Central Aerohydrodynamic Institute of Moscow, Russia

8/14/2019 Central Aerohydrodynamic Institute of Moscow, Russia

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NATIONAL ADVISORY COMMITTEE

TECHNICAL MEMORAIHXJM

CENTRAL AEROhYI)RGDYNAMICBy w.

FOR AERONAUTICS.

NO. 386..

INSTITTJTEOF MOSCOW, RUSSIA.*Margoulis.

This institute is the central establishment of the U*S.S-R.Union of Socialist Soviet Republics) for making, inaboratories at Moscow, all.scientific and technicalelating to aermau~ics. It ccmprises six sections

Section for Tncoretical Researches;Section for Aerod-yzxdm.icesearches;?Windmill Section;Section for Engin~-Propeller Groups;Section for itiaterialTesting;Section for Instrument Xaking.

its manyresearchesas follows:

he president of the faculty is Professor TchapliOaine and theection chiefs are former pupi:.s of P~ofcssor Joukowski, v~ho,athe beginning of the war, as instructors in the aerodynamic lab-ratory of the Noscow Technical High School, formed, under theirection of

erodynamicc

Professor Joukowski, a lBureaufor Aeronauticaland Tests. This bureau was first changed to theSection of the Institute of Ways and Communications

.9nd subsequently b{ecm.m-e,i~lj~,ysnder the direction of professoroukowski, the Cent~al -~rchydrodyr.am.cInstitute, which since.- .--. -From LIA+ronautique, [August, 1926, pp. 263269.


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. .. .. --- ----

A..C-A. .Technical Memorandum Ho. 386 2

he death of its founder, bears the p.ame ofProfessor Joukowski.,,-We will nou consid.e,~he ,~orkof the first three sections,it-nthe expectation-of taking up tne-forkof the remaining sec-ions in a future article.

Work of the Section for Aerody-namie Researches

Beforee ,~illsay

hich sincehe Section

describing the present equipment of the institute,a few words akout the work done since 1914 in thelaboratory of the MOSCOW Technical High School,the faunding of the institute, has been directed byfor Aerodynamic Re~earches of the institute. Theof this laboratory was given in the French transla-

ion of Professor Joukowski s Course in Aeronautics (Paris,6, Gauth.ier-Villars, publ-ishers).

Modificat ~~s in t.b_firew(zr wi:zc~ttinneu.- There were threeo-nehaving a ci~cui=r cross section of 1 m (3.28

%.) dLiam~ter>a wind r~;;.ocityof 18.5 m (60.69 ft.) per second,.6 HP., and an energy factor of O.43; one having a recta-nO@arross section 0.3 X 7-=5m (0.98 X 4.92 ft.), a Sirocco pro-

a velocity of 24.7 m (81.04 ft.) per second, 14 HP.,nd.an ener~gzfactor of 0.4; lastly, a large wind tunnel ofquare cross section, running along the main room of the labora-ory and originally designed for test:~g propellers and wind-


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.7..C.A. Technical Memorandum No. 386 3

The rcctanc@ar wind tunnel vvasused the most . In 1916,the exit cone (diffuser) was rebuilt according to a desi~l byrofessor Toupolef, and the Sirocco propeller was replaced byrofessor Joukowski ts eight~1~.dedpropeller of tho const?wn.tcirculation type, which produced a wind velocity of 44 m(144.4 ft.) per second, with 23 HP.

The aerodynamic balance, described on p. 157 of LA


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N.A.C.A. Tcchnic~l IlcmotnfidumNo. 386

Travaux uc 1In.titut, vith particularility and precision. A new nodel, withis now being constructed.

Very complete tests of wings of the

attentionautonatic

4

to its staregistration

Tchapliguine-Joukows2itype, obtained by the inversion of the paraoola, were made inthe rectangular tunnel. The results were discussed by Miss N.esnikova inenne. Theyhe wing andf a wing of

Nos . 3-4 (1923) of the E?ulZetinde la Flotte a4ri-demonstrated that, due to the small space oetweenthe walls of the tunnel, the lifts were not thoseinfinite aspect ratio, but of a wing with an aspect

ratio of 7.5. This tunnel is now used only for testin,gstrutsnd stay rires.

