Monthly Weather ReviewVOLUME 98, NUMBER 10OCTOBER 1970UDC 651.551.5:551.515.41:551.510.53:629.73:656.7ATMOSPHERIC GUSTS-A REVIEW OF THE RESULTS OF SOME RECENT RESEARCH AT THE ROYAL AIRCRAFT ESTABLISHMENT J. BURNHAMRoyal Aircraft Establishment, Bedford, England1. INTRODUCTIONThis is a brief account of what the Royal AircraftEstablishment (RAE) has learned from research onatmospheric gusts since Zbrotek's review (1965). Theperiod from that time to the present has seen the consoli-dation of several trends that were then apparent. In par-ticular, concern about design cases that are not primarilystructural but affect handling qualities and flight controlsystems has increased, and greater emphasis has beenplaced on operational aspects. (That these are intercon-nected is apparent from consideration of a number ofaccidents and incidents that became known as the "jetupsets.") In considering the usefulness of gust research,it should be noted that results that improve the abilityto predict and avoid severe gusts can be applied now tocurrent aircraft, whereas improvements in design criteriawill benefit relatively few airplanes even in 5 yr. The basicaim of recent RAE research in this field has therefore beenthe study of severe gusts and the situations in whichthey occur. This work 11a.s been done in close collaborationwith the Meteorological Office and a number of overseasorganizations. The material presented here is taken mainlyfrom unpublished RAE papers.2. SOURCES OF SEVERE GUSTSA survey of catastrophic accidents to civil transportaircraft in which encounters with gusts played a significantpart shows 20 such accidents since 1950. These are listedin table 1. Of these 20, 17 are clearly linked with thunder-storms, as probably are two others. The remaining one isthe 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with asevere gust on the lee side of the mountain where strongmountain waves existed.A further source of data (unpublished) on operationalencounters with severe gusts has been the U.K. CivilAircraft Airworthiness Data Recording Programme.During the first 6.8 million n.mi.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 in flighton 46 occasions. All were associated with gusts. Thirty-five percent of the cases mere noted by the crew as beingassociated with storms, and a further 17 percent mereprobably so; 12 percent mere noted by the crew asso-ciated wit,h jet streams, leaving 36 percent "unknown."Many of the latter, however, 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 place tended to be short (fig. 1) ; duration of half thsencounters mas less than 1 min.A significant number of injuries (and occasionallydeaths) occur to passengers and cabin crew during flightthrough turbulence, in almost all cases the unfortunateperson not having been securely strapped into his seat.Reliable statistics are difficult to obtain, but it appearst,hat many 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.123724MONTHLY WEATHER REVIEWVol. 98, No. 10TABLE 1.-Accidents to civil transport aircraft involving turbulence in which major structural failures occurred in flight*Date Location Aircraft WeatherJune 1950 United States DC 4 Line squall with thunderstormsJan. 1951 Natal Dove Dark rain cloudSept. 1951 Qreece DC 3 Scattered thunderstormsFeb. 1953 Mexico DC 6 Frontal wave with thunderstormsMay 1953 India Comet 1 ThunderstormMay 1953 United States C46F Scattered thunderstorms, accident at sqns11July 1953 Pacific DC 6A ExtremethunderstormactivityAug. 1957 Alps Learstar 18 Cold front with severe turbulence and someDec. 1957 Argentina DC4 Cold front with thunderstorms and severeMar. 1959 India DC 3 ThunderstormMay 1959 United States Viscount Cold front with large rapidly develbpingJuly 1959 United States B26C Thunderstorm DURATION , MINUTESMay 1960 Argentina C46F Cold front- Jet stream "brought drmasses FIGURE 1.-Duration of patches of moderate and severe turbulenceSept. 1960 Elba Viscount Cold front with thunderstormsJuly 1961 Argentina DC 6Nov. 1961 Australia Viscount ThunderstormsColdfrOnt with scattered thunderstormsFeb. 1963 United States B720B SqualllinewiththunderstormsJuly 1963 IndiaMar. 1966 Japan Comet 4C Monsoonthnnderstorms B 707 InleeofMountFujiinwaveconditions +Aug. 1966 United States BAC 111 Extensive linked thunderstormslinethunderstormturbulencezavwl-xE'" I 1 Iwoavthunderstorms0 I 2 3down from hills.''encountered on worldwide civil jet operations."i+ MOUNTAIN WAVES0 STORMS* Data based mainly on WorZd Aoiation Accident Di3est8 published by the CUIAviation Organization, Montreal, CanadaWa15+03. 