'

Nearest neteorological

station

Zyrene El Mm

El Adem

Cardington

El Mm

Gatwick

Carkngton

IdrlS

Gatwick

Conmgsby 6. Yaterbeach

*Spot readmgs of temperature only.

TABLE 3 - Power spectra characteristics -

Vertical component of turbulence

-- ilonzontal coqonont

of turbulence t Ratio

--

Flight conditions 7

i

1 - -_Ie--

Location

Cl Aden

El Adem Cartington

El Aden

Sussex

Cardii@or,

Idris

Sussex

‘“iid speed at height of run

ft/sec

sn (ft/sec)

3.8.I 2.19

-2.03 -2.00

3.33

2.78 2.94 2 .fL

700 70

200 -2.02

>A300 >I 300

2aI

-7.92 --1.77 -1.83

-1.80 -?.76 -1.92

2.97 2.93

3.23 3.42 3.31 3.86 y.10 I.95

-1.33 -4.38 -1.48 -1.59 -i&f5 -4.80 -?.55 -4 -20

3.34 2.G 3.87

2.81 2.80

80 130

>I 300 600 200 950

>j300 70

270

5z

>I300 400

2.70 2.78 3.27 2.72 2.87 2.55

-1.59 2.59 -1.36 2.94 -I .76 2.94

-1.53 -1.27

2.30 >93OO -1 .u, 3.34 2.81 >I300 -1.21 3.19 2.01 320 -1.40 2.78

:ftEec) f-t B&-l.

200 200

2130

500 1000

200

200 L&00 600

200 2CO

1000 yx3 2al

1000 500 2cO

200 100 500

'I 000 500

P

l- 64.02 05

77.02

!?o.oz 03 04

94.01 02 03

y9.02 03

106.01 02 03 04 05 06

q52.02 03 04

160.02 04

162.01 02 O3

10.02 IO.03 10.02

31.3 3.8 27.4 33-l 3:.2 28.5

-4.52 l,

-1 . y,

-1.68 -1.G -1 A0

-1 .:I-8 -1 l 53

-1.57

1.20 I.23 0.99 1.46 I.08 0.73

1.29 0.90 4.33

-1 A+.5 -1 A.2 -1.38

C.67 0.83 O-72

i

I

l.s b

30 02

CAUDlNGTON FLAT FARMLAND

500 UTS EAS SOOFT AGL

96 OS _- __ CARDINGTON FLAT FARMLAND

JOOKT5 EAS 1,000 FT A.Gi

INVERSE WAMLENGTN, CYCLES /FT

50 04 CARDINGTON FLAT FARMLAND

5OOKT5 EA5 ZOOFT AGI

T

FIG. 5. POWER SPECTRA - FLIGHT 90-VERTICAL TURBULENCE VELOCITY

94 01

EL ADEM “ILLI DESERT

300KTS EAS EOOFT. AGL

i

v

I

I- .Ol

-

-

- L’ 1

- -

94 02

EL ADEM HILLY DESERT

3DDKT5 EAS 400 FT AGL

-

-

\

I I

-

-

94 03

EL ADEM HILLY DESERT

300~5 EAS 600FT AGL

FIG.6.POWER SPECTRA-FLIGHT 94 -VERTICAL TURBULENCE VELOCITY.

‘Oqooo F-z-

IO L----

93.02

SUSSEX ROLLING FARMLAND

300 KTS E A.5 200FT AGL

I I I IIll] I I IIIII )’ , ,

INVERSE WAVELENGT; , CYCLES/FT

99 03

SUSSEX ROLLING FARMLAND

300KTS E A5 200 FT AGL UPWIND

I I IIIII

FlG.7. POWER SPECTRA-FLIGHT 99 - VERTICAL TURBULENCE VELOCITY.

I

\ 7

106 01

CARDlNGTON FLAT FARMLANC

3OOKTS EAS 1,000 FT A G L

-

-

-

k

- -

4 T’

106 07.

