,

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.

REPORT No. 113

TESTS ON AIR PROPELLERS IN YAW

By W. F. DURAND and E. P. LESLEY

Leland Stanford Junior Unhersity

-—

.—.—

●

REPORT NO. 113.

TESTS ON AIR PROPELLERS IN YAW.By ‘W. F. Driaum AND E.P.kSLEY.

This report was prepared by W. 1?. D&and and E. 1?.Lwley, for the National AdvisoryC?cmmitteefor Aeronautic ~d COIIta& the r~~ of t~ts tO determine the thrust (puJl) andtorque characteristic of & prop~~ ~ movamt relative to &e air in a line oblique to theline of the shaft, and specfic~y when such qle of obliquity is ]~e, aSti the case of helicopterflight with the propeller SSrV& for boti sustentation and traction.

P

eA

H 0.. H

A

*F@/ w

Diagrammaticallylet figure 1 represent SUdI a propeller attached to an aircraft of some formwith shaft OP inclined at angle 6 to the line of motion A4 which is itself inclined at tigle a tothe horizontal HH.

Let T denote the traction on the shaft. L@ R denote the traction r~tance in the lineof motion. Then assuming that T is the only force reaction of the propeller on tie structureand assuming likewise conditions of right line nonaccekrated motion, we shfl have

Tsin (et-F8)=W (1)

Tcos 8=R . (2)

The miistance R will be given by an equation of the form—

gR ==ML?? (3)

Where k= coefficient depending on the geometrical form of the aircraft hi question.A= density of air.L =Some standard or type lineal dimension of the aircraft.‘u= Velocity.

93

.-

—

_.—

--

.—

.

94 REPORT NA!WONAL ADVISORY COMMl?fTEE FOR AERONAUTICS.

It will be noted that a coefficient k thus defined id] be independent of the particular units ,employed so long as they form a homogeneous system (foo$ pound, md second, or meter,kilogram, and second.) . .

We have then:Sin (a+e) w

Cos0–“7c&%or— .

g l-v=ZAL%Ps~cy(4)

(5)

From these equations a number of elementary problems involving such motion may INsolved, once we have the means of relating the force 2’ to the general conditions of the problem.

The present investigation has then for its primary purpose the development of the relationsbetween T and the operating conditions, including at the same time the simihr relat.ions forthe torque Q.

With these relations established and suitable data known or assumed, the solution ofproblems arising in flight of this character and involying power, speed, etc., will be reduced tothe same general program as in the usual we of airplane flight.

No further discussion of these.phases of the prob~em will be given in the prm.enbreport,the primary purpose of which is to furnish the data for the investigation of flight conditions ofthe character outlined.

LIMITATION IN SIGNIFICANCE OF RESULTS OBTAINED.

As noted in the preceding paragraph, the purpose of the investigation has be~ the det,cr-mination of the thrust and torque characteristics of a~ propel~ersunder conditions of movementsharply oblique to the line of the shaft.

These forces, however, do not represent the entira force reaction between the propeller andthe aircraft. The latter will involve additional forces aria@ from two sources.

“(l) A lateral or side thrust acting from the shaft to its bearin@ and due to the lack ofsymmetry of the air stream relative to the propeller shaft and the resulting lack of symmetrybetween the two opposite blades of the propeller in their relation to the air stream.

(2) A distortion of the lines of airflow relative to the aircraft, and due to the action of thepropeller, thus modifying the free resistance of the akra.ft moving with the attitude and spcwlassumed.

It is to be hoped that the character and significance of these secondary forces maybe madethe subject of a Mer study, It may, however, be noted in this connection that certain experi-mental difficulties are foreseen in such a study in “connection with the elimination rind deter-mination of the lateral force (1) independent of (2) the efl’ect due to distorted wind streams.Them are, however, matters which are only incidentd to the present report and me mentionedordy to indicate the fact that the investigations rep~rted on herein have been restricted to astudy of the direct thrust and torque characteristics as noted, .’

—

.—

MODEIS SELECTED FOR TEST.