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 ft vertically from the top of thecloud) and in association with mountain waves. One patchof severe turbulence of the latter type found at 46,000 ftcontained a horizontal gust that reduced the indicatedairspeed of tho aircraft by 50 kt in 1 sec, a similar gust ofopposite sign occurring some 20 sec later. Large a.nd rapidchanges in air temperature 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 dangerous as penetrating thunderstorms at loweraltitudes, not only due to gusts but also to encounterswith large hail, high concentrations of liquid water, 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 neariI++02 00 +s0WWzaIuo 0.05 0.1 0.5 1.0DISTANCE , N. MILESI I I II I ' 1'1'1 I f 8 1,)0.2 0.4 0.6 0.8 I 2 4 68TIME (AT M=L).SECONOSFIGURE 2.-Examples of large and rapid changes in air temperature encountered in tho stratosphere.storm top level, at somewhat greater distances from thestorms than is the case at altitudes between 25,000 and35,000 ft. The strength of the wind near and above tro-popause level appears to be the controlling factor indetermining their strength, lateral extent, and the heightrange affected, but present data are insufficient for firmnumbers to be assigned to these relationships. It is clear,however, that many thunderstorms, at least in temperatelatitudes, will produce no noticeable disturbances at SSTcruise altitudes. Provided that the weather radar is usedcorrectly (particularly with reference to antenna tilt)and currently recommended practices followed, it appearsthat thunderstorms will be rather less of a hazard to a SSTduring cruising flight than they are to subsonic aircraft.It has been known for some time that, under favorableconditions, mountain and lee waves can propagate intoOctober 1970J. Burnham725AIR .-POSITION OF SEVERETEMPERATURE HORIZONTAL GUSTDEG. C-30 rPOSlTloWS OF -05EVERE TURBULENCE- 700 IO 20 30DISTANCE : NAUTICAL MILESFIGURE 3.-Time history of air temperature encountered during flight through a mountain wave at an altitude of 46,000 ft.TRUE VERTICALGUST VELOCITY-10 FTvDISTANCE: THOUSANDS OF FEET024TRUE VERTICALGUST VELOCITY FT/SECAPPROX. ALTITUDETHOUSANDS OF ft ____AIR TEMPERATURE0 5 IOAPPROX. HORIZONTAL SCALE:NAUTICAL MILESFIGURE 5.-Tentative model of a quasi-steady storm top (after Roach 1967).AMPLITUDEWAVE11000 PI'4500046000 FT45000 FTFIGURE 6.--Streamlines of flow in mountain waves over the WesternUnit.cd States, ba5ed on constant potential tcmperature surfaces.DISTANCE: THOUSANDS OF FEET02468FIGURE 4.-Examples of gusts measured in clear air near thunder- storm tops.the stratosphere and sometimes even amplify there.During a number of flights in the sttrat,osphere made bythe RAE over the western United States together wit,h aCanadian NAE (National Aeronautical Establishment) aircraftthat flew near tropopause level, significant disturbances asso-ciated with mountain and lee waves were found on severaldays in the stratosphere when none mere apparent nearthe tropopause. Est,imated streamlines for thc wave flowon one such day arc shown in figure 6. The occasions whensignificant wave disturbances were found in the strato-sphere were associated wit.h the existence of mountain andlee waves in the troposphere together with stable layers(near the altitude of t,he disturbandes) in the stratosphere(fig. 7). An analysis of meteorological data correspondingto the most severe gusts reported in the stratosphere inot,her 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 uncommon. Their identification with severewave disturbances in tho stratosphere is by no meanscertain and complete, nor do we know how far they arelikely to lead to significant disturbances in the absenceof a wave system in t.he t.roposphore. Further flightmeasurements are needed, together with a greater insightinto thc physical mechanisms involved. It is hoped thatbasic research on flow in stratified fluids will assist in thisprocess.At present, some airlines avoid flight through areas inwhich significant mountain wave activity is forecast in thetroposphere. In all known cases of encounters in thestratosphere with a significant mountain wave disturb-ance, such a forecast would have been made on the basisof current techniques. It therefore seems that moufitainwaves and their associated disturbances are unliiely to be726STABLE LAYERS4mMONTHLY WEATHER REVIEWBOO 'I I I 1-60 -50 -40 -30 -20 -10 0AIR TEMPERATURE, DEG CFIQURE 7.