..— -—

REPORT NO.

EXPERIMENTAL RESEARCH ON

141

AIR PROPELLERS, V

By W. F. DUBANDand lLP. LESLEY

Hand StanfordJuniorUniversity,California

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. .

.

.

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EXPERIMENTAL

REPORT No.

RESEARCHON

141

m PROPELLERS,BT W. F. IhJEUD ADIDE. P. -Y.

(1) SCOPE OF INVESTIGATION COVEBED BY PkESENT BBPOBT.

National Advisory Committeereports Nos. 14, 30, 04 comprise the redta

—v.

ofa seriesof - --—

..-.

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wind-tunneltests on ‘&odd forms of- air propeUe& &tending ‘over a three-yearprogram of.

esperimentd work. Thesereportsweremade progremivelyand each without referenceto thereds given in precedingreports tmdrelatingto forma perhapsadjacantin geometricalformand proportion. Thsse reports thus representa survey, made in three pmta, of a somewhat -extandedarea coveringa considamblenumberof model forms md proportionsand vmying invariousclmraoteristicsin a systematicand regularmanner.

At the oonclnsionof thework thuscariied on in parta,it hasseemeddesirableto reviewtheentireseriesof r~di%, to exwnine throughgraphicaland other appropriatemeans the natureof the titory of the oharactaisticaof operationas related to the syetamb variationin char-acteristicsof form, proportions, eto., through the entire sarim‘of such variations, to cheek’doubtfulpointaby repetitionof tes$ to remove inoonaistwwieswherefound, and generally todevelop,for the seriesof mod& representedby theseteats,a consistentset of resultsas judgedby the rdation of those f6r any one model b thosefor all tidds adjacentin geometricalformandproportion.

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It is thepurposeof thepresentreport to give the rsaultsof thisgeneralwmlysiaandreviewof theseseriesof experimentalobservations.

N7mmmtAN)~Im or MODEL Em3se. . . .

TIM number of modd-forms included in the mslyE&whioh is the subject of the presentreport is 33. The three reports on whioh this ana&eieis primmily hssed covered a certainnumberof additionalforms, the rESUMSfor which arenot here inchzded. These omitted forms .--”.—.representunusualor specialforms or slightvariationsfrom normal types and wereintendedtoindioate the reaultato be anticipatedby such departureafrom the more normal nmge of formand proportion. The resuha derived from these modeIs are generally without valuable orhopefd indications.

Thereremainsthe aggregateof 33 models distributedover the range of variationsin form . .and proportionas follows:

Vtiuml. .Ktimti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..- 6kofbWe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

.. .- —

ho fbMc . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2Formofcrimi mctitmofblmie . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ---------- 451deof@ti.* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..- 4

Mu

*

●

.

170 BBFOBT 194.TIONAL ADVISORY CIOMMITTBB FOR MBL!NAU?ICS.

In designating& modele,the followingnotqtionhaabeen employed:

FmdbMmWm No.l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F, (see t3g.1).Fmn of blade amtour No. 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F, (ace fig. 2).ha of blade No. 1. ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..A~(m *l. 2).&d blade No.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..A*(m*.l. q.Hti Mtidm . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . ..P1.

.

Pitch dietxibutionaccodng to constantMI@ of attack 8° . . . . . ...’.... . . . . . . . . . . . . . . . . . . . . . . .P,.Pitch dietdmtion accudngtoconntant angle ofattuck6° . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .P.,Hti Mbu&ati ti~ttie dati Qo. . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . ..P4.Drivingfaceofbladeplane ix without cm.uber. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..8. (aee ilge.8,4, 6, 6).Driving faceofbladecambemd (f@) . . . . . . . . . . . . . . . . . . . . . . . . ..= . . . . . . . . . . . . . . . . . . . . . . . ..s. (m*. 7,8,9,10).

.

Dn~&d Wem H~ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..4.(w@.ll. 12).Driv@ face of blade COllWX............................................................84(eee&. 13),

These VtUiOUS modda 00ver the fo~ow’iq OOIUbilldiOllS of ahamotmisticeof form andproportion:

&u3tant F*A,8,P* with 6 *tiolw in nominal@ch lmio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8,0.6, 0.7,0.9,1.1,1.86mmtr~&lPl titi6*timti ~#timti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.8,0.5,0.7,0.9,1.1, 1.3O~t F~z81P. titi8tih b~$timti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.9, 0.5, 0.7, 0.9, 1.1, 1.36mtit F~.P. titi6ti. ti~@timti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.9, 0.6, 0.7, 0.9, lJ, 1.88~t FlA.3#. tih8titim h.l@timtio . . . . . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6, 0.7,0.98comtant FIA#,P, with8 vwiaticminnominalpitchrati6................................... 0.6,0.7,0.96.tit F#lSIP. titi5.tiu hm. @timtio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7,0.9,1.1, L89mtit Fw.P. titi.8titiom hmti@ti mtio.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.5,0.7,0.98mWt F1A18#. titi9titi kmti@ti mti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0,6,0.7,0.98mWt F1ititi 8*timti timI@ti mti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ... . 0,6,0.7,0.98 conetmt F&,S#l with 8 titiom in nominalpitch ratio.. . ... . . . . . . . . . . . . . . . . . . . . . ...”..... . 0.6,0.7,0.98~F.&S31 titi8dkin ~titimti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7,0.9aOomtantF1A,8#, with 8 Variation in nominalpitch ratio. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0,6,0,7,0.98~t FrQ$atiti 8titi&h ti@timtio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7,0.98~t F~18#ad& 8~titi. h~@ti~tiO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7,0.98~t F#~. titi8titim h~~timti....... . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0,7,0.98~t F&lS$ltiti 8mktiwh ~$timti . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . 0.6,0.7,0.98mht F&aP. titi8titi h~fltimti . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7,0.95 conetmt F~&Pi with 5 veriatiom in nominal#t& ldO...................................0.6,0.7,0.9,1.1, 1.s6 conetit Fp4181PaWM 5 *tkM b nodnfil pitd dO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.6,0.7, 0.9, 1.1,1.86~tit F,A,S1P4titi 5vdtimh notil@ti mtio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0.5, 0.7, 0.9, lJ, 13

In addition to.the above 83 rnodds the report inoludearesultefor:Four modeleof ocmtant l?~l andnominalpitiratio 0.7, but ‘%rithmaximumtbicknesaof

orosa+mtionat 0.17, 0.25, 0.41, and 0.49 of the width from the le@ng edge. See_ 14,16,16, and 17.