TweIve models, numbered 5, 6, 7,8, 9, 10, 11, 12, 139, 144, ~45, and 146 were selected. Theprincipal chsracteristica of these models are shown in Table 1. In the above table, blade shapeNo. 1 is shown in Report No. 14,N. A. C, A., figure 14, Made &-ape No. 2 in figure 15, while thevarious blade sections applicable to these forms are shown in figurw 16, 18, 20, and 22, aHof

—

the same report. Models Nos. 5 to 12, inclusive, ire “a%”oig those tested in 1917, to determineperformance coefficients under conditions of @ht, and agaifi in 1918, when standing thrust andpower cm%kients were derived.

I

.—

—-

TESTS ON AIR PROPELLERS IN YAW.

TABLE I.-Chiuo.cteristies of mdd pmpellm.

95

..—--—.-.-.+ . .

....=,.=r

~:.—.-117

.7

.7

.7

.6

.5

.5

.5

.3

.3

::

.,-5

..-

-—

—

.—-.

:-~.

----

\

AU of the above numbered propellers are, as shown in Table 1} 3 feet in diameter, withuniform nominal pitch of driving face and are nomxunbered. There are thus represented among-the models tested two forms, straight and curved; three pitch ratios, 0.7, 0.5 and 0.3; and twoblade areaa corresponding to mean blade width ratios of 0.15 and 0.20.

—.

._-.

METHOD OF T123T.

The 0.3 pitch ratio models, Nos. 139, 144, 145, and 146, were ‘&et tested in the usual manner[described in Report No. 30, N. A. C. A.) to determine standing thrust and power coefficients.Teats to check those made in 1918 (Report No. 30) were idso made on the other models. The

- dynamometer, after slight alterations, was then turned through an angle of 90° so that thepropeller shaft was at a right angle to the wind stream through the experiment chamber. Thefdowing program was then gcmducted with each model. A wind velocity of about 30 feet persecond was set up with the tunnel fan. The model was then rotated at various speeds from 10to 50 revolutions per second and simultaneous observations of thrust, torque, or turning moment,re-rolutionG,and wind velocity were made and recorded. Seven to ten observations, represent-ing the same number of angular velocitiw, were made for each propeIIer. These tests wererepeated -witha wind velocity of about 45 feet per second and finaIIy with one of about 60 feetper second. During a siqle series of observationa the wind velocity was maintained approx-imately constant only. Because of the effect of the model itself in drawing air out of thestream and forcing it into the experiment chamber, there developed some increase in the ex-periment chamber pressure and a corresponding reduction in the veIocity of the wind stream,eqecialIy at the higher angular wlocities of the model.

Following the observations at an angle of 90°, the dynamometer was then set so that thepropeIler shaft and the axis of the tunnel formed an angIe of 85° and the same program oftests,.with the three wind velocitiea of about 30, 45, and 60 feet per second and seven to tenrotatrre speeds for each propeller, was carried out. This was repeated with angles of 80°, 70°,and 60°. The whole lot of experimental data thus represents, aside from the experiments todetermine standing thrust and power coefficients, about 1,500 simultarteoti observations of

.thrust, turning moment, angular velocity, and wind velocity, distributed about equally uverfive angles of approach, 90”, 85°,80°, 70°, and 60=. For each turning moment or torque deter-mination, an observation of torque zero was made.

——

-*-—

-.—_—--

—

...@

—

.——-.%

—

. —

REDUCTION OF DATA.

The data were reduced to the coefEcienta-

—

X torqueand C~=~AiVD’ :

In #D, }7is the wind velocity, N the rate of revolution, end D the diameter. In Ct andw

. .—

Oq, N and D have the same dues as in ~, and A is the weight per unit vohune of the me-.—

96 REPoRT NATIONAL ADVISORY

dium. H maybe DOW that them cticientslatter are homogeneous.

COMMITTEE FOR AERONAUUOS.

are independent of the units used provided the

T7

The coefficient (lt and ten tinm the coe&ient C~were plotted as ordinates, upon & as

abscissw, for each angle of approach. The result for.propeller No. 8 at 80° isshown on Plate I.As maybe noted, there is some dispersion of the plotted data from a single smooth curve, andthe data for one wind speed indicate, in general, valuas of the coeflkkuts somewhat diflereuLfrom those shown by the tests at the other wind speeds. Plate I is representative of the dis-pemion of the data from a fair curve in the average case. With some propellers it is somewhatgreater and ~th others somewhat less. As an experiment the data on Plate I were changedin form and plotted as shown on Plate. II. In this instance-

--- . .