Ada:ltchik wjnd tuny,e?..ost of the tests of wings andirplane models vere made in a wind tunnel having a circularross section (Fig. 1) and a 3iameter of 1.5 m (4.92 ft.), builtin 1915, according to Adamtchiks design, to replace the above-entioned tunn?l 2.5 m (8,2 ft.) sq-uaze.*

It had a 47 HP. motor, a six-ble.dedJoukowski propeller ofm (9.84 ft.) diameter, exit-cone angle of 19, wind velocity6 m (llElft.) per second, energy-factor 1.53.

The balance, designed by Professor A. Tou.polef,now chiefMr. Adam-tchikmade, in 1912-1914, in the laboratory of theOSCOW Technical High School, a series of tests with models ofind tunnels anti especially on the eff:ct of screens placed i-nront of the entrance cone (collector) a device which, in certainincreases the energy factor and straightens the air cur-


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1 111 111 1 1 11 11 11 11 11 1 1 I nl ml ll I III II m 1111 I III m-l, , ,,, -.. lm..m I . II m -.1.--,, -,- - . -.-- ---- -.

K.A.C.A. Technical Memorandum Ho. 386 5

of the Aeronautical Construction Section of the Institute, coa-sisted cf a steel-tubing parallelogram, one arm of wb.ich en-tered the experiment chamber, The mess~reffientsere made hy tilemethod. of the three moments.

The Propeller tests were c:adewith a device designed by Mr.Tcherew.ouchine. This deviceplaced outside the tunnel onthe tunnel and supported ;be

consisted of an electric motora vertical nount which extended inton~oaeller s:laft. The mount could

oscillate in two perpendicular direct ioilsand its balancing byveiqb.ts enabled the d eierr-ination of %F.s thrust and torque.The clevice is similar to the one lo:~q USC(%at the Yoscow Uni-v ersity and w-nit-nwas inventcd by l?rofessor Joukowski.

JOUICOWSkis larr~ ?~iqatunnel .- Like7jise in 1915, ProfessorJoukol:~skica,uscdthe construction of a wind tunnel of reinforcedconcrete (Iig. 2) having a diameter of 3 m (9.84 ft.), a 350HP. electric motor, a propeller of 6 m (19.68 ft.) diameter, ananticipated wind velocity of 50 m (164 ft.)per second, and anenergy factor of 3.1. The tunnel was entirely finished, butthe motor could not be built during the war and this vind tunnel,which was the largest in the worldused.

Tt is pa,r~ ic~la~~y rer-arlcable

in 1915, has not yet been

because Professor Joukowskiapglied in it r.cv idc?s o-.1zhiesl--a.pe: the cones, which id-eashe explai.led in his article, 1ollecteurs et Diffus3u~s desBuses pour Souff~eri~s A~rodynamiques, publisned in Travaux


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Technical Memoraildum No. 336 6

ieure Technique de Moscou, No. 6, 1918) .Professor Joukowski demonstrated t-hat, in a non-turbulent

current flowing through a conduit with parallel generatriccs, thevelocities are constant throughout the whole diameter of anygiven section. It is necessary therefore to give to the entrancecone such a,shape that the trajectories of the fluid will benearly rectilinear in the sectior-of the experiment ciarnbernearthe mouth of the entrance cone.

In his article, Professor Joukowski indicates how it isnecessary to design the entrance cone for a tunnel with a rectangular or circular cross section, the entrance to which isfree or in front of which a wall or screen is placed.

As [email protected] the exit cone, Professor Joukowski indicates theshape of the co-neitself, as also of the spinner on the propel-ler hub, which is determined by the constancy of the velocityat the entzance of tb-eexit cone and ttlenon-turbulent flow ofthe air in the exit cone.*

These wind-tunnel shapes are of double importance because,by eliminating the guide vanes, they render it possible to di-minish the power required and because the suppression of the

* Professor lVitQ3Z~-iSZi of the Insti:ut Polytechnique de Var-sovie (Warsaw} has published, during the last few years, similararticles on the shape oftunecones in closed wind tunnels.

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.A.C .A. Technical Meiiorand.u.mo. 386

This is an important contribution

7

to the theory of aerod.ynamicwind tunnels, which should be supplemented by the consid-

. ..~ationofthe effect of friction on the walls, beer.usc onc mi:;hte led.to adopt wind-tunnel shapes promoting d.etachmefitof theoundary layer and consequent loss .of power.

