Atmospheric Gusts modelling

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VOLUME 98 NUMBER 10

OCTOBER 1970

UDC 51.551.5: 551.515.41:551.510.53: 629.73:656.7

ATMOSPHERIC GUSTS-A REVIEW OF THE RESULTSOF SOME RECENT RESEARCHAT THE ROYAL AIRCRAFT ESTABLISHMENT

J. BURNHAM

Royal AircraFt Establishment, Bedford, England

ABSTRACT

Recent Royal Aircraft Establishment research on gusts has been particularly concerned with severe gusts andth e situations in which th ey occur. In t he stratosphere, mou ntain wave conditions an d the vicinity of thunderstormtops h ave been investigated. A t lower altitudes, gusts in and near thunder storms have also been studied, as have windand gust effects likely t o be significant dur ing takeoff an d landing. Th e mathem atical modeling of severe gusts relevantt o aircr aft design is described, and th e effects of pilot control activ ity duri ng flight throug h gusts are considered briefly.

Part icul ar emphasis has been placed on two aspects of the work: 1) th e stu dy of possible means by which severegusts might be avoided in aircraft operations and 2) th e limitation s of existing mathemat ical models of gusts that areused in aircraft design. Suggestions are made for models th at may pro ve to be bot h more accurate a nd more physicallyplausible.

1. INTRODUCTION

This is a brief account of what the Royal Aircraftstablishment (RAE) has learned from research o nmospheric gusts since Zbroieks review (1965). Theriod from that time to the present has seen the consoli-

ation of several trends tha t were then apparent. I n par-cular, concern about design cases that are not primarilyructural bu t affect handling qualities and flight controlstems has increased, and greater emphasis has beenaced on operational aspects. ( Th at these are intercon-cted is apparent from consideration of a number ofcidents and incidents that became known as the jet

psets.) I n considering the usefulness of gust research,should be noted t hat results t ha t improve the abilitypredict and avoid severe gusts can be applied now to

rrent aircraft, whereas improvements in design criteriaill benefit relatively few airplanes even in 5 yr. The basicm of recent RAE research in this field has therefore beene study of severe gusts and the situations in whichey occur. Th is work has been done in close collaborationth the Meteorological Office and a number of overseasganizations. Th e material presented here is taken mainlyom unpublished RAE papers.

9 . SOURCES OF SEVERE GUSTSA survey of catastrophic accidents to civil transport

rcraft in which encounters with gusts played a significantart shows 20 such accidents since 1950. These are listed

table 1. Of these 20, 17 are clearly linked with thunder-orms, as probably are two others. The remaining one is

the accident to a Boeing 707 near Mount Fuji, wherestructural failure occurred during an encounter with asevere gust on the lee side of the mountain where strongmountain waves existed.

A further source of data (unpublished) on operationalencounters with severe gusts has been the U.K. CivilAircraft Airworthiness Data Recording Programme.During the first 6.8 million n.mi. of the program, normalacceleration increments exceeding 0.6 g occurred i n flighton 46 occasions. All were associated with gusts. Thirty-five percent of the cases were noted by the crew as beingassociated with storms, and a further 17 percent wereprobably so; 12 percent were noted by the crew asso-ciated with jet streams, leaving 36 percent unknown.Many of the latter, howcver, occurred in areas of theworld at times of the year when thunderstorms arecommon.

Taking the encounters as a whole, 54 percent occurredduring climb or descent and 46 percent during cruise. Theduration of the turbulence patches in which the encounterstook pIace tended to be short (fig. 1 ) ; duration of half theencounters was less than 1 min.

A significant number of injuries (and occasionallydeaths) occur to passengers and cabin crew during flightthrough turbulencc, in almost all cases the unfortunateperson not having been securely strapped into his seat.Reliable statistics are difficult t o obtain, but it appearsth at m any incidents are connected with storm encountersand some with gusts associated with mountain wavesystems. Very few seem to be associated with clear airturbulence (CAT) in the usual sense of the term.

