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KNOTT BUILDING, DAYTON, 2, OHIO1 NCLASSI Fl E D[!UNLA

W H l

Aw.A

THE ROTATING ARM RESOLVING ANEMOMIETER

'4 Office of Naval Research Navy DepartmniotContract N7 onm-48705 PoetN 8-1

I Technical Report No. 2

:~A. K N Project 59 - Reference 54-56TI j, Arold H. Glaser

August 1954

Research Conducted 1hra-.-gh the

~~e ~ ~CasX1 A.L4./Narh ?M 0atoCOLLEGE STATION, TEXAS

Oll

JM ;iiii~ll I'i i

`I

THE AGRICULTURAL AND MECHANICAL COLLEGE OF TEXASDepartment of Oceanography

College Station, Texas

Research conducted through the

Texas A & M Research Foundation

Technical Report No. 2

A&M Project 59 Reference 54-56T

THE ROTATING ARM RESOLVING ANEMOMETIE

by

Arnold H. Glaser

August 195.4

The research reported in this document has been made possiblethrough support and sponsorship extended by the Office of NavalResearch under Contract N7onr-48705, NR No. 082-ill. It ispublished for technical information only, and does not neces-

Ik sarily reprs-ent recommendations or conclusions of the sponsor-ing agency.

John C. Freeman, Jr., Project Supervisor

5I

/:. !I

THE AGRICULTURAL AND MECHANICAL COLLEGE OF TEXASDepartment of Oceanography

College Station, Texas

Research conducted through the

Texas A & M Research Foundation

Technical Report No. 2

A&1 Project 59 Reference 54-56T

THE ROTATING ARM RESOLVING ANEMOMETER

by

Arnold H. Glaser

August 1954

The research reported in this document has been made possiblethrough support and sponsorship extended by the Office of NavalResearch under Contract N7.nr-48705, NM No. 082-111. It ispublished for technical information only, and does not neces-sarily reprezent recommendations or conclusions of the sponsor-ing agency.

John C. Freeman, Jr., Project Supervisor

K.

CONTENTS

Page

I. Introducticn 1

II. Principle of Operation 3

A. Some Aerodynamic Properties of the Cylinder 3

B. The Rotating Arm 4

C. Obtaining the Wind Velocity 5

D. The Shearing Stress 6

E. Effect of Cross Wind 7

F. Conclusion 8

III. Mechanical Features 9

IV. Electronic Circuitry 30

V. Performance 13

A. Geaeral 13

B. L1t Winds 13

C. Comparison with Other Instruments 14

VI. Proposed Future Development 14

A. Fluameter 14

B. Counter Rotating Aizs System 14

VII. Concluding Remarks 15

I. Introduction

An instrument that can resolve the instantaneous motion at a

point into components, or equivalently, indicate the vector direction and

magntude of -the instantaneous wind is of great utility in the study of

the details of the structua'e of tux~oulent motion in the atmosphere and

czean. Tim:e constants should be cufficiently short to permit the re-

solution of at least the significant range of turbulent eddies (Inoue 1954).

Instruments of this type have their greatest utility, apart from

est:Lates of the statistical properties of the turbulent velocity field,

in studies of the vertical flux of heat, moisture) or momentum. These

aro oLttined throueh the relation

F= pw9

whocre F is t',e vertical flux of the intensive property C, ,

instantaneous vertical component of the wind velocity, and the bar in-

dicates averaginr over a period of time sufficiently great to assure

reprezentation of significant eddy sizes (Swinbank, 1951; MacCready,

1953b).

Two types of in.strument have previously emerged that at least

pa:-tially satisfy the requirements of rapid response and vector resolu-

tion. One is based on the use of the bi-directional vane (Mazzarelia,

1952; Gill, 1954b) to dete-n=ne the direction of the flow and a fast re-

sponse w-emometer of some type (Parson and Bunker, 1952; Gill, 1954a).

