
v V r I THIRD PROGRESS REPORT ON THE METEOROLOGICAL ACTIVITIES AT THE DANIEL GUGGE1lliEIM AIRSHIP INSTITUTE This report covers the resulte of the meteorological research at the Daniel Guggenheim Airship Institute for the third ninety days under U S Navy Contract No 42090, of May 20, 1935, between the US Navy Department and the California Institute of Technology. The present report is restricted to the problem of gustiness and hae for its object a deeoription of those aspects of the problem which have been attacked hitherto and the main results obtained to date in the preeent investigation. A few references to previous work by other investi~ators are included in order to coordinate the information available. It DD.1st be remarked that the experimental setup which has been described in detail in Reports l and 2 v.ras restricted to measurements of one component of the wind velocity and nt only one plaoe in a given period. In other words, the following paragraphs contain the information which oan be gained by the analysis of one anemogram correlated with corresponding measurement of the temperature lapse rate, i.e. the degree of stability of the atmosphere. The desirable extension of the observations to the measurement of three components and to simultaneous measurements over an extended area is described later in the report. l. Magnitude of the wind f luctuations: The gustiness can be ch.araoter1Eed in one way by the standard deviation taken over a certain period of the wind velocity from the mean value at a 6iven point. The standard deviation is defined as the square root of the mean value or the square of the fluctuations (u U} 2 , where ~ u ie the instantaneous velocity and u the mean velocity over the time. The fluctuation velocity is denoted by u' and the standard deviation by ~. Thia quantity l~S calculated for a large number of anemograme over from 2 to 10 minute 2 periods. The intermediate positions covered periods of from 2 to 10 m1nutea eaoh. Exclusive of several runs in vmioh the anemogrnm showed no perceptible fluctuations, the values of the standard deviation varied from 0.3 llf1eec to 2.4 m/sec for mean wind velocities between 2.3 i;lsec and 15.4 ny'seo. The standard deviation is alao expressed as n percentage of the mean velocity  oalled the r elative etandard deviation. The values varied between 5 o/o nnd 51 o/o. Values of the standard deviation at the top position show e. correlation with the corresponding mean velocities. The averages of the values of the standard deviation ~ere obtained for the ranges in mean wind velocity of 24, 46, 68, 810, etc, ~s ec . The results ~ plotted in Fig l, conform fairly well with a straight line through tho origin. In other words, the mean value of the relative standard deviation, averaged over all lapse rates, is approxinnt ely oonetant, independent of the mean wind velocity. This constant is about 0.11 for the records analyzed. A definite correlation was found between tho relative standard deviation and the temperature lapse rate. To show this correlation, the observations were grouped in the follovnng v.re.y: an average value was taken of the observations between 1030 m, 3060 m, 60 90 m height and for lapse ro.tes r <. 0' 0 <. r < 0.01 , 0.0.1. <. r <. 0.015 , 1 ) 0.015. 1 is equal to  dT/dh, where T is the temperature in degr ees Centigrade and h is the height in meters. It is known tha t the adinbntio condition corresponds to about l' • 0.010 C/m. The result of thie grouping is shown in Fig 2, in whioh the abaciseae of the plotted points is the mean lapse rate of the runs ooneider ed in the intervals given above . The runa in which there were no perceptible fluctuations were not included in the averaging. It will be observed that for each layer tho seoond point lie~ above and the third below the ourvee drawn. If more observations were available, these points would probably be brought closer to tho curves drawn. The fluctuations increase quite rapidly, especially in the lov1er layer, for 3 increasing instability. Even for the low l apse rates, the value f or 1030 mis 0.15, as against 0.11 for the 6090 m layer . This difference increaees until in the most unstable range the values are 0.29 and 0.18 respectively. 2. Statistioal distribution of gust intensities: It is an interesting question how far the distribution, i.e. the relative f requency of large and suall wind fluctuations , or strong and ·.veak gusts, fol lows the pure probability laws . If the deviation in 'rlnd velocity woul d oocur in a purely random fashion , the time in which the excess wind velocity is, say, between p and p + ~ p per cents of a the mean velocity would be proportional to 0 p , wher e Pm is the average ) P2m fluctuation • the relative standard deviation mentioned in the for egoing secti~n. Let us assume, for instance, that the mean relative standard deviation or t he mean relative gustiness is 20 o/o, then the total time in which the excess wind velocity is between 0 and 5 o/o, 5 and 10 o/o, 10 and 15 o/o , and so on , would be repreFented by tl1e curve in Fig 3. The actual distributions •vere comput ed from a number of anemogiam.s . One example is shown in Fig 4. The most convenient method of oomparing the statistical distribution with the pure probability distribution is by plotting the data on a special coordinate paper. The abscissa represents the r elative magnitude or the square of the fluetuation in linear scale, the ordinate, the logarithm of the time ratio. total period With respect to these axes the error law is represented by a straight line with tho inclination  , where  2 u• 2 p m :s u!! is the square of the relative standard deviation. Records showing large values of mean gustiness appear as f lat, those with small values of mean gustiness as steep lines. Distr ibutions following the error law appear as straight lines, points above the straight line show that certain particular gust intensities are preferredj points belO\v the straight line show t.hat the corresponding intensities appear lees frequently than should be expected accor ding to the error l aw. Fig 5 shows the diagrams oorresponding to the following observations: 4 Date Run Time h r u (ny'aec) July 12* 1 4:00  4: 10 AM 84 .028 8.2 July 12* 2 5: 05  5 : 15 AU 85 .014 7.5 July 12 3 7:69  8:09 Alf 87 .010 4.9 Oct 4 1 5: 05  5 : 15 AM 83 .001 8.3 In these curves the ordinate gives the time for which u '/u will duration of record be between ± 2.5 o/o from the value indicated by the abscissa. Fig 6 givee diagrams corresponding to the observations: Date a) July 12 b) Oct 14 c) Oct 9 Run 4 1 2 Time 9:51  10:01 .AJ.a 3:38  3:48 PM 3:40  3:50 PM h 86 81 86 .013 .017 .017 u (uy'eeo) 6.5 6.8 4.5 The points for run 4 of July 12 and run 2 of October 9 deviate most from the etraight line predicted by the error law. It is possible that longer records would smooth out the differences. Giblett 1) has plotted curves similar to those shown in Figs 3 and 4 for the mean accelerations