72 3


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TABLE .-Accidents to civil trans port aircraft involving turbulence inwhich major structural failures occurred in flight

Waz

a

Dat e Location Aircraft Weather

DISTANCE , N. M I L E S0.05 0.1 0.5 1.0

I I I I

Ju n e 1950Jan. 1951Sept. 1951Feb. 1953May 1953May 1953

July 1953Aug. 1957

Dec. 1957

Mar. 1959May 1959

Ju ly 1959May 1960

Sept. 1960Ju ly 1961Nov. 1961

Feb. 1963Ju ly 1963Mar. 1966Aug. 1966

United StatesNatalGreeceMexicoIndiaUnited States

PacificAlps

Argentina

IndiaUnited States

Uni ted StaEesArgentina

Elb aArgentinaAustralia

United StatesIn d iaJapanUnited States

D C 4DoveD C 3D C 6Comet 1C46F

DC 6ALearstar 18

DC4

D C 3Viscount

B26CC46F

ViscountD C 6ViscountB720BCom et 4CB 707BAC 111

Line squall with thunderstormsDark rain cloudScattered thunderstormsFrontal wave with thunderstorm sThunderstormScattered thunderstorm s, accident at squall

Extreme h understorm activityCold front with severe turbulence a nd some

thunderstormCold front with thunderstorms and severe

turbulenceT h u n d e r s t o mCold front with large rapidly develbpiug

ThunderstormCold front. Je t strea m brought airmasses

Cold fron t with thunderstormsCold frdnt with scattered thunderstormsThunderstormsSquall inewith thunderstorm sMonsoon hunderstormsInlee ofM ount Fujiin waveconditionsExtensive linked thunderstorm s

line

thunderstorms

down from hills.

Data based mainly on World Auiation Accident Digests published by the CurlAviation Organization, Montreal, Canada

3. GUSTS IN THE STRATOSPHEREOperational experience at the altitudes at which SSTs

(supersonic transports) will cruise is very slender. Muchof the RAE gust research effort in recent years has beenspent in exploring this environment, which is essentiallythe lower stratosphere, particularly in situations in whichit is thought that severe disturbances might occur. Theresults of this work to date, together with those of theU S . Air Force HICAT (high altitude clear air turbulence)program, have recently been reviewed (Burnham 1970 .

Gusts large enough for their avoidance to be desirableby civil aircraft have been found (in the RAE work) inclear air near the tops of thunderstorms (up to 20 milaterally and 10,000 f t vertically fro m. he top of thecloud) and in association with mountain waves. One patchof severe turbulence of the latter type found at 46,000 f tcontained a horizontal gust that reduced the indicatcd

airspeed of the aircraft by 50 kt in 1 sec, a similar gust ofopposite sign occurring some 20 sec later. Large and rapidchanges in air tempera ture have been found (fig 2) in bothmountain wave (fig. 3) and storm situations. Patches ofmarked turbulence, particularly those associated withstorms, are sometimes very short (fig. 4).

The aircraft penetration of parts of thunderstormclouds that enter the stratosphere is likely to be atleast as dangcrous as penetrating thunderstorms at loweraltitudes, not only due to gusts but also to encounterswith large hail, high concentrations of liquid mater, andto possible engine malfunctions due to the intensely coldtemperatures that may well exist in the storm tops (fig. 5).There is some evidence that significant gusts exist near

\t W 1 1 I

E ou 2 3DURATION , M I N U TES

FIGURE.-Duration of patches of moderate and severe turbulenceencountered on worldwide civil jet operations.

t

+ MOUNTAIN WAVESSTORMS

+

+

+

+4-+

: +-

storm top level, at somewhat greater distances from thestorms than is the case at altitudes between 25,000 an

35,000 ft . The streng th of the mind near and above tro-popause levcl appears t o be the controlling factor indetermining their strength, lateral extent, and the heightrange affected, but present dat a are in sf ic ie nt for firmnumbers to be assigned to these relationships. I t is clear,however, th at many thunderstorms, a t least in temperatelatitudes, will produce no noticeable disturbances at SScruise altitudes. Providcd that the weather radar is usedcorrectly (particularly with reference to antenna tilt)and cur rently recommended practices followed, it appearsthat thunderstorms mill be rather less of a hazard to a SSduring cruising flight than they are t subsonic aircraft.

It has been known for some time th at, under favorableconditions, mountain and lee waves can propagate into


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c t o b e r 1970 J Burnham

.POSITION OF SEVEREI R

DEG. CT E M P E R AT U R E H O R I Z O N TA LGUST

I O S I TI O N S O F 0

aEVERETURBULENCE- 3 0 r

725

7 0 II I I

0 IO 2 0 3 0

DISTANCE: NAUTICAL MILES

IGURE .-Time history of air temperature encountered duringflight through a mountain wave at an altitude of 46,000 f t .

T R U E V E RT I C A LGUST VE L OCIT Y

F T l S E C

AIR TEMPERATUREAPPROX. ALTITUDETHOUSANDS OF f t - 6 5 --

0 5 10

APPROX. HORIZ ONTAL S C A L E :N A U T I C A L M I L E S

FIGURE .-Tentative model of a quasi-steady storm top (afterRoach 1967).