Velocity components are obtained by appropriate trigonometric calcula-

tiozis. _This tpe of instrument tends to be hampered by the rather com-

plex response of the bivane system.

A �, . • . •: :

The other type in use makes use of geometric combinations of hot

wire type instruments to determine both direction and velocity. (Shiotani,

1950 Swinbank, 1951; MacCready, 1953a). This type 1has the advantage

of cxcellent speed of response, but it is somewhat difficult to make the

indications of the instrument independent of atmospheric temperature.

Nearly all of these systems suffer from the basic non-iinearity

of the indicating system. Calculation of the flux of a p-ope:lty from

eq1lation (1) calls for the recording of the various instrument outputs,

reading from the charts at very close intervals of time, conversion of

* the non-linear indication to the actual value, performing the trifono-

metric resolution, and finally the multiplication and integration in-

dicated. If one is seeking the contribution of eddies of 0.1 second

rassage time, thiis process must be repeated each 0.05 second. Evalua-

tion of even a 5-.minute run becomes a sizeable task.

The extreme amount of calculation required makes it desirable to

use some foim of automatic calculation, either analog or digital, to

"pe.•miat somewhat more extended observations. Digital calculation can

cope with the non-linearity of rapid response instruments, but the prob-

* len of sufficiently rapid digitizing of all the quantities has not yet

been met by simple means. Analog computers offer more promise of satis-

factory performance without undue complication. Various analog methods

have been adopted to linearize the indication of hot-.ire instruments.

Parson and Bunker (1952) used a servo-operated cam system, while

MacCready used a some-what complex electronic system. Neither system gave

the flux without further cor.mputation.

* The original concept of the instrument to be described arose during

a discussion with Professor V. E. Suomi of the University of W'-isconsin

while the author was employed on an 'Air Force Cambridge Research Center

S2-

project urder Professor Suo.i. Detailed development of the princinles

and design of tl.e instrimuent ax.d computers was done by thl. present

project.

This cner:o.eter systCm was desigtred to operate directly with an

aualorg ce OrPute'" to g'ive intfC:&tcd vCAluus of the vertical flux of heat,

mn-osture, and rzomcntur. It is iLftended for continuous ope-.-ation, with

average vclues of the f.Luxes presented .eriodically, although instantane-

ous values of any of the meas*ued quantities are readily available. The

anemoueter offers linea:ity a-±d i'tLggedciess in return for some increv.se

in complication awd some aniomalies of function that will be described

S. later.

II. Princinle of Opei-ation

A. Some aeiodyna.ic prope;'ties of the cylinder

Let us exornine some of the aerodynamic pý-cperties cf the circular

cylinder. if a cylinder be plpced in a flow with its axis peipendicular

to tae direction of flow, it can be sho.;n (Milne - Thomson, 19w0, p. 152)

that the pressute distribution about the cylinder for the case of non-

viscous irrotational flow is

1/2 -r T/ ? (1- 4 sin 2F) (2)

where p is the i.:reksure rt the surface of the cylinder, i is the

static pre.,ure, pis the air density, U is the free-stream velocity,

anr i is the angle between the radius to the poit at the surface and

the direction of the flow.

Otservation shows (Mlilne-Thonrpson, 1950, IP. 152) that in real

viocous flow:s, the pressure distribution about the forward part, within

about 300 of the flow di'-ection, approximates the theoretical distribution.

* -3•-

~•.,

The pressure distribution ,.hows little r'elation to the theoretical over

the rcst of the surface of the cyllnder.

If the axis of the cylinder be inclined to the direction of the

flow, we find, in theory, that the flow may be resolved into two compo-

nur'tc. one clong the cylindler, producing no change of pressure at the our-

face of the cylinder; the other perpendicul.ar to the cylinder, producing

the pressure distribution of equation (2) but with TT now replaced by

Un - tile normal componcrt of flow. 'While experimental data is not

re.dily available; it does apPear' that this resolution is achieved v.rith

some accuracy over the region of validity of equation (2), particularly

if the flow strikes the cylinder at near right angles.

