37103422 the Gyroplane Its Principles and Its Possibilities by Louis Breguet

8/8/2019 37103422 the Gyroplane Its Principles and Its Possibilities by Louis Breguet

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No. 816._. __

THl GYRO PLANE . ITS PR.IITCIPLES AND ITS POSSIBILITIES

By Louis 13relquet

Journdes Techniques International.es de lfAdronautiqueNovember 23-27, 19%6

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WashingtonJanuary 19?7

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NATIONAL ADVISORY CtiMMiTTEE F(2.RAERONAUTICS.--

TECHNICAL MEMORANDUM NO. 816- . _ _, . . , .

THE GYROPLANE - TS PRINCIPLES AND ITS POSSIBILIT-IES*

By Louis 3reguet

To begin with, I shall explain what a gyroplane is.

The gyro.plane belongs to the helicopter family which,as the name implies, has wings in the form of propellers.

In fact, a helicopter consists of large propellers

with, substantially, vertical axes set in mo,tion by an en-gine; the reac,tion of the air on the revolving blades pro-duces an upward lift in excess of the weight of the entirea~paratus which, as a. result, can ascend in the air with-out forward speed.

It will be remembered that, in order to obtain sus-tentation without speed, a great many methcds have beenconceived intended to furnish the lifting wings with aproper movement with respect to the body.

The first inspiration was found in nature itself,

that Iincomparable model, and has actually led to the de-sign of airplanes With flapning wings whose ?cssibility ofrealization cannot be denied.

But , evei~ as man has, in the remote past, inventedthe wheel to replace the alternative movement of naturallocomotion by a rotary motion, so the rotation of liftingblades .should appear in mind as a more mechanical processthan flapping: Whence the idea, to make these wings re-volve in continuous motion around a central axis, eachwing describing a circle - the whole system constitutinga sort of individual whirling arms of which the center,fixed in the body, may be kept stationary.

The idea of sustentation of flying machines by pro-pellers is quite old, Long before Jules Verne wrote his__________________ __________________*llLe GyrOplane - Sa. Technique et ses Possibilit~s. From

Journ~es Techniques Inter,nationales de llA&ronautique,November 27-27, 1976. Published by Chambre Syndicaledes Industries A~ronautiques. .


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. . .. .. . ... .. . . ,,,, ,.. ., .-,, ...: ~, . ,.....,. , . . . . . .. . .

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2 N. A. C.A. Technical Meiorand.umNo. 816,,,

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llRobur le C0nau4rant , many inventors had.tho.ught of heli-co~ters; one of the best .knovn, studies is thatl?y Ponton?LIHe,mgcourt. More recently,

Colonel Charles Renard treat-ed. the problem comprehensively ,in his now celebrated Com-munications to the Academy of Sciences. The first, enti-tled Cn the Possibility of Sustenta..tion in the Air of aFlying ],,~~chineof the Helicopter Type bj:mm~loying theEx;plosi.on Engines in Their Actual State of Lightness,Jl~.~tes from November 27, 1907. Then on December,7, .of thesame ye>r, he presented hi: second note entitled lfCn the

QQelity of Lifting Propellers which, on November 7:, 1904,-r>.sfollo~ed by another, entit,led.A New Method of Con-,,structinq Aerial Propellers. ....

I was .in?pressed ~,t that time by the works,of ColonelP.enard, one of whose students I had the honor to k,e, andI have taken up age.in the problems treated by him by super-posing on the motion of rotation, alone considered then, amotion of translation. In effect, a. gyroFl?.ne is a heli-copter designed to move die.gonal.ly in the air at a speedas high as possible.

This translation causes the speed of rotation to corn- ~bine ~ith that of advance in every ~oint of the blade. Asthe an:le formed by these speeds changes while each blade

makes a comnlete revolution and the speed of rotation be-comes additive for half a revolution to the sneed of trans-lation, some precautions must be taken to keep the forcesfrom becoming excessive at certain moments so as to pre-verit ruFture Of the blades or throwing the eppare.tus outof ha.lance.

In my first gyroplane patent I provided for the useof flexible bla?.es with ~,utomatic incidence control. Thenin 1908, I petented a differenti~l linkage of oppositeblades for the purpose of balancing the loads by incidencevariatioLls, tile incidence of the advancing blade decreas-ing znd that of the retreating bl?de increasing.

,1 also made provision in my gyrople,ne No. ?, for themechanism described by Colonel Rena.rd in his communica-tion of 1904, and which consisted of hinging the blades tothe hub. Due to this fact, the bl?.des - being subj:ect onthe one hand to the ccntrifugn,l force, constant for a givenspeed. of rotp.tion end, on, the other hnnd., to changing aero-dynamic reactions resulting from the transition - wereable to orientate themselves at any in,st,ant, according tothe results.nt fcrces.


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N. A. C.A, Techni,pal Memora~dum. No~ .816 3

During the period of one revolution: the blades undu-late then and flap in. alternate mction, ,each at its own.,.

count; wi.t.h,a.phase .displacemera.t in.:ra$+o ..{othe air loadsand an amplitude mhich. can be .,regulated.hy an au~omaficincidence ,chan,gein. f,urictionof flapping. When the bladesadvance in the direction of transl~.tion of the body whichthey su~~ort, they are lifted up at the same time as theymove at an angle .wit,hrespect to the motion of rotation of

. the.hub. The inv.e.~s.eroc,ess takes place during -the half-revolution during which .t~e .b.lades retreat. In this maythe alternating ,l;oads to which, the rotating wings aresubjected, in their ..comb.inedmovemen,t.of translation andgyration,; as.well as. th.e,,c.ouple necessary for their en-gagement, are .r.egulated,.

. . .,The essential advin,tage of helicopters and g.y,roplanes

lies, as we have seen, ,in,thei..rpower of sustentation with-out forward. speed. Thus a helicopter can take off and.lan,dvertically without speed, whereas the modern airplanewith high specific wing loading cannot take off or landunless it has a. speed. of t~e order..of 100 kilometers (62.14m i le s) .per..,hour. As a corollary, it requires largelanding fields, leveled off and well kept. The airplanecannot , in effect, fly below a certain speed without gravedanger of instability, spoken of in aviation circles asIIdangers of pancaking..

To get away from the constraint of vast airports issomething that interests beth military and. civil aviation.For the military airPlane this release is chiefly impor-tant in time of war, when it may not only be difficult tofind suitable areas near the front but also to keep themin good shape. The landing field is apt to be a target of,bombing raids, which leave it unfit for further airplaneuse.

,.Granted that. the gyroplane can rise vertically from

any clear piece of ground: It must then be. able to fly atsuitable speeds with-out. excessive power input. With thisin mind, I wa,s particui,arly interested in ascertaining thepossible efficiency of. this me.tho.dof translation obtainedSimply by a suitable forward tilt of the blade shaft andthe extent .to which this efficiency and speed obtained arecomparable, with. those of modern airrpla.nes.

