REPORT No. 394

AIRSHIP MODEL TESTS

suMMARY

Ill THE VARIABLE DENSITY WIND TUNNEL

By IsA H. ABBOTT

.in inredigation of the aerodynamic charactem”dics C#air8hip moifek was made in the mm-able density un”ndtunnel ~f the ATational .kldrisory Cbmmittee for Aero-ml utic8. Eight Qoodyear-Zeppelk air8hip models,supplied by the Bureau of Aeronautics OJ the ATaLYDepartment, were teded in the ort”ginal closed-throattunnel. After the tunnel UXM rebuilt with an openthroat a new model tca8 te8ted, and one of the 6bodyear-Zeppelin mode18 - retes~ed. These tests were made attank prewures ra@ng from 1 to 20 aimo8phere8, and thee.rtreme range of Reynolds A%mber UW8about 1,000,000to @,000,oOO. The li$, drag, and moment coe~cientsof the mode18 xere determined, and the ejects upon the8ecoefict”ents oj p“tch.,jFnenes8 ratiol scale, surface tetiure,initial degree of air-stieam turbulence, and the e$ectsof the addition of jins and cars were investigated. Theresulting curres are included.

The res-ults show that the addition of fins and cur tothe bare hull of a model cau8es an increase in lijl atpositice angle8 of PI”tchand causes an additiomd dragwhich increa8es m“th the pitch. Little change in dragcoefficient UXISfound between a jineness ratio of about

jire and seren. !ile efect of swface roughness on draguxs found to be re)y large. T%e drag coej%ient and theapparad e~ect of scale depend upon the initial degree ofair-stream turbulence. The results indicate thut muchmay be done to determine the drag of airshipsfrom eralu-CItions of the pressure and skin- fn”ctianal drags on modelstested at large Reynold~ Numbers.

INTRODUCTION

‘i’ilnd-tunnel teats of airship modeLs have resultklin many usefuI data on the aerodynamic characteristicsof afihip huUs,and on the effects of fineness ratio, ~and control surfaces, and protuberances. These datahare been usefuI in airship desigg, but their useful-ness has been Iimited greatly by the fact that theReynolds Numbers of the task are very small ascompared to those obtained in flight. This Imitationis especially etident from a consideration of the dragcoef%cient which shows a more pronounced variationwith Reynolds iNumber than do the other chrmacter-istics.

h’ot onhj does the drag coefficient obtained from amodel apparently have little rdatkm to the fdl-scrdecoefficient, but also the drag coefficient of the samemodel as obtained in different tunneIe at the samevalue of the ReynoIda Number varies greatIy. Con-sequently, the results of wind-tunnel tests on airshipmodels ha-re been .gmerdly discredited, and airshipdesign has been hampered by the impossibility ofpredicting the drags of proposed akhips from modeltests. Work done in the past few years has indicatedthe possibility of ckifying the problem by the appli-cation of PrandtI’s boundary-layer theory, but so fewtests ha-ie been made o=rera Iarge range of ReynoldsNumbers that little experimental data have beenavadable to show that the application of this theoryis possible to a reasonable extent.

Au investigation. of the aerodynamic characteristicsof airship models was conducted over a large range ofRe-ynoIds A’umbem in the variable density windtunnel of the National Adtisry Committee forAeronautics. Some of the tests were made in theoriginal closed-throat tunnel, and the remainder weremade in the tunneI as rebuilt with an open thxoat.This arrangement made it possible to compare theresuIts of tests made over a Iarge range of ReynohkNumbers in two tunnek

The tests included the determination of lift, drag,and moment coe5cients of eight Goodyear-Zeppelinairship models, and of a model of the ZRS4 airship.Each model was tested with and without appendages,and one modeI was tested with three degrees of surfaceroughness. The models were suppfied by the Bureauof Aeronautics of the ATa-t-yDepartment.

The drags of the models were measured at zeropitch with the models mounted on two types of m.s-pension to allow the corrections made for supportdrag and interference to be checked. CorreotioQSwere made for the effect of air-stream convergence onthe drag, and they were checked by testing one modelin tunnel positions corresponding to difTerent staticpressure gradients.

Curves of lift, drag, and moment coefficients are givenfor nine modeIs. Other cumes show theeffects of pitch,fineness ratio, appendages, surface &x ture, and scale.

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●5s3

584 REPORT NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

APPARATUS were. multiples of the diameter. AH the Goodyem-Eight Goodyear-Zeppelin airship models and one Zeppelin models had the same generating curve, the

model of the ZRS-4 airship were tested in this inv@i- ordiriates of }vhich are given in Table I. The ordi-nation. Ml the models were made of mahogany with natka of the ZRS-4 model are given in Table H. Tho

.