B. The Rotatln. irra

Let us take a cylinder such as we have described and rotate it

abcut an af4s i:ePc-jnicular to the axis of the cylinder (Figure 1). Let

the axis of rotation be hoi'izontal, and let the direction of the mean

wind lie in the plane of rotation of the cylinder. At time t, the

cylinder, being rotated with vmngular velocity W•, is at an angle Q to

V•{, the horizontal. i.t the samie time, the projection V of the w.rind vector

*- • on the plane of rotation makes an angle U with the horizontal, a

being positive for winds with an upw..ard comnponent, ' small pressure hole

is located on the leading edge of the cylinder at distance R from its

a;is of ro'at.on.

Le- us fo-' the i..omnent ignore winda out of the plane of rotation

of the c.ilinder. In FiGure 1, the component of the wind normal to the

cyliinde i.-

"Vn V sin(Q a)

-4

FIGURE I

0kI

'K\

.o

'S"

e wt

ROTATING ARM ANEMOMETERSCHEMATIC

If we let 0 = wt(arm horizontal at t = W), the pressure on

the hole will be given by

p+ V]n 2 + V sin .(Wt =o)]

ia [LU21j2 2wRV sin c cos wt + 2twRV cos or sin Wat +

V2 V2 V2

V- V Cos 20ccos 2ct - 2 sin 2cosin 2wt2

It will be noted that aside from non-periodic terms, first and

second harmonlic terms are present, the first harmonic terms linear in

V, the second harmonic quadratic. It is of interest to note that the

first harmonic is a linear measure of wind speed; it is from this that

the power of this method is derived.

The pressure present at the pressure hole may be piped down hollow

shafting and converted to an alternating voltage by an appropriate pressure

transducer. Some attention must be paid to the ducting to avoid attenua-

tion of the pressure wave. Since the pressure hole is necessarily small,

it is essential that the amount of air movement through the hole be kept

as slight as possible to prevent serious pressure drops at that point.

This is accomplished principally by the use of a transducer with a stiff

diaphragm. Compressibility effects are negligible unless the ducting has

large volume. Resonance is avoided by keeping the duct shorter than a

quarter-wave organ pipe of the highest frequency to be measured.

Ixa-ne voltage output of the trazsducer will beA p, where R is the

appropriate factor of proportionality.

C. Obtaining the wind velocity

A number of methods may be used to recover the wind velocity'-.

Filtering is the most obvious, but does not easily permit the recovery of

p 5

the angle of the wind. The method chosen here is phase rectification,

which makes use of the familiar orthogonality principles:"•/ O• (5)

Lim 1 sinat siulbtdt Lir cos at cos bt dt O (a b)

and Lim inat cos bt dt= 0

Lm 1 2Lim 1j 2Li sin2at dt cooatdt(6)

S j

so that if we zuultiply/tp from (3) electrically by sin iut and obtain

an average, we haeve

. *,i/P s!nut dt 2 I ,•P,(Vcos.) (7)

The approximation impro-res with increase of averaging time *-', but if the

spectra of V and o- 6o not contain significant harmonic components of

frequency •' the approximation is excellent after a very few cyces.

The quantity V coso- will be recognized as the horizontal com-

ponent of the wind velocity in tue p:.ane of rotation of the cylinder. If

we muitiply/, p by cos wt and integrate, we have

r c cos t dt = wR(Vsin.) (8)

where the quantity V sin o4 is the vertical component of the wind velocity.

The Lorizontal and vertical components may be separately recorded.

