Technical Report 3

MEASUREMENT BY TIMED SPARK SHADOWGRAPHS OF SHOCK VELOCITIES IN THE SHOCK TUBE

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HERBERT I.. HOOVER

Submltti'd l.y R. J Knirich

1 July 19T.3

Project NK 0R1-H63 Contract NTonr 39302

Office of Naval Research

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MEASUREMENT BY TIMED SPARK

SHADOWGRAPHS OF SHOCK VELOCITIES

TO TT'E ">"OCK TUB*?

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Herbert L, Hoover

Technical Report 3 Project NR 061-063

issued under contract N7 onr 39302 between the Office of Naval Research

and the Institute of Research, Lehigh University

This report which comprises the M.S. thesis of the author describes research carried out in the Physics Department of Lehigh University from June 1950 to June 1953. The work. Jointly supported by ONR and the Physics Department, is part of a program of study of transient flow of gases in a tube. The measurements reported herein were performed to ex» tend those reported in Technical Report 2 whioh appeared in the March 1953 issue of the Journal of •\pplled Physics.

R. J. Emrioh C. «• Curtis

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IT ir Abstract

Using a rectangular shock tube with glass walls, shock

propagation noar the diaphragm has been studied quantitatively

by means of double spark shadowgraphs. The cross-section of

the tube had dimensions oi' 0.64 and 7.6 cm. For positions be-

tween 100 and 250 hydraulic radii from the diaphragm, «3hock

velocities were measured by timing the interval between the

©parks • Within this reeion the shock velocity is greatest at

the position nearest the diaphragm, but not as large as pre-

dicted by ideal theory.

INTRODUCTION

The velocities of shock travelling in a shock tube of

rectangular cross section .64 by 7.6 cm were measured in a

series of experiments to determine) the attenuation with traveli/.

The shock voloolty docroasod continuously with travel over tho

range studied by those measuremr-r.ts , which wore made by timing

the arrival of the shock at opt! nl detection stations located

at 50 cm Intervals alone the tubo. These tests however did not

include measurements very noar to the diaphragm. The tests to

bo described studied tho shock propagation within tho 75 cm of

channel (250 hydraulic radii) nearest the diaphragm*

1/ R. J. Emrich and C. W. Curtis, Journ. Appl. Phy3lca 24, 360 11953)

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2.

These measurements of shock velocity near the diaphragm

employed a section of channel with plate glass walls. Spark

shadowgraphs of the shock within the channel determined its

position and configuration at two successive times, and these

times at which the 3parks flashed, together with the time at

which the shock arrived at an optical detection station at the

end of the glass channol, wore recorded on a chronograph.

The configuration of the shock within tho 30 cm nearest

the diaphragm differs markedly from a plane shock. In Figure

1, tracings of shadowgraphs?/indicate the way in which the

initially curved shock undergoes a series of Mach reflections

until a nearly plane shock is formed. Since different parts

Of the shock front, e.g. the center and the part adjacent to

the wall, move with different velocities during thi3 stage of

propagation, velocity measurements worr made only in the inter-

val from 30 cmt>jD 7E> cm front the diaphragm*

'fhe study of shock propagation near the diaphragm by timed

spark shadowgraphs wa.s proposed by <-. ft, Curti3. W, R, Smith

ana R, A. Shunk constructed apparatus and performed a series

of preliminary tests of the typo described herein, and their

contributions to this work are gratefully acknowledged, R, M,

Wileox also assisted in the construction of electronic equip-

mefft»

2/ These shadowgraphs were made by R, A, Shunk,

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30 35 DIAPHRAGM (CM ) i I

7 6 CM

INITIAL DIAPHRAGM POSITION

FIG. I SHOCK FORMATION IN SHOCK TUBE ft/-MB

Tracings from spark photographs 4{%

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APPARATUS AND METHOD OF MEASUREMENT

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Figure 2 -hows the relative positioning of the apparatus

oxcopt for tho pronsuro and electronics oquipraont. Figure 3,

which is a block diagram showing tho sequence of oporations

for obtaining a rocord, indicates tho functions of various

units and their interconnections.