of the 'vind over five seconds and also for the deviations from the mean direction at a height of 50 feet above the ground. He finds that the dictribution of t...hese components is approximately aooording to the error law. Best 2) ha3 obtained similar results for the velocity fluctuations in the immediate vicinity or the ground (up to 4 meters) . The measurements presented in this report are the first similar investigations, to our knowledge, at greater height. The general result of the analysis is that eapeoially when the atmosphere * The lapse rates given for runs 1 and 2 of July 12 are slightly different from those givon for the same runs in the preceding report. These corrected values wore obtained from a plot of the temperatures at the 30 and 80 meter levels against the time at whioh the inatrul'!lent was actually at that level for the four runs of that dnte. The lapse rate given is that for the time hnlfv.JB.y between the t\vo points corresponding to ea.oh run. Thie method \vas used to obtain the lapse rates for all runs made before the temperature difference instrument was installed. • 5 ia stable, the distribution or guetintensities conforms approxll:ntel y wit h the error law. Thia means practically, that the relative frequency of str ong and weak gusts is about the eame independent of mean wind velocity nnd mean guatineaa. Therefore, if the mean gustiness is known, it can be fairly well eatinnted in 'Nha·l; percentuge of a. total period considered , the wind velocity is likel y t o exceed n certain limit or be below a certain value. However, it must be emphas i zed that a.a yet nothing onn be said regar ding "how oft en" gusts of certa in i ntensity appear. This depends not only on the added sum or the time cl€11lents in whioh a certain intensity prevails, but on the average duration or an individual gust. This question has perhaps more practical importance than the statistical distribution itself, and 'vill be discussed in the next section. 5. Analysis of correlations. Duration and Size of gusts: It is believed that th~ time or duration of a certain gust at a given plnce depends on the size of more or less "coherent" e.ir masses. It is difficult to obtain reliuble infor mation about the average sizo of such :masses. The apparatus available in Akron did not allovr takinz simultaneous recor ds of the velooity componenta at various stations distr ibuted at distances along and across the menn flow. Ho\rever, quite valuable informution can be obtained by the analysis of a single anemogram,at l east as far as the size of the perturbations in the direction or the mean wind is concerned. To a firRt approximation the sequence of velooities as thoy are r ecorded at a fixed place correspond to the velocities occurring simultaneousl y up~tream, so the. t the velocity devi ation u' , 1mioh corresponds to the time Ii t, is of tho same order as the differ ence between velocities at two points separated by a distance A x. • u At, wi1ere t is tlle mean velocity. Henoe the duration of a certaln period of excessive velocity gives a measure for the linear extension of a col1erent uir maea 'vi th excessive velocity . To be sure, this reasoning neglects first the deformation or the air m.9.sses coneider~d ; second, their vertical and lateral motion. Unfortunately we know very little about the dero?'l!'~tion or 6 such "gusts"; however, observations show that their shape ohanges relatively slowly. As for the influence of the vertioal and lateral motion of gusts, it is believed that they do not affect materially the conclusions drawn from the anal ysis of the anemogram. In fact , if we compare two oases, assuming that a gust traverses the point of location of the anelilometer horizontally or under a slight inclination, the period in whioh the anemometer r ecords ahow higher or lower velocities will be only slightly changed. This is demonstrated in Fig 7, in which the gust is r epresented as elliptical. Whether the ms.ea passes the station along th~ direction a or b intr oduces only a amall error in its apparent size as judged from the anemogram. TVJO methods were used in order to obtain information on the average size of gusts: a) The first method consists or averaging the exoess or defect of velocity u', (i e . the actual velocity  mean velocity) over a given time ~ t and oalculating the standaru deviation for suoh averaged velocity fluctuations. In order to explain the physical meaning of this method, let us take an exampl e. Assuming the mean velocity ;:.; 10 n;/sec, then 1 time interval or 6.t ,. 15 seo corresponds to a length o!' 150 m in the wind direction . Hence, if the average value of u' for the 15 seo period is found to be equal to 1.5 z;/seo, thie means that over the whole 150 m length, the wind volooi ty vm.s on the average 15 o/ o higher tl'l.8.n the mean velocity. Computing now the standard deviation for such "150 m segments", we obtain the "mean gustiness" experienced by a body of 150 m linear dimension. The rate or decrease o!' the standard deviation 1 U' 2 •vith the length of the eegments considered is a relative measure, whether more or lees gusts of considerable extension are present in the wind . Some of the oharaeteristio ourve~ are represented in Fig 8. These represent the four runs of July 12 and are der ived from the curves given in the preceding report . For the first three runs r epr esenting a wide range in stability , the curves fall very nenr to each other . These differ ences might be smoothed out if 7 records longer than 10 minutes were considered. If we consider a body 300 meters long, the curves ehow that in the stable atmosphere the standard deviation over thie range ie around 5060 o/ o of the value calculated f rom instantaneous values of the velocities. On the other hand, if the at mosphere is unstable the value rises to around 80 o/o. b) The sec\Jnd method used for the analysis is the computation of "correlation coeffici ents" between pairs of wind velocity values following each other in a certain constant time interval ~ t or, accor ding to our hypothesis, occurring simultaneousl y at t\vo points separated by the distance llx • u At in the mean vrind dir ection. The correlation coefficient is defined by the product or If 6 x is so small that the two points x and x + 6 x are practically always in t11e same gust a·nd havo the same vcl oci ty, the correlation coefficient will be nearly 1. If tho vel ooi ties u' x and U' x .,. fl x are independent, the oorrelation coefficient 1111 be zero. The occurrence of negative correlation ooeffioients is a sign for "wavy" or poriodica.1 oharaoter of' the gust distribution. Fig 9 s)lov1s the corr elation coefficients computed for the f ollowing runs: 1. 2 . 3. 