B.~f.ore launching into t.hikproblem, I want to answer-,a question which has so, often been posed to me: What isthe difference between a gyroplane and a helicopter?


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4;.. ~,,AGc.Ao Technical Memorandum No. 816, ..:..... .. .. .

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,I$tymological.ly, gyroplane mea,ns Ilan apparatus which ll.an~.this name WaS. ,ceined .dllr.i.~ga cOn --o+~ejs-yturni,~.g,

,v.rsati,cinI.had in .1905with-t:h.e:la,te~rofe.ss,or~bharle,sRichet, Agyroplane ha# no pro.pwl-e.ive.pro.pel:lei,since.i,ts,r.otatin~ in~s driven by tihe ..eng,i.n:es, ,,r.,s,i-f ficie,ntbqth for propulsion ~andor su~tentation. : , ,.,,. .,,. .- . .

An ,autogiro-, such as that of Mr. d.e..laCierv,a,,he.e,r, nent ,Spanish- engineer-, i-s.an a.pparatuswhos. wings ro-tat,e in ,aitorotation. In autogi.ros, in effect, the re -voltii~lgblades are not controlled ]y the, engine %tit.mount-ed. free on the central shaflii The engine drives, as in .the airplane, one or more regular propellers ; itis therejative wind, dtieto the translat ion, previded %y thesi

gro?ellers, that sets the revolving. blades in auto rotation -the plane of the blades, of necessity, being tilted withrespect to the planeof rotati on..

.,In brief, the autogirb i,s actually an airplane whose

wings are free to rotate a%,out a central axis, as a wind-mill set nearly horizontal;. in revolving, these wings ma-terialize, in some may; according to mind--tunnel tests, alifting disk, arid themachine, behaves a.s,if it had a fixedwing, but of considerably larger ar~a,. equal to. the swept-disk area of the bltides. It is, by virtue. of this enlargedarea, that the au.tog.irb can fly at 10.wspeed.

In the a,utogiro the plane of ~he blades is tilted to-,~a~d the rear and is drag-producing, -,...therag being over-come by the propeller thfust; :, hile in the gyroplane the~lane of the blades tilts forward in. order to assure pro-pulsion.

., .,..The gyroplane - quite apart from. the faculty of ver-

tical flight, mkich the autogiro w.~th free m.ings does notpossess - offers additional advantages, particularly inregard to the over-all efficiency, which is enhanced by the

absence of the pro~ulsive propeller. Propulsion and sus-t.entati,on by the same rotating wing system, allows, muchnigher forward speeds, and. it has been proved that thep.ropulsiv.eefficiency is then practically equal to unity.

My first gyroplane with flexible ~ings was built dur-ing 1905-1906, at Douai, and. made its first free flightin 1907, with one man aho.ard. This achievement, - thefirst of its kind - formed the subject of a report pre-sented to the Academy of.,Sciences by.M~. Lipmann (reference 1).


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N-A. C,A. Technical Mem.orandum. No. .816 5

Before building this gyroplane, I had made a greatnu.m~er of systems.ti.c experiments on a. large mind-tunnelbalance. The first resnlts of these-tests were equallypresented in a communication at the Fourth AeronauticalCongress, held at Nancy, in September 1909.

The conclusions et which I arrived from the study ofthe best airfoils and especially from the introduction ofa new con~eqt, that of the solidit,y ratio or ratio ofbl~.de zrea to swept-disk area., had already been verY en-couraging,.

For e given lifted weight P, with a propeller rad.i-Us D, and e. power W, I had obtained a lifting qualitY

q . 2:!:; which was distinctly superior to that indicptedDT

by Colonel Renard,, mk~ose nro~ellers had an excessive rel-ative width, es~eci~lly tovard the tip.

Moreover, it seemefi to me that the translation shol~ldim~rove this ouelity which would, un to certain speeds,compensate the ~ower necessary for translation.

I vrote, in Yact, in 1909: I!The trouble met with Onsurfaces ~orkin~ successively on the same air columnshould lead us to think that, fcr a lifting TroDeller india~onal motion, the supporting column of ?ir being con-stantly renewed., the inconvenience of the surfaces betweenthem should, due to this fzct, be notably less great thanwhen at rest.

I have, indeed, checked this fact but without beingable to put it in figures. On a day of average and inter-mittent ~ind~ I have observed that at every gust the lift-ing force developed by my gyroplane No.. 1, increased quitefreely.

III also noted another fact: While testing my secondgyroplane, which was a combination of helicopter an,d.air-glane, the center of thrust of the propellers - which, atrest, coincided with the axis of rotation - was, duringflight, shifted quite freely forward, the shift of thee.g.. amounting, grobably, to as much a.s 50 cm (19.67 in.);the propeller diameter being 8 m (26.25 ft.), and the f6r-ward speed of the order of 10 m/s (~2.808 ft./Sec.)B

I have reproduced the sketch and photograph of the


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llal~,hcewl~lch~~cbnst~tititedfor my experiment salong withtlie.graph ondirect-lift propellers; anda piciur~of my1907 gyroplane. (figsi 1; 2, 3;.4). : ~~ .. -

. ..... ... . ,. ... .,.~ot~~ithstan dir.~ th~~e result s..~;nd:the Very end OUr&.g-

ir.g trials of my machine, I was due to abandon the solu-tiofi of this importsnt yroblembecatise of Iack of funds.

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TiiQn; too, whi].e devoting myself to these researches,Santos-Dumont; Voisin, B16riot, and Esnault~Pelterie hadmade successful fiigh.ts in regular airplanes. And SO Idecided to build an airplane but on the basis of the re-sults of my own .experiments.

The win:s of my airplane were therefore conceived assc:~,led-up versions of my gyroplane tilade


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H.A,.C.A,. Technical Memorandum No. 816 7

plate mounted on ball bearings, which the pilot could con-trol either for changing the incidence in any meridian orfor changing-the whol,e system affecting the pitch. !Che

direction was assured by & differential control of thepitch of two systems of coaxial blades revolving in oppo-site direction. This arrangement had the advantage of as-suring direction even when hovering.

The last gyroplane I constructed was, in fact, onlya laboratory model. Its lines, as seen in figures 5 and 6,were not refined, and its drag was quite high. The solepurpose was to aid my experiments on blade-control mechan-ism and !naneuver?,bility.

Concurrently, I launched into a theoretical study oftranslation - a study Which was to confirm the tests madeat the Eiffel l,l~oratory and as published in 1927 in theBulletin of the S.T.Ad. These tests mere made by Mr. La-presle on rigid. ~ro~c].lers With fairly large solidity and~: wide r,ange of incidence v~.riations. These experimmts,carried out in systematic order, confirmed in startlingma,nner everything I had suspected, and were of inestimablevalue to me.