Shock Tube. The chamber of the shock tube was constructed

of 3/4" by 6" duralumin plate? separated by 1/4" Lucite strips

whoso oides wore polished to porrr.it transmission of a light

beam; it:-, cross suction was 0,64 by 7,6 cm and length about

75 en. It was support.;! on rollers which permitted about one

lncn travel away from tho channel for inserting a diaphragm,

A flango with - n cvnl ^roov-.; to receive a rubbor gasket ring

provided :::eans to cl?mp together chamber and channel and to

seel the chamber when a diaphragm was in placo. A slot in

tho lower plat'..- contained a solenoid which, when energized,

thruat 1 3harp pointer against the diaphragm causing it to

rupture. At thu opposite end of the chamber was a fitting for

connection to tho pressure system,

Tho pressure in tho chamber "as raised by uso of a tiro

pump connected with rubber tubing to the chamber and to the

pressure measuring dovicu. Pressure was sot with an accuracy

of 0,01 atmos by using a closed arm mercury manometor, Bofore

taking a series of velocity records, one arm of tho manomoter

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FIG. 2 SHOCK TUBE and SHADOWGRAPH EQUIPMENT

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FIG. 3 SEQUENCE of OPERATIONS

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strip a small 1-1/4 by 1-1/4" Luclto ploco was insertod as a

window for the shock detection station. The inner surface

of the long Lucite strip forming ono wall was polishod with

fino grit emery paper and oil, and buffed to oliminate

irregularities. Tho outer odgo was also polishod at oach end

to allow tran3iJission of light beams usod for measuring pur-

poses.

Tho brass and Lucite strips were comontod to one glass

plato with stationers rubber cemont which had boon thinned

with 2 parts of bonzeno to ono part cement. Throo layors

wore appliod to oach surfaco of the Joint and allo^od to dry

partially. The strips wore placed in accurato position on tho

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was calibrated for tho particular pressure of interont by com-

parison with a hydraulic doad weight gago. Tho cancmefceJr

provided a simplo and sensitive means for repeating tho

initial pressure sotting from one trial to the next. For

the sotting of higher pressures (above 45 pslg) tho doad

weight gage alone was used. Atmosphoric pre?"-uxc -va^ recorded

from a barometer.

Tho 7,6 cm channel walls were formod by twe p;oces of

plato plans 1/4" by 6" and 30" long, Ono of tho ,64 cm thick

walls wa3 a strip of brass 1-1/4" wido by 28-3/4" long; tho

other was a 1" wido 3trip of Lucite milled to tho *64 cm thick-

noss for it? cntiro length of 30". At tho end of tho brass

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glass, hold lightly with C clamp3 which woro then tightonod

at intorvals of about 15 minutes. Uso of thick rubbor comont

resulted in a coating of non-uniform thickness; too rapid

application of pressuro with the C clamps squeczod the comont

out so that a «as tirht seal was net obtained. Tho other glass

plate was comontod in piece by a similar procoduro. Excess

comont was removed from the insido of tho assembled tube by

rubbing with a brass strip inserted at tho open onds,

^ho ond of tho channel near the diaphragm was surrounded

with a 3-1/2" by 8" split woodon yoke v/hich could be clamped

against tho steel flange of tho cht-mbcr holding the rubber

gasket for tho diaphragm seal. This woodon yoke was set

slightly away from th? ond of the £lass section to pormit

tho glass to exert positivo pressure against tuo diaphragm.