CARDINGTON

FLAT FARMLAND ,OOKTS LA5 SOOFT AGL

-

6

\

106 03

CARDINGTON FLAT FARMLAND

300KT5 EA5 ZOOFT A‘L

FIG.8 (a>. POWER SPECTRA - FLIGHT 106 -VERTICAL TURBULENCE VELOCITY

I1111 001

I I I III1 -

i

:

-LLLL 31

FIG.8@ POWER SPECTRA-FLlGHT 106-FORE-AND-AFT TURBULENCE VELOCITY

.I- 001

I I lllll]

-

-

-

\

-

-

106 05 CARDlNCTON FLAT FARMLAND

300KT6 EAS 500FT A GL

*-- --‘; \ A \

d 4’

I- 301

I I I Ill11

-

-

- ‘k - -

FIG. 8.(c) POWER SPECTRA -FLIGHT 106-VERTICAL TURBULENCE VELOCITY

I I IIIIL I

106 06 CARDINGTON FLAT FARMLAND

300KTS LAS ZOOFT AGL

-

\ 6

-

-

F IG. 8.(d) POWER SPECTRA- FLIGHT 106- FORE-AND-AFT TURBULENCE VELOCITY

L

L

\\

I \

li

‘- P i f c’ 1

L-l 0, FIG.9.bJPOWER SPECTRA-FLIGHT 152 -VERTICAL TURBULENCE VELOCITY.

\

-

I I Illll

-

\ ii

I I1111

FIG. IMa, POWER SPECTRA-FLIGHT 162-VERTICAL TURBULENCE VELOCITY

162 01

E ANGLIA FLAT FENLANO

300KT.s EAG

2OOFT AGL UPWIND

162 02

E ANGLIA

FLAT FENLAND 300~TS EAS

ZOOFT AGL DOWNWIND

,N”ERSE WAVELENGTH, CYCLES /FT

-

-

- 4 9

-

-

162 03 E ANGLIA

FLAT FENLAND

JOOKTS EAS LOOFT A G L

CROSS-WIND

FIG. II(b). POWER SPECTRA- FLIGHT 162- FORE-AND-AFT TURBULENCE VEUXITY

1000 FT.

IO, 000

F

i

& N

v) -p- 1,000.

&

9002, 03 AND 04

CARDINqTON

FLAT FARMLAND

300 KTS E.A.S.

500 FT

II I I I IIIII .,

INVERSE WAVELENCjTH -CYCLES/ FT.

FJG.12. COMPARATIVE POWER SPECTRA AT DIFFERENT HEIGHTS

VERTICAL VELOCITY OF TURBULENCE.

100

IO

I I I IllI] 0001 c

94.01 02 AND 03

EL ADEM

HILLY DESERT

300 KTS E.A S

INVERSE WAVELENGTH -CYCLES/FT.

FIG.13 COMPARATIVE POWER SPECTRA AT DIFFERENT HEIGHTS VERTICAL VELOCITY OF TURBULENCE.

:\ \\

,

I I I I lllll I ll1llll . 0001 -001 *Ol

k, 7 \ \ \ \

106.01, 02 AND OS

CARDlNCiTON

FLAT FARMLAND

300 KTS E.A S

/

I, 000 FT

INVERSE WAVELENqTH -CYCLES/ FT.

FIG.I4.(a)COMPARATIVE POWER SPECTRA AT DIFFERENT HEIGHTS VERTICAL VELOCITY OF TURBULENCE.

100,000 1

106~01, 02 AND 03

CARDINGTON

FLAT FARMLAND

300KT.S EAS

to, 000

t’

&II J

t .

N

T 2

t L 1,000

t

5

::

: d

“l 100 \\ \

5 ‘1‘ \ \ \

‘\ ’ \

IO

I I I I IIll I I I IIIII .oooi *ODi .Ol

INVERSE WAVELENqTH-CYCLES/FT.

FIG 14Xb)COMPARATlVE POWER SPECTRA AT DIFFERENT HEIGHTS FORE-AND-AFT VELOCITY OF TURBULENCE.

IO, 000

1,ooc

100

IC

200 FT.

I I IIIII

\ , \

Y’

\

L

106.04, 05 AND 06

CARDlNqTON

FLAT FARMLAND

300 KTS. E A.S

SOOFT.

I 1 I III11 .OOOl .OOl

INVERSE WAVELENGTH-CYCLES/FT.