I have established in this respect, various generalformulas, and requested my collaborator, Mr. Devillers, tohelp me put them in mathematical form. They appear, atfirst glance, quite complicated, which is but natural.But they are in full accord with both the Eiffel tests andmy own past and recent ex-oerirnents.

I shall commence by indicating several simple princi-ples concernin~ the velocity distribution over the bladesof a lifting propeller of diameter D, revolving at nrevolutions per second, and animated by a horizontal move-ment of translation at speed V..

The calculation, compared with the test data~ has

shown me that the aerodynamic action of the air on theblades depends practically only on the velocity componentsin a plane at right angles to the blade span. In otherwords, the radial velocities or velocities of sidesliphave no substantial effect on the lift and power coeffi-cients - this assumption being, moreover, unfavorable..

Other scientists or technicians who have treated thisCroblem, arrived at the same conclusion (reference 2)..,.

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8 N.A.C.A. Technical Memorandum No. 816.,,

At ~.ny one instant there is thus introduced into the.vel.ocity distribution, the component of the speed of trans-l.atinn V ,alongthe normal to the span of each clade,~.~ch as, for instance, Vl for the ll,ade A, and Va forIlade B (fig. 7)0

1. Consider blade A advancing in the.direction cftranslation by rctating about axis 0; the effective re-s~~ltent velocity at the tip then is the sum V3 = U-4 + VIof the speed ~f rotP.tion UA = mnD and of the componentVI perpendicular to the span of the speed of tyanslati?nv.

The extremity of the resultant speed U! at any one

point M of the blade, is therefore found on the straightline EF to he deduced from the straight line CUA , theplace of the extremities of the speeds ~f rotation by atranslation> VI in the direction of the advance.

The line El? meets the axis CIA of the blade at (l!which is the point of zero velocity or the instantaneouscenter of rotation.

The triangles 01OE and OAUA forthwith give:

001 _~E~o!.

VI CA %. _3_ = ,001 . _ILTTnD 2i-rn2

Let H represent a point on the perpendicular to thedirection V of the translation and in such a manner that001 is the projection of OH.

The triangles 00IH and @vE are similar as theirres~ective sides are ~erpendicular.

001 - c@ =!2E,- _ OH = l CO! = Q_ =.constoQE VI v VI 2nn

The angle ()@lH being straight when the blade Aetfects its r~tatien, the instantaneous center fJ1 is

shifted on the circle I, passing through O and the di-

ameter d= OH = .-~2nn

perpendicular to the direction of

translation, the directi


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N. A. C..Ai Technical Memorandum No. 816 9.

The distribution of the aerodynamic velocities isthe .s,ameas ifl:~a.t each instant, the blade turned about

the. instantaneous ceftel O! attH@ angularvelocity%n.,.which it has


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10 N. A..C..A. Technical Memorandum No. 816..

This theory of the gyroplan.e, as outlined above, isbase,d on the.fact that it is possible to effect the sum-mation of the elementary actions of the air on the rotat-in~ klades, considere~, as wings of an airplane having acerta,in aspect ratio A and a minimum drag coefficientCXO* The problem then reduces to finding the fictitious

as~ect ratio 1 to be applied to this blade.,.

Obviously, this A depends on the blade number ii,tl.leratio ho of blade area to swept-disk area, which Ihave called. solidity ratio,ll on the parameter of transla-tion Y = V/nD, and lastly, on a residual aspect ratio,to which a fictitious residual solidity ratio hr corre-s:oond.s.

It will be remembered that the geometrical aspectratio Ag of a surface S1 is the ratio E2/ SI betweenthe square of the span and the surface - that is to say,

~g . R$ . :22 for a blade of surface S1* But , on consid-

ering it as a propeller with N blades, by definition

Nsl . ho ~::, it gives for the geometrical aspect ratio .of a blade:

AK = ~hQ

it

It is known that the interference of the blades, operatingbecause of their rotation in their mutual downflow, ismanifested by a rise in induced velocities norqal to theplane of rotation, aild ,proceed.s, as concerns the induced

2drag cxi = -%, a. function of Cz,

TTAas if the geometric

aspect ratio A,g was lowered and replaced by a fictitious

asFect ratio A so much smaller as the interference ismore pronounced.. It was this which decided me, in thefi:~st place, for operation at a fixed point (static thrust)to multiply ho by N+l which, for N = 2, gave afictitious aspect ratio three times smaller than the geo-metric aspect ratio Ag.

Then I had to introduce the residual aspect ratio hrwhich I express in terms of a. fictitious solidity ratioh r, the introduction of which simplifies the mathematical

representation, and so that Ar -2-2nhr

at a fixed point..


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N.A. C.A. Technical Memorandum No. 816 11

The wind-tunnel tests Warranted the use of x= = 35for an isolated wing in translation, and A= = 10.5 for

the wings in rotation, such as those of a wing system ro-tating at a fixed point, the latter value corresponding tohr = 0.015. Thus the formula for the fictitious aspectratio of a helicopter blade ~t a fixed. point, .,reads asfollotvs:

?tO = --1

(.-

T 1 ho >N + 1 + ahr

N.

In effect, hr may be dependent on the blade number,but this formula is intended to be applied to gyroplaneshaving at least four, and no more than 8, %lades, and itis sufficiently approximate for the study under consider-ation.

The coefficient hr represents an altogether new no-tion in aerodynamics and signifies that, for blades -whichare infinitely extended, a residual aspect ratio corre-sponding to an interference limit, should he considared~

In the Eiffel wi.nd.-tunnel tests on a four-blade pro-peller yielding ho = 0,28, the geometric ~.spect ratio of

a ble.de being Ag = 4.5, me observed. at ,n fixed point, re-sults corresponding to a fictitious aqpect ratio of Ad =0.9: thrt is, r.mn.rked. d,ecrep,sewith resnect to Ag, an dexplaining the quite mediocre results obtained experimen-.t?.llym

It is only by adopting a fictitious aspect ratiocomprising the residual term, that use can be made of theinduced ~Oarabola of prandtl Is theory for each blade sec-tion. Otherwise, it is impossible to find even the senseand magnitude of the experimentally observed results.

This was confirmed in my experiments of 1907 on the dyna-mometric balance - according to which the variation of thesolidity ratio ho results in the lifting quality passingthrough a maximum for a value of ho proportional to hr;or else, when hr is neglected, it increases indefinite-ly in proportion as the bladesbecome smaller. The solidcurves in the chart (fig. 8) represent the results of mytests of 1907, and the dashed curves the theoretical resultcorresponding to hr = 0.015 for blades extending as faras the huh.. The disc~;,epancy between the experimental andthe theoretical curves is due to the fact that the blades


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12 it.A.C.A. Technical Memorand.urn N0.-816

of my propellers in 1907, did not rea,ch to the hub.