Slippage of tho woodon yoke on tho glass was prevented by

two U-shaped 3tocl strap3 extending the full length of the

channel and surrounding it; these straps wcro fixod to tho

yoko at tho open ends of the U and pressed against the ends

of tho glass plates at tho closed onds of the U, The stoel

straps woro separated from tho glass by cardboard pads, and C

clamps at 4" intervals served brth t-f* >""*>ld fhr straps to t-be

glass and to maintain pros3uro on tho rubber sealed Joints

between glass and brass and Lucitc strips,

Boforo the yoko and stool straps wero attachod in tho

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final aaaombly, tho end of tho channel at tho diaphragm was

ground flat and smooth with a bolt sandor. Care waa takon

to :nako this flat surface porpondicular to tho inaido edgo

of the brass strip and also to the glass plato3• This

assured that tho walls of the channel would bo perpendicular

to the diaphjjd'.-m and parallel to thoso of the chambor when the

tubo was a33er;;blcd with a diaphrarm In place. The direction

of motion of the belt wes along the 6" dimension of tho

glass so that chipping at the edro would not affoct tho soal-

ing at tho diaphragm. Tho sanding operation caused tho

Lucitc to hoat and swell so that after cooling a gap existed

at it3 end. This was offectively filled with throe layora

of scotch cellophane tape, carefully fitted, and an oxcellent

acal was always obtained.

Dowel pins in holes in tho wooden yoko and in tho stool

flange of the chamber allgnod the two acctiona of tho shock

tubo, Tho end of tho channel noar tho diaphragm waa supportod

by chains from the coiling. Tho othor ond waa rigidly supportod

by a woodon block fastened to a laboratory tablo.

Two Lucito acaloa woro fastened along ono side of tho

channel by means of small clips. Those transparent acaloa

providod tho rcforonco for determining tho position of tho

shocks in tho photographs. Tho scales woro rulod by uso of

a spectrographic comparator; a dot was scribed for oach

millimotor and a lino for oach contimetor. Each scale was

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72 om long. Ono sculo was abovo tho ohanncl, tho othor bulow,

and their shadows overlapped In tho photographs, por/nitting

the correction for 3hock position duo to parallax. Tho divi-

sions on tho two scales woro aligned by observing the ;riultiplo

reflections of a lino of tho upper scclo in tho glas3 platos

benoath it and tho corresponding line of tho lower scale.

Photocell Stations, Tho first photocell station providod

a signal it dt'iphregm rupture which startod tho delay circuits

and chronograph. A narrow light beam passod obliquely through

tho dlaphrafm to p. 931-A photocell. Tho sudden increase in

light when the diaphragm shattorod rosultod in a signal from

the photocoil which was amplified and transmitted to a "gate"

unit. Tho "gato" unit both shaped tho pulso to a standard

form for transmission to tho dolay, and prevented later signals

resulting from fluctuations in light intensity on tho photocell at

from passing to and interfering with the delay circuit,

Tho second photocell station at the far end of the channel

^cnoratcd three signals at the times oach of two 3parks flashed

and at tho time the shock passod a knife edge optical detection

station. Tho ldttor was ono of the standard arrangements of

threo knifo odgc3 which provent a light boam from falling on

tho photocoll oxcept during tho few inicrosoconds that a shock

is passing tho plane of tho knifo odgos.

Delay units. Tho dolay unit3 woro doublo triodo univibrators

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with variable resistance and capacitance in ono arm. Tho

delayed pulse from tho first univibrator was solectod, shapod,

and dclivorcd to a thyratron grid; it w«3 also transmitted

to a second univibrator delay unit of similr.r construction,

whoso output was applied to a socond thyratron.

Spark Ans.,-:r.blleg. Each of the thyratrons refcrrod to

above dischargoa a capacitor through tho primary of an auto-

mobile ignition coil. The voltaic pulse inducod in the

secondary triggored the main spark. Tho construction and wir-

ing of the spark aseonbly is shown in Figure 4. Tho spark

source consisted of three clcctrodos axially aligned in a

hollow Luclte cylinder 2/. The first elcctrodo v.-a3 a brass

plug which screv/cd in an end plate to permit adjustment of

the electrode spacing; tho socond was an iron slug with a

pin at the end to slido in a hollow insulator of soapstono;

the third electrode was a stool insert with a 1 mm diaraoter

hole through its center. Light from tho spark confined within

the soapstono emerged through the 1 mm hole; tho duration of

the spark was approximately 1 ^soc, and tho inton3ity was

sufficient to give a 3hadowgram through glass on F-l Kodabromlde

onlarginK pupor at a distance of 100 cm.