.-mH8.-, ...-..—....—.-..Fm’cEEl.-Oc@’eer.=ppeIin drehlp models

metal nose and tail caps, and the cross.sections were24-eided polygons, fair& to drcles at the nose andto 16-aided polygons at the tail.The fineness ratioof the ZRS-4 model was 5.9. The Goodyear-zeppelinseries consisted of four basic models with finenessratios of 3.6, 4.8, 6.0, and 7.2, having the same maxi-

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FIQURZ2.–@odyear-=ppeflneirahfpmcdels. lVoQCIV fine+ Thebrimdneammadeofbrassplata. They are of the same general plan form.%sthe woodVflusandare)ii bob thfok

mum diameter, but varying in length. Four addi-tional models with fineness ratios of 5.3, 5.6, 5.8, and6.8 were obtained by inserting paralhd middle bodiesin the two smallest basic models. Figure 1 illustratesthe models and the means used to Iengthen the smallerones. The middle bodies had a constant diameterequal to the maximum of the mode~, and their lengths

center of buoyancy positions and volumes” for allmodels are given in Table. III. The models wereequipped with removable & and cars. Brass finswere fitted to the G&3.6 and the GZ-7.2 models, andwooden fins to all others. (Fig. 2.)

AU models had rubbed varnish finishes. One modelwas also tested with a highly polished surface, andwith a surface coated ‘with No. 180 Carborundum(grai~ ranging from about 0.003 to 0.007 inch inraaiimum dimension). The granular Carborundumwas >prayed over the, freshly varnished surface by“mea~ of a smaIl air jet to obtain a uniform distri-butkm.

A description of the original close-throat variabledensity wind tunnel and a diecwtion of the principlesof its operation are given in reference 1. tide fromth6 change to an open throat, the rebuilt tunnel wasmuch” like the original, the chief diflerencea being inthe h.ape of the air passages and in the balance details.(Ii& 3.) Sphere drag tests (reference 2) showed thatthe open-throat tunnel had leas air-stream turbulencethan the old closed-throat tunnel.

Figures 4 and 5 show the method of mounting themodels on the main balance in the original tunnel.Special supports were used with the outer ends fastanod

4

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1

AIRSHIP MODEII TESTS IN THE VARIABLE DENSITY WIND TUNNEL

1

IIFmuEx3.-Open4broatYerfsbledeneltywfndtunnel

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FmcmzL-Om@er-Zep~ alrshfpmodelmountedat zeropitchon the mrdnbelanmofthe cIosed.throettunnel

SWOO-324

586 REPORT NATIONAL ADVISORY

to the baIance ring, and the others extended into abrass bushing in the model. This bushing formed thebearing around which the model pivoted with chang-ing pitih. A streamline wire attaohed to the shielded,angle-of-pitch bar supported the tail of the model.Streamlined shields covered the supports.

The models were mounted on the main balance inthe open-throat tunnel as shown in Figure 6. Themain supports were fastened to the balance cradle atthe bottom of the test chamber and were partlyshielded, The exposed portions were streamlined.The models, which were mounted on a horizontal

. . -. .—COMMITTEE FOR AERONAUTICS

R~ETHOD

The tests were made in the usual manner in the “--variable density wind tunnel. (Reference 1.) TheresuItant force. on the balance included the following:

1.

2.

_3.4.

I “5”

The desired aerodpamic forces on the mod~.Forces on the model duo to air-stream con-

vergence.Forcgs on supports of model.Forces due to mutual interference of model

and supports.Forces due to windage on parts of the balance

located outside the air stream,

FIGUEIr5.-Ooodgear.Zepp?lfnairshipmodelmounhd at 23°pitchon the main balanceof thechxad-throethm.nel

streamlined rod between the supports, contained brassbushings to form the bearings on which they pivotedwith changing pitch. A partly ahieIded, strea.ndinewire fastened to the angle+ f-pitch bar formed the tailsupport.

.4 photograph of a model mounted on the auxiliarybalance in the old, closed-throat tunnel is shown inFigure 7, This balance and mounting are fullydescribed in reference 3. The mounting in the open-throat tunnel was the same, except that four roundunshielded wires were used b support the modelinstead of three partly shielded streamline wires, andthat a 45° linkage was used instead of a bell crank totransmit the force of a counterweight. (l@. 8.)

The eflects of the last four items had to be e~aluatedin order to determine the desired forces on the model.

The additional drag on the model due to air-streamconvergence was calculated from the formula for anellipsoid with a volume and fineness ratio equal tothat of the model placed in a stream converging insuch a manner as to have a Iincar static pressuregradient. (References 4 and 5,) The formula forthis correction is given in the Appendix, and is similmto that for the more conventional horizontal buoyancycorrection. Howeverj the actual static pressure gradi-ents of the tunnels were not linear. (Table IV andfig. 9.) The locatiogs of the models in the tunneIsare given in Table lT. For the open-throat tunnel

AIRSHIP MODEL TESTS IN THE VARIABLE DENSITY WIND T13NXEL 587

I?lauu 6.–ZIM-4ahshlp modelmmmtedIn Pitch on the mdu Mance of Ihe ormkthrcattnod

588 REPORT NATIONAL ADVISORY

tests, a process of graphical integration was used tcarrive at this correction. For the closed-throat tunneltests the models were divided into three sections andan average linear static pressure gradient was used foreach part. Thwe gradients were close approximationsto the existing gradients for the sections. Thesemethods have little theoretical justification, but theresults justify their use. It is thought that they givecloser approximations to the correct results than theusual horizontal buoyancy correction. A check was

COMMITTEE FOR AERONAUTICS

instead of the dummy model. The main balancewindage was included in the balance rendings,

The discrepancy between the resultson the main andauxiliary balances in the closed-throat tunnel testsindicates that the corrections for the interference ofthe main balance model supports on the model wereinaccurate. Therefore, in the open-throat tunneltests, this interference effect was determined bymeasuting the drag of the model mounted on theauxiliary balance with the main balance model sup-

F1OUR~7.—Ctodyear-2%ppelindrsbipmodelmountedontheatiry dragb&m&in th?cloged.throsttunnel

made by testing one model in the open-throat tunnelin two positions having greatly di.fTerentstatic pressuregradients. The gradients in the closed-throat tunnelcaused much smaIIercorrections than thobein the open-throat tunnel, The effects of stream convergence onlift and the effects of cross-tunnel static pressuregradients were considered negligible.