4 . Date July 12 Oct ober 4 July 12 October 14 Run 1 4 1 Time 4:00  4: 10 AM 5 : 05  5 : 16 AM 9:51  10:01 _lli 3:38  3:48 PM h 84 83 85 81 .028 .001 .013 .017 u (o/seo) 8.2 8.3 6.1 6.8 The curves are repeated in Fig 10 with x • u ~t for abscissa. The comparison of the correlation curves of Figs 9 and 10 shows strikingly the incr ease of gust sizes with increasing instabil ity. Anot her feature of some of the correlation curves is sho~n in Fig 11 , where the computation of the oorrelation coefficient is carried out to a time interval of 6.t = 120 sec, corresponding to D>. x a 1000 m. The corresponding temperature lapse rate is f • 0.001 , • 8 indicating a medium degree of stability. The correlation curve shows two negative minima and two positive maxima with an average half' "wave length" of about 200  250 m. The correlation curves undoubtedly Give a proper measure for the relative size of the gusts or coher ent air masses. As f'ar as the absolute measure of their extension is concerned, some indioations can be given by caloulation of the correlation curve f or some idealized conditions: a) Let us assume that : velocity fluctuations of equal magnitude ooour in equal time intervals r , oorresponding to equal alternating gusts of the length i . The correspondine; correlation curve is shown in Fig 12 . The correlation is zero for A x • Q./2 and the length l is given by the distance between the origin and the location of the first negative minimum. The computation for a pure sine wave leads to a similar result. except that the train of straight lines is replaced by a oine curve. b) Let us assume now that ± velocity fluctuations of equal magnitude ocour , but the duration of the gusts is variable, the mean value of the duration being equal to ~ • In this case there is no periodicity in the distribution of the gusts, e.nd we assume that their distribution is of a purely statistical oharacter . The correlation coefficient can also be oaloulated in this case and the result is shown in Fig 13. The initial tangent to the ourve intersects the abscissa at the distance Ax• J*tm , where lm is the square root of' the mean value of the square of the lengths of the gusts. The tl\vidth of the correlation curve" corresponding to 50 o/o correlation is equal to .5 em· These idealized cases may give some idea of the actual size of the guats. For the stable oases given in Fig 10, the value of' A x for which tho correlation coefficient is 0.5 is 30 meters . This gives 60 meters forLm. For the unstable oases the values are Pm = 250 and 270 meters respectively. This seems to indicate that the predominant vmve lengths for the unstable cases is four or f'ive times that for the stable oases. If we estimate the gust length by means of the 9 method (a) (Fig 12) from the ourve of Fig 11 the indicated length of the longest gusts on the anemogram is around 260 meters. For the unstabl e cases , if any wave lengths were indicated by the ~~vinesa of the correlation curves, they are muoh longer and it wne not considered safe to carry out the oorrelatione in the tenminute reoorde of the time intervals neoessary to ehow up the wavy oharacter. Whether the waves indicated in Fig 11 are of thermoaerodynamic origin or are due to the topography of the country surrounding Akron oannot be deoided from the reoords available. Giblett 1) carried out some correlations along and aorosa the mean wind. The investigation invol ved the simultaneous recording of wind speed and direction at four stations, three of which were arranged in an equilateral t r iangle, the fourth bisecting the aide of the triangle in the direotion of the pr evailing wind. The instruments were fi1'ty feet above the ground. He finde correlation factors of 0.8 and 0.6 at distances of 360 and 700 feet respectively , in the direction 6 x of the mean wind for a time difference between the records equal to u , where u is the mean velocity and {lx • 360 and 700 feet respectively. The records were made under what were considered approxiimtely about 0.5, the distance bet ween stations being about 600 feet. Sinoe this correlation faotor has a high negative value, it wae concluded that the breadth of gusts was of the order of 600 feet. A calculation of the correlation factors from the records of one etati on shoVTed that a minimum factor was reached o.t 6 x • u At = 2000 feet. It "W&.8, therefore, oonoluded that under adiabatic conditions a class of gusts exists whose domiwind and orossvnnd di mensions are of the order of 5000 by 600 feet respectively. Giblett also carried out·a few correlations in the vertical direc't"Aon (between 60 feet and 40 feet and bet\veen 50 feet and 30 feet above the ground) . He finds correlation factors up to 0.94 between the simultaneous velocity . fluotuntions at 60 feet and 30 feet for the s~ble atmospher e. 10 Some measurements of crosswind and vertical correlation faotors in the lower six meters over flat meadow land were oarr1ed out by W Schmidt 3). The apparatus consisted of a frame 6 x 10 meters, with pressure plates arranged at vertical and horizontal distances of one meter. The deflection of the plates was recorded photographically as a function of the time. Analysi s of t he photographs gave a picture of the wind velocity as a function of the ti.nb:. at eaoh of the anemometer positions. He finds that, even at six meter s height, the crosswind correlation factors drop to 0.5 at such a relatively large distance as 5 meters. The vertical corr elation factors dropped to 0.5 over a distance or 2.6 meters (between 3.5 meters and 6 meters above the ground). If the analysis which led to Fig 13 is applied to the vertical and crosswind dimensions of the gusts, it would indicate that at a height of six meters the crosswind extent of the gusts ie about twice the vertical extent. A series of measurements of the cross sectional structure of the wind at high velocities was made by RH Sherlock 4). The apparatus consisted of one 250 foot tower, with anemometers at 50 foot intervals, and seven 50foot towers with anemometers at the top. The towers were arranged in a northsouth direction at intervals of 60 feet . The anemometers were of a special pressure plate type, and all wind velocities were recorded simultaneously by means of a 12element oso1llograph. The structure of the wind is r epresented by isovelooity lines as a function of the time and vertical or hori zontal distance. It is believed that the computation of correlation curves is a promising method for obtaining information on the relative size of gusts. S1nn1ltaneous measurements over a network of stations are obviously necessary if the extension of the gust in all three dimensione shall be measured. However, even t he one station measurements seem to reveal inter esting relations between gust size and stability of the atmosphere. It is believed that the statistical method of correlation coefficients leads further than the pure descriptive method of "gust formations." Sohmidt's and 11 Sherlock's isovelocity map and the interpretation of' gusts as "vortices" are very instructive, but the types of gust formations are so various that it is believed the Etatistical method is likely to yield easier quanti tative results of practical importance. S1111111ary: 1) The standard deviation at the top of the tower (8085 meters above the ground) was determined for different values of' the mean wind velocity (Fig 1). 