I estimate that the method of conducting the calcula-tions is more exact that that frequently resorted to fora.uto~iro rotor blades; i.e., computing the interferenceon the basis of induced vertical velocity uniformly dis-tributed over the swept-disk-area, this velocity being de-termined by comparing the disk constituted by this areato an airplane wing. It is, in effect, difficult to ac-knowledge such a distribution - much too advantageous intra,nslaticn - of the vertical flow of the air for largepropellers revolving considerably slower than the propul-sive propellers - at a speed of from 2 to 4 revolutions

per second, for example, and where the blades during halfof a revolution are inactive while sweeping the reversed-velocity region.

I effected the calculations on the basis of a meanand uniform lift coefficient, but proceeded from an experi-mental polar when, in the reversed-velocity region, thesections are attacked at their trailing edge.

Wit~,out automatic incidence adaptation, this wouldchange periodically because of the tilting of the axis ofthe pro]?ellers, but the vertical flapping motions of the

blades permitted by the articulations play, on that ac-count, the part of a regulator.

To compute the lift and the power input, I then ef-tected the integrations of the air action along the bladeshy replacing for each section the square ~ , 2 of the re-sultant aerodynamic velocity by its mean value derivedfrom the integraticzi in the period. The integrations weremade separately for the exterior and the interior of thereversed-velccity regione For the interior, I assumedCx f = 2CX and Czl = -0.5 Cz, Cx and Cz being the lift

and drag coefficients on the active parts of the blades.

I also computed the resistance offered to the rota-tional speed generated by the blades in their plane of ro-tation, with consideration for the unsymmetry of the airloads set up when the propeller is in translation. Addingthe dra< of the body to that of the accessories gives thetotal drag.

This drag necessitates an angle of forward propulsiveinclination of the axis of the propellers and its effectis included in .t.heterm for the power input W to keepthe propellers rotating.


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N.A. C.A. Technical Memorandum No. 816 13

I confined myself to the case wh,erethe reversed-. velocity region remains within the swept-disk area, whence

my. formulas are valid up to v = n., which seemed to me;5to be sufficient. In this manner I have obtained (refer-ence %) for blades substantially rectangular in plan form,the following formulas (in meter, kilogram, second units).

Gyroplane Formulas

ho = ~z 9 effective solidity ratio for total blade area s.nD4

N, number ?f blades.

h r, residual solidity ratio (0.015 for my actual gyro-planes).

v, forward speed. .*

n, revolutions per second of the coaxial propellers.

D, propeller radius.

Y=V yarameter of translation.;5

ma , parasite drag at zero altitude.

?/, fictitious aspect ratio of the blades.

Czf -s lift coefficient corresponding to the fine-

ness ratio of an element, for a minimumdrag coefficient Cxo.

Cz = Wczf , lift coefficient of an element, assumed con-

stant for all active parts of the hades...

Cx = (1+V2) Cxo, drag coefficient of an element.

P, total weight, equal to the lift in horizontal flight.

w, power input at propeller shaft.

c, sum of engine torques applied at propellers.

8, relative air density at contemplated altitude offlight.

. .


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14

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11-

N. A. C.A. Technical:. Memorandum ITo..816

Fictitious aspect ratio: -

.A= 1 .

ho ho + hrl-l +hr+

N 1+ 1.28 7Lift coefficient:

Paz = ____ =

6n2 D*

/

%o0.162 @O

h +h(1+0.15 Y2.-0.01Y3)

;~ + hr + __~~1+1.28Y

(1)

(2)

111. Power coefficient:

@ = ! = 0s383 (1+IL2) Cxo ho (1+0. 3Y2+0.006f4) + ~a~ Y3(3)6n3 D5

IV. Angle of propulsive inclination b:

tan b =

(4)

v. Lifting quality:

p 3 / 2 ~ / 2 ~ 3 / 2 q = - - . -

DW =6 ..

P

tan ma being the relative drag of the wing systen alone;that is, for o- = 0,. so that

(5)

(6)

(6a)


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N*A. C.A. Technical Memorandum No. 816 15

VII,

,.

VIII*

IX,

x.

XI.

Propeller torque:

Lift referred to speed V:

P= 6 + D2 V2

Power referred to speedV:

(7)

(8)

(9)

Pola,r versus swept-disk area S:

c 64>x= (lo)~ Y=

64 azCz =

l-l?=

(11)

(12)

(13)

Semicubic induced parabola asymptotic to the polar:

Cx =c z 3 / 2 (14)2

corresponding to the quality at fixed point q = 0.443 61/2deduced from the l?roud.e theory.

It follows from formula (l), which allows for thetranslation , that the blade interference decreases veryquickly in function of the translation parameter V, thisphenomenon being analytically expressed by the rise infictitious aspect ratio A interposed in the induced pa-rabola of a blade (fig. 9). This A is minimum at staticthrust (Y = O) and then takes the aforementioned value:

0 *


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16 N.A.C.A. Technical Menorandurn No. 816

In forward motion, when the propeller makes a completerevolution, it advances by V/n , thus sweeps the total area:

2The ratio of the actual blade area s = ho & to

this area S! is:

s ho hO= = .-;; ~++J_ 1 + 1.28 ?

R nD

Formula (1) shows that, on condition of increasingho of the residual solidity ratio hr, it is preciselythis characteristic ratio which intervenes to cause, throughits decrease, the increzse of A in function of the trans-lation.

Lastly, if Y becomes very great, the limit of thefictitious aspect ratio is reached at:

Am 1_-.

(%+h \l - r\N r)which is ide~~tical to the geometi-ic aspect ratio Ag ofthe blade except for the added residual solidity ratio hr.

Yigure 9 shows for gyron-lanes with 4 or 6 blades, therapid increase of A with tile translation parameter Y,the fictitious aspect r~,tio becoming substantially 2.5times greater when passing from$=3.

Y = O (static thrust) to

In the expression (2) of the lift coefficient mz thecomposition of the velocities gives the parenthesis (1 +0.15 Y2 - 0.01 Y3 ) the fairly small subtractive term0.01 Y3 arising from the passage of the blades into thereversed-veloci ty region.

It is surprising to note that. up to the limit of va-lidity Y=l-r of my formulas, the reversed-velocity re-gion remains within the swept-disk area; the passage ofthe blades into this circle lowers the aerodynamic quali-ties of a propeller in transition very little.