WAY EA M P L I T U D E

F T

0 2 4D I S TA N C E : T H OU S A ND S OF F E E T

T R U E V E RT I C A LGUST V E L O C I T Y

F T l S E C

20 I O o I O 2 0 30 4 0 5 0 6 0 7 0 B OD I ST A N C E N A U T I C A L M I L E S

FIGURE .-Streamlines of f l o ~n mountain waves over th e WesternUnited States, bawd on constant potential temperature surfaces.

0 2 4 6 8D I S TA N C E : T H OU S A ND S O F F E E T

GURE .-Examples of gusts measured in clear air near thu nder-storm tops.

e stratosphere and sometimes even amplify there.uring a number of flights in the stratosphere made bye RAE over the western United States together with anadian NAE (National Aeronautical Establishment) aircraft

at flew near tropopause level, significant disturbances asso-ated with mountain and lee waves were found on severalys in the stratosphere when none mere apparent neare tropopause. Estimated streamlines for thc wave flowone such da y are shown in figure 6. The occasions whennificant wave disturbances mere found in the strato-

here were associated with the existence of mountain andwaves in the troposphere together with stable layers

ear the altitude of the disturbances) in the stratosphere

ig. 7). An analysis of meteorological data corresponding

to the most severe gusts reported in the stratosphere inother studies shows similar stable layers.

Little is known from a climatological point of viewabout the existence of these stable layers, but it appearsthat they are uncomnioii. Their identification with severewave disturbances in tho stratospherc is by no means

certain and complete, nor do we know how far they arelikely to lead to significant disturbances in the absenceof a wave system in the troposphere. Further flightmeasurements are needed, together with a greater insightinto the physical mechanisms involved. It is hoped thatbasic research on flow in stratified fluids will assist in thisprocess.

At pre/sent, some airlines avoid flight through areas inwhich significant mountain wave activity is forecast in thetroposphere. I n all known cases of encounters in thestratosphere with a significant mountain wave disturb-ance, such a forecast mould have been made on the basisof current techniques. It therefore seems that mouhtainwaves and their associated disturbances are unlikely t o be


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726 MONTHLY WEATHER REVIEW

STABLE LAYERS

TROPOPAUSE

a5a

5 -

BOO I I II I

60 - 5 0 -40 30 - 2 0 -10A I R TEMPERATURE, DEG C

FIGURE 7.-Examples of upper air temperatures showing theexistence of stable layers in th e stratosphere.

greater operational problems t o a SST than they are t ocurrent aircraft

While the possibility exists that severe disturbances canoccur in the stratosphere in other than thunderstormand mountain wave situations, no reliable reports of themare known. It appears, largely from the results of theUSAF HICAT program, that gusts in the stratosphereare less frequent an d less severe tha n a t lower altitudes.Nevertheless, HICAT and RAE programs show that, insome par ts of the world at certain times of the year, aSST may occasionally spend 10 t o 15 percent of i ts cruisetime in turbulence sufficiently intense to be noticeable t othe passengers.

4. GUSTS AT ALTITUDES USEDBY PRESENT TRANSPORT AIRCRAFT

The predominant part played by thunderstorms inturbulence accidents and incidents involving currenttransport aircraft has been described in section 2. Thishas been reflected in RAE studies of gusts in and aroundthunderstorms at currently used altitudes and of the useof weather radar to avoid them. Much of this work hasbeen done in collaboration with the U.S. National SevereStorms Laboratory (NSSL) Gust measurements inthunderstorms had been made in a number of test series

in the United Kingdom and the United States; but withthe exception of some NASA (National Aeronautics andSpace Administration) measurements made in the early1960s, no true gust velocity measurements mere avail-able. In only a very few cases could the data be comparedwith quanti tat ive rad ar measurements of the storms.

The RAE-NSSL work has allowed the relationshipbetween gust intensity and properties of the radar echoesof Oklahoma storms t o be firmly established over an al-titude range from 23,000 to 35,000 ft (Burnham and Lee1969). A clear relationship exists between the probability

1 This comment an d a similar one about thunderstormsassume th a t SSTs will notbe much different from current aircraft in the wayin which they respond to atmos-

pheric disturbances. Thi s assumption is reasonable for the types ofSSTs h a t we have sofar considered.