D. Th-e Shearing Str'ecs

A rather surprising feature of the instrument appears if we iso-

late the second haimonic coiisponent of the pressure signal by multiplying

by sin 2 cj t and aveo'aging:

Tp sin 2wt dt-"'O- sin 2 (9)

o 6

Since V2 sin 2e= 2 V2 sin ae cos c,

rin 2wt dt - o p(V sinc) (V cosc) 2o

where -,uw will be recognized as the shearing stress or the vertical

flux of horizontal riementum. Because of calibration difficulties, this

relation has not yet been exploited, but it is planned to do so at the

earliest opportunity.

E. Effect of cross wind

SThus far it has been assumed that the wind is in the plane of ro-

tation of the cylinder. In General, the wind will have an additional

componcnt perpendicular to the plane of rotation. It would be desirable

that the instrument ignore this component, so that direct readings of u

end w may be obtained. It can readily be seen that this condition would

be satisfied if equation (2) readPd x=1 2 2 (1- 3t u I 09 O (c)

d. 2

This differs from equation (2) by

P 1 - U2 su2 (12)2

or fractionally,

'2 = -. tan2 1 (13)Pd -

Shas its maxinum value when the cylinder is retreating with the

wind

t:an fmax 4v (l).R -V

where v is the cross-com.onent of the wind, the other notation as before.

The minimum value is found where the: cylinder is advancing into the wind

tan .inn .R(15)

"-7-

It will be seen that this varyi4 p gives rise to a spurious

pressure alternation of amplitude approximatelV

t~'I~ "'R [(~ 2V)2 (WR +V)2 +v ]=R vt + V2 + v2)2] (16)

and of the same phase (but opposite sign) as the first harmonic oWRV.

In a typical case, we may take

V=a = 0. 3 V (Friedman, 1953) (17)

Then the bracketed quantity in equation (16) has the value .053,

corresponding to a decrease in instrument response of some 5%.

While this quantity is by no means insignificantp, it cannot be con-

sidered as a source of major error.

F. Conclusion

It will be seen from the foregoing that the principle of operation,

while perhaps somewhat involved trigonometricaliy, is reasonably straight-

*! forward. Perhaps the most attractive feature of the instrument is its en-

forced linearity of operation; any non-linearity appearing at any point in

the alternating pressure or voltage system appears as a higher harmonic,

and is rejected by the rectification system. Tests of the system have

shown such false higher harmonics to be insignificant in magnitude.

i -8-

-. - - .. O-S

III. Mechanical Features

The first model of the resolving annemorticter, which forms the subject of

this report, was rather elementary in construction and perhaps somewhat crude.

It consisted of an angJle iron frar.ework supporting the rotating arm

mcchanisrn at 120 cm from the ground. It was oriented into the mean wind by

hazd. The m.echanism was dcsigne" to rotate a short arm at 1500 rpn. This

rmlatively high rate of rotation was chosen because of the convenience of the

25 cycles per second fi'equenc, produced and because of the availability of

stendard 25 and 50 cycle components for computational use.

Details of const:-uction"

(1) A hollow shaft (one-,ie.lf inch outside diameter) supported by bear-

ings at each end. with provision for mounting the rotating arm at the center

of the shaft.

(2) One of the bear'ings forms a rotating shaft seal to permit trans-

mission of the pressure to a stationary pressure transducer.

(3) Drive shafting and gearing to peimit rotation of the shaft by a

rather bulky icotor without interference with the air stream. The right-

angle kea.Jing was through unenclosed spiral miter gears, speed reduction at

the n.otor through unenclosed fiber and steel spur gears. Rates of rotation

were somewhat excessive for this type of gearing, and it was found impossible

to keep e.en special coxn-picher grease on them. As a result they howled

diszressingly, although wear did not seeri serious.

(4) Generator to produce the necessary reference voltage at phases

fixed w-ith respect to the position of the rotating arm. An Electric

Indicator Co. type F-16 A-C rate generator was used, providing two alter-

natJng voltages of excellent harmonic purity and quite accurately in quad-

rature with each other. This was geared to the drive motor to produce a

- 9

frequency of 25 cycies per second. Provision was made for rotational

adjustment of the body of the generator to permit accurate phasing.