Onemodel of oonetantF,A1& with bladm made adjuetablefor.ohangeof pitoh, the pitahbeinguniformat 0.7pitohratio.

The oharactarieticaof thesevariouamodelsin detailwill be found in.Table I.

#

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Im%%.“g%% I O& %%.

i

171

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b

—.. -

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. ...-.

._.-

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_.-k

.. _ ,,-.-

-.__. k. ..._

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—-.-. .

. . ..-..-.

-.. ..-. —.. ..— -...—._. :-.-. Z .-

●

BEPORT l.T&CIOIUL AWCSORY 00~ FOR AEROITADTICS.

TABLE I.L-Dkmiow OfWtiO?U(bbb~. 18).

172●

-.. .. ,_L ..,.

,.

.

. ..U-r. .

.F

. . .

A&

?,

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-.

. .- .: .....7-

----

., .-c” -.:- .= ,

.:l—

I.-

‘-----Lkmbou. B. lkcbw. tih

r, :’.;% “%# & FI AI.. zmIa

.90%m .W.’”. . 16. 9m .W. . ..... .

4- &w”hLm

[T

4 slF:&...$$ :R”““”:SJj6;;,&@i“’”b. oo “.L”M-.

b 4#”FgA.&.7 La “LI7I10 S14 Lobla 906 .m10 1.90 ..aI

....MMJ.. . . . . . . . .

60

-—.It

1“1.................................................................lo......... .................. ..... ....,-------.................... ................... lb:......... ..........

—..:LIO

L4N.84.66.UL10LOI.84%LlbLOl.2,..&

M.b4.m.4QL14LOl%.4b

l%:!

L“tiLOl.s4

...:“LMLOl+

“L;LOl:%.9LM104:#..a

.,.:.,:.

...

-.:....

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II...........................................-..................... .ai-,

1.

. . . . .

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......... ..........i. .

.-””~iy HH;:!

# ::::::::::..........

-“””y ::::::::::.......-

. lb ...........

.10..........

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1

:3 :~;::;g.............,-

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&rl As...I.,.! IIEIF’*AL..’

.8

9

10

11

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...........10..........

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1

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:% ‘--.---””.07‘---”--”--p H::::

......... .la

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......... :%

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......... .ln

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1

la

Kti .alh= .e4a14 . . . ,6a“a69LW .:.:%

a.m .“ ,:j

i% . .7b9.60 .U1Loo .U

14

14

la

17

iI1

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I......... la’......... ................... .................. ................... ..........

.-

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\

.JA1......... .................. ..........I........ ........“.”::.:. :-m+.

1

I \

...—. -.— .-.

The dimaueioneof the sectioneshown in @urea 8 to 17 are given in Table II, referencebeingmade b figure18..

EXPERIMENTAL EE8EABCEOl!fAn PRo~ v. 178

D&-x?

\

I

.

.—

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174 RID?ORT lVATIOITAL “ADWSOBY OOMMITTEB FOE AERONAUTICS.

,

D&*

\ T/k 6/‘

-.

.34

\

—.

-1.mk

-L6/=&

—.—

F2 Al FZ9.2

. .

.

FE /4=

i

\I.— . . . . .

—

ExPERITIENW RESEARCH ON AIR PROPELLERS, V.175i

, ./6-Rad

16”Rad

!3”RadL3”Rad.

4-Rad.

Fig. 3 S&Al

16”Rad.

7-ha!

4-Rad.

Fig. 4 S, ~ A2

16-&d.

13‘Rad.

/OaRm!

4-f?ad. 4-&d.

Fig. 5“ S, GA, Fig. 6S, ~ A2

. . . ...

176 REPORT I!WI!IOHALADYISORY OO~EE FOE AERoNAuTIcs.

16”&d. Iii’”t?ad

13=i?od.

7%bd

L9-,J?d.

#

m ‘Rod.t!m~f! i!-J

7nKbd

4“/?od 4 “Rod.

Fiq. 7 5P F/ A, Fig.’&3. S=F,AZ

16-RaOI. 16wxi

Lm?d. 13=Rod.

T.Rod. 7=&d.

4“Rod. 4“f?od.

Fig.9 S=&A, Fig./U .~ ‘“ ~ sea.@%...... . . .

EXPERIMENTAL.IRESEARCH ON AIR PROPELLERS, V. . 177

16-I%L+. Ils-i%gf.

L3-Rad. [3‘Rod.

fO”Rad. 10“hi ...—

II

7-Rad~\R!$iiii\ “~.‘

7-Rm’.

4’”l?c7d. 4-/?ad.

fiq.11 S3 ~ A, F19.IP

/6-Rd.

[3”Rod.

al

.

4“Raa’.

S3&. A2

f6-Rud.

13-Rad.

m -Rod.

7-&d.

“4”bd.

.

.:—

—.

178 BEPoB!l!lm!J!Iol!?ALADVISORY00mam!l!m FOB.4m0K-u!mls.

16”Rod.

13-Rod.

*e

10“Rod. e!

~f3

7-R#.

4-W.

Fig IS ~fiAl

16”W.

U“Rod.

10‘Rod.

7-&d.

#“w.

—._

-.