PERCENTAGE OFPENETRATIONS ONWHICH DERIVED

vol. 98, No. 1

GUST VELOCITIESEXCEEDING GIVEN

VALUES WEREENCOUNTERED

Z o m o x IS MAXIMUM RADARREFLECTIVITY OF

STORM: m m b / m J

0 1 2 0 3 0 40DERIVED GUST VELOCITY: f t / sec EAS

FIGURE .-Effect of the maximum radar reflectivity of the stormon the maximum derived gust velocity cncountered on thunder-storm penetration.

that the largest derived gust velocity encountered on agiven storm penetration exceeds a given value and themaximum radar reflectivity of the storm penetrated (fig.8). Measurements made in convective clouds in theUnited Kingdom in which derived and true gust velocitystatistics were compared and found to be in good agree-

ment (fig. 9) suggest that results similar to those of figure8 apply also t o the true gust velocities. Gust intensitywas found to be unrelated to other properties of the radarechoes such as average reflectivity or maximum or averagereflectivity gradient. For storms of a given intensity asmeasured by rada r, a higher probability of encounteringa large value of derived gust velocity was found on thosepenetrations th at passed through the most reflective partof the sto rm (tha t is, its core) than for those tha t, whilestill passing through a part of the storm giving an echoon the ground radar used in the tests, missed the core bymore than 5 mi (fig. 10). For those aircraft penetrationsth at passed through storm cores, the design values

of derived gust velocity were encountered on approx-imately 10 percent of the occasions.

The Oklahoma and U.K. results are probably suitableguides t o storm turbulence in other par ts of the world;further evidence on this point is greatly desirable. Airborne weather radars are not so powerful, so sensitive,or so stable as the ground radar used in the tests. Althoughavailable comparisons between airborne and groundweather radars are few, they provide no reason for be

2 True gust velocities are actua l componentso i r motion . Derivcd gust ve locitiesobtained directly from measurementsof incremental norm al acceleration, being thesiof gust of a particular shape that would have produced that accelerationsee appendo Burnham and Lee1969).Derived gust velocities areoften quoted in terms of equivale

airspeed EAS), this being the product of the actual true air velocityTAS)

and tsquare root o the relative density.


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October 1910 J. Burnham 727

ERCENTAGE OF RUNS ONWHICH GIVEN VALUE5

ARE EXCEEDED

DERIVED GUSTS \

IO I O

r m 5

iI I0 5 IO

rims GUST VELOCITY: t t /sec TAS h

MAXIMUM

-XIMUM GUST VELOCITY:f t / sec TAS

IGURE .-Probabilities of encountering given rms and maxi-mum gust velocities from flights through convective cloud.

eving that airborne systems are significantly worse soa r as the detection of the positions of storms is concerned.

should be noted tha t there is a period of a few minutest the beginning of any storm cells life when the visibleoud and air motion are present, but there is as yet in-

ufficient liquid mater to give a ra dar echo.Reference has already been made t o the meteorologists

resent ability t o forecast regions of the tropospherekely t o be affected by mountain and lee waves and as-ociated disturbances. These can be severe and have been

sponsible for a t least one catastrophic accident. Al-hough no measurements of severe gusts in troposphericaves have been attempted by the RAE, some measure-ents made by a USAF instrumented aircraft in thee of a high mountain ridge in strong wind conditionsave been analyzed and are referred t o in section 6.

Although RAE research has concentrated on convectiveouds and wave situations in which operationally dan-erous gusts are likely, the much more common but lesstense CAT is a significant nuisance to airlines andeir passengers. The current situation regarding therecasting of C AT has been described by Jones (1967) asllows : The present position is, therefore, that we

now a great deal abou t the possible locations of CAT,ufficient t o be able t o predict general areas where thehance of encountering turbulence is greater thansewhere. This is possible mainly by identifying theosition of the jetstream and predicting its intensificationr decay, and its movement . . . . We are not, however, inposition t o forecast with certainty where in the general

reas, air motion will suddenly break down into turbu-nce. A great deal more research is required before wean hope t o narrow down these areas and give the pilotore precise warnings of rough patches.I n recent years, much effort has been spent, particularly

n the United States, in attempts to develop an airborne

PE RCE N TA G E OFPE N E T R AT IONS

ON WH I CH G I V E NVALUES ARE

EXCEEDEDIC

- H RO U G HCO RE

I

2 0 4 0 6 0M A X I M U M D E R I V E D G U S T

V E L O CI T Y : f L / s e c E A S

FIGURE 0.-Effect of passing thr oug h or missing the storm coreon maximum gust velocities encountered on thunderstormpenetrations (at heights between 23,000 and 28,000 f t throughstorms with maximum reflectivity factors between lo4 and 105.6 .

device that will detect CAT ahead of an aircraft. On thewhole, the proponents of the various techniques th at havebeen tried appear to have become less optimistic astime progresses. At present, only one technique appears t ohave a worthwhile chance of success. This is infraredradiometry used to detect temperature changes ahead ofthe aircraft, it being hoped that the tem perature of thepat ch of CAT differs from tha t of the surrounding air.It is known from RAE and Meteorological Office workthat this is not always the case, but it is possible thatthe correlation may improve as the intensity of the CATincreases. If the range discrimination of radiometerscan be improved, there is hope that an operationallyuseful instrument will result.