Chronograph. Tho time intervals botwoon the three signals

r 6/ Tho spark sourco design was furnished by D. E. Allmand and R. L. Kramor of tho Hydrodynamics Subdivision, Naval Ordnance Laboratory, White Oak, Md.

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FIG. 4 SPARK ASSEMBLY

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genorated at the second photocell station were measured ->?ith a

rotating drum chronograph. In thi3 chronograph, a timo base

on a cathode ray tuba scroon is photographed on 35 mm film

moving in a rotating drum. Linear motion of the cathodo ray

spot transversely to tho motion of the film is synchronized

to a crystal controlled oscillator for 50 ^socj tho direction

of tho spot motion thon reverses for 50 uscc. Timing markers

at 5 u-scc intervals and the signals to bo timod deflect the

sect in the direction of film motion. Interpolation octv.'oen

timing markers permits the time intervals botwoon tho signals

to bo determined to within 1 ^sec . Tho cathode my spot was

brightened by the signal resulting from diaphragm rupture and

remained bright for just slightly lcs3 than one revolution of

tho drum, i.e. 1/30 sec. A typical chronograph record is

shown in Figure 1 of tho first reference.

Shadowgraphs . As indicated in Figure 2 tho spark sources

were placed on tho floor 90 cm below the glass channel and

photographic paper in a holder was placod 10 cm above tho

channel. A typical shadowgraph appoars in Figuro 5.

If the spark fleshed at the instant whon the shock was

directly above the spark source, i.o., whon tho piano of tho

shock included the source, the shadow of the shock was an ox-

tromoly fino lino. Usually the shock was displaced by a few

centimotcrs from the vortical through tho sourco so that

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FIG. 5 SHADOWGRAPH

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the shadow consisted of neighboring bright and derk linos*

Tho position of the center of ther.c linos is dotorminod rolatlvu

to the shadows of both the upper and lower transparent scalos ;

the avora^o of tho two scale- readings is the position of tho

shock relative to cither of the accurately aligned scales,

Tosition of Shock Dotoctlon Station* The position of tho

knife edge dctoction station had to bo determined relative to

tho scr.lo appearing in the photographs • An operational method

of taking thi3 determination wa3 employed. The spark sources

and photographic paper were arranged to make a measurcnont of

the shock velocity from two shadowgraphs over an interval of

about 10 cm just ahead of the shock detection station* Tho

shadow of the shock fron the second spark was about 1 cm ahead

of the detection station, Ey assuming that the 3hock moved

with constant speed over tho interval betwoon tho first shadow

and tho detection station, the measured volocity between tho

shadows and the time intorval r.oasur^d botwoon tho second spark

and th: detoction station pulso permitted calculation of tho

position of tho station relative to tho scalo appearing in

tho photograph. Three such ^cts of measurements at oach of

t-;o shock strongths all indlcatod the samo position of tho

detection station within * 0*5 ran*

RESULTS

Four groups of position-time measurements woro mado for

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chambor pressures 15, 30, 45, and 60 pslg; channol prossures

woro atmosphoric, Those correspond to prossure ratios PQ/P0

= 2.03, 3*02, 4,09, 5.14 respectively. Actually Pc/P0 varied

slightly from one trial to tho next within a given group and

tnorc noticeably ao «hon rana were ma do or. different- diyg.

However, tho differences were always small and an adjustment

of results to a common bas*3 as described in tho paragraph

following fie next compensates for variations in initial

pressure ratios.

In crdar to attain as nearly perfect diaphragm breakage

as possible, different strengths of cellophane were usod at

tho different pressure ratios. The diaphragms used wore as

follows:

PQ/PQ Cellophane Typo and Treatmom;

2.03 .0008" DuPont 300PKT, charred at 250°C for 3 hours, dehydrated; vory fragilo, noar ultimate breaking strength

3.02 ,0008"DuPont 300PHT, charred at 175°C ror 1 hour, ro-hydrated at room humidity (50^); somewhat below ultimate strength

4.09 .0008 DuPont 300PHT, uncharred, dehydrated; near ultimate strength

5,14 ,0022" Dobcckmun laminated Red Zip, dehydrated; near ultimate strength

For each trial, the positions and corresponding times of

tho 3hock at three placos woro roeordod. Prom those the avoraga

velocity over three intorvals were computed. Corrections for

17

small lack of rcproducibillty from ono trial to tho next wore

made. The positions of tho first shock picturos woro kopt tho

samo, Thon all volocitios woro altorod in such a ratio as

to bring to a common valuo all avcrago volocitios ovor tho

interval from tho first shock picturo to tho detection station.