0 —.c.B

Fig.??3R

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l?l~ EES3UEOH OH An PrtoPEuiaRE,v. 1’79

Thesemodelsfurthermorepermit of groupingin such maunsrss to give remltafor the fol-lowingseriesof gradedvariations:6 variation d “~ti ratio with 4 combimticmi of. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .FAil P.6titiom d@timtio titi40ha ~timd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..FASP.stitioM d@timti titi 18tia~ti d . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. FABP.2*tiad~ti&M ~tid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .AEPwithpitchraticL2variationo dbMeareatiti36 combiitio?. wd. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 Pwithpitchnkio.2vaziatimu of blade eectionwith24 comhimtimsof -- . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3A P m“th @t& rstio.Svariatiom of bhademction ti&6*~ti d . . . . . . . . . . . . . . . . . . . . . . ..--. . . . . . .FAPwithpitchratio.4mwiations dbladeeectionw5tlt 60tkruxnbktiomd .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .YAPtithpitdIra&2 VMiatiom of pita Cwibutioxl with 26Comhindionllof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .F A S with @ch ~tiO.4muMioJMd pitdiditkributkmwith 6 other aunhinatiom of. . . . . . . . . . . . . . . . . . . . . . . . . . --- _FAi3withpikhrati.

The generalmethod,of test lus alreadybeen describedin precedingreports (Nos. 14, 20)and need not he more espmiallyreferredta at thispoint.

(2) EEDUCJZON OF ECPEIUMENTAL REsuLmO

For ther~udion of experimentalmodelresultsto forms suitedto useinpraotigalproblems,the folIowingnotation is employed.

D- dkneter.N-revolutions.

.

V-velooity.A-density of air.H-altitude.T-thrust.Q==tmque. 0

P-edkotive power Qxmerdeliveredby engineto propeller).“Pl=IUaefUlpower (utilizedby propellerfor propulsionof phme).

q= efEoiemy-P1 +P.B, 0- ooefiicientsvariouslyspeoifiedby subsmipt,and servingto relate T, Q, P, or PI to some

function of V, D, N.z- V/ND. . ‘-

oomRKmwrsor ~, TORQUE%AND POWER

Thelaw of oompariaonwhiahis accaptedfor the dkuawon- of experimentalxwndtaon modelair propellersand for the purpose of making use of such resultsin mnneotionwith practicglproblemsrdating to full size propellers,maybe stated thus:

For propelIeraof similargeometricalform and at equal values of the fumhion V/ND thefollowingrelationshold

T- V*D2 (1)Q- PLP GO

These relationsmay be expressedin the form of equations by the introduction ofooeWtits l?,, l?,. In orderfurthermoreto makethe mfficientsnondimensionalwhileat thesametime mwuring T and Q themselvmin gravitationalunits,we may introduoethe faotor g, thus@% quatim as fOUOwa:

gT- B,AVW (3)

gQ-BAPD’ (4)

—.—

——

——

.—

—

This gives for the coefioientaB, end B, the dues:.

(5)

.“-A%’ (6)

.

180 RBPOET IWATIOI?ALADVISORYC4)M.M193!EEFOB MRONAUTIC9.

We may now rsatatetheumuuedlaw of comparisonasfollows:Forpropelksof similargeometricalform andat equalvalueaof thefunction V/ND, valuca

of B1in (5) will be the sameindependentof absohe ~e; andlilmwieefor valuesof B, in (6).If thenwe multiply equation (5) by the equationz’- (V/ND)’ it iEsrvidsmtthat we shall

have, on the left, a new cmd3Ment,likewiseindependentof absolutesize,and expressedin formaa determimidby the right hand memberof the resql$ingequatiom

Thiswillbe dear by holdingin mindtwopropellers.ofeimilsr~metical form andoperating “-at thesamevalueof V/ND. For th~e partioidarconditions,thevaluesof the CmdMentB,, foreachpropeller,will be the same. If. then this singlevalue of B, be multipliedby the value ofV/iVD we shsUhave a newsinglevslue, likewieeappficableto thsaetwo propelkreoperatingattbia value of V/ND. We may similarlymultiply or divide by ‘any power of V/ND orby(V/ND)* where n may have any valuepoeitiveor negative.

We may thus derive an indehite seriseof co.ellicients,all relating to thrust,and in eachctwefuMUingthe oondition.of equalvalueaof caefllg@t for.equalvalueaof V/ND for two pro-pellersof eimilargeornetrioalform; and if for some two propdlere, thenfor any two aad hencofor my number,so long as they belong to thesamef-y as regaqiegeometricaltype or form.

Thusbyway of ~ample, by suitablyealeotingthe”indexof V/ND, we derivecoeihienta forT r$ated M follows to the variables V, D, N, A:

%&A ‘A%’ A*’&, mIt willbe noted thatof thsaefour eixamplea,theflretinvolves Vand D, tb secondNand D,

the third Vtmd Ntidthefourth. V, N;D. ““”” -We may deriveaimilsrlyocdcienta for Q m follows:

,

(8)

Turningnow topower we have immedktaly from (3) and (4)

gP, -gTV-BIAVW (9)

gP I=8@N=BW1B,ANTD’ . (lo)H6noe . ...”. . . :.- - - . .

.—-—- ..—

3-”-A,“ A : (11) - ““But formy two pOpSUSIISgSOrnI@C@y ,@nilsr in form and atthesame due of V/NP, ._

the two valuesof B1 are the -, andlike~ for B,, whileby epecifimtionP/ND is thesame.llen~ from (11),the.aflhkm~ will be the sam~

This meansspeoMcRUythat for any pair of propellersgeometricallysimilarin form andop”hratingat equal,v~uea of V/ND, the eflioieneimyin be the smae; or more broadly, thatthroughout all the memb of a given family of propellemof the same gwmekricalform, agiven value of V/ND willfix the efikienq; or otheryiee, that for a given family of the samegmnetricil form, dhkmoy is a fmmtionof V/ND oiily.