I

\

b t

L- 01

FIG.lS(a) COMPARATIVE POWER SPECTRA AT DIFFERENT HEIGHTS VERTICAL VELOCITY OF TURBULENCE.

IO _

I I I IIIII I I IIIII *oooi 001

INVERSE WAVELENC,TH -CYCLES/FT.

FIG.I5.(b)COMPARATlVE POWER SPECTRA AT DIFFERENT HEIGHTS FORE-AND-AFT VELOCITY OF TURBULENCE.

--. -. ‘\

y 1,000 L-

ii L

03 a

IO

I I I llill 0001 .C

,

\

a,

\\

\ \ \

\ \

\ \ \’

\ \ 1

I I I I IIll .(

INVERSE WAVELENqTH - CYCLES/FT.

152.02,03 AND 04

I DRIS

CULTIVATED DESERT

300 KTS EA S.

\

\ ,’ \ \ \ \ \ s \ \

FIG.l6.@COMPARATIVE POWER SPECTRA AT DIFFERENT HEIGHTS VERTICAL VELOCITY OF TURBULENCE.

I

00 FT

10,000

t I I lllll

152.02, 03 AND 04

lDRl.5

CULTIVATED DESERT

300 UTS E A S.

\ a

\ T \ \ \ \ \ \

I I Ill1 ~Ooa .OOl 01 INVERSE WAVELENG,TH - CYCLES/ FT.

i\ \ \’ ‘\’ \

FIG.l6(b)COMPARATlVE POWER SPECTRA AT DIFFERENT HEIGHTS FORE-AND-AFT VELOCITY OF TURBULENCE

‘oo’ooo L------l 64.02 AN0 05

EL ADEM

FLAT AND HILLY DESERT \ ‘\ \ \ \ \ \ \ HILL \

l0,000 \ / \

\ .

\ \ \ \

\

-A

1,000

FLAT DESE. T k- 100

300 KTS E.A.S.

200 FT. A ‘+L

DESERT

.o 0ol; .OOl .OI ‘. . INVERSE WAVELENGTH-CYCLES/FT.

FIG.17. COMPARATIVE POWER SPECTRA OVER FLAT 8, HILLY DESERT VERTICAL VELOCITY OF TURBULENCE.

99.02 AND 03

SuSSEX

ROLLIt+ FARMLAND

300 KTS E AS.

200FT. AGL

1,000 L-

100 L-

‘“ET----- l I I IllIll

.OOOl a

\ \

\ \

-.\.\

INVERSE WAVELENCjTH CYCLES/FT.

\

\

\ \

\

FIG.18. COMPARATIVE POWER SPECTRA Up, AND DOWNWIND VERTICAL VELOCITY OF TURBULENCE.

‘oo’ooo~

‘Or------

162.01 02 AND OS

E. ANqUA

FLAT FENLAND

300KTS E:f’.S

200 FT. A.G,.L

I I Lllllj [II ‘*b.@s *OOl ‘01

INVERSE WAVELENqTH-CYCLES/ FT.

FIG. 19. COMPARATIVE POWER SPECTRA UP, DOWN, AND CROSSWIND VERTICAL VELOCITY OF TURBULENCE.

L

-2mFT

10,000

2 1,000 “,

-2

500 FT \ 1,000 FT

INVERSE WAVELENGTH-CYCLES/FT

1

\ \\ 4

\ \

IT 001

106.01, 02 AND.03

CARDlNClTON

FLAT FARMLAND

300 UT.3 E.A 3

\ \ \ \ 4 \ \ /

I I lillli I

-

-

‘\ P -

FIG20.COMPARATIVE POWER SPECTRA OF VERTICAL AND FORE-AND-AFT TURBULENCE AT DIFFERENT HEIGHTS.