The forces due to the main balance modeI supports,and the interference of the mode~on the supports weredetermined in the closed-throat tunnel tssts by placingdummy models in the model position so that they didnot touch the supports. This force was then measureddirectly on the balance. The same general pro~durewas used in the open-throat tunnel tests, except thatthe model mounted on the auxiliary balance was used

ports in place but not touching the model, and withthem removed,

Tbg. drag of the auxiliary bnhmce model supportties “was calculated in the closed-throat tunnel tests.(Reference 6.) The interferences were small becnusc ofthe location of the wires, and they were ncgloctwl, Inthe open-throat tunnel tests, nn attempt was made todetermine the wire drag nnd interforcnces by measuringthe drag of the model mounted on the main balancewith and without the auxiliary balance model supportwires in place, It was found, however, that thismethod was subject- to considerable error because ofthe small magnitude of the correction. Consequentlyjthis correction was calculated as in the previoustests.

AIRSHIP MODEL TESTS IN TH13 VARIABLE DENSITY WTND TWNXEL 589.-

The formulas used in the calculation of the results moment near zero pitch, which are probably lessare given in the Appendix. It will be noted that the accurate:coefficients are based on (vol)~, and that the Reynolds ; Lift, +3 per cent.Numbers are based on the lengths of the models. I Moment, * 5 per cent.

TESTSDrag on main balance, +3 per cent.fDrag on auxdiary balance, &2 per cent.

I The large magnitude of these possible errors WM due .._The modeIs were tested under the following con- ~ditions: bare Ml, hti with b, and hulI with fins and ~ mainly to an unsteady air stream and to vibratio~ of ._car. Brass and wooden V-shaped fms were attached ! the tunnel strnc@re to which the balances were ~to the different modeIs as requested by the Navy I attached. Changes in surface texture between runs . .,_

FIQ~~ 8.-Owdrear-Zep@1ncJm?JIPmodelmountsclCMaaxWcYdragbaknca in theopen-thmnttumud

Department. Two sizes of cars mere attached for thetests on hull with fine and car, a small car be~w usedon the smaIImodeIs and a krge one on the large models.The tests were made at tank pressur= of 1, 2.5, 5, 10,and 20 atmosphem for the bare-hull condition, rind atpressures of 1, 10, and 20 atmospheres for the otherconditions. A tabulation of the tests is given inTable VI.

PRECISION

The accuracy of the measured gross forces is believedto be within the following limits except for the Iift and

caused additional errors, which may be of about thesame magnitude as those listed abcwe. The measured .—corrections were obtained from the ~erence of ..,_measured gross force measurements, and they containau the above SITOI’S.

The accuiacy of the calculation of the wire drag for —-.modeIs on the auxiky balance is beIieved to be asgreat as that of the measured corrections. There is an .additional error due to the neglected mutual inter-ference of wires and model, but this error probably isand because of the location of the wires. The dragcorrection for air-stream con-rergence is thought to be .—

590 REPOiT NATIOIWU ADVISORY

more nearly accurate than the conventional horizontalbuoyancy correction.

No correction has been applied to the lift for theeffect of air-stream convergence, and no correctionshave been made for the influence of cross-streamstatic pressure gradients or for wail effects. Theerrors due to these effects are belie~ed to be less than1 per cent. The same correction for the effect of air-stream convergence on drag has been applied nt allangles of pitch, and this additional drag has beenassumed to act at the center of buoyancy of the modelsfor the purpose of moment calculations. The modelsupport and baIance windage corrections for any one

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open-throattnnnel. StetIupresure referredto Pmsom of stfll sir intentchamtwrw zero

model have been assumed to be the same for allangles of pitch. These assumptions may havecaused appreciable consistent errors.

Fkure 10 shows that the a.meement betweendrag-coefficiente for the GZ-4.~ model as testedin two positions in the open-throat tunnel withgreatly different static pressure grfidients andin the closed throat tunnel is within + 8 percent, except at the lowest Reynolds Numberswhere air-stream turbulence effects are appreci-able. This agreement may be taken as n generalindication of the accuracy of the tests.

CtiMMI@lXE FOR AERONAUTICS--- : .=

The results of the drag tests on the bare-hull modelswithout parallel middle bodies fit zero pitch on thermxihary balance are given in Figure 17 (A). Thecurves of drag coefficient.are plotted against ReynoldsNumber on logarithmic scales. similar curves aregiven for the bare-hull models with partdlel middlebodies in Figure 17 (El), and for the models testedwith and without appcndqysw in Figure 18. Curvesfor the GZ-4.8 and ZRS-4 bare-hull models as testedat zero pitch on the auxiliary balance in the open-throattunnel are given in Figure 19, The results of the close-throat tunnel test on the GZ-4.8 model are also givenfor comparkon.