2) The relative standard deviation was correlated with the temperature lapse rate for the three layers: 1030 m, 3060 m, 6090 m (Fig 2). The gustiness increases with lapse rate; the influence of the lapse rate is greatest in the 1030 m layer. 3) Statistical distribution of the wind speed fluctuations for various lapse rates com.po.red with the error law. The conclusion is that when the atmosphere is stable , the fluctuations are distributed approximately according to the error law. In the unstable atmosphere, essential deviations from the error law are shown (Figs 4, 6, and 6). 4) The averaged standard deviation was. calculated by averaging the flu~tuation velocities over time periods of various length (Fig 8). Putting A x = u Ot, 'vhere o t is the interval over vmioh the fluctuations are averaged, it is assumed that 6 x rNJ.y be interpreted as the linear dovmstream dimension of a body immersed in the flow, and the averaged fluotuation ae the mean gustiness experienced by suoh a body. The resul te show the reduction of the standard deviation as 6 x increases , e. g. then, for a body 300 meters long, if the atmosphere is stable, the apparent standard deviation is around 60 o/o of its value for a snall body. For the same body in an unstable atmosphere, the corresponding ratio is 80 o/o. 5) Correlations between the fluctuation velocities at a time t and those at a time t + At were carried out for several runs at the top of the tower and for several values of 6. t. Curves are given in Fig 9. It is assumed again that 12 the fluctuations measured at one point nt a time t will be approximately the same at a. time t ... ~t at o. point a distance A.,_ downstream, where A x • u At. The curves of Fig 9 are reproduced in Fig 10 , with Ax as abscissa . The linear dimensions of the gust in the wind direction is discussed, based on the oorrelati on curves. 6) In some oases of stable stratification, the curves have a definitely vte.vy character, indicating the existence of disturbanoea with wave lengths around 400500 meters. References 1) Giblett  Geophysical Memorandum. #54. 2) Best  Geophysical Memorandum #65. 3) W Schmidt  Journal of the Royal Aeronautical Society, May 1935 , p 365. 4) R ll Sherlock  Civil Engineering, June 1932, p 358. 12736 lf    • Al.RS ...... Al:.. z.o w to 0 4 8 12 f (, u (n/sEc) J?igur e 1 . Jependence b t~ce~ stan~ard deviation~ a~d meaP velocity at h = 85 meters. 0.3 .17: O.i:.. y 'f , ... l ( C'.1 ., "!  r ...~. .. r.,,., I L ' J •  / ()  ..J J ''I' ,L. r ...J ')  ....; 1  6 1 / • J._ / Cr 0 A  <" "'1J 1 1' I C /..._ r._ F/(, I_ 'f(£" Rel f t i vc standard deviation J u 1 2ju functio::: of the lapse rate 1 . in various layerc as T"l ·. .it.. VMF 1 ./)U!fAT/ON OF R£CC'R..D () .04 .6  .4 .2 0 u: .z .4 . '7 ti£Loc1 rY DEFE::.cr..( ...  u c; • ligur e 3 . Theor.tinal ~ist r ibution of fluctuati ons a ccording t o the pr obabi lity l o.vi . I Figure 4 . Distribution of velocity fluctuations . .3  .2  ./ .3 . / 0 . / I , ~ '·/ . .{ Ocf. ~ ,JJS Jt:'t 1 1:01 A1 I )"' : (".. "t t'> I ~ = ~ ..J ,~/c ~r. ; (/ i..( : < ·..:>I~ .... <..C . " .z 3 /.0 .9 .8 .7 .6 .s .4 .3 . 2. G Ourofion of Re ord . / .O'J .08 .07 . 05 .04 .03 .oz . 0/ 0 • 8 .02_ Dote • July }Z r:J July 12 l::J J vly 12. 0 Def 4 • DANI~ Al ') A~ Run Time ~ ~ ll. I 4'00 ·4:10 IJ.P'/. 84  .028 t3.2 2 ..5:os s: 15 A/1. 85  .014 7. S 3 7:5'18 :091111. 8 7 .0/0 19 I 5:os · 5 : 1.5 J/.ft1 ~3 .Oo/ 8 .3 '!<' • ~ ~ igure .., . Distribution of velocity fluctuations for four t s a.o ,... . e cases . .04 (~Ji .08 ./o r.1 .ttl 0 .BO .60 .'10 \ ,30 \ .20 \ \ .10 \ .08 . • O'I .02 \ \ \ \ \ Date aJu(y 12 •Oct. 1¥ 60cl:9 \ \ \ \. \ \ \ \ Run ~ I 2 \ \ 7ime ~ .9.:5/10: 01 AM as ..J:38.J:'l8PM 81 .J:'lo.J:SOPM ~s D 't' .oo .0/7 .011 a 6.S 6.8 9S Lf ll!} l) Fieure 6. ~ist ribution of velocity fluc+'l0 t inn~ for three unst!bl0 caf.:es. \ \ \ ..t. D ... ._ Fi5 ure 7 . Representation of a cust passing: the a.nemorr.eter. Dot~ Run Time ~ t' 1.0 •July 12.. I ~:IXJ'1.10 AH 8't .02" XJu/y Iii! ,z, .s:osS:JSAM 85 .01~ Cf)Juty 12 J 7."S"98:o9Al1 87 .010 . ' ~ &Ju{y IZ If 9:56/0;06Al1 8S ,0/3 .8 ...._ _. AI 1  lL~t ~ ..__A U't. ' ' .6 ' ' ' ~ .... ...,. ,:......_ ' ... ..................  . ....... ~ . ~ ........... , .... , .... . z 0 0 ~00 "00 6 00 8 00 1000 L1 X = U/Jt (!'1erER.5) Figure 8. Relative ~aLiard deviation as a function of the avora~ing interval A x . ,,. . f; «.. 8.Z 7.5" Jf.8 6./ A Dofe Time ( y /() Rvn AJvl_y /2, "/':oo  '1:10 AH I 8'f .OJ?.13 ' 00ct. ¥ J:os  s:1s Al1 d3 . 00/ \ aJu(y12 9:S/ 10:01 AM A/ 8.5 . 01.3 ·" :x Ocf. /JI J;JljJ: Jt& PH I di .017 \,\, '," ' "t "t+11t.6 ~'x,  "' U!~ \~ ~ \, )c' 'c:i..__ \ "' .............. , _A.~ .2, '~ t:\, "' . ' \ ~ ' ' ' ' ' ' ~ b ~ ' 0 0" ti 8 ' .2. .6 t (second.s) I Figure 9 . Correla.tio: c ... rvee over various time inter vals ~ t , or stable and unE abl cases. ' 0 "' ~.2 8.3 6.1 6.8 OafG Time Run ~ 'II"  /,0 u A Ju(y 12 'f:()O ¥.·10 AH I d'I .OZ8 8.Z \ t!J Oct. 'I s:os5:1.s AM 83 .001 lJ.J ~ eJvly 12 9:.51  10:01 AH 'I 85 .O/J 6./ .\ 8 x Ocf l'f J .:38:J:*J #1 I 81 . 017 6.8 \ \  \ \ \ \~ .6 hi '~ ' ~  Figure 10. The correlation curvoG  ~· .I. ~ Lgure 9 't:l plotted against /l x = u A~. ' ~ .¥ :."'. iJ: IJ.r • ' t; tttlt )C~ ":'~ IC.#2. • ' A"'et. .2 ' ')t ' "'' ' ,"' ' "'A '·"~ ~ • ·' 0 • , .¥  • lO • • .8 .6 . 2 0  ./ .2  .,3 .__ . ' ....... .¥ • Date e Ocf 'I~ 193.5 fr .001 £( 7ime " ·3 s:oss:1s AM Figure 11. Correlation curve carried out to Ax = 1000 meters , sho· ir'.g v·avy cha1~a.cter . 600 • 0 1000 tf .. .1 ~ • • 1.0 .8 «xu;fll?: .6 lJ.•">' .4 .2 0 • 4 • 6 • :8 :lo     ,._   ...........   • JlM ..  u • • 12. Anemoc: ram a.nd correlation euri.·c f'or gi_lst::: of equal ma 11jtucle a.nd ec1t1al •  • size. I'·  "1 : (/) ..,,. . 0 I • d H ,:,i, ,+ I'• c+ i:: c+ (!) ll .8 I  • . 2 .4  _ __ _... ___ 4_ ~~  U I .8 t.2 'X Figur e 13 . f\.nemogra1n and correlation curve for gus·ts of equ.o.1 a1n1)li tude but of ra)1dom size . /.>{, 2.o 28 I  • c
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Title  (Third) Report on Meteorological Activities at the DGAI (21836) 
Creator  Daniel Guggenheim Airship Institute 
Date Original  19360218 
Date Notes  19360218 
Description  This report covers the results of the meteorological research at the Daniel Guggenheim Airship Institute in Akron, Ohio for the third ninety days under U.S. Navy Contract No. 42090, of May 20, 1935, between the U.S. Navy Department and the California Institute of Technology. The present report is restricted to the problem of gustiness and had for its object a description of those aspects of the problem which have been attacked hitherto and the main results obtained to date in the present investigation. A few references to previous work by other investigators are included in order to coordinate the information available. 