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N.A.,C,A. Technical Memorandum No. 816 17

Intuitively, it is seen that .- the aerodynamic reac-tions being proportional to the square of the resultant

velocity - the blade which recede; with fespect to trans-lation is, by reason of the smallness of the existing re=sultant velocity, bound to be practically inactive overits whole area lying within the reversed-velocity region-

The power coefficient @ in formula (3) assumes,at each instant, the propulsive equilibrium realized inhorizontal flight. The power absorbed by the drag of thebody and of the accessories is, according to (3), derivedfrom the integrations:

A w = 8(T ZE_m y=D2

or, substituting V/nD for Y and simplifying:

A w = 6GV3

This power is equal to that of traction, with an efficiencyCqUal. to unity, whatever the translation parameter maybe.

This conclusion is exact only when, as I have done,the qu.~.ntities of the second order ,~wreneglected with. re-s~ect to the angle of mronulsive inclination 6$ Cos eh~ving been compared t; u~~ity and sin b to b during myc?.lculationso

The chart (fig. 10) illustrates the application of myformulas to propellers tested during 1925-27 in the Eiffelwind tU~lilel- propellers with excessive solidity and verydrag-producing hub, M reaching as high as 309.

Chart 31 ~homs the evolution of the lift coefficients

Z and the power coefficients @ against Y = V/nD for

two gyro~lanes. The one of considerable parasite drag andhaving four blades, is substantially the same as the ex-perimental aircraft I have tested; the other, fitted withsix blades, represents a very refined gyroplane of the fu-ture.

Figure 12shoys the angle of propulsive inclinationa, insuring propulsion in horizontal flight independentof the relative air density for the two types of gyroplane.

Figure 13 gives the aFParent relative drag changes


19/56

18 N..A..A.Technicnlcnl l?emorandum.~q.. .1~l~

tp+~ @ independent of, the altitude, andgainst Y = V/n D, ._the lifting quality. q.. at sea,level for the tested gyro-

plane a,gainst that,ofthe future.. : Itwill be seen that a,passes through somuch higher a maximum as tll.eparasitedr,a~sarelower; ,t~ismaxirnum, reached for,fa value of ,/ nD, decfeases as these drags:increase., By the same ar-

flumeat, the relative drags tan @ pass through so muchlower aminimum anfi.reach so.much higher a vaiue V/nD asthe Farasite drags are smaller., For aerodynamically cleanmachines, as the future oneswill he; this minimum rangesaround 0s11 for a Value of V/nD: approaching 2-5, and itis surprisiilg to note that over a very large. region therelative drag remains practically constant and equal toits minimum. . .. ...,

This is an advanta~e not possessed by the airplane andenables a.gyro,plane:in cruising flig.htto increase itsspeed while conservin:q its power in proportion to itslighter weight with fuel consu.mption.

Another remarkable feature is, that at the regime.ofminimum tan 01 the angle of propulsive, inclination brem?ins practically constant and equal to a slope of .around 10, as a glance at figures 12 and 13 reveals.

The graph 14 shows t~,n OP., tan b and the-liftingquality q plotted ~.~r,inst t= V/nD for a gyroplanewith zero parasite dr,>g (0 = 0) nt sea-level altitude(corresponding to ~ing system rotating only).

Qu~.lity q increases to a maximum of 0.64 on approach-

ing V=2 then dro~s alittle to reach 6.615 at v = 3;5 ED

The apparent. relative drag,, tan @a, decreases. Constantly

a s far ,as J_=3nrl where it reaches substantially its

minimum o: 0.069.

!i!heslo>e tan 6, corresponding to the ~ing system

aione, is inferior. to tan @a as far as -L=3 thesenD

two quantities t~en becoming equal.

Now, for any gyroplane, let R = Ilr.+ Rn De the totaldr?.g balanced .by the angle of. propulsive inclination b:

, Ra being the drag ?.ue to the reyolving blades, e,nd. Rnthe drag due to lod.y, huh, and accessories.

.,., ,


20/56

N.A.C.A. Technical Memorandum No. 816 19

The condition of propulsion in longitudinal flightgives, obviously, t&nEl = R/P. But , as the apparent over-

all relative drag is tan @ = W/PV, the substitution ofR/tan 9 for the weight P in the formula for tan Elgives:

tan @ = i$v tan 6

According to the charts for @ and tan 0, it seemsthat up to the minimum of tan @,. tan.@ being greaterthan tan b, the power input W is greater than RV and,beyond, W may be inferior to RV q

This paradoxical result follows from evaluating Rwith respect to V/nD rather than V. In the regime ofminimum tan 0, w/RP is very close to unity for,a cleangyroplane, and approaches 0.5 when the gyroplane has a highdrag, such as that ana,lyzed in this study.

Finally, it may be noted that in vier of formula (6),the poiver equation of a gyroplane can be put in the follow-ing form:

(15)

wherein the parasite drags CIO not interfere except in theirrelation tc the total weight of the gyroplane,

For a very o- 1clean apparatus, -me may put .; = 350000

to 1_.-_ . Formula (15) shows that, f,or a gyroplane of4000D0

given parasite drag, vveight, and horsepower, the highestspeed V is obtained when tan @a is minimum, or at valu-es V/nD much higher than considered here, i.e.,v

The most favorable value for w is unity, as is read-ily apparent from formula (6a), although tan @a increas-es slowly with w so long as this coefficient does not ex-ceed 1.5.

gAssume, for example, that p = ~O~ooo, 6 = 0.74.

(3,000 meters = 9,842 ft.) ~ild that it is possible toadapt the propellers for avalue of V/nD = 2.3 to 2.6 orsubstantially, tan @a = 0,072. Then the preceding formula


21/56

.. . . . . . ,

2,0 N~A. C.A, Technic al~emorandum Nog 816,,.. ....,.

.,.enables us to compute the hor~epower per kilogram of total:weight or the total weight per horsepower with respect. to

the maximum speed at this altitude. The result is:,.

Altitude of Ilight, 3,000 m (9,842 ft.)

Maximum speedkm/h 350 400 450 500

Horsepower perkilogram 0.116. .140 .169 .200

r

Total. weight imkilogr:t.ms ~er 8s65 7.13 5*92 5horsepower .

550

.235

4.25

km/h x 0.62137 = mi./hrc kg x,2.20462 = lbe

-

600-

.27,6

3*62%

65.0 70.0

.320 .370

3.12 2e70

,, 1

Now v~e attempt to find the speed of translation V,Up to which the resultant velocity at the tip of an ad-vancing blade does not exceed the velocity of sound. Fora speed of translation V and a tip speed mn D of theblades, the resultant maximum aerodynamic velocity at thetip of the advancing blade is:

(16)

It is seen that for a given speed V, U? will be somuch lower as the translation parameter Y itself isgreater. So, to prevent U? from reaching some velocityand thereby vitiating theaerodynamic qualities of theblades, it is advantageous in this respect that f shouldapproach IT. With Y = m, the velocity U! = 2V reachesthat of sound; that is, ~~o m/~ for a forward speed ofV = 185 m/s, or 595 km/h.