-Examples of upper air temperatures showing the existence of stable layers in thc stratosphere.greater operational problems to a SST than they are tocurrent 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 and less severe than at lower alt,itudes.Nevertheless, HICAT and RAE programs show that, insome parts of the world at certain times of the year, aSST may occasionally spend 10 t.o 15 percent of its cruisetime in turbulence sufficiently intense to be noticeable t,othe passengers.4. GUSTS AT ALTITUDES USEDBY PRESENT TRANSPORT AIRCRAFTThe 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 seriesin the United Kingdom and the United States; but withthe exception of some NASA (National Aeronautics andSpace Administration) measurements made in the early1960~~ no true gust velocity measurements mere avail-able. In only a very few cases could the data be comparedwith quantitative radar measurements of the storms.The RAE-NSSL work has allowed the relationshipbetween gust intensity and properties of the radar echoesof Oklahoma storms to be firmly established over an al-titude range from 23,000 to 35,000 ft (Burnham and Lee1969). A clear relationship exists between the probability1 Thh comment and a similar one about thunderstorms assume that SSTs Will notmuoh different from current aircraft in the way in which they respond to atmos-pherlc disturbances. This assumption is reasonable for the types of SSTs that we have s0far considered.PERCENTAGE OFPENETRATIONS ONGUST VEWHICH IEXCEEDMVALUESENCOUNIOC50ICIVol. 98, No. 10IEF:LoIC 1WITE?IVEOCITIESGIVEN Zr,,, IS MAXIMUM RADARIREREDREFLECTIVITY OFSTORM: mm6/m30 IO 20 30 40DERIVED GUST VELOCITY: lt/uc ASFIGURE 8.-Effect of the maximum radar reflectivity of the stormon the maximum derived gust velocity encountered 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 st.orm 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.0 the true gust velocities. Gust intensitywas found to be unrelated to other properties of the radarechoes such as average reflectivity or maximum or avera,gereflectivity gradient. For storms of a given intensity asmeasured by radar, a higher probability of encounteringa large value of derived gust velocity was found on thosepenetrations that passed through the most reflective partof the storm (that is, its core) than for those that, 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 penetrationsthat passed through storm cores, the design valuesof derived gust velocity were encountered on approx-imately 10 percent of the occasions.The Oklahoma and U.K. results are probably suitableguides to storm turbulence in other parts of the world;further evidence on this point is greatly desirable. Air-borne 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-obtained directly from measurements of incremental normal acceleration, being tho Size2 True gust velocities are actual components of air motion. Derived gust velocities areof gust of a particular shape that would have produced that acceleration (see appendixof Burnham and Lee 1989). Derived gust velocities are often quoted in termSOfeqUivalentairspeed (EAS), this being the product of the actual true air velocity (TAS) and thesquare mot of the relative density.October 1970PERCENTACE OF RUNS ONWHICH GIVEN VALUESJ. Burnham727ARE EXCEEDEDDERIVED GUSTS \IO - \ IO -IIMAXIMUMI0rms GUST VELOCITY : it/=. rAs MAXIMUM GUST VELOCTTY: ft/sec Tfi5 10 0 IO 20 30FIQURE 9.-Probabilities of encountering given rms and maxi-mum gust velocities from flights through convective cloud.lieving that airborne systems are significantly worse sofar as the detection of the positions of storms is concerned.It should be noted that there is a period of a few minutesat the beginning of any storm cell's life when the visiblecloud and air motion are present, but there is as yet in-sufficient liquid mater to give a radar echo.Reference has already been made to the meteorologist'spresent ability to forecast regions of the tropospherelikely to be affected by mountain and lee waves and as-sociated disturbances. These can be severe and have