Subject Terms 
Daniel Guggenheim Airship Institute University of Akron. College of Engineering United States. Navy Department California Institute of Technology Meteorology in aeronautics 
Location  Akron (Ohio) 
Type  Text 
Publisher  Daniel Guggenheim Airship Institute 
Digital Publisher  University of Akron. Archival Services 
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transcript  v V r I THIRD PROGRESS REPORT ON THE METEOROLOGICAL ACTIVITIES AT THE DANIEL GUGGE1lliEIM AIRSHIP INSTITUTE This report covers the resulte of the meteorological research at the Daniel Guggenheim Airship Institute for the third ninety days under U S Navy Contract No 42090, of May 20, 1935, between the US Navy Department and the California Institute of Technology. The present report is restricted to the problem of gustiness and hae for its object a deeoription of those aspects of the problem which have been attacked hitherto and the main results obtained to date in the preeent investigation. A few references to previous work by other investi~ators are included in order to coordinate the information available. It DD.1st be remarked that the experimental setup which has been described in detail in Reports l and 2 v.ras restricted to measurements of one component of the wind velocity and nt only one plaoe in a given period. In other words, the following paragraphs contain the information which oan be gained by the analysis of one anemogram correlated with corresponding measurement of the temperature lapse rate, i.e. the degree of stability of the atmosphere. The desirable extension of the observations to the measurement of three components and to simultaneous measurements over an extended area is described later in the report. l. Magnitude of the wind f luctuations: The gustiness can be ch.araoter1Eed in one way by the standard deviation taken over a certain period of the wind velocity from the mean value at a 6iven point. The standard deviation is defined as the square root of the mean value or the square of the fluctuations (u U} 2 , where ~ u ie the instantaneous velocity and u the mean velocity over the time. The fluctuation velocity is denoted by u' and the standard deviation by ~. Thia quantity l~S calculated for a large number of anemograme over from 2 to 10 minute 2 periods. The intermediate positions covered periods of from 2 to 10 m1nutea eaoh. Exclusive of several runs in vmioh the anemogrnm showed no perceptible fluctuations, the values of the standard deviation varied from 0.3 llf1eec to 2.4 m/sec for mean wind velocities between 2.3 i;lsec and 15.4 ny'seo. The standard deviation is alao expressed as n percentage of the mean velocity  oalled the r elative etandard deviation. The values varied between 5 o/o nnd 51 o/o. Values of the standard deviation at the top position show e. correlation with the corresponding mean velocities. The averages of the values of the standard deviation ~ere obtained for the ranges in mean wind velocity of 24, 46, 68, 810, etc, ~s ec . The results ~ plotted in Fig l, conform fairly well with a straight line through tho origin. In other words, the mean value of the relative standard deviation, averaged over all lapse rates, is approxinnt ely oonetant, independent of the mean wind velocity. This constant is about 0.11 for the records analyzed. A definite correlation was found between tho relative standard deviation and the temperature lapse rate. To show this correlation, the observations were grouped in the follovnng v.re.y: an average value was taken of the observations between 1030 m, 3060 m, 60 90 m height and for lapse ro.tes r <. 0' 0 <. r < 0.01 , 0.0.1. <. r <. 0.015 , 1 ) 0.015. 1 is equal to  dT/dh, where T is the temperature in degr ees Centigrade and h is the height in meters. It is known tha t the adinbntio condition corresponds to about l' • 0.010 C/m. The result of thie grouping is shown in Fig 2, in whioh the abaciseae of the plotted points is the mean lapse rate of the runs ooneider ed in the intervals given above . The runa in which there were no perceptible fluctuations were not included in the averaging. It will be observed that for each layer tho seoond point lie~ above and the third below the ourvee drawn. If more observations were available, these points would probably be brought closer to tho curves drawn. The fluctuations increase quite rapidly, especially in the lov1er layer, for 3 increasing instability. Even for the low l apse rates, the value f or 1030 mis 0.15, as against 0.11 for the 6090 m layer . This difference increaees until in the most unstable range the values are 0.29 and 0.18 respectively. 2. Statistioal distribution of gust intensities: It is an interesting question how far the distribution, i.e. the relative f requency of large and suall wind fluctuations , or strong and ·.veak gusts, fol lows the pure probability laws . If the deviation in 'rlnd velocity woul d oocur in a purely random fashion , the time in which the excess wind velocity is, say, between p and p + ~ p per cents of a the mean velocity would be proportional to 0 p , wher e Pm is the average ) P2m fluctuation • the relative standard deviation mentioned in the for egoing secti~n. Let us assume, for instance, that the mean relative standard deviation or t he mean relative gustiness is 20 o/o, then the total time in which the excess wind velocity is between 0 and 5 o/o, 5 and 10 o/o, 10 and 15 o/o , and so on , would be repreFented by tl1e curve in Fig 3. The actual distributions •vere comput ed from a number of anemogiam.s . One example is shown in Fig 4. The most convenient method of oomparing the statistical distribution with the pure probability distribution is by plotting the data on a special coordinate paper. The abscissa represents the r elative magnitude or the square of the fluetuation in linear scale, the ordinate, the logarithm of the time ratio. total period With respect to these axes the error law is represented by a straight line with tho inclination  , where  2 u• 2 p m :s u!! is the square of the relative standard deviation. Records showing large values of mean gustiness appear as f lat, those with small values of mean gustiness as steep lines. Distr ibutions following the error law appear as straight lines, points above the straight line show that certain particular gust intensities are preferredj points belO\v the straight line show t.hat the corresponding intensities appear lees frequently than should be expected accor ding to the error l aw. Fig 5 shows the diagrams oorresponding to the following observations: 4 Date Run Time h r u (ny'aec) July 12* 1 4:00  4: 10 AM 84 .028 8.2 July 12* 2 5: 05  5 : 15 AU 85 .014 7.5 July 12 3 7:69  8:09 Alf 87 .010 4.9 Oct 4 1 5: 05  5 : 15 AM 83 .001 8.3 In these curves the ordinate gives the time for which u '/u will duration of record be between ± 2.5 o/o from the value indicated by