(5) Drive motor, Bodine synchronous type USY-55, 1/8 h.p. A

synchronous motor was chosen to permit accurate maintenance of rate of

rotation, so that calibration would be as stable as possible and rotational

transients would be minimized. The sjnclronous motor is consi.derably bulkier

than an ordinary A-C motor of the same power, and somewhat noisier.

(6) Pressure transducer, Statham Laboratories Model P58-0.15D-i400,

chosen for its sunsitivity and its high resonant frequency (275 cps), which

permits it to follow the relatively high frequenoy alternating pressure

(25 and 10 cps) without c;,tt•..uation or distortion. The transducer was

shockmounted together with its preanplifier and connected to the rotating

pressure joint by a short length of stiff plastic tubing. The total pneu-

matic circuit was about 40 cm in length, which coapares quite favorably w.rith

the 166 cm lengtii of a 50-cycle 1/4-wave organ pipe.

(7) The rotating arm itself. A number of different configurations

were tried, but none seemed any more effective than a simple cylindrical

tube of 3 16 inch outside diameter, 15 cm in length, with a .045 inch hole

drilled about 12 cm from the axis of rotation. This produced a circum- -

'ferertial speed of the pressure hole of just under 20 m isecond at a rota-

tional rate of 25 rps.

The total ensemble was somewhat bulky and distinctly noisy in

operation. An improved model, under construction at the time of this report,

will have better characteristics.

IV. Electronic Circuitri

* A wide range of electronic circuits may be used, probably with equal

success, to reduce the electrical output of the pressure transducer

- 10 -

'I""

_ _ _ _ _ -

(equation If) to the desired form for recording. Each must perform the

folloviiig orexrations:

(1) Amplification of the relatively weak signeal from the pressure

transducer.

(2) Phase demodulation. This is essentially multiplication by the

a_,propriate trigonometric function. (See equation (7)).

(3) Integration. This may be an actual integration, but resistance-

capacitance pseudo-integration is far riore convenient for purposes of in-

d:*.cation. The time constant of the resistance-capacitance integrator estab-

lishes the effective time constant of the instrtmient.

Al•,i. circuits that have been used in this first model are quite

standard and 'rilL no• be reproduced here. Figure 2 gives a block diagram

of the sstem.

The pressure transducer is of a strain-gauge bridge type, producing

a sigrnal of the oider of a few millivolts. ,2.plification brings it up to a

few volts amplitude.

The phuse rectifiers chosen were of the type using addition of

voltag4es at the grids of a paIr of push-pull cathode follow;ers. This type

of rectifier niuitiplies the input signal by *:hat is essentially a square

wave i-ather than by a sine function. A square iave is composed only of

odd harmonics, so that there is nothing in the input signal that will pro-

duce spurious reuponse. Any odd harmonics generated by harmonic distortion

in the transducer or amplifier will be recovered at this point.

The phase rectifiers contain as an integral part the resistance-

capacitance network that produces pseudo-integration (a running meaning

process). Time constants were set at 0.5 seconds to produce a reasonably

smooth record on the recorder used. Tnis relatively large time constant

- 11 -

F IGURE 2ROT. ARM

PRESS. AMP PHASE R-C

X-DUCER P RECT. INT.

ROTATING ARM ANEMOMETERCOMPUTER SYSTEM

.,

R E. -------. .. • •.

is a matter of convenience rather than of necessity; it represents 12.5

cycles at 25 cps, which is probably mole than enough to make the approxi.-

mation of equation (7) excellent for most atmospheric conditions.

A two-ckA.nxel Brush recorder was used to produce a graphic record,

with 1 cm o2 chait length representing one second. The speed of response

of the recorder is so high that it does not add appreciably to the time

constant of the system. Appropriate scalin- voltage 6ividers were intro-

duced earlier in the System to expand the scale of the vertical component

relativ,°e to that of the horizontal.