-71 106 04, 05 AND 06

500 FT \ lOOOFT CARDINCITON

k \ \ FLAT FARMLAND

300KTS EAS

\ VERTICAL \ VERTICAL - ’

x FORE-AND-AFT \

-. 1 I I I I,,,,

,I 001 01 I I I IIIII

000, 001 INVERSE WAVELENG,TH -CYCLES/ FT

FIGt21.’ C0~;1~~~TI~~‘~~-~““‘-~~ER SPECTRA OF VERTICAL AND FORE-AND-AFT TURBULENCE AT DIFFERENT HEIGHTS.

t\ FORE-I

IO I I I I III,, I I I III,,

0001 001

0001 c

SO0 FT

INVERSE WAVLLENqTH-CYCLES/FT

152~02,03 04

IORIS

CULTIVATED DESERT

300 KT3 EAS

I,,/ 01

FIG.22. COMPARATIVE POWER SPECTRA OF VERTICAL AND FORE-AND - AFT TURBULENCE AT DIFFERENT HEIGHTS.

1,000

CROSSWIND

162 01, 02 AN0 03

E ANGLIA

FLAT FENLAND

3OOKTS EAS

200 FT Aq L

FORE-AND-AFT

1 ,Ol 001

I I I I Illl“’ I I I IIIL 0001 001

INVERSE WAVELENGTH-CYCLES/FT

FIG. 23. COMPARATIVE POWER SPECTRA OF VERTICAL AND FORE-AND-AFT TURBULENCE FOR DIFFERENT WIND

DIRECTIONS RELATIVE TO FLIGHT PATH.

HANDS ON

160 03 AND 04

SUSSEX-ROLLING FARMLAND

300 KTS E.A.5.

SOOFT. ACiL

STICK FREE \ \ \ \ \ \ \ \ \ \ \ \

\-

\ \ \ \ \ \ 1 \ \ \ \ \ \ \ \ \ \ \ \

\. \ \

\ \ I I IIIII

INVERSE WAVELENG,TH- CYCLES/ FT

‘\ \

\

\ \

/

FIG24.(a)COMPARATIVE POWER SPECTRA-HANDS ON 8 STICK FREE VERTICAL VELOCITY OF TURBULENCE,

-\ \ - \ \ \ \ 10,000

t Y 0 s I-

160.01 AND 02

SUSSEX- ROLLINS FARMLAND

300 KTS E A.S

IOOOFT. AGL

1E.E

INVERSE WAVELENqTH - CYCLES/FT.

FIG.24.(b)COMPARATlVE POWER SPECTRA-HANDS ON & STICK FREE VERTICAL VELOC 17-Y OF TURBULENCE.

100,000

IO, 000

I,OOC

ioo

IO

-

-\

-

:3c

-

-

; I I I IIIIII I I I I I I/III *OOOl .OOl .Ol

INVERSE WAVELENGTH, CYCLES/ FT.

/

475 KTS

‘\ J ‘\* 400 KTS

‘\ J

77 01,02,03 AND 04

EL ADEM -FLAT DESERT

200 FT.

FIG.25. COMPARATIVE POWER SPECTRA AT VARIOUS AIRSPEEDS VERTICAL VELOCITY OF TURBULENCE.

N AFRICAN FLIGHTS 64,77,94,152 106 01 UK FLlqiTS 90,106,160,162

0001 001 01

INVERSE WAVELENqTH-CYCLES/FT

FIG.26 COMPOSITES OF NORMALISED POWER SPECTRA OF VERTICAL TURBULENCE AT DIFFERENT HEIGHTS.

I I IIIllll I I I IIIIL] \ IJC.b-t

aa 01 I I Illllll I I IllIll

) \ 106 65

0 01 “P’ I I I I I I II? I I I Ii

INVERSE WAVELENGTH- CYCLES/FT

-

16.64

FIG .27. COMPOSITES OF NORMALISED POWER SPECTRA OF FORE-AND-AFT TURBULENCE

AT DIFFERENT HEIGHTS.

EXPRESSION (I), 1 = 200 FT.

I I

j)

oqor ,

INVERSE WAVELENc;TH-CYCLES/FT.

FIG.28. MEASURED AND FITTED NORMALISED POWER SPECTRA VERTICAL TURBULENCE AT 200 FT,

.^ I u,ooo I /EXPRESSION (2) x=540 F-f.

-BAND OF MCASURED-

-SPECTRA

I 000

t

-iii- EXPRESSION (I) et?=

i:

5 ->

I

INVERSE WAVELENqTH -CYCLES/FT.