From (9) we have the coefEcient,

“=A% ““ ‘“(12)

.Ththesamemannw as for T tmd (J wemay titi derive a &of cotiaients from that

defbiedas in (12), by multiplicationor divisionby powersof V/ND. We may thusdwive inparticularthreeCOatbnia 8s follows:

Z$i9’x%’A* ‘ ““- (12)

ElmMUMEI!7TAL BEEEABOHOH=PR ~ v. 181

!l!kre will obviously be threeaimi.hmcoefbients for the effeothe powerP which may bederivedfrom (10) in the same mannerin whioh those expressedin (13) are derivedfrom (9}.

..—

It is olear, however, that if for two similarpropellersat the same value of ~/ND there is anumericalcoalTwimtrelatingPI to some funotion of T, N, D, and which numericalcoefljcientis the samefor both propellers,thenskce the efficiencyis also the same, therewill be auother

..

numericalcoe13iohntrelatingP to the same funtion of ~, 1?, D, imd whiohrmmeriealcoeffi-oientwill Iikewiaebe the samefor both propellers.

We may thereforeuse coeflioientehaving the forms given in (13] and derived eitherfromP, or from P.

.-

For presentpurposeswe shall use the efleotive power P se the primary power quantityand we shall denote the three coefficientsderived from effeotivepow= and having forms asabove, reapeotivelyby Cl, (?I,0~.

--

We shaIIhave thenfor theseooeilioients:

“ -A% (14a)

C’=x%Q, .*4

-/The foIlowingrelationswill be noted: “>

... ..,

(14b)

(14C) .

(15)

TVitih any conaiskntsetofunits,vieshaU thenhave a get of ooefkienta 0,, (7W(2,inde- . _pendentof thesyetamof unitsassmh, andhencethesmnefor eithermetrioor E@sh me=-. - ..-----

It reaultafurthermorethat in the Mlc fcmnuhelpower is measuredin Mogram-meters .._=.per seoond or foot-pounds per second and not horsepower. Lkwiee speed is measured inmetersper seoondor feet per seocmd and not kilometers@r hour or mihe per hour.

C&dingthasevario= equationstie have as folIofi: ‘ -gP - OIAWDS

gP = (7,APD’

g~= O,APAW .

.Y - Viw

P, -VP

q- funotion of V/JVD as in tables or diagrams

T-PI+ P

Q_P+~=~

In theuseoftheseequationsitmust be rememberedthat the units are:Metrio: meter, kilogram,second.English: foot, pound, second.

Henoe D is measuredin metersor feet.N is measuredin revcdutionsper second.V is measuredinmetersper second, or feet per seoond.A is measuredin kilos.Peroubiometer, or Boundspei oubiofoot.

(16).

(17). (18)

(19)

(20)

(21)

- (22)

.

--.

- -—

P is measuredin EIogr”- metem.per&co;d, orloot-poundspersecond.T is measured in kilograma, orpounds.Q ismeasured”inklogram-metene,orpound-feet.

182 REPORTIUTIO19fi 4DV’ISOBY COMMITTEE FOR URONAU~a. , . u-.

With these units, as previouslynoted,thevsluee,ofCl,C,,C,willbe nondimensional,andhence thesame.with eithermetrk or B@sh uniti..

Ifany ofthse variousquantitiesme expressed in terms of othw unitssuch MIhomepoww ‘- -.:(metricor English),kilometwa per hour, or miles per hour, they must be reducedto valueaintSRUSof the above unitsbefore direct UMiEI~de of the fo~b ~th the n~eric~ V@CZIOf .+.Cl, U,, C, as in Table V~ or fiw= 19 to 52.

The dual testrebsultaare thenput in the form of the followingseriesof items. .-.—TABULAR.

Valuesof cc@oi~t Cl on V/ND as argument.Valueaof ccdbkmt C, on V/iVD as argwqent.Valuesof cdefhiant (Ison V/ND as mgument.Valuw of efficiencyv on V/ND”ae “iughiitit.

See Table VIII.GEAPmc.

.- .-.

.- --—

Valucaof caefkient G plotted on V/ND se independentvariable.Values of etlicienq 7 spotted on curvesof Cl as above.

._..—.

(See @s. 19 to 52.)

APPLIWTION, W EQUATIONS (1S), (1?), (IS) TO =CMCML PBOELEMS.

Of the nine quantiti~~ V, ~, D, A, E ~, Z, with the ~W COfi~eR~ Qi, OS, f%

some combinationofwtichm .mk @JO SUChpmbl.~~ we may note@t ~t;P,, is dependenton q andP, beingrelatedas”in (20)UJmis depended on z, being de-ad and axpreaeed both in tabdar form and graphically as

R funotion of z alone. k-(% also (11).)

The three coeflichta (YI, 0.., (?,, are dependent-cm z and are so ~etermined and given in tabular . -

and graphh form.(SeeTable VIII ind @. 19 to 52.)

His dependenton A beingconnectedby therelation@tw~,altitude andthedensityof theair.Thereremainthensix variables,P, V, N, D, & z, anY four of which (with ono exception “”-” ““””

----

to be noted later) maybe taken as the necessaryand sufficientspecificationof a problem.The number of type problems“whiohmay thus ariseinvolving combinationsof thesesix

qwtiti= wouldbe th~ the n-bw.mf COIP~DtiORS.of ~ ~gs t~kenfo~ at a the. ~isnumberis 16 and thecombinationaare asshownin QCJUMR1 of Table ID. ___

TABLE HI. -

‘ww-●\./ ● I

I.

-x. ;I; ”““i ●4 ,...............................$D .......... .......... “y ..........XN ~,j........... ..... .... ...... ...AV

, ●● I

. ., ..

.

-

. .

J-

>-—

.—.

-.