5. GUSTS IN RELATION TO TAKEOFF AND LANDING

I n recent years, there has been considerable interest i nthe United Kingdom in gust problems in relation t o takeoffand landing, particularly in connection with the manuallanding of large aircraft and th e assessment of the safetyof automatic landing systems. Although gusts are likely

t o be small in the poor visibility conditions fo r whichthe latter were originally intended, it is necessary tobuild up confidence in the system by operation in clearweather, and Some operators wish t o use these systemsin all weather.

Large gusts are, of course, most likely to occw in strongwinds and where the terrain is irregular. Since much infor-mation on gusts near the ground comes from measurementsmade on instrumented masts on sites th a t are :flatcompared with the neighborhood of most airfields, its appli-cability to takeoff and landing problems is doubtful. Thisapplies particularly t o measurements of vertical gusts atheights below about 200 f t . Much work needs to be done


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T I M E , H O U R S

FIGURE 1.-Anemogram of a large squall.

in conditions similar t o those of practical interest beforeconditions can be defined confidently.

From th e operational point of view, both for giving aneeded improvement i n the prediction of t he severityof conditions for present day piloted aircraft and fo rallowing the placing (where necessary) of sensible limitson the conditions in which automatic landing systemsmay be used, it is essential that the severity of gustslikely t o be met on the landing approach be related togeneral meteorological parameters, or their forecastingbe facilitated by some other means.

The importance of wind shear effects (in the sense ofwind variations with height that persist for a minute ormore) can be much overrated. At altitudes of primaryconcern t o landing safety (below about 200 f t ) , such shearsare likely to break down into turbulent fluctuations thatare sensed more by an aircraft than the shear would be.Large shears are much more likely to occur above 200 ftthan below; and at these altitudes, the gusts primarilyaffect glide path performance rather than directly affectlanding safety. A system, either human or automatic,th at can cope with the average level of gusts likely in a30- t o 40-kt wind is not likely to be greatly troubled bywind shear, except perhaps for the human pilot who istaken by surprise. However, significant shears may beassociated with large temperature stratification, andimportant wave effects may occur occasionally at a fewairports.

Large and rapid fluctuations of wind are not confinedto situations in which the mean wind preceding them isstrong. Large gusts that follow light winds are associatedwith convection around and above the earths boundarylayer; and larger gusts, which have resulted in a number ofaccidents, are associated with thunderstorms and areusually referred to as squalls. The anemogram of aparticularly horrendous example is shown in figure 11.Smaller troublesome squalls occur relatively frequently

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Vol. 98 No 10

DIRECTION

WIND SPEED

k n o t s

1 6 0 0 1 7 0 0B EDFOR D15 NOV. 6 6

1 5 0 0 1bOO 1 7 0 0 I600BEDFORD31 M A R . 6 2

FIGURE 2.-Anemograms of squalls recorded a t Bedford, England.

in the United Kingdom. The average number per yearover the last 5 yr at the RAE at Bedford has been 40.Two examples of these are given in figure 12. A transport-

type aircraft was flaring prior to a landing (on a westerlyheading) when the squal l of Nov. 15, 1966, occurred.The aircraft touched down with a large sideways velocity,but an accident was averted because the runway was wet,allowing the aircraft to slide sideways.

A very large number of squall records are availablefrom the Meteorological Office, but they do not resolvethe fluctuations with the accuracy needed t o determinetheir effects. In an attem pt to obta in further information,continuous records of windspeed a t heights of 30, 50and 100 ft are being obtained on an expanded time scaleusing an instrumented tower at the RAE at Bedford.An interesting record of an almost steplike gust obtainedwith this system is shown in figuro 13.

The coming operation of VTQL (verticle takeoff andlanding) and STQL (short takeoff and landing) aircraft islikely to lead to new demands for knowledge of the gustenvironment in urban areas.

6. DESCRIPTION OF GUSTS

GUST SPECTRA

Up to the mid-1950s, the discrete gust approach togust loads was practically universal. In this, gusts areconsidered to be a fixed and relatively simple shape (aramp or 1 - cosine function with a fixed length in feetor aircraft chord lengths) and variable amplitude.Although gusts are not really like this, the approach hasworked well and is still the primary one used by theaircraft industry.