beenresponsible for at least one catastrophic accident. Al-though no measurements of severe gusts in troposphericwaves have been attempted by the RAE, some measure-ments made by a USAF instrumented aircraft in thelee of a high mountain ridge in strong wind conditionshave been analyzed and are referred to in section 6.Although RAE research has concentrated on convectiveclouds and wave situations in which operationally dan-gerous gusts are likely, the much more common but lessintense CAT is a significant nuisance to airlines andtheir passengers. The current situation regarding t.heforecasting of CAT has been described by Jones (1967) asfollows: "The present position is, therefore, that weknow a great deal about the possible locations of CAT,sufficient to be able to predict general areas where thechance of encountering turbulence is greater thanelsewhere. This is possible mainly by identifying theposition of the jetstream and predicting its intensificationor decay, and its movement . . . . We are not, however, ina position to forecast with certainty where in the generalareas, air motion will suddenly break down into turbu-lence. A great deal more research is required before wecan hope to narrow down these areas and give the pilotmore precise warnings of rough patches."In recent years, much effort has been spent, particularlyin the United States, in attempts to develop an airbornePERCENTAGE OFPENETRATIONSON WHICH GIVENVALUES AREEXCEEDED100-10.PASSING 1STORM MISSING \BY MORE THAN- STORM CORE5 MILES`HROUGHCOREII I0 20 40 60MAXIMUM DERIVED GUSTVELOCITY : lt/sec EASFIGURE 10.-Effect of passing through or missing the storm coreon maximum gust velocities encountered on thunderstormpenetrations (at heights between 23,000 and 28,000 ft throughstorms with maximum reflectivity factors between 104 and 101.9.device that will detect CAT ahead of an aircraft. On thewhole, the proponents of the various techniques that havebeen tried appear to have become less optimistic astime progresses. At present, only one technique appears tohave a worthwhile chance of success. This is infraredradiometry used to detect temperature changes ahead ofthe aircraft, it being hoped that the temperature of thepatch of CAT differs from that 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 LANDINGIn recent years, there has been considerable interest inthe United Kingdom in gust problems in relation t,o takeoffand landing, particularly in connection wiith the manuallanding of large aircraft and the assessment of the safetyof automatic landing systems. Although gusts are likelyto be small in the poor visibility condit,ions for whichthe latter were originally intended, it is necessary tobuild up confidence in the system by operation in clearweather, and some operators wish to use these systemsin all weather.Large gusts are, of course, most likely to occur 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 that are .flatcompared with the neighborhood of most airfields, its appli-cability to takeoff and landing problems is doubtful. Thisapplies particularly to measurements of vertical gusts atheights below about 200 ft. Much work needs to be done728MONTHLY WEATHER REVIEWVol. 98, No. 10TENNANT CREEK(AUSTRALIA 1 12 DEC.61II I 1 I I I I t16 17 18 19 20 21 22 23TIME , HOURSFIGURE 11.-Anemogram of a large squall.in conditions similar to those of practical interest beforeconditions can be defined confidently.From the operational point of view, both for giving aneeded improvement in the prediction of the severityof conditions for present day piloted aircraft and forallowing the placing (where necessary) of sensible limitson the conditions in which automatic landing systemsmay be used, it is essential that the severity of gustslikely to 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 to landing safety (below about 200 ft), 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,that can cope with the average level of gusts likely in a30- to 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 earth's 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 frequentlyWINDDIRECTIONWIND SPEED knotsI600 1700 1500 1600 1700 I800 BEDFORD BEDFORD 15 NOV 66 31 MAR.62FIGURE 12.