--

Of thcae 16 combinations,all representpossiblephyEiicalproblems exoept the second, in-volvingx, V, D, N. Shoe i- V/ZVDit is olearthat we can not arbitrarilytake valuesof more .than three of theseparticularfo~ quantities. ~ is the exception refd ~ above,

mmEmmmT4L maEABcmol?Am PMPmxam ,‘v. . 188

In oolumn (2) are gimn the unkownsfor the sevaml easesss noteii If the velue of z isamong the lmowns, the value of the e&.aienq will follow immediatdy frmn Table VIII or@uree19t062. Othmwise,i fziswnongthe unbowns, itsvaluewillrmultimmediatdy homequation(19) as soon es V, D, and N are known. Onoe q is known, the useful power P, tog-ether with the thrust 2’ and torque Q, may be readilyfound from equations (20), (21), (22),if desired.

lk oohunn(8) a oheokmark indioatestheoaseswhioh may be solved by equation(14a)orthrough the eodhient 0, as defined by this equation. Similarly, in 00Iumns(4) and (6),oheokmarksdenotatheeaseswhiohmay be solved mpeotively by equations(14b) and (140)orthroughthe ooeftleientsUM~ as dabed by theseequations.

Th90SSS3OheOkedin 00h1?nD(8) arein tied thosein WhiOh the fourkIIOWUSOf00h1mll(1)arefoundinequation(1)and simikrlyforthoseofoohmme (4)and (5).

The starsinwhunn (6)denotetheoeseswhioh areoheokedinallthreeoolumns-that is,theeaseswhich may-be solvedby any or allofthethreeequations.

In additionto theseeightoesas,itwillbe noted thatoases(12),(14),and (15)maybesolvedby eitherorboth of two equations,whilenumbers (7),(8),(9)permiteachofsolutionthroughone equationonlyasindieatd .

By theuseoftheseequations,asohoieeor neoessitymay diotate, any of the 14 oombirwtime of quautitieaas noted in TabIe III. and representingpossible probIems“revolvingtkevsriablesmaybe solved by suitablemethodsof computation.

Jn most problamsin design or of like praotioal oharaoter,the geometrical@pe form ofthe propelIeris first assumed. Suoh assumptionis, of oourse,ody tentative,but it is usuallyconvenientto oemy on the programof searehfor a suitable designthroughtrial of a seriesofsehmtedtype forms. k suohease,with a type form ohoseq the rehbtionbetween the oodh-oienta(?I,~, ~, and V/ND is immediattdyfixed, and,asmmingit to be oneof the88 type.formaooveredby the presentreport, referenoemay be made direotlyto the oorresponchg diagramor.table for VEJUSSof the fienoy tmd of the ooii3itieJIts0“ 0,, CJ,M ftmotionsof V/ND. ha~m~-, ti, m~duedb*oy qordtifmotin V/~fl~-ately determinethe vsluea of the ooefhients and the solution will prooeed along lines asindioated.

In certainoases,however (oMee7,8,9, TabIe III), iihevalue of the eoefEoientmay be leftse an unknown, the various othar quantitieshaving been detamuinedindependentof any se-leobd type form of propeller. The solution will then give the value of the ecdioient ~ ~,~. This eoeffioientvalue may then be sought in the table or on the diagramEfor varioustype forma. ‘iYhareverit is found it will at the ssme time determinea value of z, and hemsof eflioianoy,and the value of the latterwilInaturaRybe a guidein the ohoieeof the type formb be ultimatelyaocaptwi If no aoeeptableresultsin these reepeetaoan be found, it meansnaturallythat suitableahangeamust be made in the basio data-es, for exm@e, an inoreaseor dearessein the diameter or in the revolutions or speed or some combination ohange inthesebss+iodata wbiehwill-give a difkrent due of the m-t and thenoeperhapsa moreaooeptableE@OklOy.

In a similarmanner,with otbr @pea of problems,es in Table III, the seleotedtype formwiththe resultantvaIueof Umaybesuoh sstogivean unaooeptableresult,eepe@y in termsof D, N,or V. Iniiimhoase,likewim,t hebasioassruuptionsmustbe modbhdinsuehmanneras to give My en acceptable combinationof valuw

(8)NOMO GRAPHIC DIAGRAMS

——

.-

.-..-

. .

For the rapid graphioalsolution of probkimssnob es those ooneidaredin the pmoedingseo$io~ nomographicdiagram hava bean preparedas in PIateaI-m the tit four being in “metrh and the seeondfour in Euglishunits. k the earlierreports, ooveringprogrdvely the

184 REB3RTNATIONAL ADVISORY CIO~ EOEtAEBONAUTWS.

sties of tests forming the mibjeot of the present report, this feature was represented by theEiffel logsrithmio diagram,~th curveqE$owingvalyM of 0, for ue@d and effective powerdrawnthereon ‘Me form of diagram,whilefag a solution for au combinations of data “- “ ““involved in designproblems,is, however,subject td two disadvantages:

(1) The operativeprogramwith referenoeto the eequenoeand direotionof the vectors isnot easy to wry in mindwith only occasionaluse, aud thisfad h= undoubtedlydiscouraged,in some measure,the use of this exceedinglyingeniousform of grapbioalsolution for designproblems. —

(2) Valuesarenot -uen~y de- “hyintarseotionaof lima at rathermute angles, ‘-thus tendi.ugto magnifythe probable errorof oonstruotion.

For thsaereasonsthe nomogmpbioform of diagramhsabeen ~= ~ the p~t ~Port. - _k diagramsof this type the operative program is simpler than in the Eihl diagram,and theintameotions,maybe madeless aoute. To oover all combinationsof the data whiohmay enter

.-

into smh p~blems, however,four diagmmearerequiredratherthanone;Thus, refem%gto the diagramsi@ended for me@c unjta,Plates I, II, III arelaid out for-

--

the use of equations(16), (17), (18), respectively,whilePlate IV is providedfor the solutionof ‘-equation (19) or generally.foroonneoti.ggtogetherthg_fourqusmtitieaz, V, N, D.

Any dimussionof the theory of nomographicdiagramsor .of tie detailsof oonstruotionof “”” ‘-”suohdiagramsis beyond the mope of the presentreport. It @l be desirable,however,to givesome descriptionof the die. as they are, togetherwith SUWBtiOm wwdiw their UM%and with suoh data as maybe requiredshouIdit be desiredto reinstruct such diagramsona huger smileor to axtandthe soaleon any of the axes of the diagramsas given.