The results of the tests+on eflcct of surface texture _“ondr~g ati given in Fi&re 20. Cufi’es of drag coeffi-cient. at zero pitch for the GZ-4.8 bare-hull modelwith three degrees of surface roughness are plotted onlogarithmic scales ag~inst Reynolds Number. Thecurve$” show, greatly increased drag resulting fromincressed surface roughne~~.

z. DISCUSSION ..

Pitc~,.-The effect of pitch on the aerodynamic chur-actcristics of the models is shown in Figures 11 to 161inclusive. The lift and moment at zero pitch me notexactly zero because of air flow and modcd eccentricity.The lift coefficient incre.asmto values of about 0,10 to0.12 for the bare-hull m~dels at 15° positive pitch, and

RESULTS

The results of the tests iR pitch of the bare-hullGoodyear-Zeppelin airship models without parallelmiddle bodies are given in Figure 11. The curves of~ift-;drag, and moment coefficients at five values ofReynolds Number are plotted against the angle ofpitch for the GZ-3.6, G7+.8, GZ-6.0, and the GZ-7.2models. Similar curves for the bare-hull models withpardleI middle bodies, namely, the GZ-5.3, GZ-5.6,GZ–5.8, and the GZ-6.8 models, are given in Figure12, and for the models tested with appendages inF’igures 13, 14, and 15. Figure 16 shows similar curvesfor the GZ-4.8 and the ZRS-4 models, both with andwithout appendage+ as teted in the open-throattunnel.

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FIQuErr10.—Ihngcoellicfenbof the Goodyear.ZepIWOahab[pmodeI. Finenesemtlo,4%ZWO pita herehull

to values of about 0.25 to 0.35 for the models at thesame attitude with fins and cars.

The moment coefficients for the bare-hull modeIsincrease from approximately zero at zero pitch to avalue of about 0.06 to 0.08 at 15° positive pitch. Thotheoretical moment coefkients have been calculatedfrom the values of KZ–.KI (reference 7) given in Figure21, and F@.me 22 shows the ratio of the.actual to thotheoretical moment coefficients plotted against angloof pitch, This ratio is about 0.70 at the larger angleswhere the erros due to eccentricity are unimportant.This value is the one usually found for this ratio.(Reference 7.) The moment coefficients for the nlodeIswith h and cars, and with fins onIy, increase withincreasing pitch to a maximum at an angle of roughly

AIRSHIP MODEL TESTS IN TEE VARKBLE DENSITY WIND TUNNEL 591

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592 “ REPORT NATIONAL ADVLSORY COMM-E FOR AERONAUTICS

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596 REPORT NATIONAL ADllfSORT COMMITTEE FOR AERONAUTICS

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-.

-HIP MODEL TESTS IN THE VARNLE DENSITY ~ TUNNEL 597

g“, above which the slope of the moment curve be-comes negative.

The drag coeftlcients are”Ieaet at zero pitch. Therate of increase with pitch is and at amalI sngIes ofpitch, but it becomes greater as the pitch increases.

Fins and cars.—The magnitude of all effects of ti

Fineness ratio.-Fineness ratio is defined for thepurpose of this report as the ratio of the major axisof the airship to its greatest diametm. An tipwith a fineness ratio near unity would ha~e a wry

largepressure drag. If only airships of good shape areconsidered, that part of the drag coeflkient due to

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Q

FIG- ‘B.-Aerodymnio&araoMetiesin pitchcdthe W-M airshipmoddas tastedwi~ andwithoutappendagesIIIthecIosedmd open throat hmuele

and cars upon the aerodynamic characteristics of air- prwure drag ia greatIy decreased as the tienas ratioships is dependant maidy upon the relative sizes of the is increased; but, if the increase is continual, a pointhuUand appendages. Consequently, it is impossible to ~ is reached where the decrease in the pressure ~Ucompare directIy theeffectson the Merent modelsbecause the relative sizesvary. The iduence ofthefis and cam for the combinations tested can beseen from a comparison of Figur= 11 and 12 withFigures 13,14, and 15, and from Figures 16 and23.The lift is increased at positive angles of pitch.The moment due to the b and car of the C%6.Omodel ia shown in Figure 24. The appendagescause a decrease in moment when the ship is inpositi~e pitch.

The increase in drag due to appendages with themodel atzeropitch isshown in Figure 18 to be from15 to 20 per cent of the bare-hull drag at the hugerReynolds Numbem and more at the smaller Rey-nolds Numbe~. This increasers greater at lsxgerangles of pitch and is about 100 per cent at 15°,except for the GZ-3.6 model, which shows an in-crease of about 150 percent of the bare-hull dragat that attitude.

Tests on the GZ+.O model (@s.15 and 24),withb and car, and with h onIy, show that thecar has no effect on lift and moment with

.——

-—

--

.

Ang(e of pitdz ~

Fmum 2L—Moment due to iim or Sm and oar. Omdye+Zep@ln airehIPmodel.Finenessratio,8.0;_JZIOldSN- i=XIOC

the I coefficient is too small to be appreciable. That partaccuracy of the tests, and onIy a alight effect on

Iof the drag coef%cient due to skin friction is increased

drag. as the fineness ratio is increased, because the ratio of.