Chart 15 compares tan @ for a gyroplane of the fu-ture and an aerodynamically cler.n airmlane correspondingto Cxo = 0.018 and a 170 kg/ma loading against the speed

at 3,000 m. The over-all relative drag of the airplaneis equal to its relative aerodynamic drag divided by theproueller efficiency ~, which has been fixed at 0*77.It is seen that the gyr.oplane prevails over the airplaneas soon as the speed exceeds 380 km/h, and likewise, atspeeds below 130 km/h, unattainable by the airplane whichassumedly has been fitted with the best high-lift devices-_.________________ _______________ ___- _

m/s x 3.28083 = ft./see. kg/m X 0..2O4818 = 111./sq.ft.


22/56

.

N. A. C..A. Technical Memorandum .NQi .816 21

In proof of the fo.egoing, the diagram (fig.. 16). shows, plotted ,agains.tthe speedat.. 3,.O.OO.meters, the

power absorption for the airplane and for the ,gyroplane,and for the latter the development of quality q at thisaltitude; q varying in inverse: ratio of the horsepower.

..,,Bet~.ee,n 1.30 ,and ~,80.kilorn,ete,rsper hour, ,the airplane

needs less,.pow..er,to ~f,lythan a gyroplane, but the gyro-plane can maka 500 .kilometer~ per. hour with only 2,900horsepower, whereas the airplane, notwithstanding its highfineness ratio, needs 4,700 horsepower.

~Chart 17 represents, .in function of Y = nD, the

changes in speed of advance, speed of propeller rotation,power absorption,. and of the total propeller torque forhorizontal flight at 3,oOO meters - that is, for the en-tire speed range of horizontal flight, from hovering tomaximum forward speed.

The surprising fact is, that contrary to what occurswith .th.eordinary propeller, the number of revolutionsper second of the propellers decreases consistently as thespeed V increases, which is evident as a result of thecorrelative increase in lift coefficient az.

Thus the tip speed nnD of the blades decreases inproportion to the increase in forward speed V, so thatthe sum V + nnD may be almost considered as being aconstant. This explains why, with this particular .gyro-plane, the tip speed at static thrust is 260 meters persecond, and at 480 kilometers per hour, the resultantspeed V + nnD will only be 274 meters per second; i-e.,only 5 percent higher and well below that of the velocitYof sound.

This va~iation in the number of revolutions can, ob-viously, be mitigated by modifying the blade incidence,but there is a possibility that it will be necessary toprovide a speed change for the gyroplane of the futurewith its high forward speeds. .,

According to figures 16 and 17, the gyroplane absorbs~hesame power at statiti thrust as at 450 kilometers perhour, which indicates quite clearly that this type of air-craft affords in some fashion, gratuitously, a translationat already very high speed. The power input is minimum forv = 0.9, corresponding to a ,speed;5

V of 225 kilometers


23/56

22 N*A. G.A. Techtiical~ Merntiraridum No. 8716

per hour, w:hilefhe.:@r pellertorque itself is minimum ata slightly lower speed,such,as V/n D = 0~6 ,and v= 150kilometers per ,hoi.ir. ,,,,., . Cfiart 8 shows the changes is coefficient 13/uz ofthe propeller torque against V/nD for the investigatedand the futureg~~roplan . As for the airplane, the speedof minimumtorque. is that of the ceiling, and that ,is alenthe most &dv&ntageoUs foi flightwith one or more enginescut out.

.

C,harts 19 and 20 reveal -@tt:d,;@:;; ;$;:,-r;:eslope of the lift and power curves z

zpectivtily mhich follow when horsepowei and, lift are re-ferred to s~eed of advance V, as for the conventionalairplane, rather thanto the number of revolutions n.

.-

Lastly, chart 21 gives the polars versus swept-diskarea conformable to formulas (10,) and (12) for the testedgyroplan,e and for that of the future. The coefficient Cxis defined by the power equation (11) and coefficient Czby the lift equation ,(13).

Drag tan0 and lifti; g quality q are given in

terms of Cx and Cz by the formulas:

(17)

p 3 / 2f i

3 / 2&2 Cz= _ _ _ . , 8

c ~ (18)

When Y tends toward zero, i. e., upon approachings,tatic sustentation, Cx and Cz increase indefinitely,

and the polar has an, infinitely .ris.ingbranch; tan @then. increases i.ndefi:nitely, the asymptotic direction be-ing the axis of Cx. The que.lity at zero altitude thentends toward ~ limit !IO* ,aking the polar asymptoticto the semicubic induced parabola:

Cx= _~cz3/~ (19)..Sqo

.,. Froude!s th:eoryaffords a -satisfactory approximationof the quqlity q. at static thrust, an,d without gr..ound

interference. It supposes the induced speed to be uni-


24/56

N. A. C.A. Technical Memo,randurn ,~o. 816 23.. .,

formly distributed over the swept-disk area, the value uon p,assing into this area, and 2U after passage. It fi-

nally o.ffordsthe powerinput Pu- and the quality at zeroaltitude !10 = ___ = 0.443, with the corresponding semi-

cubic induced parabola previously cited and..

1 ~z31acx=~ (20)

1have indicated in the foregoing that, in order tomove c,t sufficient speeds, it was indispensable both fromthe point of view of design ,and of the stability, to hingetlie rotating blades to the hub, and gave the reasons whythis is justified. when the ~lade,s are rigid - and thisis important - and the.parameter of translation is quitehigh, the momentoue v?,riations in the lifting force exert-ed dn a, bl~,de during rotation, produce periodic bendingstresses which ~.re not ~~dmissible unless the structure isvery heavy. Besides, it undoubtedly engenders criticalvibrations. The ce.lculation of which I have given the re-sults, ,are predicated on the assumption, from the aerody-namic point of view, that the blades are rigid and conse-quently make no allow~.nce for the .fiap~in~ action Fermit-ted by the ~rticul~tions, ~.nd whose analysis is a verydifficult problem.

Suffice it to, spy thr.t this flapping, even for highvalues of Y, has practically no detrimental effect ontan 0. I shall demonstrate, moreover, the necessity, fromthe aerodynamic point of view, for allowing the blades 2of freedom about the two perpendicular axes - one in themeridian plane, the other in a parallel plane in order torecover the power,s brought into p~ay.

.