Rakrring to Plata I, the diagram@ intandedfor-.ihesolutionof the equation

flP- OIANSDE

Attentionmay tit be direotadto the followingpoints:(1) The faotor g does not appearin the construction. It is “absorbed” in the program

of developmentof the disgrmy This remarkapplk equally to-the diagramsof Plates II, III.(2) The quantityA does not appear directly ~,. the Ngstyuction. I@ placwis taken by

altitudeH. This is simply a matter of the numberingof the graduationson this axis. TheaotuaIdistancewhiohis involved in the graphiml 00JMtruoti~ti rdy A to a mitab~efit!but the numberingon the male. repreaentathe o@wsponding idue of the altitudeH. Thus :the scalesmay be read dimdy in termsof altitude,whilethedensityA is the quantity really .employed in the computation. This remark applies equally to the diagrtuus of plates II, HT.

(3) The diagram oontaina axes, one eaoh for the five quantities P; C,, ~(A), ~, 11,as noted, .

tugether with two auxiliary axw Y,, Y,.(4) M thsaebe arrangedin orderas follows

D H(A) N Y, Y, 0, P

(5) These may then be taken in thressumessivegroups of three eaeh as folIows (see ahosmallkey diagramson plates):

“H Y, O,iv Y, Y,DY, P”

(6) Th”mhtim00neis@inefkt, then,ofdrawingthreestraightlines acrossthesethreegroups of axss, as in (6), in suohmannsras to contain the Imowndata and to have mrmnonpoints on the auxiliary SXeaY1 and Y*. Oneof these lima wiU then cuttheaxisoftheunlmownatthevaluerequiredfor the solutiom (See aIsosmaUkey diagramsas above.)

(7) It should be eamoiaUY notd that the eevemaxes are associatedin three groups ofthreek abovs and in tl& way-only.

(8) The foUowingpoints regarding

—

the units of PIateaI, 11, III, ~ shouldbe notod.

\

.

(aj The unit of P is the metrichorsepowerdirect and not the kilogrammeter per second,as in the case of nu.mericdcomputation.

(h) The unit of N is one revolution per minute instead of per second, as in the case ofnumericalcomputation.

(c) The unit of V is one kiIometerw hour insteadof one meter per second, es in the caseof numericalcomputation.

These changes are made possible by suitable changesin the units used for the variousscalesof the =es of P, V, N, and thuspermit the direct use of tke quantitiesin termsof thecommon engineeringunitsof mmmmment. -

The scaleson thesediaggwns,therefore,indicate as follows:V in kilometersper hour.Ninr. p.r.uDin meters.~~ h~aesewer=(metrio).

01, iJ,, (?s, kndunenaionfd.

-.

.-. ——

RLusrBATn’E PBooBA?bls.

More noting a few illustrativeprograms,attentionmaybe called to the followingpoints:The solutionin each mse will call for the determinationof the unknowTMSEnoted in the —.

severalcasesof Table 131,and thisw’111requirethe useof two d@rams-ti, PlateIV andeither”...—

PlatesI, II, or III. The formerwill detmmineone of the four quantitiesV, N, D, or z and the. ..—

latter the r- *-The coefilckda (7,,U,, ~ aredependenton z - V/ND and may be determine! fkom figures

19t0620r Table VIHessoonaszis known...-

-.. ..——

In caseswherez is one of the knowns,the vahmsof ~,, (7,,C,becamelmownfrom @wee 19ta 52 and Table VIII. h such cases the nomographicdiagramsare to be used in such order ..-es may be requiredby the detaiIsof the csse-that is, Plate IV fit and then Plate 1, II, or ‘III, or vice verqa. @ee cases3,4,5, 10, 11, 12, 13, 14, 15, Table III.)

In caseswheres is one of the unlamwns,its determinationmay fti under either of twoprogram:

(1) If the lmowneinclude P, N, D, thenz is found immediatelyfrom the diagramof P1ate .IV. (Seecases 1,6; Table Ill)

.._—

(2) If the imownsdo not include F, IN,D, they will includefour quantit.k permittingthedirect use of eitherPlate 1, Plate II, or Plate Ill. This will give the due of ~, U,,or C,, andthis through@ures 19 to 52 or Tabh VIII will give S- V/ND, and this throughPlate IV will - ‘- ‘-.@v&ther . .. . unknown. (Seecases7,8,9, Table Ul)

By way of illustrationsaeumefit case 1, Table III. The values F, D, iVserve immedi-ately to determinez or V/ND by the diagramof Plate IV. A“Iineis drawnthroughthe valuesof Vand D,cutting Y. Amndtih tib-ti@ Nmdhpokton Y. Thislineextendedto theaxisof z or V/AIDwill thengive thevaluedesired.

.

With z Jmown,we findhn thesuitablediagramof figures19 to 62 or from TabIeVIII thevalue of Cl.

..-

We havenow es lmownsall valuesinvolvedin the @gram of plate 1 -mpt ~. Ths Mad .groups are then as follows:

HY, i71-N Y, Y,D3?, (P).

The Iinefor the first triad being drawn, the point on Y, is determined. This point withN serves to determine3?, in the second triad, and this point with D serves to determine P inthe third triad, and thus the SOIutionis completd

.m.

186 EWOBT N,A3!IOI’UIIADY180BYW~ EOB -XA~~

Supposewith the same data it were ohosemto use Plata 2. The programfi proceed kentirelysimiIarfashion. The value of z is tit found and then 0,. Then in Plate II the triaddevelop aafollows:

HY, D

;g(~

In an entirelysimilarmannerPlate 8 may be wed if desired.hume next the data of oaee10,Table III. The valueaof z, D, N beinggiven, Vie found

by Plate IV. The valuesof 0,, U,, ~-resdt humediatelyfrom z throughmea 19 to 52 andTableVIII. In easePlateI isemployed,thetriadgroupsresultasfollows:

(H) Y, 01N Y, Y,D Y* P

audHisdeterminedasthe ~ -0=Assumeagain the data of we 7, Table IIL The kWIIS 1’,A,~, N tidcah Hak I MI

the only one availablefor this combination. The triadgroups result ss ffi:

HND

Y,Y,Y,

($)

P’

The value of U, thus redta, and this gives, throughilgurea19 to 52 or Table VIII, thevalueof#, mdthenoethrough Plate~mMV.