-

.—.-.

598 REPORT NATLONAL ADVISORY

surface area to voIume is increased. It follows thatfor airships with the same generating curve, therewill be a definite tieness ratio at which the drag co-efficient will be a minimum, although there may belittle increase in drag for airships with iineness ratiosvarying somewhat from the one giving minimum drag.Figure 25 (A) shows that- there is actually littledifference in tie drag coefficients of the models withiineness ratios between 4.8 and 7,2. The scatteringof the points is due to the inclusion of models withparallel middle bodies, to inaccuracies of measurement,and also, very likely, to different test conditions causingditYerencesin the boundary-layer flow.

If an airship form is used for the fairing of objects,the important drag coefficient is one based on themaximum cross-sectional mea instead of on (vol)i.In Figure 25 (B) this coefficient (CB.) is shown plottedagainst fineness ratio for the Goodyear-Zeppelin bare-hull models at a Reynolds Number of 20,000,000.The results indicate that CD. is a minimum for thisgenerating curve at a fineness ratio of about 4.5.

These tests show no consistent variation of lift co-efficient with fineness ratio, either for the models withthe samegenerating curve or for thosewith pnrallelmid-dle bodies. (Fig. 26.) In general, the lift coefficientsare higher for themodels with the larger iheness ratios,but this variation is small and not very systematic.

The rnomentweflicients are higher for the bare-hullmodels with the smaller fineness ratios (fig. 27); butthis effect is not entirely systematic, probably becauseall the models do not have the same generating curve.From consideration of the theoretical moments, themoment coefficients of the Goodyear-Zeppelin bare-hull models would be expected to increase as the fine-ness ratio is decreased. The following table gives thetheoretical and actual moment coefficients of thesemodels expressed as a function of the pitch. (Refer-ence 7.)

C. AS A FUNCTION OF THE PITCH

Fhmose

d .“

‘Theore$icsl (F&~p@ntA.%Oressure-xl atmoephered

8.6 a?t8eIn2a a;~~g48 .%7sin2a

lb.8 J&a;ag15.8 :%%%6.0 .2U8in2a .lasinti

16.8 .210sin2U .142SiII?a7.2 .197sin 2U .12astn2u

1 Models with pmrdlel mfddIe bodies.

Surface rou~hness.—The lame increase in drag co-efllcient for the GZ-4.8 bare-hull model due to increasein surface roughness is shown in F@me 20. At thehighest Keynolds Numbers reached, the drag coefficientfor the model coatad with No. 180 Carborundum is 200per cent-f the drag coefficient for the model with anormal rubbed-varnish surface, and this coefihient forthe model with a highly polished surfwe is 93 per centof that for the normal model. Although the Carborun-dum surface is far rougher than anything that would

—.COMB&l’EE FOR .4ERONA&ICS

be obtained in practice, the large magnitude of theeffect of surface roughness makes it imperative thatconsideration be given to the condition of the surfacoof the model in any interpretation of airship mode]tests.

Reynolds Number.—The effect of Reynolds Numberon the lift and moment coefllcients is show-nin Figures11 to 16, inclusive. There is no consistent variationof lift coefficient with Reynolds Number, probablybecause the data are not snfllciently accurate to shuwthis effect, which is small. Most of the models show anappreciable increase in the moment coefficient at largeReynolds Numbers. This increase”is greater for Jhemodels equipped with fine and cars thtin for tho btire-hull models.

The drag coefficients for the models in pitch do nvtshow any consistent variation with Reynolds Number.This fact is probably due to the inaccuracy of the re-silts. .The drag coefficients at zero pitch for the modelstested in the closed-throat tunnel decreasowith incrms-ing Reynolds Number (figs. 17 and 18), but- the de-cream is not systematic for rdl models. The rate ofdecrease is greater at small than at large ReynoldsNumbers, especially for the models equipped with finsand cars,.and the curves of dr~~ coef%c.ieuw of the bnrr-hull models plotted against Reynolds Numbers approxi-mate straight lines when plotted on logmithmic scales.The apparently high drag coeficionts shown by somoof the models a.tthe highest Reynolds Number roachedmay have been due to the use of insufhient counter-weight to keep those modek steady at 20 atmosphorcstank pressure. The drag coefficients for both models .tested in the open-throat tunnel at zero pitch inrrenscat low Reynokls Numbers and decrease at high Roy-nokls Numbers. (Fig. 19.)

Initial degree of air-stream turbulence.-Tho dragof airahip hulls with good forms is very largely clue toskin friction. Pressure distribution tests on airshipsand models have repeatedly shown Tory small pressuredrag ,coeflicients. The rgagnitude of the skin friction,and hence the magnitude of the drag coefficient for theairship, aro dependent upon the type of ffow existingin the boundary layer. The type of flow depends notonIy upon the scale, but also upon the steadiness of theair approaching the airship, or, to state this differently,upon the initial degree of air-strmm turbulence. ThcIboumku-y-layer flow is also partly dependent upon theshape of the airship.