Varying the position of the shock for the second photograph

p:rmittod measurement of averse velocities ovor different

intervals. By assuming tho average velocity over an interval

to be tho velocity at tho mid-point, data for a velocity-dis-

tance curve were obtainod.

The* results appear in tho graphs of Figures 6, 7, 8, and

9, Each is a plot ofsnocic Mach number vs. distanco from

the diaphragm.- By-using tho ratio of tho shock vcoeity to

the sound speed in tho air ahoad of the shock, M = U/'c , the

erf foots of variations in room temperature among trials is

Glimin-Ttod, The vaiw; for sound speed is determined from tho

formula e= 347*4 £l + (t-25,5)/597.2 ^ m/soc

where t is contigrado temperature dotcrminod by a thermometer

in good thermal contact with tho metal walls of tho shock tube

chamber.; Tho short horizontal lino above tho experimental points

indicates tho value of velocity predicted by tho ideal thoory

of shock tube flow for the portinont valuo of P„/F^ !/• The

solid diagonal lino is "an extrapolation from the measurements

4/ Blcaknoy, Woimor, and Fletcher, Rov. 3cl. Instr, 20, 807 (1949 )oquation (10)

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i Figure £ Mach mahar of Shook •£ DiaUnc* from

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DUptoHP. Pc/P0 « 3.02

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Figure 8 Mach Suab«r of Shook *£ DisUaoo fraa

Di*phra«». p0/p0 = 4.09

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of Emrich and Curtis 1/, In thoao caaos <vhorc the P /p„ valuo c* o

for their data differs slightly from that applying to tho

proaontly reported rosultn, a dashed lino is also drawn in to

indicato tho difforencos in Mach number to bo oxpoctod on this

Account. The vortical intervals associated with tho measured

Much numbers uro estimates of the indofinitcness arising from

errors in reading tho records alone; thoao refloct a possible

error of + 1 u-scc in each tiino intorval moasurcment and of

+0,3 ram in oach distanco Interval moaaurorocnt• Such orrors

aro presumably random.

The poasiblo sourcoa of sy3tomatic orror in loach nunbor

determinations arc in distance and tlmo intorvals and in sound

volocity. Variations of Mach numbor with travel might also bo

influenced by a non-uniform cross section of the shock tube.

The latter influence is believed to bo small ainco caroful

measurements of the glass walled channel after assembly

indicated changes in cross sectional aroa in tho diroction

of propagation of ]c33 than 0.2 percent. Tho transparent

pla3tic ccalos were found to have ch°.ngcd dimonsion aft or thoy

were ruled, but appropriate corrocticnx were made to bring tho

scalo rcr.iings into conformity with an accurately ongravod

stool scalo. Tho time baso in the chronograph is known with

greet accuracy by comparison with timo signals broadcast by

station WV.'V. Tho largest systematic orror that may bo present

is associated with tomporaturo gradionts oxisting in the glass

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walled chamber. Caro wr.3 takon to keop hoat s our cos such as i

lamps and oloctronic dovicos ns distant as possible and to hnvo I

lamps on only for tho minimum times ncodod during each trial*

If ton.poraturc difforoncos along the channol of as much a3 3 ,

Centigrade degrees v/cro prosont, thoso difforoncos would reflect,

tlirough the sound spo^d values, changos in Mach number with

distanco of 0.5 percent. Unfortunately tho magnitudo of this

source of orror was not realized during tho tests and no

moasuroments of temperature gradients woro maao.