In all of theseoaseathe value of the efhienoy n will naturallyplay an importantpart indetmminingthe ooume of treatment of a dwign problem This value follows immediatelyfromz, through@a.19t062and TableVIU. Ihmauyoases ?willbesssumed asatidxat some value whioh it is desiredto realizeif possible. Or otherwisethe value of z==V/NDwillbe assumedwith primaryreferenoeti the eorrapomhg value of the afiieieney.

Diagram of the nomographic type are eqwoidly wall adapted to the purpose of indicatingquiokly the oorralative ohanges in any two variablea of eithar end triad, all other quantitisaremainingthe same. Thus, a Iimsin either and triad may be revolved about ita Y axispoint without disturbing the remainder of the diagram. In this manner the correlative_ of eitherof thesetwo pti of variablesare -y usmined.

Thus, in ease (l), V, N, and D are asiumedImown. The value of z follows and thenoeG’land the solutionproceeds,as previoueIyindicated, to a resultantvalue of P. In this triad Pis sssooiatedwith D. We may thentilt the line back andforth about thepoint on Yaas oentwandreadoff thevalueaof P for a seriesof diameters,d othar-“tics onthisdiagramremainingth UnM.

In order to realize the latter oond.ition, however, it is dear that if Cl is to raua.in the samewith the same type of propeller, then z - V/ND must_remainthesame, andhence(Nremain@the same) Vmust be assumedto vmy diredy with the varyingvaluesof D. ~us if the D betaken 10 per oent largerthan the fit value resumed, then the value of P for a speed also 10per cent greaterat thes- r. p. mawill be givanby tiltingthelineabout the intersectiononY, as indicatedabov~

Again inPlate~, supposethat the vahe of z_isone which gives a value of the eflioienoyundesirablylow. In thisdiagramz is aasooiatedwith N. We may themtilt thezYNline abouttie Y~kt=a=tidnoti tietitionkW- _ehhr. p.m. md_ekxmdham ehaugein edlkdeney,the ratio of V to D being suppmedta remainthe same.

Othersimilarapplicationsof thisconvenientfeaturewiJlocaurto theintarededreader.It is apparent that in all of these various oases the solution maybe tied on through

equations(2o), (21), (22), to inolude,if desired,valuesof umfulpower, thrust,and torque.

.—.

=E~TAL BESEKEOH OH “AIRPEOJ3mhms, v. 187

Nomographicdiagram might, of oourse,be preparedfor the mrrying out of the indicatedcomputations,but their relatively lesserimportsnoe lms not seemed to justify the extensionof the p-t report to inoludethepreparationof sudhdiagrams.

While the preoedingdisoumionof thesediagrms has applied especiallyto those of PIatssI-Iv adapted to metrio meseume,the smne generalremsrks apply equally wdl to those ofPlates v-m adaptd to Ihglish mssurw.

The soak of theseindioateas follows:Vin mik pm hour.Nkr. p. m.Din feet.Pin horsepower.H in feet.

. 0,, (7. U,nondimeneiomdas in Plates I-IY.Pmporticm and mz7m—A nomographicdiagrmneuoh es thatofPIateI for the solution

of anequationsuohas(16)maybe MniteIy vtxciedinproportionandinthescaleunitsemployed,allhowever,sorelatedastofulfdlthebasioconditionsrequiredforthesolnhn. The parthdarproportionsend soaks employed in PIateaI–m have besn chosenprimarilym suob man-nerastogivea fairly eqpable Wributicm of ases ovar the diagnun,oombinedwith the rangesof valuesohcaenfor the dHerentvariables.

In osseit shouldbe desiredto lay down eny of thesediagram largeror _ than theserepresentedin plates I . . . VIII, or cuveringdifhmt rangesof values, the following methodmay be followed:

T- ~.+x OjtZtU.

HATES.

D ........E........k%F........4.440Y........ ........m

g:::::~~

&::: :SJY—..... 7.2M

._ . . . . ..lLM11 . . .._.Jm7P........s.am

k-xP—.....mm

%.......am

The spaoingof~themmedve axesisgivenin Table IV. h the originalsfrom whiohPlates I... ~ were reproduced, the unit was 1 imih. This unit maybe similmly takenat any value whatever, thus giving diagram with spmings shays in the same proportionsssthose of PMesI.. . ~, butofmy aetualsize esmaybed=ired.

Next we must oonsiderthe mid wihwa; that is, the values.lying on a single wntinuousstraight line drawn through the oentar of the field oovered by the diagram. These valuesare given in Table V eaahin termsof the speoialunit appropriateto the quantityin qudon.

TA31rlnv.—Miiwdu44.

PLATES.

I L v. nVL m. Vm. m. mm

, %::1 4s 16Jlll 2:::::::% $% 2::::::%! ‘%! +Z15% ~% .; F.....~ #.... AL: lwJ f:::: aq

. . . .. A.SIO lsJcQ D..-...Z6 kS .a? E...... m m E.....-WW1,~

! --”-- ....... m H......J,810I,mfI

Next, for themalesubdivisions,thereis, for eadhh, a faotor~~ definedby the equation

-..-—

-.

.. ..—

.—.--

-----—=.

.-.-..

—..

..-..——

.-_.. —

-. . .- -+=

whm (%-~ -distenoe, in krms of my arbkry unit, between graduation for values %d% (%>%).

188..-

REPORT U“OI.WL tikUORY 00MMrM!EE FOB kiItOXAUTICS.

These factom j are givemunder,the appropriateheading in Table VI.mmdentof the matem of measurescmdoved d are thereforethe same for

.