The following equation of B1asiusexpressesthe arcr-age @n-frictional drag coefficient for aIl laminmboundary-layer flow on rectangular flat plates. (Ref-erences 8 and 9):

C,=I.3W

Burgefi md Hansen have established this equationas a good approximation to wiperimental values.J?rand”tl’sequation

c,= o.0741F

.-

—

AIRSHIP MODEL TESTS IN TEE VARLKSLE DEWJTY WIND TUNNEL

.03

.02

G

0

.0s

.04

c%

.C12 I I I I I I O WiWmufpa-allef middle bodes t I t I I i1 I , t t r, I 1 1 I 1 t , 1 1 I t b 1 1 , ,

–(B) Drw cueftikt”enf bused w mo~m GZLSs-sectim w-eo–

I I I I 1.[ I t I I I 1 f I Iliiiiii iiiiiii i’’’’’’’’’’’”” J..-

0 I 2 3F-ss r%

5 6“7

.28

24

20

.16

.12

.08

G

.04

0

-.04

-.08

-.tg9 _6 -3 ~ ~ ~ ~ /2 [5 ,8

.-@fe ofptfc~”deg-ees

~GUSE !28.-Ef&Ct Of I%WJIESSE3ti0~ ~tOWfttCht. Qoo&ar-ZeppelinnlmhtpmddaLiftmdl?.cfentsat 21ntm~here+%bars hu testedin tbeclmed.throatWmeI

599

.. —

.—

—-

—

600 ‘ REPORT NATIONAL MWISORY

expresses the average skin-frictional drag coefficient

for all eddying boundary-layer flow ou rectangular flatplates. (Reference 10.) Curves of c= are plotted onlogarithmic scaIcM against Reynolds ~umber inJ?@we 28.

As explained in the above references, the laminnrtype of boundary-layer flow exists only at sma~Reynolds Numbers; and, if the Reynolds Number isinoreued, the flow in the boundary layer becomeseddying on the surface of the downstream portion ofthe plate, and the transition line between the two

types of flow progresses upstream. in wind tunnel

*

c.

-.

-.

-.

-.

-9 -6 -3 0 3 6 9 12 /5 mAngk ofpifch, degrees

FIauRr H’.-Effect of llneness ratio on moment OcefScIent. C?O@im-ZePpdlndmbipmodeh. Moment aenh at a atmospheres; bare hti testd In the closad-thnmt

COMl&%E” FOR AERONAUTICS—

to the upstream edge of the plate, The value of the .._critical Reynolds Number is dependent upon the initinldegree of air-stream turbulence (References 9 and 11),and decreases as the initial turbulence increases. Theusual values of Rx for wind tunnel work are veryroughly 100,000 to 3,000,000.

The transition curve of the skin-frictional dragcoefficient can be calculated approximately for a flntplate and a value of the critical Reynolds Number.The foIlowing assumptions give two Iimiting transitioncurves between which the true curve must lie, (Iiof-erence 9.)

tomd

tests the Reynolds Numbers are such that the Howis neither entirely laminar nor so largely eddying thatthe Iaminarupstream portion can be neglected, Underthese conditions the skin-frictional drag coefficient Iieson a transition curve between the two curves dascribedabove.

The value of the Reynolds Number at which thetransition from laminar to eddying flow takes placein any given case is called the critical Reynolds Num-ber. The scale at the transition line, i. e,, the criticalReynolds Number, may be expressed by Rx in whichthe characteristic length is the distance from the line

1. The lmninar flow does not affect tlm ed-dying flow behind it at roll.

2. The eddying portion over the rear ofthe plate acts as though the layer wereeddying over tho whole plate.

Two typical transition curves for rectangular flatplates have been cnlculated for a critical Rey-nolds Number of 600,000, and have been plottcdin Figure 28.

The tot~l drags of some of the airship modclahave been expressed in the form of skin-frictionaldrag coefficients (C=J. This coefficient is bnmdon the surface areas of the models, The inclusionof the pressure drag is not very important bectiusethis drag is comparatively small, and prol.mblyvaries little with the Reynolds Number. Curvesof this coefficient are plottod agnimk ReynoldsNumber in Figure 28 for the GZ-4.8 model as~ested in the old closed-throat tunnel, nnd as ‘“tested in two positions with thrco degreesof surfaceroughness in the open-throat tunneL The curvefor the GZ-7,2 model is also included.

The @m-e shows that the curvea,for the modelstested in the open-throat turd rosemblo transi-tion curves for recttingular flat plates at the lowerReynolds Numbem, and closely approxixnatc thocmrve for all eddying boundary-layer flow at thehigher Reynolds Numbers. The curves from the“closed-throat tunnel tests lie nearly parallel with

.-

those for all eddying boundary-layer flow on flatplates, The turbulence in this tunnel was muchgreater than that in the opcm-throat tunnel (ref-erence 2), and the critical Rev-nolds Number wss

apparently so “farbelow the test r&ge that the curwesshow no resemblance to transition curves at thelower Reynolds Numbem.