the abscissa. Fig 6 givee diagrams corresponding to the observations: Date a) July 12 b) Oct 14 c) Oct 9 Run 4 1 2 Time 9:51  10:01 .AJ.a 3:38  3:48 PM 3:40  3:50 PM h 86 81 86 .013 .017 .017 u (uy'eeo) 6.5 6.8 4.5 The points for run 4 of July 12 and run 2 of October 9 deviate most from the etraight line predicted by the error law. It is possible that longer records would smooth out the differences. Giblett 1) has plotted curves similar to those shown in Figs 3 and 4 for the mean accelerations of the 'vind over five seconds and also for the deviations from the mean direction at a height of 50 feet above the ground. He finds that the dictribution of t...hese components is approximately aooording to the error law. Best 2) ha3 obtained similar results for the velocity fluctuations in the immediate vicinity or the ground (up to 4 meters) . The measurements presented in this report are the first similar investigations, to our knowledge, at greater height. The general result of the analysis is that eapeoially when the atmosphere * The lapse rates given for runs 1 and 2 of July 12 are slightly different from those givon for the same runs in the preceding report. These corrected values wore obtained from a plot of the temperatures at the 30 and 80 meter levels against the time at whioh the inatrul'!lent was actually at that level for the four runs of that dnte. The lapse rate given is that for the time hnlfv.JB.y between the t\vo points corresponding to ea.oh run. Thie method \vas used to obtain the lapse rates for all runs made before the temperature difference instrument was installed. • 5 ia stable, the distribution or guetintensities conforms approxll:ntel y wit h the error law. Thia means practically, that the relative frequency of str ong and weak gusts is about the eame independent of mean wind velocity nnd mean guatineaa. Therefore, if the mean gustiness is known, it can be fairly well eatinnted in 'Nha·l; percentuge of a. total period considered , the wind velocity is likel y t o exceed n certain limit or be below a certain value. However, it must be emphas i zed that a.a yet nothing onn be said regar ding "how oft en" gusts of certa in i ntensity appear. This depends not only on the added sum or the time cl€11lents in whioh a certain intensity prevails, but on the average duration or an individual gust. This question has perhaps more practical importance than the statistical distribution itself, and 'vill be discussed in the next section. 5. Analysis of correlations. Duration and Size of gusts: It is believed that th~ time or duration of a certain gust at a given plnce depends on the size of more or less "coherent" e.ir masses. It is difficult to obtain reliuble infor mation about the average sizo of such :masses. The apparatus available in Akron did not allovr takinz simultaneous recor ds of the velooity componenta at various stations distr ibuted at distances along and across the menn flow. Ho\rever, quite valuable informution can be obtained by the analysis of a single anemogram,at l east as far as the size of the perturbations in the direction or the mean wind is concerned. To a firRt approximation the sequence of velooities as thoy are r ecorded at a fixed place correspond to the velocities occurring simultaneousl y up~tream, so the. t the velocity devi ation u' , 1mioh corresponds to the time Ii t, is of tho same order as the differ ence between velocities at two points separated by a distance A x. • u At, wi1ere t is tlle mean velocity. Henoe the duration of a certaln period of excessive velocity gives a measure for the linear extension of a col1erent uir maea 'vi th excessive velocity . To be sure, this reasoning neglects first the deformation or the air m.9.sses coneider~d ; second, their vertical and lateral motion. Unfortunately we know very little about the dero?'l!'~tion or 6 such "gusts"; however, observations show that their shape ohanges relatively slowly. As for the influence of the vertioal and lateral motion of gusts, it is believed that they do not affect materially the conclusions drawn from the anal ysis of the anemogram. In fact , if we compare two oases, assuming that a gust traverses the point of location of the anelilometer horizontally or under a slight inclination, the period in whioh the anemometer r ecords ahow higher or lower velocities will be only slightly changed. This is demonstrated in Fig 7, in which the gust is r epresented as elliptical. Whether the ms.ea passes the station along th~ direction a or b intr oduces only a amall error in its apparent size as judged from the anemogram. TVJO methods were used in order to obtain information on the average size of gusts: a) The first method consists or averaging the exoess or defect of velocity u', (i e . the actual velocity  mean velocity) over a given time ~ t and oalculating the standaru deviation for suoh averaged velocity fluctuations. In order to explain the physical meaning of this method, let us take an exampl e. Assuming the mean velocity ;:.; 10 n;/sec, then 1 time interval or 6.t ,. 15 seo corresponds to a length o!' 150 m in the wind direction . Hence, if the average value of u' for the 15 seo period is found to be equal to 1.5 z;/seo, thie means that over the whole 150 m length, the wind volooi ty vm.s on the average 15 o/ o higher tl'l.8.n the mean velocity. Computing now the standard deviation for such "150 m segments", we obtain the "mean gustiness" experienced by a body of 150 m linear dimension. The rate or decrease o!' the standard deviation 1 U' 2 •vith the length of the eegments considered is a relative measure, whether more or lees gusts of considerable extension are present in the wind . Some of the oharaeteristio ourve~ are represented in Fig 8. These represent the four runs of July 12 and are der ived from the curves given in the preceding report . For the first three runs r epr esenting a wide range in stability , the curves fall very nenr to each other . These differ ences might be smoothed out if 7 records longer than 10 minutes were considered. If we consider a body 300 meters long, the curves ehow that in the stable atmosphere the standard deviation over thie range ie around 5060 o/ o of the value calculated f rom instantaneous values of the velocities. On the other hand, if the at mosphere is unstable the value rises to around 80 o/o. b) The sec\Jnd method used for the analysis is the computation of "correlation coeffici ents" between pairs of wind velocity values following each other in a certain constant time interval ~ t or, accor ding to our hypothesis, occurring simultaneousl y at t\vo points separated by the distance llx • u At in the mean vrind dir ection. The correlation coefficient is defined by the product or If 6 x is so small that the two points x and x + 6 x are practically always in t11e same gust a·nd havo the same vcl oci ty, the correlation coefficient will be nearly 1. If tho vel ooi ties u' x and U' x .,. fl x are independent, the oorrelation coefficient 1111 be zero. The occurrence of negative correlation ooeffioients is a sign for "wavy" or poriodica.1 oharaoter of' the gust distribution. Fig 9 s)lov1s the corr elation coefficients computed for the f ollowing runs: 1. 