— . .

my are indc- -both metrio aud

“ihgliahmeaaur& It will, of mime, “k kdaretood that the unit of measureemployedmustb the emuethroughoutany one diagrmu.

TABLE VI.-Vi of fadora ~.

PLATE8...

1,v. Q VI. m,@. ; Iv,vm.

.........lam O..........am 0.....:—L= x;wan ,V “’-””-’--:?

! & ......l%b% ;..~~:::am 2?:::::7M%,Z::::::>&& -“.

I ‘:’::::::’‘= “’’’::::%+-‘::::3:1:!i=---v. “:.— . . . .To k the ideas, take Plata I, axisof D. The midvslue is 2.8 (metric). The distanceto

the graduationfor 2 (metem)will then be measuredby 18.33log. 1.4==2.678. This may thenbe laid down to any convenientunit, having in view the size of diagrampermissibleand thew of V4dUM desired.

If thereshould be reasonfor deriding tha diagramto include, say, values of 1 and 10,the distancefrom 2.8 to 1 wouldbe measumdby 18.’32log. 2.8=8.197, and, again,the distancefrom 1 to Owould be measuredby 18.33log. 10==18.33.

Instaadof using factcm as given@ Table VI wi~ a unit adapted to the aim of diagramdesired,a tied tit such as 1 cm or 1 inch maybe adopted, and -may multiply or dividothesti of factorsiu Table VI by any cod%hientat wiU,thusgivingvariousswim of numbem,but alwaysin the proportionof threein the table.

Thusjby way of ihstration, in PIateI, axisD, the total rangeis from about 1.876to about4.182. The log. of the ratio of thesetwo numbersii 0.8483, and with a unit of 1 cm. and thefactor 18.33 as in Table VI the Wal length of this axis would equal 6.384 cm. By taking aunit of 5 cm. or otherwiseby usinga faator 6 xik33 ~91.65j the over-alllengthwouldbecome3L92 cm. ““

.—. . .. ... . ..—

In thismmmer,then,thegraduationaon agy axisnmybe laid out accordingto conv@ence.Obtiouily the sameunit mustbe used throughoutfor any one diagram.

If for any reasonit shouldbe desiredto subdivide the graduations~n Plates I . . . VIIIes printed,or to extend thein to somewhat higherorlowerIimits,thefollowingstepsmay botaken: ..—.

(1)Measureti-~tie thelinearc&ance betweentwo convenientnumbem suchas 1 and

6 or1 and 10orany otherconvenientpair,takingthem,howsver,insuchmmncr astoincludea cmsiderablepartofthescalelength

(2)Take thelog.oftheratioofthetwo numbers and divideitintothedistance.The quotientwdl establishthefactor~fortheparticularunitofmeasureemployedand for

theplateas actuallyprided. .!t’hisfactar-~nuiythenbe usedinmanner as indicatedabovetadeterminethedistancebetweenthegraduationafm any two numbers on themale asdcsimd.

The scakaforaltituderequiresomewhat diilenmttreatment. -

. . . .

_.. ....-

.-. . ..—

.,

—-

.-

-,-

.-—

.

.

----

,

IKU?EEIMENTAL REsEARcm ON ATE PBOPBLLERS,

TABLBVIL-ReMionbatwn altitudkand dimdy.

v.

. —.—-. ..-.. -.. ..-.? .-----

.’

●

. .... ..

.—-.. . -.L-.—. . .

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

. .....L

. ..—. . .=.

.-:-.— - .,..--—

.

_—-. -

.-..b— —

. . . ..—. .. ..-.

----- -, -----*, .-.

LTable VII givm the rdations amployed between altitudeand densityin both metric and

Englishmeeeti.--

& pretioudy noted,the mtual quantityinvolvedin the oomputdion isdensityA, but forconveniencethieierepresentedon the diagmun by altitudeH. The f~tor~ * gi~ in fible .

.

VI iefor density. IIinme,in order to determinethe distanoebetween the graduation for any -, “-——

two dll~ Ofthe altitude,we In8ypI’00&3dM fOUOWS:(1) Convertthe two valuesof H into valum of A throughTable VII by interpolation,or

.

graphicallyby mrve+splotkd from thesetables.

(2) Then divide the largervahie of A by the smaller,find the log. of the ratio, multiply—_-

by the faotor-fiand the produotwill give the *~M d- . ——-.

.,. —-PBoPm&EE No.1. PEOPELLEB NO. P.

d’d d+- :--t%! -ai ~.-&w.4U.479.m7.6Q.=.Wz “.ml.m.na.Tm

:%!.ma.m.i’m

r.&90.%.ao.as..M.4a.m.56.m.06.70

1

i :~

“._

MO::

.a6

.40

.a

.m

.=

.a

.as

.7Q

.?5

.m

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190 mmlxr NATIONAL ADvIE?mY ao~ FOE AiEOl!?AUW&.T- VlW40d&ued.

PROPELLEENo.a PROPEi&E~NO.4. ..

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TABLE VII14antinueL

191” —

PBOPELLEE NO.lL.

PEOPELLEB No.14.

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192 BEPOBT NATIONAL AlW180RY COMMITTEE FOE AEBOHAUm~

TABLE VIII+ontinued.PROPELLEB NO.M. PBOPELLEE NO.%

1“ .“. —.=-.—-.-

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T- VTII-Oautinued..PROPELLER NO.44.

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196 REPORT NATIONAL ADVISORY GOMkmmlm ROE AERONAUTICS.

TABLE VIII-Continued.-—-—--———-- —.. -. — . .-

.. ----PEOFEIAER No. m (ANGLE INUBBA8ED 8“).

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197

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198 REPORT NA!cIolrA14

PBOPELLER NO. IW.

ADVISORY UoIkmnmlm

TABLEViii-Continued.

FOB AERONAU!CKJS.

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\PROPELLMW 1,80 AND Ill .

LCOEFFICDIIUT C!,AND EFFICIENCY

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PROPELLERS 2,81 AND 112

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r

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PROPELLERS 16,20 AA?D 24

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