Recommendations for future work,—The curves ofthe drags of airship models, when mqnwsscd as skin-frictional drag coefficients, r~emble the curves forskin friotion on flat plates. The indications arc thatmuch may be done to predict fuLscale drag cocffLcients of airship models from separate evaluations ofpressure and friction drags. In order to calculat~ thofriction drags it will be neoeasary to mako experimentsto determine the effect of pressure gradients, curva-

AIRSHIPMODEL TESTS IN THE VARIABLE DENSITY WIND TUNNEL 601

ture, and taper of a body of revolution upon tha

boundary layer. This work should be undertaken inconjunction with an extensive study of turbulence.Although the determination of turbulence by plots ofsphere or streamline-body tests has been used fairlysuccessfully, this method is subject to error becausethe assumption is made that the turbuhnoe is con-

&

i

2. The drag coefficients for the airship models withthe Goodyear-Zeppelin generating curve vary little ‘betwaen fineness ratios of 4.8 and 7.2.

3. Wind tunnel teats of @ship models may lead toerroneous conclusions because of the effect of ●theinitial degree of air-stream turbulence, and because ofdifferences in surface roughness.

J-U-L HkIHY polisheo’-JJ

1

.2 3 4 56789[0 m 30x10gReynaIds Mmber

Fmo’Ex 28.-Oomp3rk$on M akin Metfon on drehlp modeh end reckn@mthtpIak Deshed Iinesrepresmtt heoretiesle mvesforektnMetIon numctun@aaatplate% EOIIdlfneere~tteatreenltSon bamAnlI air8hJp nmdeIs. These eumes are for the GZ-4.S model testd fn the normal @tIon with normal snr-Caeein theown-three.t tninel exeepte.snoted

st.ant,whereas it probably varies with Reynolds Num-ber. The work should be combined with completeboundary-layer surveys, force tests, and pressure-dis-tribution tests on an airship model, and, if possible,on the fti-sized airship.

CONCLUSIONS

1. The addition of iine and cars to mrship modeIs inthe combinations tested increases the drag from 15 to20 per cent at zero pitch.

8~

4. The variation of the resistance of airship modelsat the large ReynoMe Numbers obtained in thesetests is apparently a determinable function of theReynoIds Number.

LANGLEY L~EMOBIAL AERONAUTICAL LABORATORY,

JNATIONAL ADVISORY COMMITTEE FOR AERONAUTICS,L.UTGLEYFIELD?VA.,January WI 1931.

—.-

—

.— -

—

APPENDIX

Lu — I liftcoefhient.

g(vol)iill= — J moment codcient.

l#(vol)*.27= —~ drag coefhient.

g(vo~)+_ D , drag caticient based on maximum–~ crossi-sectionaIarea.

=q~> skin frictional drag coefficient.

=-D skin frictional drag coefkient based onqx’ assumption totaI drag is skin frictional.

‘m Reynokls Number..—,

– ‘~x, Reynolds Number at point(X).P

(K,– El) (voI)* sin 2a theoretical moment‘~’ coefficient about

center of buoyancy.

. #L,

(Tol)l’ *CD’ = ~(vol)l , drag coefhient due to stream con-

vergmce.

(Tel),’ = (Tel)+ (Vol),”.

(Vol),’ = (-rol)+ (Vol),”.

~1= (TOY),”— .(Vol)

Where

L, fif~.M, moment about center of buoyancy.D, drag.F, force due to skin friction.cc,angle of pitch in degrees.1, Iength of model..4, maximum cross-sectional area of model normfd

to axis.8, total surface area.d, distance downstream aIong ask of tunnel meas-

ured from selected stations.

X, distance dovmstream measured from upstreamedge of plate.

——

V, airspeed.—

p, static pressure.q, dynamic pressure.p, mass density of the fluid.p, coeilicient of viscosity.(vol), vohune of model.(vol),’, virtual ~olume of the body placed longitudi-

r.dy in an accelerating stream.- —

(-rol),’, virtual ~ohrne of the body placed trans-~=ely in amaccelerating stream.

(vol)l”, apparent additional vohune of the bodyplaced longitudimilIy in an accekratingstream.

(vo1),”, apparent additional volume of the bodyplaced transwrsely in an accekratingstream.

REFERENCES

1. Munk, Max M., aud Miller, Elton W.: The VariabIe Den-sity Wiid Tunnel of the NationaI Advisory Committee —.

for Aeronautics. N. A. C. A. TeohrdcaI Report No. 227,1926.

2. Jacobs, Eastman N.: Sphere Drag Teste in the VariableDensity Wind Tunnel. N. A. C. A. Technical NoteNO. 312, 1929.

3. Higgins, George J.:Testsof the N. P. L. AirshipModeIsin the VariaMe Density Wiid Tunnel. N. A. C. A.TechnicaI Note No. 264, 1927.

4. Taylor, G. L: The Force Acting on a Body Plaaed fn aCurved and Converging Strecun of Fiuid. British -A. R. C. R&M NO. 1166, 1928.

5. Lamb, H.: Notes on the Forces Experienced by EllipsoidalBodies Placed Unsymmetrically in a Converging orDlvarging Stream British A. R. C. R&hI NO. 1164,1928.