FIG.29. MEASURED AND FITTED NORMALISED POWER SPECTRA VERTICAL TURBULENCE AT 500 FT.

EXPRESSION (2) J& = 620 FT

~2 = 1000 FT

IBAND Ok MEhJRED SPf CTRA

I I I Kill 1 ;~ I I III11 I I III1 .OOdlj .OOl

INVERSE WAVELEN5Tt-kCYCLES/FT

FIG.30. MEASURED AND FITTED NORMALISED POWER SPECTRA VERTICAL TURBULENCE AT 1000 FT.

3,

SCL

IO

o-5

I.5

IO’

o-5

0 w 1,000 HEIqHT ABOVE qROUND- FT.

FIG.31. RATIO OF INTENSITY OF VERTICAL TO FORE-AND-AFT TURBULENCE AT DIFFERENT HEIGHTS.

SCALES > 1300 FT. 1

-l-A 0

yi XFLK 0 0

R x x

r OR SLIG,HTLY

Q HILLY DESERT

I I ,

500 1000

HEIGHT ABOVE GROUND-FT.

HILLY TERRAIN

FIG.32. SCALE LENGTH OF VERTICAL TURBULENCE AT DIFFERENT HEIGHTS.

A.R.C C.P. mo.733 551.551: I A.R.C. C.P. No.i33 551.551: 539.Wl 539.431

WWLT SPECTRA OF LOW LEGL A~FXERIC TGXBlJlWZE f?UXRLZ FROM AN PUIER SPEClRA OF Low LWEL AlXEPiiD.IC WRDLZXE PlEAsum FRON AN

AIRCRAFT. Burns. A. API-11, 1%3. AIRCRAFT. Suns. A. April, 1963.

me note presents 30 power 8pectra 01 the vertical component or atmori- me note present* 30 pmfer spectra or the vertical cent or amos- pherlc turbulence and 12 wwr spectra 01 the horizontal co”p~“e”t measured pherle turbulence end 12 poner ~pec%ra or the horizontal ccrmp~nent meamzred on a Canberra alrcrait ifbIle flying at low altitude. The epxtm relate to on a cmberra aIrcraft while flying at low altitude. The ~pectm relate to various types of teml” 1” U.K. and N. Africa. Comparatlw spectra are films types of terral” In U.K. and N. Africa. Compsrative 8pectra are given for dllierent heights above ground wlthl” the belght band 200 to ~1~” Ior diffemnt heights above gm”“d Wlthi” the helEbt band x0 20 im rt. sor& :nlormatlon Is giw” on the associated meteorological lom ft. Sone lnfrmatlon 1s glwn on the assoclsted reteomloglcal condltlons. cc”d1tlo”s.

The results are tiacussed briefly with a view to rzenerallslns the basic The ms”1t.s m discussed briefly wlth a view to @“emllSlng the basic shape of the spectra for the purpose 01 ~edlctlng fatigue loads. Comparl- atap of the spectra for the purpose of predlcclng fatigue loads. COmparI-

son is made with pmgosed a”e.lyClcal expresslo”s deflnlw the basic ahape.

I-

son 1s lOade with Toposed analytlcel expressIons defining the bask IBulpe.

A.R.C. C.P. No.733 551.551: !539&1

POWER SPEC’IRA OF I.&’ LEVEL ATMBPHERIC lXWJLZXE MEAWPJD FROM rW AIRCRAFr. I9.mu. A. April, 19611.

The note p-esents 30 power spectra or th? vertical compo”e”t of atmos- pherlc turbulence and (2 paver apec~1.8 of the horizontal cor!w”e”t meamd on a Canberra aircraft id11l.s flying at low altitude. The spectra relate to various types of terrain 1” U.K. and N. Africa. Cconparatlve 8PctPB are given for dllfemnt heiehts above ground within the helght bend ZOO to loco ft. Some inforuatlon is given on the associated meteomloglcal condltlons.

The malts are discussed briefly with a view to !@“erallsing the basic shape oi the spectra IOI‘ the plrpose oi pedlctlng fatl!&“e loads. Comparl- so” Is made with proposed analytical expressIons deflnlng the basic sl!ape.

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