2 . 3. 4 . Date July 12 Oct ober 4 July 12 October 14 Run 1 4 1 Time 4:00  4: 10 AM 5 : 05  5 : 16 AM 9:51  10:01 _lli 3:38  3:48 PM h 84 83 85 81 .028 .001 .013 .017 u (o/seo) 8.2 8.3 6.1 6.8 The curves are repeated in Fig 10 with x • u ~t for abscissa. The comparison of the correlation curves of Figs 9 and 10 shows strikingly the incr ease of gust sizes with increasing instabil ity. Anot her feature of some of the correlation curves is sho~n in Fig 11 , where the computation of the oorrelation coefficient is carried out to a time interval of 6.t = 120 sec, corresponding to D>. x a 1000 m. The corresponding temperature lapse rate is f • 0.001 , • 8 indicating a medium degree of stability. The correlation curve shows two negative minima and two positive maxima with an average half' "wave length" of about 200  250 m. The correlation curves undoubtedly Give a proper measure for the relative size of the gusts or coher ent air masses. As f'ar as the absolute measure of their extension is concerned, some indioations can be given by caloulation of the correlation curve f or some idealized conditions: a) Let us assume that : velocity fluctuations of equal magnitude ooour in equal time intervals r , oorresponding to equal alternating gusts of the length i . The correspondine; correlation curve is shown in Fig 12 . The correlation is zero for A x • Q./2 and the length l is given by the distance between the origin and the location of the first negative minimum. The computation for a pure sine wave leads to a similar result. except that the train of straight lines is replaced by a oine curve. b) Let us assume now that ± velocity fluctuations of equal magnitude ocour , but the duration of the gusts is variable, the mean value of the duration being equal to ~ • In this case there is no periodicity in the distribution of the gusts, e.nd we assume that their distribution is of a purely statistical oharacter . The correlation coefficient can also be oaloulated in this case and the result is shown in Fig 13. The initial tangent to the ourve intersects the abscissa at the distance Ax• J*tm , where lm is the square root of' the mean value of the square of the lengths of the gusts. The tl\vidth of the correlation curve" corresponding to 50 o/o correlation is equal to .5 em· These idealized cases may give some idea of the actual size of the guats. For the stable oases given in Fig 10, the value of' A x for which tho correlation coefficient is 0.5 is 30 meters . This gives 60 meters forLm. For the unstable oases the values are Pm = 250 and 270 meters respectively. This seems to indicate that the predominant vmve lengths for the unstable cases is four or f'ive times that for the stable oases. If we estimate the gust length by means of the 9 method (a) (Fig 12) from the ourve of Fig 11 the indicated length of the longest gusts on the anemogram is around 260 meters. For the unstabl e cases , if any wave lengths were indicated by the ~~vinesa of the correlation curves, they are muoh longer and it wne not considered safe to carry out the oorrelatione in the tenminute reoorde of the time intervals neoessary to ehow up the wavy oharacter. Whether the waves indicated in Fig 11 are of thermoaerodynamic origin or are due to the topography of the country surrounding Akron oannot be deoided from the reoords available. Giblett 1) carried out some correlations along and aorosa the mean wind. The investigation invol ved the simultaneous recording of wind speed and direction at four stations, three of which were arranged in an equilateral t r iangle, the fourth bisecting the aide of the triangle in the direotion of the pr evailing wind. The instruments were fi1'ty feet above the ground. He finde correlation factors of 0.8 and 0.6 at distances of 360 and 700 feet respectively , in the direction 6 x of the mean wind for a time difference between the records equal to u , where u is the mean velocity and {lx • 360 and 700 feet respectively. The records were made under what were considered approxiimtely about 0.5, the distance bet ween stations being about 600 feet. Sinoe this correlation faotor has a high negative value, it wae concluded that the breadth of gusts was of the order of 600 feet. A calculation of the correlation factors from the records of one etati on shoVTed that a minimum factor was reached o.t 6 x • u At = 2000 feet. It "W&.8, therefore, oonoluded that under adiabatic conditions a class of gusts exists whose domiwind and orossvnnd di mensions are of the order of 5000 by 600 feet respectively. Giblett also carried out·a few correlations in the vertical direc't"Aon (between 60 feet and 40 feet and bet\veen 50 feet and 30 feet above the ground) . He finds correlation factors up to 0.94 between the simultaneous velocity . fluotuntions at 60 feet and 30 feet for the s~ble atmospher e. 10 Some measurements of crosswind and vertical correlation faotors in the lower six meters over flat meadow land were oarr1ed out by W Schmidt 3). The apparatus consisted of a frame 6 x 10 meters, with pressure plates arranged at vertical and horizontal distances of one meter. The deflection of the plates was recorded photographically as a function of the time. Analysi s of t he photographs gave a picture of the wind velocity as a function of the ti.nb:. at eaoh of the anemometer positions. He finds that, even at six meter s height, the crosswind correlation factors drop to 0.5 at such a relatively large distance as 5 meters. The vertical corr elation factors dropped to 0.5 over a distance or 2.6 meters (between 3.5 meters and 6 meters above the ground). If the analysis which led to Fig 13 is applied to the vertical and crosswind dimensions of the gusts, it would indicate that at a height of six meters the crosswind extent of the gusts ie about twice the vertical extent. A series of measurements of the cross sectional structure of the wind at high velocities was made by RH Sherlock 4). The apparatus consisted of one 250 foot tower, with anemometers at 50 foot intervals, and seven 50foot towers with anemometers at the top. The towers were arranged in a northsouth direction at intervals of 60 feet . The anemometers were of a special pressure plate type, and all wind velocities were recorded simultaneously by means of a 12element oso1llograph. The structure of the wind is r epresented by isovelooity lines as a function of the time and vertical or hori zontal distance. It is believed that the computation of correlation curves is a promising method for obtaining information on the relative size of gusts. S1nn1ltaneous measurements over a network of stations are obviously necessary if the extension of the gust in all three dimensione shall be measured. However, even t he one station measurements seem to reveal inter esting relations between gust size and stability of the atmosphere. It is believed that the statistical method of correlation coefficients leads further than the pure descriptive method of "gust formations." Sohmidt's and 11 Sherlock's isovelocity map and the interpretation of' gusts as "vortices" are very instructive, but the types of gust formations are so various that it is believed the Etatistical method is likely to yield easier quanti tative results of practical importance. S1111111ary: 1) The standard deviation at the top of the tower (8085 meters above the ground) was determined for different values of' the mean wind velocity (Fig 1). 