Spectral methods were introduced t o gust load studiesin the lat e 1940s, having been used in the fluid mechanicaldescription of turbulence for th e previous 20 yr. T he gustsare here conceived as examples from a random processwith a determine spectral density (average variation oenergy with frequency o r wavelength). Knowledge of thisspectral density with the dynamics of the aircraft (varia-tion of response with input frequency) allows the spectral


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c t o b e r 1970 J. Burnham 129

1 ...... , - - - --...... ....... -......

EEDFORD.......... 20 AUG. 68

1326 G M T00 FEET50 F E E T- -I

l o t33 FEET

I 10 I O 20 30 40 5 0

T I M E , S E C O N D S

FIGURE 3.-Time history of a rapid change of windspeed.

ensity of the response to be calculated if the system isnear. Th us rational account could be ta ken of the effects

aircraft rigid body a nd aeroelastic dynamics.If in a homogeneous region of stationary random airrbulence, energy is fed in only at the long wavelengths,olmogoroffs well-known result is that the spectralnsities of the turbulence components decay as the five-irds power of wavelength over a range (known as theertial subrange) from around the shortest wavelengthwhich energy is being fed in down to wavelengths of a

w centimeters where viscous effects begin to predominate.hen given the assumptions made, the five-thirds powerm is a reflection of the physical properties of air. How-er, if th e turbulence is no t homogeneous-for example,energy is fed in where measurements are made, but thecay takes place somewhere else-a slope steeper than

ve-thirds would be expected over part of the frequencynge. Many examples of spectra measured in this kindsituat ion show a square law deca.y, figure 17 for example.As wavelength increases t o values near those at whichergy is being fed into the turbulence, the spectral densitygins t o flatten. T he wavelength at which the bend occursa measure of the scale of the turbulence. Most of theany definitions of scale give its numerical value as ef-ctively proportional t o but not equal to this wavelength.e generally used theoretical turbulence spectra dueDryden and von KBrm n, or examples, shorn a fairly

rupt bend and an almost flat spectrum at long wave-gths. The available evidence suggests that in practicee bend is not so abrupt, as indicated in figure 15. Manyasured spectra do not show a bend at all, and measure-nts a t the long wavelengths involved are very demand-

g on instrumentation accuracy. During the last 10 yr,instrumentation has improved, the generally recom-

nded value of turbulence scale has increased tenfold.Taking, rather arbitrarily, the Dryden formula and

atching the appropriate autocorrelation functions withose measured (fig. 16), turbulence scales ranging from750 to 7,800 f t have been obtained from examples of the

The utocorrelation and spectral density are Fouriertransfoms of each other.

LOG

I x 1 0 4LOG FREOUENCY

FIGURE 4.-Shapes of spectral densities of true vertical gustvelocity measured during flights through thunderstorms.

LOGSPECTRALDENSITY

LOG FREQUENCY

FIGURE Fi-Shapc of theoretical gust spectra compared withpossible shape of actual spcetra a t long wavelengths.

vertical component of turbulence measured in clear airnear storm tops. Corresponding values inside the thun-derstorms range from 750 t o 2,300 ft, these being for thespectra shown in figure 14. Some rather unexpected resultshave recently been obtained by the RAE from measure-ments of vertical gusts at heights between 50 and 200 ftover Bedford Airfield. These give scales that tended to begreatest at the lower altitude, contrary t o expectations,and the numerical value at .50 ft is much longer than wasthought likely. While it is not suggested that these fewresults at low altitudes call for an immediate revision ofideas, more evidence is badly needed from sites ofpractical interest such as airfields and their approachareas.


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730 MONTHLY WEATHER REVIEW v o l . 98 No . 1

2

o I - 3

0.5hHEORYITTED

' . t i t-XPERIMENT0 .-

IO

S P EC

-L I

0 2 4 6 8 1 0

T RUM

T I M E S E C ON D S L \.,IO* IO

WAV E L E N G T H :

FIGURE 6.-Experimental gust autocorrelatio n function, fittedtheoretical curve, and corresponding spectral densities.

P E R C E N TA G E OF R U N SON WHICH No E X C E E D S

G I V E N VA L U E S

oar--I N C R E M E N TA LN O R M A LA C C E L E R AT I O N

\\

\

P I0 2 4 6

Z E R O CROSSING F R E Q U E N C Y : N 0P ER N A U T I C A L MILE

FIGVEE 7.-Percentage of runs on which zero crossings of t ruegust velocity and incremental normal acceleration cxcecd givenvalues, obtained on flights through convective clouds.

The spectral densities described above shorn how, onthe average, the energy of the turbulence varies withwavelength. Spectral methods also provide a. valuabletool for comparing measured aircraft loads and motionswith theoretical predictions. The primary question thatconcerns the aircraft designer, however, is usually howoften a relatively extreme and rare event will occur.Th e spectra.1 density, alone, will not tell him this.