It is said that when a wing in uniform tr hSa tiOII is

actuated by a vertical, sustained,tion, periodic flapping mo-it is possible to effect a decrease and even a nul-lification of the drag by combining the oscillation of theaerodynamic resultant with the incidence variations (ref-erence 4). .,

The di,miliut.ion fthe power necessary for the advanceis found in the. po,l~,eronsumed for upholding the flappingmotion, with a propulsive efficiency solely a function ofthe effective ,aspect ratio of the wing. The efficiency isimprov,ed when the wing,scillates about an axis parallel to


25/56


26/56

. .NiA.C..Ai Technical Memorand:urnl~o.816 25

the automatic pitch decrease , with the aid of an eccentriclever, in direct ratio tO the rise. .Themaximum speed and,.. elongation are thus ie&.cliedsooner. I sha~ll ,confine my-self, on this subject, to the following little-known funda-. mental phenomena which underlie the theory of flapping mo-tion.

1) Every vertical flapping motion develops - due tothe fact that it superposes itself on the rotation of thepropellers - combined centrifugal forces, perpendicular tothe meridian plane of this flapping, which tend to maketh~, blade advancewhen it is r~,ised and retreat when it islowered. , :

Every vertical fla-pping motion is therefore, necessa-rily, accempmied by a horizontal flapping motion of loweramplitude, these two flapping mo,tions being not in phase.

2) The increase in power necessary for the rotationdue to the drag increas-e in the plane of rotation, is com-pensated - at efficiency approaching flapping - by thepower supplied in vertical flapping by the displacement of,the lift.. -

,, ,~) This recovery is effected through the energy, in

the horizontal flapping motion; of the combined centrif-

ugal forces which, in this fashion, play the role of trans-formers of energy. As these combined centrifugal forcesare due to vertical flapping, it is readily seen that therecovery of energy is contingent upon the combined flap-ping motions, vertical and horizontal: whence follows thejustification of the principle of. double articulation; nofraction of the considerable energy employed in the verti-cal flapping motion can be transformed and recovered ex-cept by permitting the horizontal flapping to be effectedfreelye

I shall give the mathematical demonstration of thesefundamental properties, ~~

The motive, force CI.fa: blade being its rotation aboutits own axis at tiniform speed UJ, the vertical flappingconstitutes a, relati,ve motion and gives rise to comple-mentary accelerations.

.

Let ~ be the upwardinclination ofthe blade in the,..d$

.piane of rotation,

=rwthe speed of rise of an ele-


27/56

I ,,. . .,, ,,, ,,. - ,,, ,,, , ,... .. . . .... . ,, ., ....-

,. ..-,,. . .: .:. ..,... .

26 lTqA...A. Technical Memorandum No.. 81,6 .

., . . .

ment dm of the, mass of theblade..situated at distance. r,v forrning, with the axis ofrotation, the.%ngle P. The....

elementi?;.r.combi,ned cen.trifuga.lforce of mass dm is per-pentiictiiar.o ,V and to the axis of rotation, hence tothe meridian of the blade and has, by virtte of the Corio-lis theorem, the value:

dFc = 2WV ~ dm = 2w.r dm. ~ $$

With M, the total mass of the blade

(21).,.

g distance of its center of gravity fromthe axis Of rotation, we have:,

Z r dm = MTg

The resultant combine?! centrifugal force then has, afterintegrating f~r the whole blade, the magnitude:

It is seen that this force Fc h,as the same magni-tude as if the total mass were concentr&ted in the centerof gravity, although this is not to be interpreted as be-ing applied at that point.

If H=MuJ2rg is the centrifugal force to whichthe bla.dc is subject in its rotation about its axis, wemr,y write:

(23)

which shows thnt this force can become relatively very im-:?orttwltm

An the blade rises, this force - directed in thesense of motion due to rotation w - is active. Contrari-wise, it is resistant vhen the blade is lowered, and zerowhen the blade is perpendicular to the axis of rotation(P = O), . or when itsinc~ination is maximum or minimum

(:$=O). By integrating along the blade ata given in-stant , the resultant couple in relation to the articula-tion parallel to the axis of rotation, due to the forcesdFc, h~-s the value:


28/56

N, A. C.A. TechnicaL, Memorandum No. 8.16 ~7

,,., J =z r dl?c = >W ~ ~~ X ~a @m = 2I w ~ :$ 2,4)

. . .,,. .,

. ::. ,.where I = Xradm=Mp2 is the moment of inertia of theblade. in ratio to, the articulation, and p the corre-sponding radiizsf gyraton. Thus it isseen that {heforce Fc is applied at a ~.istance a from the axis, sothat al?c =@. From formui.as (22) a,nd (24) !follbwh:

,..,. I MP2 2 . :a , = = = ~ - :Mrg - Mrg ~

(25)

.,, ,But if. pg is the. radius of gyration relative to the cen-

ter Qf gravity, pa = pg~ + r 2, ~ence: .g

Pg2a=r +-~ rg

(26)

the well-known fcrm.u]a, defin.illg the center of shock withrespect to the axis rhich, ia consequence, is the point ofapplication of force . Fc farther avay from the axis than,t.hecenter of gravity; .,

The combined centrifugal couple J thus defined, is.periedic and of partic-ular value; it contributes directlyto, the conservation of, the horizontal flapping motion.

Then l,et $ be the ,elongation of horizontal flapping.at time interval t, positive when in direction of motiondue to rotation w, all flapping motions having as commonperiod that T . ~w.? of a nrope.ller revolution.

I shall demonstrate this important theorem in the fol-lowing manner: The recoverable ~ertical flapping energyet each propeller. revolution is. precisely the work of the

combined centrifugal couple J .in the ho,r.izontalflappingmotion. The work of cou~le J in the pe:riod is evidentlythe sum of the work ~ and T! of ,this couple in the ro-tation at uniform angular vel~~ity ~ on one hand, and inthe horizontal flapping superposed on this motion, on theother.

,., ,..The differential of the work ~ is

aftcr Substitutingd@2 for

28 d~: : :


29/56

28 N.A. C.A. lechnical Memorandum No. 816

As elongation ~, and consequently its square, alsoassume the same values a-t the end of an interval equal to

the period, it is seen that the work ~ within the periodis zero.,

The couple J can therefore furnish work only in thehorizontal flapping motion, and the value of this work inperiod T is:

Now it remains to be ~roved that this work is preciselyequal to that of the F.erodynamic lift during ver t i ca lflapping. With this in view, I shall write the equationfor verticr.1 flapping.