-Anemograms of squalls recorded at 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 squall 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 to determinetheir effects. In an attempt to obtain further information,continuous records of windspeed at heights of 30, 50,and 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 figure 13.The coming operation of VTOL (verticle takeoff andlanding) and STOL (short takeoff and landing) aircraft islikely to lead to new demands for knowledge of the gustenvironment in urban areas.6. DESCRIPTION OF GUSTSGUST SPECTRAUp to t,he mid-l950s, 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 to gust load studiesin the late 1940s, having been used in the fluid mechanicaldescription of turbulence for the previous 20 yr. The gustsare here conceived as examples from a random processwith a determine spectral density (average variation ofenergy with frequency or wavelength). Knowledge of thisspectral density with the dynamics of the aircraft (varia-tion of response with input frequency) allows the spectralOctober 1970 J. Burnham 729z..e....PWW BEDFORDlot..........100 FEET50 FEET33 FEET20 AUG. 681326 GMT"-z3-LOG"0 IO 20 30 40 50 TIME, SECONDSFIGURE 13.-Time hist.ory of a rapid change of windspeed.XI04LOG F REOUENCYFIGURE 14.-Shapes of spect.ral densities of true vertical gust velocity measured during flights through thunderstorms.density of the response to be calculated if the system islinear. Thus rational account could be taken of the effect,sof aircraft rigid body and aeroelastic dynamics.If in a homogeneous region of stationary random airturbulence, energy is fed in only at t,he long n-arelengths,Eolmogoroff's n-ell-known result is that the spectraldensities of the turbulence component,s decay as the five-thirds power of wavelength over a range (known as theinertial subrange) from around t.he shortest wavelengthat which energy is being fed in down to wavelengths of afew centimeters where viscous effects begin t,o predominate.When given the assumptions made, the fire-thirds powerlaw is a reflection of the physical properties of air. Hon--ever, if the turbulence is not homogeneous-for example,if energy is fed in where measurements are made, but thedecay takes place somewhere elsea slope steeper thanfiv+thirds would be expected over part of the frequencyrange. Many exawples of spectra measured in this kindof situation show a square lam decay, figure 17 for example.As wavelength increases to values near those at whichenergy is being fed into the turbulence, the spectral densitybegins to flatten. The wavelength at which the bend occursis B measure of the "scale" of t.he turbulence. Most of themany definitions of scale give its numerical value as ef-fectively proportional to but not equal to this v-arelength.The generally used "theoretical" turbulence spect.ra dueto Dryden and von KRrmRn, for esamples, show n fairlyabrupt bend and an almost flat spect,rum at long wave-lengths. The available evidence suggest.s that in practicethe bend is not so abrupt, as indicat,ed in figure 15. Manymeasured spectra do not show n bend at dl, and measure-ments at the long wavelengths involved are very demand-ing on instrumentation accuracy. During the last 10 yr,as instrumentation has improved, the generally recom-mended value of turbulence scale has increased tenfold.Taking, rather arbitrarily, the Dryden formula andmatching the appropriate a~~tocorrelat,ion functions withthose measured (fig. 16), turbulence scales ranging from1,750 to 7,800 ft have been obtained from examples of theI The autocorrelation and spectral density are Fourier transforms of each other.LOGSPECTRALDENSITYLOG FREQUENCYFIGURE 15.-Shapc of "theoretical" gust spectra compared with possible shape of actual spectra at long wavelengths.vertical component of t,urbulence measured in clear airnear st80rm tops. Corre,sponding values inside the thun-derstorms range from 750 to 2,300 ft, these being for thespectra shown in figure 14. Some rather unexpected result,shave recently been obtnined 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, controry to 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 ofidees, more evidence is badly needed from sites ofpractical interest such as airfields and their approachareas.730MONTHLY WEATHER REVIEW Vol. 98, No. 101IOI.o AUTOCORRELATIONFITTEDEXPERIMENT0110246810TIME SECONDS IWAVELENGTH: 1 tFIGURE 16.-Experimental gust autocorrelation function, fittedtheoretical curve, and corresponding spectral densities.PERCENTAGE OF RUNSON WHICH No EXCEEDS GIVEN VALUESINCREMENTALNORMAL\ J ACCELERATON\\*L I 1 0 2 4 6ZERO CROSSING FREQUENCY: No; PER NAUTICAL MILEFIGURE 17.