In 1S16-1917, Professor Toupolef made a series of tests onodels of exit cones of varioufi lengths. As a result of theseests, he desi~ned a C1OSN3eturned through an ar.nula.rroper, si~.ilarto the plan

wind tunnel, in whichspate surrounding theof the wind tunnel of

dvisory Committee for Aeronautics, just built at

the air waswind tu~ elthe NationalLangley Field

U.S.A.), for makin,g tests in air of variable density.

New wind tunnel of the Moscow Tedhnicp,l School .- The 1.5 n4.92 ft.) circular vind tunnel did not Sive complete so.isfac-ionj due to the irregularity of the current. It was thereforeeplaced in 1924-by a ~rindtunnel of a ile~:~ type, proposed byr. Juricff, Chief of the Section for Aerodynamic Researches,nd built according to the calculations and drawings of V-shakoffnd Boun. kin.e. A model having one-quarter the dimensions of thisind tu.nn.elis renrc.~er.cd by Fig. 3.* Fig. 4 shows the full-This figure is taken from an article by Mr. 3aulin, Recherchesxperimentales sur les souffle:ies adrody-namiques in Tm.vauxe lInstitut central a~rohydrodynamique, No. 7, 1924. Thisork, performed in t-neaerodynamic laboratory of the MoscowSchnical Hi&h Schobly e~:t (asitlefrom tests of the imodel ofhe Jurie~f wind tun~.el;-it-nliecros+sectional shapes (circu-square and octagonal), the generatrices (straight and para-olic) of the exit conss, the effect of t:hecontraction of their stream behiild the propeller, the calculation of the latter,nd the energy factor of the wind tunnel.

*


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8*A.G.A. ~~c~m~.ca.l Ilemlorandum~~o 396

Size -h_lr.rlelas seen from the entrance-cone end.The wind tunrielhas twc experiment chambers, one with a,.

c?iameter of 1.5 m (4.92 ft.) and the other 2.25 m (7.38 ft.).When working in the large chamber, part 4 of the exit cone isremoved and the air enters through the annular opening thusformed. With a 48 HP. electric motor, driving a four-bladedpropeller with constant circulation along the radius and re-volving at 960 R.P.U., there was attained, in the 1.5 m (4.92ft.) section, a velocity of ~1 m (157.5 ft.) per s~ccmd, co~re-sponding to an energy factor of 3.5, which is one of the high-est, if not the highest, foz any existing wind tunnel? In the2.25 m (7.38 ft.) section, the energy factor is 0.75, likewisea very high v a l u e for a wind tunnel without an exit cone and -due to a good arrangement of the returiiair conduits.

The experiment char.lker,shcvn in Fig. 4, is designed toprotect the experimenters from the returning air strea,m,the ve-locity of which may reach 7 m (23 ft.) per second. It is stream-lined, with the nropeller in_the larger end, in such a way asto ~Lire& the air symmetrically with respect to the tunnel andthus obtain in the experiment chamber a good regularity in bothtime and space. In fact, we thus succeeded in o-otaining,with-out .puidevanes, a very regular field in both experiment chanbe=.

The halau.ce, y:~ith horizontal parallelogram suspended fromthe ceiling by three rods, has an ele~tror:agnetic device forvarying the angle of attack of tb.emodel.


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o

A larger wind tunnel of the same type, with an experinert -clm,mber3 m (9.84 ft.) in diameter, is now under cons trtictionat the institute. Fig. 5 shows the aerodyn%nic laboratory Gfthe institute in process of construction.

In addition to thewings, we must mention,Section for Aerodynamic

1. Experiments on

above-meritioned tests of Joulcowkj.1samong the experiments performed by theResearches:

LfieIoilgitudir.alstatic stability ofairplane models, for the Tm-:pcse of determining practically thedimensions of the contrcl surfaces ?.ndto supplement the workof Professor ~~etthinkine on the general mj.culation of the con-trol surfaces.

2. E:rperime,ntswith i~odel-sof exit cones for wind. tu-nznelsjthe exit cone consisting of two sheets of ca,rdboa,d placed be-tween t-woglasses, which renders it possible to vary its shapeeasily.

3. Determining the distribution of wind pressures on huild--ings. A theory of Professor S. Tchapliguine renders it possibleto determine the air flow about edifices of different shapes.