‘“d“:’gw”As maybe seen, these cdicients are of the form used p~eviously in plotting data for tests

of models under the condition.of flight or of axial wind, and are derived from the cofllcient.sshown on Plate I by dividing the values of Ct and C~there indicated by the square of the corre-

sponding &. It is interesting to note that although mathematically the data as shown on

Plates I and II are the same, the appearances are in the two came very diflerent.The form as shown on Plate I was seIected for presentation since coficienb without the

factor V in the denominator are necessary in order to permit of graphic representation a~v——~~ – o.

In Plates 111 b XIV are shoti.the results as determined for the twelve propellers. Eachcurve as shown represents an average of points pIotted. The actual marking of tie spots isomitted in order to avoid confusion. The original observations, reduced to the coefficients

C?tand Oa,are, however, given in Table II agatit the various values of ~~mas resulting from

the three diflerent wind speeds employed. The curves of Plates 111 to XIV are in somoinstamea slightly different from those at fiat-drawn through the plotted data. Thesemodifications were the result of drawing cro~ curves SEshown on Plates XV to XXVI. Forthese latter plates the ordinatea are as before, Ckand C~jbut the absciesm are valuw of ~gleof approach,

DISCUSSIONOF RESULTS.

Thrust.-& may be seen by reference ta Plates III to XXITI,”the tiect of side wind at any“~le of approach greater than a certain value for .s.uyone propelter is to increase the thrus~developed at a tied tip speed. For the propellers of 0.7 pitch ~atio (propellers 5, 6, 7, and 8)the angle at which there is no change in thrust with change in wind speed is about 70°. For . .angles less than this the thrust varies inversely with wind velocity. For the 0.5 pitch ratio(propelkrs, 9, 10,11, and 12)the angle of approach for approximately constant thrust with con-stant tip speed but variable wind velocity is between 72° and 74°. Not only is there greatervariation in this angle for the 0.5 pitch ratio propellers than for those of 0.7 pitch ratio, but &othe angle is, for a given propeller, usually less defi-te. For the 0.3 pitch ratio (propellers 139,144, 145, and 146) the constant th&t aggle lies between 73° and 78°, showing a wider variationthan for the 0.5 pitch ratio as well as, in some cases, a more pronounced lack of definition.

For a constant value of & the thrust coticient Ct varies directly with the angle of

approach.Torque.-The-&anges in torque with variatiori of side wind velocity are less marked than

those in thrust. They” appear to be in general somewhat Iws consistent. For the 90° angle

TkXTS ON AIR PROPELLERS IN YAW.a

9?

of approach it appears that the torque at first generally decreases with increase of wind velocityand later increases. An ewseption to this general rule is noted in the propeller No. 139 (PL .Xl)where the trend of the torque coefficient curve is slightly downward throughout its length. 1tmay be noted, however, that for 85° and SOOthe previoudy stated generaI rule appears to be

‘r-foIiowed. For the angle of 60° the torque coefficient curv~ on abscissmof fi are generally

convex upward instead of downward m with 90°. For” other m@es the torque coefficientT7

— have a generally rising characteristic except at smaI1 values ofcum- ‘n absck~ ‘f i;D

—

& where in some cases they have very simdar characteristics to the 90° curve.

An examination of Plates XIV to SSVI shows that with fe~ exceptions there is artangleof approach for which the torque is practicality constant ;or varying wind velocity. This angleis generalIy from 6° to 10° less than the angle for constant &rust. It may be also noted thatwhile the torque coefficient curves of Plates HI to XIY appear in some instances inconsistent,the cross curves on Plates XV to XXVI show in general simihw characteristics. With fewexceptions they are con~ex upward and show, with decreasing angle of approach, at first a riseand later a fall in the value of (?q.

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TESTS OX AIR PROPELLEES IN YAW. 99

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