GUST PROBABILITIES

If gusts were a Gaussian process, knowledge of theirspectrum and root-mean-square value would allow any

desired probability t o be calculated. I n particular, if

P ERCEN TA G E OFRUNS ON WHICHM A X I M U M N O RM A L

ACCELERATION

TIMES THE r m 5E X C E E D E D n

I 4

FIGURE 8.-Percentagc of runs through convective clouds andthunderstorms on which the maximum normal accelerationexceeds n times the rms.

aircr aft behaved as linear systems, th e average frequen-cies at which given loads are likely to be exceeded couldreadily be obtained. Unfortunately, the overall proba-bility distribut ions of gust loads encountered opera-tionally are nothing like Gaussian. Rather, the largeloads ar e usually a good approximation to an exponentialdistribution. The usual way around the associateddifficulties is to assume th at each individual turbulenceencounter is with a Gaussian process but that the rmsvalues corresponding to each encounter may be different.

Th e usual method of calculating the average frequencyof a functions zero crossings per unit time from knowl-edge of its rms and spectrum shape is mathematicallycorrect only if both the function and its first derivativeare Gaussian. I n this situation, there is good agreementbetween experiment and theory. However, results ob-tained on flights through convective clouds, where theprobctbili ty distributions during individual cloud pene-trations do not appear to have been near Gaussian, showwide variations i n the zero crossing frequencies of bothcg normal acceleration and true vertical gust velocity(fig. 17.) Th e percentage of runs on which the maximumexceeds a given factor times the rms is much greater,in both the convective cloud and thunderstorm flights,than would be obtained with a Gaussian process (fig. 18

In relation t o aircraft response, a property of the truegust velocity that can usefully be considered is t3he ransi-tion function, the change in gust velocity that occursover a fixed time or distance lag. The rms of thtransition function is usually called the structure functionand is uniquely related to the autocovariance, whether

not the process is Gaussian. For a given patch of moderate


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W LEE O F M O U N TA IN S

mI 2 0 8 st

N 15 NUMBER OF GUSTS OFL E N G T H H WHlCH EXCEED W SI0 \

*100

G U S TSIZEw

t t / s e c

TWVN DE RSTORM S

2 0

0 l v . e . . .100 500 I O 0 3 0 0

G U S T LENGTH, H, f t

FIGURE 3.-Variation of gust size with gust length for constantvalues of the product of gust length an d thc number of gustsof t ha t leng th exceeding W in size.

other by a constant factor when an exponent of gust sizedivided by the square roo t of gust length, rat her t han ofgust size itself, was used (as shown in figures 20 and 21) .Curves showing the variation with gust length of lines ofequal probability of gust velocity exceedance are shownin figure 22. I n comparing the behavior of different sizesof aircraft, it is sometimes convenient to consider thebehavior of isopleths of the product of the number ofgusts exceeding a given size with the gust length, and suchcurves are shown in figure 2 3 .

A fur ther example of the practical application of theGaussian assumption concerns the use of synthetic tur-burlence made with Gaussian noise generators, the outputof which is filtered to give the correct spectral density.These have frequently been used in rig testing of auto-

matic flight control systems and in simulators. So far asthe prediction of extreme values is concerned, this syn-thetic turbulence does not have the same properties asthe atmosphere.

It is clear that the Gaussian representation of atmos-pheric gusts, on the whole o r as individual patches, lacksphysical reality. Nevertheless, spectral techniques basedon the Gaussian assumption are a useful advance, froman empirical point of view, on what has gonc before.But they are not rational design methods based on aphysical understanding of atmospheric gusts.

THEORETICAL MODELS OF GUSTS

G U STS I ZE

W

NUMBER

OFG U S T S

5

0 2 0 0 4 0 0 6 0 0 8 0 0 1000G U S T LENGTH, H, f t .

FIGURE 4.-Variation with gust lengt h of a num ber of gustsa given Qize for self-similar g usts wit h a spectral density thavaries as th e square of waveleng th and exponential probabilitydistribution.