4. Mr. Korostelef invented an instrument for tracing the~?-dfiles of wings and wopellers and named it Esp6rographe(Pig. 6), which enaklcd very rapid tr? :ing (uP to 100 profileser minute) in a contiu.r.ous~aruner(not by points, as ordinari-1y done) of profiles of widely differing shapes, including some


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. B n . . .,---m... . ..--.. .- -.-. --,. -.. -------- -

N.A. C=A. Technical Memorandum No. 386 10

very similar to the ones obtained by Professor Tchapliq--ine,oyin~:ertingthe ellipse, a,ndfo: rhich LIr. Wesselowsky h.W d~s-covered ametfi.otof tracin~ by points similar to that of ~re=ftz.The aerodynamic section proposes to make very cociplete SYSt~iQ?).t-ic wind-tunnel tests of the profiles traced vith this in:tnment.r

Kd. Experiments with Iifting-propel.lers of constant circu-lation, for the purpose of verifying Professor Joukowskif s vor-tex theory of the ~rope.1.ierand-determinirig ~heexperimentalcoefficients . Prof. Jurieff has inven~ecl very ingeniousmethod for measuring the real angle of attack in any sectionof the olade. This method is based. on the fact that the ratioof the p~essu~e differences at thee points of any scctioildoesnot depend on the spcedj cut only on.t-neangle of attack. Itis only necessary tb.erefore to m,easure these differences, inorder to determine the angle of attack. For this purpose, open-ings are made in each section and tk.e pressure differences aredetermined by means of tuoessunk in the prope:.ler and of aspecial hub enabling the transmission of the pressures to a m.ano-~eter.

Professor Jurieffls relative nron elier theory .- Otherexperime:ltalresearches were made on Professor Jurieff s rela-tive theory of pro_peTlers.* .


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IT A. C..A. Technical ]jcmorandum Xo. 386

Sabinine and Jurieff first entertained theing the stresses uilclcrgoneby an element of they assuming t-natthe velocity along the pro-pellcr shaft ~as equalto the translational velocity plus a certain velocity of aspira-tion, as determined by the theorem of the qaantity of motion.Thus they combined, for the first time, V. Froudel s theory ofthe element of the blade (1878) and F..3. l?rou.tietth.toryof theideal propeller (1282). lheir I:0k, dating from 19il, was recount ed by Joukorski ii~his lecture course of 19111.912,at theOSCOW Technical-digh School.

It is known that Joukowskis vortex theory of the propeller,eveloped by ?~of es~or Jettchi-nkine,considera the absolute mo-tion of the fluid with rsspect to the circle s~ept oythe propel.er and calculates the menn inducedfvelocities by the actionof an infinity of helicoidal vortices distributed over coi~cenric cylindrical surfaces (Fig. 7), of an infinite nurllbcrofortices bound to the blades in the plane of rotation antibyn axial vortex behi-nd the propeller. *

In his first dissertation on the vortex theory of the pro-published in 1912~ Jculsowskivrote: IInefu-fld~~::entc.ldea

of bound vo~tices, vilichccmstitutes tb.e oasis of my ~rork,would


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.A,C.A. Technical

render it possibleiwe -velocities of

Memorandum No. 386 12

to make calculations founded on the real rela-the fluid, but this discussion would be too

Having found that JoukowskiIs theory, in certa,in cases,ave results slightly different from the expe.zimental-results,rofessor Jurieff formulated a newhe considerations of the relativeeference to the blade, z:idof the

propeller thecry founded onmotion of the fluid, withmmenta. ry velocities. Pro-

ssor Jurieff co,~sid.:s the action of tilehslicoidal verticalurface nl-o&~~~e~.y a ~ropclier in the same wa-ythat we study.he action of the vertical su~face t.cvelope3_belind a wingFig. 8). He thus comes to the very important conclusion tkatpropeller, with.a constant circulation al.cng its radius, does

ot give, in front of the propeller3 the ccnstant induced axialelocities assumed by the old vortex theo~y, outvelocities i-nreasing toward the circumference. Fig. 9 shows the distribuion of these velocities for-a wing (likewise with uniform cirulation) and a propeller. From tnesethe writer draws the con-lusion that we car.not :?akea prOpeller with uniform Circulation,ince the velocities at the blade tips can not be infinite and

in a progel.ler with uniform ci~culation,designed accordng to Joukowski, the cizc-il~.tionand the real axial inducedmvel.ocityave values as sti.ownin Fig. 10.