Isolating amplifiers with negligible phase shift were introduced

between the reference voltaZe generator and the phase rectifiers las•ely

as a precautionary measwue.

Once the few initial "bts" were removed, the electrornc system

peiforned fairlyv atisfactorily.

- 12 -

77.1 ,

V. Performance

A. Generl&.

The basic instrinueznt was tested at the Air Force Cvlabridge Research

Center's Great Plains Turbulence Field Prograri, held at O'Neill, Nebraska,

during AMSust and the early paý-t of September 1955. It functioned apprcxi-

mat ely a4 calculated under all but light wind conditions, when the rotating

a= Zet ur a circulatron that gave completely spurious results.

Figure 3 shows a short length of the record obtained with the

S, instrument. The excellent time resolutions will be noted, as well as the

relatively open scale for the vertical velocity.

Actual operation of the inst:'t=ment ras somewhat more complex than

had been originally hoped. It was found that the D-C output of the phase

rectiftiers had a strong tendency to drift in spite of the relatively high

levels at w.hich they were operated. This necessitated frequent zeroing

of the apyaratus. The phase rectifiers occasionally overloaded on strong

transients and would give obviously spurious indications until they hadrecovered from the overload. h�'is prevented operation at anw.here near

f,'ll-scale of the recorder, and required frequent range-switchling as wind

velocities asd turbulence increased or decreased.

B. Light Winds

0eration in light winds set up a whirl about the rotating arm

that gave a record suggesting the wind approaching the instrument at some

angle to the horizontal. For not-too-light winds, this angle was not too

great, and could fairly well be compensated for by a slight rotation of

the phase of the reference voltages. However, it is felt that this pro-

cedure has little to recommend it, as it is not known to, what extent this

may distozt the record.

-15-

_ II t . . _ - . . . . . . ...i /.- . - • - . . . . . . . - ' . ; - .

- -r- -7 -T-. -

• .• • • ", ... k_...L -. +,.--..+-.• "- .- ', " - - " - - - ,-

-i ,r--*--1--i-----T I

iIXI LLA2 evrA rimsU 4.ew *vA~faO1 ffEffW6UASA 3~4~ /~3 CART NO0. BL 0

" I'] - T - ' , "I I !

I_ _ L ± • I . " L - _ . . . . + -- - . - - . + -+ - - . - -

A SAMPLE RECORD -- FIGURE 3

O;*

•- . . . . .. . . . . . . . . . . . . . . . . .. . . . . . . .. r /-- - -l . ,8,e ".A1 " ."I"A , .

Figure 4 shows the apparent engle of the wind found for a 1/4."

diameter cylindrical arm. Data are not yet available to indicate the

relation of cylinder diameter to this effect. As a rough estimate, it

might be anticipated that it will be in proportion to the diameter and

wo-ld be reduced for a streamlined nrofile.

C. Comnparison with other Instruments

Unfortunately, it was not possible to make a side-by-side comparison

of the output of the rotating arm anemometer with another instrument measur-

ing the same quantities. An attempt was made to compare it with the Sonic

Anemometer of Prof. Suomi. of the University of Wisconsin, but because of

dissimilar presentations of data, only very general egreement could be

established.

The cbservations made at O'Neill will be the suboct of another

re-;ort.

VI. Proposed Further Development

.A. Fluxmeter

The circuit of Figure 2 may be expanded wzithout great increase of

comple'Jty to that of a flu:m~eter for the measurement of the vertical flux

of heat or moisture. In this case, multiplication of the velocity by the

tempe::ature or by the mixing ratio may be accomplished by passing the signal

from the transducer through an appropriate resistance bridge circuit before

phase demodulation.