N=NUMBER OF G U S r S OFL E N G T H H WHICH E X C E E D W

GUST S I Z Ew f t j S C C /

I O 0

8 0

6 0

4 0

2 0

0 00 1000

.GUST LENGTH, H,ft

FIGURE 5.-Variation of gust size wit h gust length for const antvalues of t he product of g ust length and th e number of guststhe length that exceed W in size, for self-similar gusts withspectral density that varies as the square of wavelength andexponential probability distribution.

representations of turbulence has led t o a search fortheoretical models that, while utilizing spectral ideas inconsidering the averagc distribution of energy with wave-length, have probability characteristics that match thoseof the real atmosphere. A number of concepts are beingstudied, including those of the transition function

The above doubts about the validity of Gaussian process mentioned earlier and of similar intermittent random


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734 MONTHLY WEATHER REVIEWS Q U A R E O F MODULUS OF

A P PA R E N T A I R C R A F TFREQUENCY RESPONSE

FROM RATIO OF M E A SU RE D( N O R M A L A C C E L E R AT I O N

AND G U S T S P E C T R A LDEN SI T I E S

lo L I G H T T U R BU L E NC E

Vol. 98 No,

RATIO OF r m sDERIVED GUST

VELOCITY TO rrnsTRUE GUST VELOCITY

SY .biBOLS DENOTE+ A DIFFERENT PILOTS

0 6 12r m s T R U E ,VERTICAL GUST

VELOCITY f t / s e c~~

I O * l o 3 FIGURE 0.-Ratio of maximum-derivcd gust velocity t o maximum

true gust velocity versus maximum truc gust velocity for flightsb y different pilots thro ugh convcctive clouds.

WAV E L E N G T H : t l

FIGURE 9.-Effect of turbulence intensity on the square of modulusof apparent aircraft frequency response.

cloud penetration indicates that the effect of gust intensityon the ratio of maximum acceleration to maximum truegust velocity is less marked tha n on the r ms (fig. 30) .

Operational flight recording data also show that pilot

control actions can have a significant effect on the loadsexperienced during flight through moderate or severegusts. At the present time, there is no way of takingaccount of such pilot effects; and in this case, gust loadprediction must be an inexact business, however good ourknowledge of the atmosphere.

8. CONCLUDING REMARKS

The past few years has seen an increasing concern b ythose involved in aircraft operations about the effects ofatmospheric gusts and the means of avoiding particularlythe more severe ones. The grea t concern expressed in some

quarters abou t CAT appears, in the light of accident andincident data, t o be somewhat misplaced. The thunder-storm is still the greatest hazard, bu t the severe gusts tha tcan occur in mountain wave conditions, long recognizedas a hazard by some, are now widely known.

Many airlines have, in recent years, increased efforts increw training in tho use of airborne weather radar forstorm avoidance. Although it might be suggested that nogreat improvements in the radar itself can be foreseen,improvements in thc display of information to the pilotare possible. Convincing arguments can be advanced, hom-ever, t o suggest that airborne radar alone is not alwaysgood enough, and a good weather display to the air trafficcontroller is also needed.

Although no great improvements in gust aspects oweather forecasting seem likely in the immediate future,considerable advances have been made in understandingthe physical mechanisms responsible for severe gusts.There are, however, still large gaps in our knowledge. Threalization that severe gusts are not just larger versionsof the more common less severe ones, but may differ fromthem in kind as well as in degree, implies that measure-ments must be made of the severe gusts themselves and soincreases the difficulties an d dangers of experimental work.

The use of gust statistics such as the spectral density todescribe averages from which extreme values may bepredicted is a questionable procedure unless adequateregard is paid to other probability properties. There isnom clear evidence that tho gust probabilities are notGaussian. Work on theoretical models of extreme guststhat are more physically plausible than those used in thepast is showing good progress and should lead to improveddesign criteria. It has, however, been indicated thataccount must be taken not only of the gusts bu t also ofthe resulting control activity of the hum an pilot.

REFERENCES

Burnham, J., Atmospheric Turbulencc a t th e Cruise Altitudes oSupersonic Transport Aircraft, Progress in Aerospace SciencePergamon Press, New York, 1970 pp. 183-234.

Burnham, J., and Lee, J. T., Thunderstorm Turbulence and ItsRelationship to Weather Radar Echoes, A I M Jo u rn a l of Aircraft, Vol. 6, No. 5, Sept.-Oct. 1969, p. 438-445.

Jones, Robcrt F., Clear Air Turbulence,, Science Journ al , Vol. 3,No. 2, London, Feb. 1967, pp. 34-39.

Roach, W . T., On the Nature of thc Summit Areas of SevercStornis in Oklahoma, Quarter ly Journal of the Royal MeteoroZoyicaZ Society,Vol. 93, No. 379, July 1967, pp. 318-336.

Zbroiek, J . K., Atmospheric Gusts: Present State of the Art andFurther Research, Jo u rn a l of the Royal Aeronautical SocietVol. 69, No. 649, Jan. 1965, p. 27-45.

[Received October 7 1969; rewise Apri l 16 19701

Atmospheric Gusts modelling

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