DISCUSSION OF RZGULT3

The purposo of these tosts omploying 3park shadowfjrrph

v methods was to extond moaourcmonts of shock velocity back I

as noar to tho diaphragm as possible for comparison with

mc,suromcnt3 made in the samo size tube at relatively groat

distances from tho diaphragm. Shock Mach numbers mecsurod

at 75 cm from the diaphragm by tho two raothods differ sig-

nificantly in tho caso of tho two higher starting prossuro

ratio3 Pc/P0» Thus, it does not soem possiblo to interprot

thoso velocity loss measurements by spark shadowgraphs as

moroly extending t'ao oarlior measurements.

rto havo no explanation of the discrepancy noted in tho

procoding paragraph. Tho most apparent difference In the

apparatus usod for the two moasuromonts is in the shock tubo

walls; the glass walls aro poorer hoat conductors ana super-

ficially aro smoothor than tho duralumin walls.

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The observation from the measurements at greater distances

from the diaphragm that shock velocities docroase continually

with travel suggested that, if tho volocity could bo measured

near onough to tho diaphragm, tho value prodiotod by tho

idealized shock tubo theory might bo found. Thoso moasuro- l I monte by spark shadowgraphs indioato highor vclocitios noaror

to the diaphragm but tho idoal thoory value is not attainod

notod that strongor shocks loso volocity loss rapidly. This

is in contradiction with the results obtained at larger dis-

tances from the d'.^.phragm. It may bo that wavos resulting

from tho diaphragm rupturo procoss continuo to strongthon tho

shock over tho region studiod and counteract to somo oxtont

tho wall dissipation which tonds to docroaso tho shock volocity.

by the timo a reasonably plane shock has formed. •

As a final observation from thoso raoasuromonts, it may be i

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1 Director, NACA Langloy Aeronautical Laboratory Langloy Air Force Base, Vu. Attn: Mr. J. Stack

1 Director, NACA Lewis Flight Propulsion Lab. Cleveland 11, Ohio Attn: Mr, A. Silversteln

1 Research and Development Board Department of Defense

1 Armed Forces Special -capons Project Pentagon, Washington, D.C. P.O. Box 2610 Attn: Info. Reqt.Board Washington, D.C. Attn: Col. G. F. Blunda

Associated Individuals and Government Sponsored Laboratories

1 Dr. -iin, Bollay P.O. Box 89 Downey, California

1 Dr. L. R. Hafstad 1901 Constitution Ive. Washington 25, D. C.

1 Dr» R, M. Mott-Smith 50 Memorial Drive Cambridge, Mass.

1 Dr. G. N. Patterson 17 Langmulr Crescent Toronto 9, Ontario

1 Dr. D. R. White

Applied Physics Laboratory 8621 Ooorgia Avonuo SiIvor Spring, Maryland

1 Attn: Supervisor Tech. Reports

1 Attn: Dr. F. K. Elder

1 Arnold Research Organiza- tion, Inc. Rm. 210, 522 Olive Stroet St. Louis, Missouri Attn: Mr. F, Smelt

Cornoll Aeronautical Laboratory

4455 Gonosoe Stroot Buffalo 21, Now York

Goneral Electric Resoarch Laboratory 1 Attn: Dr. J. V. Foa Schonectady, N. Y, 1 Attn: Dr, 0. Rudingor

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1 Jot Propulsion Laboratory Pasadena, California Attn: Librarian

1 Arthur D, Little, Ino. 30 iacmorlal Drive Cambridge 42, Mass* Attn: Dr. »"»m. Gordon

1 Los Alamos Scientific Laboratory Santa ?c, N. &ox4 Attn: J-l Division

1 niclpar Electronics Inc. 452 Swann Avenue Alexandria, Va. Attn: Mr. W. L. Mttlg

1 Midwest Rosoarch Institute Physics Department 4049 Pennsylvania Avenuo Kansas City, Uo, Attn: Mr. K. L. Sandefur

1 Ordnance Aerophyslcs Laboratory Daingorfiold, Texas Attn: Mr. J. B. Arnold

1 Projoot METEOR Mass. Institute of Technology Cambridge 33, Mass* Attn: Librarian, Rr.

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1 Project SQUID Princeton Univorslty Princoton, N-. J. Attn: Librarian