-Percentage of runs on which zero crossings of truegust velocity and incremental normal acceleration exceed givenvalues, obtained on flights through convective clouds.The spectral densities described above show 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.The spectra,l density, alone, mill not tell him this.GUST PROBABILITIESIf gusts were a Gaussian process, knowledge of theirspectrum and root-mean-square value would allow anydesired probability to be calculated. In particular, ifPERCENTAGE OFRUNS ON WHICHMAXIMUM NORMALACCELERATIONTIMES THE rrnsEXCEEDED nIC+FIGURE 18.-Percentage of runs through convective clouds andthunderstorms on which the maximum normal accelerationexceeds n times the rms.aircraft behaved as linear systems, the average frequen-cies at which given loads are likely to be exceeded couldreadily be obtained. Unfortunately, the overall proba-bility distributions of gust loads encountered opera-tionally are nothing like Gaussian. Rather, the largeloads are usually a good approximation to an exponentialdistribution. The usual may around the associateddifficulties is to assume that each individual turbulenceencounter is with a Gaussian process but that the rmsvalues corresponding to each encounter may be different.The usual method of calculating the average frequencyof a function's zero crossings per unit time from knowl-edge of its rms and spectrum shape is mathematicallycorrect only if both the function and its first den'vativeare Gaussian. In this situation, there is good agreementbetween experiment and theory. However, results ob-tained on flights through convective clouds, where theprobability distributions during individual cloud pene-trations do not appear to have been near Gaussian, showwide variations in the zero crossing frequencies of bothcg normal accelerat.ion and true vertical gust velocity(fig. 17.) The 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 to aircraft response, a property of the truegust velocity that can usefully be considered is t.he transi-tion function, the change in gust velocity that occursover a fixed time or distance "lag." The rms of thetransition function is usually called the structure functionand is uniquely related to the autocovariance, whether ornot the process is Gaussian. For a given patch of moderateJ. Burnham731October 1970PERCENTAGE OFTRANSITIONS WHICH THEIR rrnsEXCEED n TIMESIO0GAUSSIAN CURVEIO\\\\\\~0 In2 3FIGURE 19.-Percentage of transitions with lags of %, 1, lj6, 2, 3,4, and 5 min that exceed 7 times their rms from measurementsmade at a height of 1,458 ft on an instrumented mast.NUMBER OF GUSTS OFLENGTH H WHICHARE BIGGER THAN WGUST LENGTH, H, fto 00+ 160300 -200 -100 -50 -10 -SL#0IWH 3" 1 2FIGURE 20.---Number of gusts of length H that are greater than W, for thunderstorm data.or severe turbulence, the probability that transitions inexcess of a given value will occur tends to be exponentialfor values more than about twice the rms in all the405-235 0-7-NUMBER OF GUSTS OF GUST LENGTH* H, 'ILENGTH H WHICH ARE . 70+ 140x 2100 2800 350BIGGER THAN WIO -0 2WH-241FIGURE 21.--Number of gusts of length H that are greater than W, for gusts in the lee of a mountain range. 0 5 GUSTS EXCEEDING W o 20 - IO x 50GUST SIZE 0 100w tr@c0THUNDERSTORMS50 200 400 6000-00GUST LENGTH H ftFIGURE 22.--T'ariation with gust length of the number of gusts of a given size encountered.examples so far examined and sometimes is close to ex-ponential even for small values, 8s shown in figure 19.A more subject3ive approach to the analysis of largegusts has recently been made. This is an examination oftime histories of true vertical gust velocity measured inthunderstorms by the RAE and of some US. measure-ments made immediately in the lee of a mountain rangein strong winds. Changes in gust velocity that occurredover given distances mere picked out by eye. Any changeexceeding the threshold used was considered to be a gustof some length, and gusts of different lengths were notpermitted to occur simultaneously. The probability dis-tributions of gusts exceeding a given size were found tobe exponential for each gust length. For different sourcesof gusts, the probability distributions differed from each732N 15 NUMBER OF GUSTS OFLENGTH H WHICH EXCEED WGUSTSIZEwt t/sec6orTHUNDERSTORMSI 000.: * +100 500MONTHLY WEATHER REVIEWW LEE OF MOUNTAINSI2010080604020C,*.I SLIO0 300GUST LENGTH;H. ftFIGURE 23.