This brief sum~marywill render it-possible to comprehendhe importar.ce of the new theory, wb.osedevelopment ad e~eri-


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rental verification are now being pursued by t-ncSection

1z,

for

The ~indmill sectipn, directed by lJIi-.rassovsky, studiesthe construct ion p.ndfmlcti.oning conditions of uindzvills, P-Salso the structure and distrioution of the winds.

The first work of t-hissection wr.sdone, since 1921, at t>eInstitut de Physique cosmiaue c?-eou.tcF.ino(the fo~er In~ti_tut A drcd~m.amiqu. o: ]Ir.F.iabouchinski). It consisted in thedct crnination of the functioning conditions (no::entsand revolution speeds) of d-ifferent windmills rind-especi~lly of an Ar-,ri-cail eighteen-bladed uindnill and r.six-blwi cd vil:iklll fiadcaccording to an article ky Frof essor Joukowskij Wirxl??ilIsof t:hcNEJ type, in which the miter appliei to -rinti:illsis vortextheory of the propel ler.* Tkesenabaral ni-ndon a special tower,

Following these researches,

tests vere nadc either in 2or on models in a vind tunnel.tke section milt, according

type 6 m (1.69 fi.) ill@-i?.metr, which ?, exhibited :~ttheexnosition. Fig. li pictures the first one

of these ~indnills.


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.A.C.A. Technical Memorandum No. 386 14Theposition of the blades is controlled by tail pl?.acsand

by-the.actian of additioilalmasses on the tail planes, in sucha,nrieras to assure a maximum motive moment *7hent-hetiil~nlillas set in motion, a high constant rotational speed, whateverhe wind velocity and the moment of resistance, and a good utili-ation (40~) of the wind energy.* This windm~ll had nothingo fear from tempests, because the blades straightened out inhe wind so as to offer only a slight resistance.

One investigation mad-eby this section, at the request ofhe Azneft Company (petroleum wells of Azerba~djan) showed ito be possible, by means of windmills, to dlminjsh appreciablyhe cost of producing petroleum. A winikfiillwith three adjusta-le blades of 14 m (46 ft.) diameter and giving 50 HP., waslaced in service and tes~eciin a wind of 18 m (59 ft.) per

Subsequently it witnstooda tempest of 25 m (82 ft.)er second.

This section made a.thorough investigation of the questionf utilizing the energy of the mind, especially by means of hy-raulic accumulators. For this purpose, tabI.esand graphics ofhe wind velocities were prepared for all Russia..

Most of these investigations were recounted in Ncs. 2 and 4f the ~~orksof the Central Aerohvdrodynamic Institute, cor,-.rising the Ipl.oblfinsf t:leUtilization of the Enermv of theind by N. Kr~,s~~vslcyand G. Sahiv.inc;A New Blade for ~SSian. - -- .According to Pmf essor ,Juj}.o~ski:theo~y, the m.aximurnvaluef the energy factor is 0,522.


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.A.C.AO Technical Memorandum Eo. 386 15indmills by lJ.Krassovsky; and Instructions for Mounting Wind-ill Blades by W. Utkia Egorcff.,, -. ,.. -.

Work of the Section for Theoretical Researches

Among the works of the Section for Theoretical Researches,he first place is occupied by those of Professor W. Wettchin-

Chief of the Section, on the lDynamics of Airplane Flight,he Calculation of the Dimensions and Effects of the Controlurfaces and the Strength of the Materials Employed in the

We will1. His

ade in 191.8

of Airplanes. note:experiments nith a nonrecording faccelograph,for measurin? the stresses undergone by airplanes

uring acrobatic maneuvers.* Subseq7~ently,Mr. ;(esselowsky,anngineer in the section, made a,recording a,ccelograph whichave excellent results.

.2. A theoretical treatise on the Landing and TakeOff ofand especially, on the motion of an airplane when,

efore landing and after having .t~,kenthe angle of attack pro-ucing themaximum lift, it is flying parallel with the ground.y assuming that the aerodynamic resultant has a.fixed directionn space, the writer arrived at ,a differential equation of the----- -- ----iccati type, who~e integration enablel him to establish tables-.Travaux du Laboratoire volant, founded.by tb.epilot, E.ossins-ky, Uo. 1, lSi8.


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.A.C .A. Technical Mcmorandurn No.

iving the vcrtic~.1 speed ~.tthein terms.of the hcxi.zontal speed

386 16

inst:)ltof tcucb.ingthe ground,

ift) , of tb.efir.eness, and of the Z>titud.cat vhich the lt?r.dingneuver began.* In connection with this work, the section

studied thcconstruction of landing gears r.rldespeci~.llythe dif-erent kinds of shock absorbers: oil and air, oil and sando?-s,nd oil springs.