1 RAND Corporation 1500 4tti Stroot Santa Monica, California Attn: Dr. R. VU • Kruogor

1 San?.la Corporation c/o CG, Sandia Baso Albuquorquo, N. Mox. Attn: Appl. Physics Div.

Project HERMES General Eloctric Company Schonootady, New York Attn: Mr. C. K. Bauor

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1 Amherst College Department of Physics Amhorst, Mass. Attn: Prof. A, Arons

1 Polytochnlc Institute of Brooklyn 85-89 Livingston Stroot Brooklyn 2, New York Attn: Dr. A. Porri

Brown University Providence 12, Rhode Island

1 Mctcalf Resoarch Laboratory Attn: Dr. D. P. Hornig

1 Engineering Division Attn: Professor J. Kostin

California Instltuto of Technology Pasadena 4, California

1 Attn: Dr. H. W. Leipmann 1 Attn: Dr. H. T. Nagamatau

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1 John Hopkins University Lcpt. of Aeronautical Engineering Baltimore 18, Maryland Attn: Dr. P. H. Clausor

1 Harvard University Dopt. of Appliod Physics Cambridge 38, IJass • Attn: Dr. H, V. Emmons

University of Illinois Urbana, Illinois

1 Attn: Dr. C. H. Fletcher 1 Attn: Dr. A. H. Taub

1 Armour Rosoarch Fonndati* Illinois Institute of » Technology 3300 Federal Street Chicago 10, Illinois Attn t Dr. 5. RavnO?

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1 University of California Engineering Research Projects Berkeley 4, California Attn: Dr. R. 0. Polsom

1 Case Instituto of Technology Clovuland 6, Ohio Attn: Prof. Guatav Kuortl Div. of Aeronautical Engr.

1 Lehigh University Phyaica Departnent Botrlehcra, Pennsylvania Attn: Dr. R, J, Emrich

1 University of Maryland Institute for Fluid Dynamics College Park, Maryland Attns Dr, M, M, Martin

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1 University of Chicago Yorkos Observatory William Bay, .iceens in Attn: Dr. S. Chandrasokhar

1 Cornell University Grad, School of Aero. Engr. Ithaca, New York Attn: Dr. A. Kantrowitz

University of Michigan Ann Arbor, Michigan

1 At en: Dr. A. M. Kuethe Dept. of Aeronautical Engr.

1 Attn: Dr. Otto Laporte Department of Physics

1 University of Minnesota Dept. of Aeronautical Engr. i-inneapolia 14, Minnesota Attn; Dr. J. D. Akomian

Now York University Institute of Math and Moch. 53 :<aahin^ton Squaro So, Hew York 12, New York

1 Attn: Dr. h. U. Courant 1 ;.ttn: Dr. K. 0. Pricdrichs

Mass. Institute of Technology Cambridge 39, Mass. Attn: Dr. J. C. Kunsakor Aeronautical Engineering Dept, Attn: Dr. H. Guyford Stover Aeronautical Engineering Dept, Attn: Dr. C. C. Lin Mathematics Department

Pennsylvania State College Physics Department State Collogo, Pennsylvania Attn: Dr, R, G, Stonor

Princeton University Princeton, Now Jorroy

L Attn: Dr. W. Bloakney Palmer Physioal Laboratory

I. At In; Dr. D, Bershador Aeronautioal Attn: Mr, L, Aeronauticul Httn: Dr. J.

Engr, Dopt, Lees Engr, Dopt, vonNeumann

Instituto for Advanced Sl;udy

1 University of Virginia Department of ?hy3ics Charlottosvlllo, Va, Attn: Dr, J, »*• Beams

University of Wisconsin Department of Chomistry Madison, is cons in Attn: Dr. J, 0. Hirschfelder

Yalo University Now Haven, Connecticut Attn: Dr. J. G, Kirkwood Department of Chomistry

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