B. Cour ter-: otating Armn System

Design calculations indicate that much of the error resulting from

the circuia-uion caused by the arm in low wind speeds can be avoided by

building the instrument with tvo counter-rotating arms, the difference in

- 14 -

DIRECTIONAL ERROR AT

40 'LOW WIND SPEEDS

30

20-DEGREES

ERROR

10 0

0 1 2 3 4 6 7

M/SEC

SME A N H O R IZ O N TA L V E L O C IT Y

FIGURE 4

I.'I..A

pressure between the tv.-o leading edges being measured. The signal corre-

sponding to the horizontal velocity is cancelled out, however. This causes

some loss of general utility, but is, if anything, desirable for use of the

ir.strzwent as a -'ertical flu.neter. Cancellation of the relatively large

horizontal signal permiita greater accuracy in the handling of the vertical

ccm.mic:nt,. It is feuad thathe only other signal retained after cancel-

lation is that of tLe shecaring stress (see ceuation (1O)), which should be-

come quite manageable. Such a counter-rotating arri sr.,stem with associated

gearing anC. pressu:-e dtvcting is under construction.

VII. Concludinm Reniaros

The rotating arm ane..ometer as presented here, wuhile not a finished

instrumcnt, shows enough promise of becoming a useful addition to the in- -

str mientation of micrometeorology to justify the further development out-

linQc. above.

Pcrhc.ps it- g.-eatest utili'ty may come in introducing a somewhat new

concept in msteovological instrumeatation - that of rotating a sensing

element in a field of a vaxriab~le. A fairly obvicus example is the rotation

of a thermnl eleuient in a la:'ge ver'tical circle to measure the vertical

Gralient of temperature. The use of a si.gle element eliLinates many of

the difficulties fcequent].y er.countered with this measurearent.

11t is believed t,-at the completed fluxaeter asser.bly will be capable

of amassing large quantities cf useful data in easily assimilable fornn. If

its operation can be reduced to a fairly si.rile routine, it may become of

consideý:able util.ityr iii gine;ýal micrometeorological research•.

IA

R VFEREINCES

Friedman. Dor G., 1957: The height variation of lateral gustiness anditbs e'ftect on lateral diffwuion, J. Met.. IO 372-79-'

Gill, G. C., 1354: A fast response anem.ometer for ricrometeorologicalinvest12ation6, BAMZ 55, 69-75.

Gill, G. C.; 19'l4b: L fast response bivano for micrometeorologicalinvestigations, (to be published).

Inoue, Eiich., 2.954: On the smallest scale of turbulence in the atnosishere,Texas P. & M nesearch Foundation, 01 contract 1U7onr-48705,Technical Report No. 1.

.MacCready, Paul B., Jr., 1955a: Atmospheric tui-bulence measurements anda.).Lysis, J. let. 10, 525-357.

MacCrez.dy, Paul B.1 Jr., 195,7b: Structure of atmospheric turbulence,! J. Ilet. 1C, 4ý4-449.

Mazzarella, Daniel A., 1952: An all weather, remote recording b-vane,BP'IS 35, 6o0-66.

Milne -Thomp.son, L. 1., 1950: "Theoretical ?'vdrodynamics", Nevi York,. aC il..'l•an.

Parson, D., Jr. and A. F. Burke-, 1952: A recording co.'.puter for. thedirect measurcner.t c-f the turbulent heat exchange in the at-mosohere, Interi.atiore.l Cymosium on At::ios-heric Turbulencein the bo~urdaly ieyýr, M. I. T., Air Force Combridee ResecrchCenter, Geo•,hysical Research Papers No. 10, 369-379.

ShLotani, M., 1950: Turbulence in the lcweuit layers of the atmosphere,Sci. Rej. of the T&hoku Univ., Ser. 5,_2, 167-201.

Swinbank, 14. C., 1951: The m.easurement cf ver-tical transfer of heat andweatcr vapor by eddles in the lower atmnosphere, J. Met._8, 133-145.

L.

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