-Variation of gust size with gust length for constantvalues of the product of gust length and the number of gustsof that length exceeding W in size.other by a constant factor when an exponent of gust sizedivided by the square root of gust length, rather than 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. In 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 23.A further 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 syst,ems 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 or as individual patches, lacksphysical reality. Nevertheless, spectral techniques basedon the Gaussian assumption are a useful advance, froman empirical point of view, on what has gone before.But they are not "rational design methods" based on aphysical understanding of atmospheric gusts.THEORETICAL MODELS OF GUSTSThe above doubts about the validity of Gaussian processGUSTSIZEWIO050ICIVol. 98, No. 10NUMBEROFGUSTS510 200 400 600 000 1000GUST LENGTH, H, ft.FIGURE 24.-Variation with gust length of a number of gusts ofa given size for self-similar gusts with a spectral density thatvaries as the square of wavelength and exponential probabilitydistribution.LENGTH H WHICH EXCEED WN=NUMEER OF GUSTS OFGUST SIZEW ftisec/I 1100 1000GUST LENGTH, H,ftFIGURE 25.-Variation of gust size with gust length for constantvalues of the product of gust length and the number of gusts ofthe length that exceed 11' in size, for self-similar gusts with aspectral density that varies as the square of wavelength andexponential probability distribution.representations of turbulence has led to a search fortheoretical models that, while utilizing spectral ideas inconsidering the average 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 functionmentioned earlier and of similar intermittent randomOctober 1970J. Burnham7330 20- +UPVertical gust velocity-or-20 -Normal accelerationOY)E2-2uo01 I I I I I I I I0 25 50 75 100 125 150 175 200TIME . SECONDSFIGURE 26.-Time histories of true vertical gust velocit.y, normalacceleration elevator deflection, and pitch attitude measuredduring flight through a convective cloud.VISUAL FLIGHT INSTRUMENT FLIGHTFIQURE 27.-Comparison of incremental cg normal acceleration andelevator deflection for instrument and visual flight by the sameaircraft and pilot through similar gusts.processes, and several promising ideas have emerged.This Tvork has been of great value in suggesting ways oflooking at severe gust data and of considering suchquestions as the effect of turbulence scale on thc proba-bility properties of t.he gush. For example, the equalslopes of the curves on figure 20 from the spectrum shapeshown in figure 14 can be predicted. Curves comparablewith those of figures 22 and 23 (although t,he dcfinitionsof "gusts" are somewhat different), calculated for self-similar gusts with spectral density varying as the squarcof wavelength and infinite scale, arc shown in figures 24and 25.More experimental data on severe gusts, as well astheoretical interpretation, are needed before a physicallyvalid model of them can be put forward for usc in design.Good progress is, however, being made toward this end.7. THE EFFECTS OF PILOT CONTROL ACTIONS ON FLIGHT THROUGH GUSTSAlthough t.he researc-h described above mas done pri-marily to study t,hc gush t'hemselves, their effects on thetest aircraft and crew have also been considered.RATIO OFMAXIMUMDERIVED TOMAXIMUM TRUEGUST VELOCITYASYMBOLS DENOTEDIFFERENT PILOTS2-I-A0Ih00 15 30MAXIMUM TRUE VERTICALGUST VELOCITY: ft/secFIGURE 28.-Ratio of rms-derived gust velocity to rms true gustvelocity versus rms true gust velocity for flights by differentpilots through convective clouds.Mention was made earlier of a series of gust accidentsand incidents known as the jet upsets; similar accidentsappear to have happened to propeller-driven aircraft. Afeature of thc jet upset,s mas a pitching oscillation with aperiod of about 20 sec t,hat tended to be divergent, theaircraft, finally cntcring n dive. A similar oscillation (fig. 26)occurrcd on one of the RAE flights through convectivecloud \vit,h afightcr aircraft and was damped out only whenthe pilot regained visual reference.Comparative studies illustrated by figure 27 showgreat,er control activity