3* Researches on tke looping(Bulletin de ,laFlotte adrienne,

aildturnir-gof airplanesifos.3, 4, 6, 1923) .

4. Researches on the calculation of the tail surf~ccs nndilerons, l:~hic~~homed that the dcterminat ion of their di:flcn-ions mus t be b,lsed nrir.cipally on considerations of nr.neuvera-

and not of stability (~ulletin d.ela Flotte a6ricnne, 5, 1923).

It is known ti,atthe elcmentary methods of starting vith.he strength of the nlaterials does not cnable the calculationf w.ost of the airplane parts, since they fail from local defort ion. Professor Wettcfiinkine has ~iven special attention tohe solutim of questions of stability of shap~of these parts.


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N.A.C .A. Technic?.1Mcmorzuldum IJo. 386 17

cross section. He discovered ?.form of sirut -nhich, for a finiteof the fineiless ratio (fleche), gives equal tensions at

ll points-of the length and .vhichenables a snvin~ of 13? ineight and 8% in aerodynamic r esi st ?.n ce d r eg , a s compared wi~hsimilar strut of uniform cross section sv.bjected to the same

stress.Another research was on the stability of twisted sheet metal

(ventilator vanes, for exlmple) .Mr. Wettchinkine also investigated the

i th dciublecurves. The first part of thisinin

the Bulletin des Ingenieurs , 1924; thepress.

flexure of partswork was publishedsecond part is now

Lastly, we will f~ention an instrument for measuring mcmentsinertia ar.dfor determining the effect of t-hei~ass of airy

scillating witiz the airplane, on its moment ofMr. Waltk.er, one of the assistants in this

mportant investi~ation cf the forces acting on

inertia.*section, made anthe vanes of

ydraulic turbines plun[


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N.A. C.A. Tcchnic~.1ll~~orandum No. 386 18

Of the dissertations on technical questions published inthe Travaux de 1Institut, rreI,Tilllention: Sur Ie mouvenentde 1e~Ludam les canau.xet des gaz clanslcs conduitcs by Pro-fessor Jouko~ski (No. 1); Application de la th60rie des pcr-siennes a Ihblices 1by W. Alexandrof (No. 6); 11e calcul d-es

pales dh~lices 5 la torsion by L. Leibenson (Nr. 8); Tenp%tesde neige avec et sa,nschute de neige by F- Eouchkowsky (NO. 11).

The institute has published since 1923, 18 dissertationsin P.ussianwith summaries in Znglish. It also proposes to pub-lish in foreign languages certain particularly important works,notably the French translation of Professor Joukowskis fourdissertations on his IVortexTheory of the Propeller, and theEnglish translations of two dissertations of Professor Tchap-liguine on the Theory of the Slotted ~l~ngand on tb.eGeneraltheory of the Monoplane ?:~ing.~

Translation by IlwightY Miner,National Ad.viso~:yCom;ittee.for Aeronautics.


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N.A.C .A. Technical l~eillor~.ndwflITO.86 Figs.1,2 & 3.

Fig.1 Adaimtchikwind.tunnel.

1----------~--l-. 1Fig.2 Joukowski wind tunnel..

k 6050 IFig.3 Model of i~ewvind tunnel of the ~~oscovTechnical School.

..-.


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-,.,.- . ... . . . . .

~~.A.~.A. Technical Memorandum No.386 Figs.4,5,6 & 11

lFig.4 View from entrancecone end of new windtunnel of Moscow Teohnica3School .

-.

Fig.5 New aerodynamiclaboratory with thetower for testing windmills

Flg.1-i First Sabininew lndmill.


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----- .-.,..., . .IT.A.C .A, Technico.1l[~tilor~.nd~i.lO.3E S Figs.7,8,9 & 10

Fig,8 Vertical surface behind a wing and behinda propeller.

Fig.7 Tilehelicoidalof Jonkowskis vorticesvortex

oFig.10 Circulationand axialinduced velocity in apropeller with .circulation uniform.

theory of the propeller. o:6 2810I i=const. i

Fig.9 Values of the induced velocities accordingto the formula Vz = azn~ A. \


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Central Aerohydrodynamic Institute of Moscow, Russia

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