2) The relative standard deviation was correlated with the temperature lapse rate for the three layers: 1030 m, 3060 m, 6090 m (Fig 2). The gustiness increases with lapse rate; the influence of the lapse rate is greatest in the 1030 m layer. 3) Statistical distribution of the wind speed fluctuations for various lapse rates com.po.red with the error law. The conclusion is that when the atmosphere is stable , the fluctuations are distributed approximately according to the error law. In the unstable atmosphere, essential deviations from the error law are shown (Figs 4, 6, and 6). 4) The averaged standard deviation was. calculated by averaging the flu~tuation velocities over time periods of various length (Fig 8). Putting A x = u Ot, 'vhere o t is the interval over vmioh the fluctuations are averaged, it is assumed that 6 x rNJ.y be interpreted as the linear dovmstream dimension of a body immersed in the flow, and the averaged fluotuation ae the mean gustiness experienced by suoh a body. The resul te show the reduction of the standard deviation as 6 x increases , e. g. then, for a body 300 meters long, if the atmosphere is stable, the apparent standard deviation is around 60 o/o of its value for a snall body. For the same body in an unstable atmosphere, the corresponding ratio is 80 o/o. 5) Correlations between the fluctuation velocities at a time t and those at a time t + At were carried out for several runs at the top of the tower and for several values of 6. t. Curves are given in Fig 9. It is assumed again that 12 the fluctuations measured at one point nt a time t will be approximately the same at a. time t ... ~t at o. point a distance A.,_ downstream, where A x • u At. The curves of Fig 9 are reproduced in Fig 10 , with Ax as abscissa . The linear dimensions of the gust in the wind direction is discussed, based on the oorrelati on curves. 6) In some oases of stable stratification, the curves have a definitely vte.vy character, indicating the existence of disturbanoea with wave lengths around 400500 meters. References 1) Giblett  Geophysical Memorandum. #54. 2) Best  Geophysical Memorandum #65. 3) W Schmidt  Journal of the Royal Aeronautical Society, May 1935 , p 365. 4) R ll Sherlock  Civil Engineering, June 1932, p 358. 12736 lf    • Al.RS ...... Al:.. z.o w to 0 4 8 12 f (, u (n/sEc) J?igur e 1 . Jependence b t~ce~ stan~ard deviation~ a~d meaP velocity at h = 85 meters. 0.3 .17: O.i:.. y 'f , ... l ( C'.1 ., "!  r ...~. .. r.,,., I L ' J •  / ()  ..J J ''I' ,L. r ...J ')  ....; 1  6 1 / • J._ / Cr 0 A  <" "'1J 1 1' I C /..._ r._ F/(, I_ 'f(£" Rel f t i vc standard deviation J u 1 2ju functio::: of the lapse rate 1 . in various layerc as T"l ·. .it.. VMF 1 ./)U!fAT/ON OF R£CC'R..D () .04 .6  .4 .2 0 u: .z .4 . '7 ti£Loc1 rY DEFE::.cr..( ...  u c; • ligur e 3 . Theor.tinal ~ist r ibution of fluctuati ons a ccording t o the pr obabi lity l o.vi . I Figure 4 . Distribution of velocity fluctuations . .3  .2  ./ .3 . / 0 . / I , ~ '·/ . .{ Ocf. ~ ,JJS Jt:'t 1 1:01 A1 I )"' : (".. "t t'> I ~ = ~ ..J ,~/c ~r. ; (/ i..( : < ·..:>I~ .... <..C . " .z 3 /.0 .9 .8 .7 .6 .s .4 .3 . 2. G Ourofion of Re ord . / .O'J .08 .07 . 05 .04 .03 .oz . 0/ 0 • 8 .02_ Dote • July }Z r:J July 12 l::J J vly 12. 0 Def 4 • DANI~ Al ') A~ Run Time ~ ~ ll. I 4'00 ·4:10 IJ.P'/. 84  .028 t3.2 2 ..5:os s: 15 A/1. 85  .014 7. S 3 7:5'18 :091111. 8 7 .0/0 19 I 5:os · 5 : 1.5 J/.ft1 ~3 .Oo/ 8 .3 '!<' • ~ ~ igure .., . Distribution of velocity fluctuations for four t s a.o ,... . e cases . .04 (~Ji .08 ./o r.1 .ttl 0 .BO .60 .'10 \ ,30 \ .20 \ \ .10 \ .08 . • O'I .02 \ \ \ \ \ Date aJu(y 12 •Oct. 1¥ 60cl:9 \ \ \ \. \ \ \ \ Run ~ I 2 \ \ 7ime ~ .9.:5/10: 01 AM as ..J:38.J:'l8PM 81 .J:'lo.J:SOPM ~s D 't' .oo .0/7 .011 a 6.S 6.8 9S Lf ll!} l) Fieure 6. ~ist ribution of velocity fluc+'l0 t inn~ for three unst!bl0 caf.:es. \ \ \ ..t. D ... ._ Fi5 ure 7 . Representation of a cust passing: the a.nemorr.eter. Dot~ Run Time ~ t' 1.0 •July 12.. I ~:IXJ'1.10 AH 8't .02" XJu/y Iii! ,z, .s:osS:JSAM 85 .01~ Cf)Juty 12 J 7."S"98:o9Al1 87 .010 . ' ~ &Ju{y IZ If 9:56/0;06Al1 8S ,0/3 .8 ...._ _. AI 1  lL~t ~ ..__A U't. ' ' .6 ' ' ' ~ .... ...,. ,:......_ ' ... ..................  . ....... ~ . ~ ........... , .... , .... . z 0 0 ~00 "00 6 00 8 00 1000 L1 X = U/Jt (!'1erER.5) Figure 8. Relative ~aLiard deviation as a function of the avora~ing interval A x . ,,. . f; «.. 8.Z 7.5" Jf.8 6./ A Dofe Time ( y /() Rvn AJvl_y /2, "/':oo  '1:10 AH I 8'f .OJ?.13 ' 00ct. ¥ J:os  s:1s Al1 d3 . 00/ \ aJu(y12 9:S/ 10:01 AM A/ 8.5 . 01.3 ·" :x Ocf. /JI J;JljJ: Jt& PH I di .017 \,\, '," ' "t "t+11t.6 ~'x,  "' U!~ \~ ~ \, )c' 'c:i..__ \ "' .............. , _A.~ .2, '~ t:\, "' . ' \ ~ ' ' ' ' ' ' ~ b ~ ' 0 0" ti 8 ' .2. .6 t (second.s) I Figure 9 . Correla.tio: c ... rvee over various time inter vals ~ t , or stable and unE abl cases. ' 0 "' ~.2 8.3 6.1 6.8 OafG Time Run ~ 'II"  /,0 u A Ju(y 12 'f:()O ¥.·10 AH I d'I .OZ8 8.Z \ t!J Oct. 'I s:os5:1.s AM 83 .001 lJ.J ~ eJvly 12 9:.51  10:01 AH 'I 85 .O/J 6./ .\ 8 x Ocf l'f J .:38:J:*J #1 I 81 . 017 6.8 \ \  \ \ \ \~ .6 hi '~ ' ~  Figure 10. The correlation curvoG  ~· .I. ~ Lgure 9 't:l plotted against /l x = u A~. ' ~ .¥ :."'. iJ: IJ.r • ' t; tttlt )C~ ":'~ IC.#2. • ' A"'et. .2 ' ')t ' "'' ' ,"' ' "'A '·"~ ~ • ·' 0 • , .¥  • lO • • .8 .6 . 2 0  ./ .2  .,3 .__ . ' ....... .¥ • Date e Ocf 'I~ 193.5 fr .001 £( 7ime " ·3 s:oss:1s AM Figure 11. Correlation curve carried out to Ax = 1000 meters , sho· ir'.g v·avy cha1~a.cter . 600 • 0 1000 tf .. .1 ~ • • 1.0 .8 «xu;fll?: .6 lJ.•">' .4 .2 0 • 4 • 6 • :8 :lo     ,._   ...........   • JlM ..  u • • 12. Anemoc: ram a.nd correlation euri.·c f'or gi_lst::: of equal ma 11jtucle a.nd ec1t1al •  • size. I'·  "1 : (/) ..,,. . 0 I • d H ,:,i, ,+ I'• c+ i:: c+ (!) ll .8 I  • . 2 .4  _ __ _... ___ 4_ ~~  U I .8 t.2 'X Figur e 13 . f\.nemogra1n and correlation curve for gus·ts of equ.o.1 a1n1)li tude but of ra)1dom size . /.>{, 2.o 28 I  • c 



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