in relation t,o t.he turbulencc levelduring true instrument conditions than during visualflight, with R strong tcndcncy in IFR (instrument flightrules) flight for t,he larger accelerations to be closely relatedto elevat,or deflection. Figure 28 shows horn the ratio ofrms-derived gust velocity to rms true gust velocityvaries with the truc gust velocity for a series of flights witha fighter aircraft through convective cloud. Since therms-derived gust velocity can be taken as proport,ionalto the rms cg normal accelerations, corrected for theeffects of height, weight, and speed, figure 28 shows atendency for pilot, control actions to have a decreusingly-deleterious effect on accelerations (and so on loads) asgust intensity increases. An unpublished analysis byZbroiek (RAE) shows a similar effect (fig. 29). However,data on the maximum acceleration experienced on each134 MONTHLY WESQUARE OF MODULUS OFAPPARENT AIRCRAFTFREQUENCY RESPONSENORMAL ACCELERATIONAND GUST SPECTRAL(FROM RATIO OF MEASURED DENSITIES)10 r LIGHT TURBULENCE1 I Ilo4 lo3WAVELENGTH: tiFIGURE 29.-Effect of turbulence intensity on the square of modulus of apparent aircraft frequency response.cloud penetration indicates that t,he effect of gust intensityon the ratio of maximum acceleration to maximum truegust velocity is less marked than on the rms (fig. 30).Operational flight recording data also show that pilotcontrol actions can have a significant effect on the loadsexperienced during flight through moderate or severegust,s. At the present timc, 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 REMARKSThe past fern years has seen an increasing concern bythose involved in aircraft operations about the effects ofatmospheric gusts and the means of avoiding particularlythe more severe ones. The great concern expressed in somequarters about CAT appears, in the light of accident andincident data, to be somewhat misplaced. The thunder-storm is still the greatest hazard, but the severe gusts thatcan occur in mountain wave conditions, long recognizedas a hazard by some, re now widely known.Many airlines have, in recent years, increased efforts increw training in the use of airborne weather radar forstorm avoidance. Although it might be suggested that nogreat improvements in the radar itself can be foreseen,improvements in the display of information to the pilotare possible. Convincing arguments can be advanced, how-ever, to suggest that airborne radar alone is not alwaysgood enough, and a good weather display to the air trafficcontroller is also needed.:ATHER REVIEW RATIO OF rmsDERIVED GUSTTRUE GUST VELOCITYVELOCITY TO rmsASY ,moLs DENOTE+ + DIFFERENT PILOTSA+OO0 6 12rmc TRUE VERTICAL GUST VELOCITY f tpecFIGURE 30.-Ratio of maximum-derived gust velocity to maximumtrue gust velocity versus maximum true gust velocity for flightsby different pilots through convective clouds.Although no great improvements in gust aspects ofweather 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. Therealization that severe gusts are not just larger versionsof the more common less severe ones, but may differ fromthem in kind as v-ell as in degree, implies that measure-ments must be made of the severe gusts themselves and soincreases the difficulties and 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 isnow clear evidence that the 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 crit,eria. It has, however, been indicated thataccount must be taken not only of the gusts but also ofthe resulting control activity of the human pilot.REFERENCESBurnham, J., "Atmospheric Turbulence at the Cruise Altitudes ofSupersonic Transport Aircraft," Progress in Aerospace Sciences,Pergamon Press, New York, 1970, pp. 183-234.Burnham, J., and Lee, J. T., "Thunderstorm Turbulence and ItsRelationship to Weather Radar Echoes," AZAA Journal of Air-craft, Vol. 6, No. 5, Sept.-Oct. 1969, pp. 438-145.Jones, Robert F., ``Clear Air Turbulence," Science Journal, Vol. 3,No. 2, London, Feb. 1967, pp. 34-39.Roach, W. T., "On the Nature of the Summit Areas of SevereStorms in Oklahoma," Quarterly Journal of the Royal Meteor-ological Society, Vol. 93, No. 379, July 1967, pp. 318-336.Zbroiek, J. K., "Atmospheric Gusts: Present State of the Art andFurther Research," Journal of the Royal Aeronautical Society,Vol. 69, No. 649, Jan. 1965, pp. 2745.[Received Odober 7,1969; revised April 16,1970]