6. DeFoe, George L.: Resistance of StJ ‘. e TWres.N. A. C. A. Technical Note No. 279, 1928.

7. Munk, ifSX hi.: The Aerodynamic Forces on AiMhipHulls. N. A. C. A. Technical Report No. l&4, 1024.

S. Bladus, H.: Zeitechrift fiir Mathematik und Physik. 56,1908, p. 1.

9. Jones, B. M.: Skin Friction and the Drag of StreadineBodies. British A. R. C. R&hf No. li99, 1928.

. .-

10. Prandtl, II., and Betz, A.: Ergebniese. der Aerodynamieohen—

Versuchsanstalt zu GMtingen. 111 Liefrun~ 1927, p. 1.11. Dryden, H. L., and Keuthe, A. M.: Effect of Turbulence

in Wind TunneI Measurements. N. A. C. A. TechnicalReport No. 342, 1930.

—_—

003

604 REPORT NATIONAL ADVLSORY COMWITEE FOR AERONAUTIC%●

TABLE V

LOCATION OF MODELS IN TUNNELS

OLD OLOLJED.TH130AT TuN~L

TABLE I

ORDINATES OF THE GO:C)~ARZEPPELIN AIIWEIP

st8tfor4pae0nk4rt#

tatfon, permtkn@hkom nose

R:

RU67.007L2672 ‘#

8X2086. s689.6093.16

ii%Ml. 00

Ordfnatw Ordfnatw

D&m&l

honeycomb

Ifctin#S6.la36. la

Ena~44#g

&A&m

a 76!4L 6!?32.%2.766a lC$aam8.662awam.oa776& 798& a07amsaaasa.aoa

rnchtw

%?&am2.470& Sla

:%

;$$

L 49$0. 97a0.6200.Oal

M&!6.66

Ml16.6020.162a. 8027.468L 10U. 76

Hi4h m49.86

Gz-a 6432-4.8m-h aW% 6W-& 8Qz-a oCM-&8QZ-7. 2

OPEN-THROAT TUNNEL (NORMAL PO81TION)

TABLEHORDINATES OF THE ZRS-4 MODEL

I *tatIon I 0rdInete3 ~ Station Ordinatee I

TABLE .VI

TESTS

Model Fkctcng Tank prosaarea(atmoapheme) I Mae I CarTABLE 111

C ENTER OF BUOY~$C~o:OiSiTION AND VOLUM14C?Z-2.S...-...-.

Do-_--—-Do--------Do-..-——

13z4J......._._. . . . . ..-—

Do_______Do.~--. -.._Do. L------DoJ . . . . .._-D&l S_____Dal I :_____

Do.1 * L----Qz-&o_______

Do.-.._Do._..__Do. . . . . . . . . . .lYrk..-._.

02-7.2.....———po---——

.— ___Do___ . . . . .

GOD:.. _:-–...—

W=6.6. . . . . . . ..__Do_.-—-

Gz-6.8 --------lM-..–-——Do_____

f3z-Dy-----.—- ... . . .

ZRB41 . ..--. .—Do.l ______Do.l ______

~@~;&&m. I.----..................-—-8.6 brass ~... SrnelL

TModel Gong&ofCentsofbmyanog

e%%%now

.-_ao-_... ______ . .._._-_L la AL... ______ a.obr8sL_ Do.I, 2% & I& !im.._..-.. . ..--_—-.volume ..._dO __________ .._____l1, 1($Xl.. --._. . . . . 4.a wII.._. Do.~l#rn . . ..-__. - .i-;rw;: . . . .

. . . .. -.--—-d 2% al IQ20. . . . . ..-. ..1.—--Zr—h#y

CM-2. oCK4-4.8 24:6W-a. o 46.7Cu?W.2 6L8Gz-h a 40,3GZ-L 6 ~:W-6. 813Z-&w8 al. 7

47.4

46, 8a46.9246.8846.864a aa47.8048.647.14fi 7

...--dO.....-..-------- ........ ..._do.. . . . —.— II. . . . . . . . . . . . . .

:::::*:=::::::_l-6:Fwc::lLame,

--l..-—-..._—..........-LlL3d&......-.__ 6.0“v”__._do-------- -_Ao_—-.

.!3&!?:IL.. “KiiliG.IDo.

Do.

Do.

Do.

TABLE IV .__ao ______ . . .._-._1,10,m-._.-__—_ 7.1 b4u?s.-

:R$k’v?:

1

. . . . . . . . . . ..-— —

L 34 alii m.::.-= ::::::::::=1, la m.._. -.._ .._-._L3$L10,20 . . . ----- ..-—-—

AVERAGE STATIC pREmE GRADmNTS IN OLDCLOSED-THROAT TUNNEL .L

Statlo pre.smre gradbts (**)m .-.——~--- ...—.——

1~lQ Al.. _...___. 6.f-f“v’’___: 2#&J:20......._ ---——

-. —---- -— ,L 2%4 mla..----— ...---...—.

--—?%% helm fromhonegmmb

23ta81! “’0” k=.

.. ..ilo._..-..-- . . . . . . . . . . . . . .

.-–-do-—————— ZRZ-4..._ ZRS-4.+0. 076

i.6 -.066-. lao

1:15 +::_.20

+4 104

\

.(s3

.110,m.117. U4

-a 014-.018-.018-. ma-.022–. 024

1bfodal temadill Op+lrl.thmattmmeLs Modal tested 8 faches downstream from normal @tIon.I Modef @Sad Wtth hkhly PO]hb&d 91Uf8C0.~Model tti with roaghened earface.I Fin nmnbere are the fineness ratio of the modeI for wh!eh the fins ware made.