The blade rotates at speed d~u+~t, so t,hat the cen-

trifug,~l returning moment due to an element of mass dmis:

dCi = r2 dm(w+ #Y

(29)

()u 2Disregarding dt ,before W2 an d 2UI ~~ and designat-ing the mement of inertia of a blade with respect to onearticulation with I - (it is practically the same thing,vhether considering on e or the other of the two articula-tions) - 17e have :

(30)

With Ca as constant couple due to the lift, and. Cm

as constant couple due to the weight of the blade, the differential equation of the vertical flapping motionreads as follows:

I#Lca-cp - Ci (31)

That is, by replacing Ci,,

by its value:

(32)

This equation is absolutely general, whatever t,he laws of


30/56


31/56

30 N.A.C.A. Technical Memorandum No. !316

The engines, four in number, housed in one compart-ment of the aircraft, should develop, at 3,000 meters, atotal maximum power of around 3,600 horsepower. The gyro-plane should be able to fly at 3,000 meters, with only2,000 horsepower, at a forward speed of 250 kilometers perhour (155 miles per hour), whereas with 2,400 horsepower,the speed is to be 400 kilometers per hour (248 miles perhour). The drag of the body and of the accessories corre-sponds to that, of a 0.56 m2 thin flat plate.

I have compared, as seen, the possibilities of sucha gyroplane with those of an airplane of the same tonnage,loth in horizontal flight with full load, at 3,000 meters.

The ~weight balance for a design of the same qualityis in favor of the gyroplane, whose rotating wing system -not being su?)jected to any appreciable bending moment -is definitely much lighter than the fixed wings of an air-planem One may figure the gain in dead weight at 10 per-cent o,f the total weight. The airplane, to counteractthis added weight, would have to be equipped with lesspowerful engines, which in turn would lower its top speed.

lTow, in regard to cruising flight, the gradual reduc-tion in weight due to fuel consumption must be borne inmindo Then, by judiciously combining the altitude increasewith that of Y = V/nD, it is possible to realize the con-dition of flight with. constant horsepower, while remainingwithin the limits between which the over-all finenesstan 0 changes little - in fact, remains practically con-stant over fairly large speed ranges, as I have alreadyindicated

Under these conditions, the formula V = ~ t,an ~ ..

shows that the speed increases continuously in ifiverse ra-tio of the total tveight without the altitude reached atthe end of the trip becoming excessive.

.,.If the fuel consumption amounts to 36 percent of the

total weight, which is equivalent to stages of 4,600 kilo-meters in still a i r $ the speed of 400 kilometers may evenbe raised to 625 kilometers pe~ hour, which corresponds toa mean speed of 500 kilometers,

Such a result is impossible to achieve with the air-plane considered here, because tan 0 increases muchfaster vith the speed than it does for the gyroplane and,to raise the speed, it would have to reach heights where


32/56

N. A; C.A. Technical Memorandtirn No..836-. 31\

the power of its enigines could not oe maintained. In-fact,it does not seem possible, withthe very best airplanes,

actually to envisage a mean speed of over 400 kilometersper hour, at the time, at 8,000 or 10;000 meters altitude.

. . Objections may be raised tomy assumed 130 kg/m?,wingloading of the airplane. But these are figures actuallyin use, and 1have chosen for a gyroplane a somewhat largediameter, carrying at full load only 446 kg/ma blade load-ing, so as to provide a margin of excess sustentation attake-off in order to be a%leg with engines cut out, todescend in a glide, like an autogiro, the wings - with aloading of only 31 kg/m2 - being in autorotation with re-spect to swept-disk area; and lastly, to be able to flywith one of the four engines stopped.

,. ,

If an airplane of 200 kg/m2 loading could be realized,it vvould necessarily have to be launched by catapult. Thereduction in wing structure involves, probably cX. = 0.021.

That .~eing,s6,. the gyroplane which I have considered shouldnot have a higher. over-all fineness than the airplane at?,000 meters, except at speeds above 420 kilometers perhour instea,d of 780 kilometers per hour, as before.

Quite apart from the advantages df speed and light-ness of design, the gyroplane has other particular quali-ties not possessed by any other type Qf aircraft - and im-portant enough tojustify the studies undertaken, even ifthe maximum speed should not exceed that of our conven-tional airplanes. These are:

1. Practically no response, to aerial eddies, the flex-ibility of the articulated revolving rotors forming a par-ticularly efficacious aerodynamic suspension.

2. The absence of stalling, since stationary susten-tation is possible, and the facility in case of enginefailure, to descend in the manner of airplanes with lo~Ywing loading, like the autogiro descends.

3.. Possibility of joining several engines to the cen-trql shaft and installation in a comfortable engine corn-partment , affording uninterrupted inspection and ease ofaccessibility, with liberty of cutting out the engines atwill. .._.___ _______ _______ _____ .____________________km/hx 0.62137 + mio/.hr.

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


33/56

32 iS~AqC...~.~lechn.ic,alMemorandum ,No... 816

With the high reduction gear ra,.io .(10 to ,20) betweenengiqe and propellers, a simmle yorm (endless screw)couldbe used nnd which actually ~I~S teen developed and is ofsufficient efficiency. . . .,

4. Possibility of vertical ascent on ground or wateroThe gyroplanes will be more or less amphibians. 0n6 caneven visualize refueling ~eing effected &ith much lessdifficulty than with seaplanes.

E Small: over-all dimensions for storage, since theartic~~atei!.blades are easily folded.

,,. . .

6, Inappr,eciable military qualities, since agyro-plane can take observations in cases where ab-sence of mo-tion is ~?articularly de~ired; small gyroplanes seem to hemade: for ~rtillery spotting.

,7. As re~ards ,naval aviation, gyroplanes of from 2-4tons could replace the actually used deckplane, along withthe bulky ~.nd heavy catapults,to good. advantage- Air-plane carriers will, undoubtedly, no longer. 0$ necessary.

Deck-landing gy.roplanes, with their small bulk, oncethe blades are folded, can he used in much larger numberson every battleship.

..

Such tempting results are, quite obviously, not ob-tainable beforeovercoming certain di,ffic!ulties beset-ting every new development, and mhich are beyond the scopeof this report. 3ut I do feel that it is fitting to makeknown at this time the conclusions to which my investiga-tions have enabled me to arrive. .

Certain readers - even among techniciansmost famil-ir.r with aeronautical problems - may be surprised, but I

arnfirmly convinced that when they have studied my formu-lr.s and reflected on the posed proll.em, their final con-clusiofis will be similar to mine.

I may have been led to assume, in my examples, quali-ties beyond reach in the near future, but even so, thejudgment and nature of my conclusions. p.re, I believe, in-contestable.

1 hope I have been a31e to make you share my pers,onalopinion , that the gyzoplane prollem should not be given Up

but , on the contrary, attacked in all ,seriousness. suc-. .


34/56

N.A.C,A. Technical Memorandum No. 816 33

cess will so much more quickly crown the efforts still nec-essary, as these efforts are more unanimous, better under-

stood, more encouraged and coordinates, and it is hopedthat France will again take first place in this new stageof progress in aerial navigation.

Translation by J. Vanier,National Advisory Committeefor Aeronautics.

REFERENCES

1. Comptes Rendus 145, 1907, m. 523.

2. Wheatley, John B.: An Aerodynamic Analysis of the AutP-giro Rotcr with a Comparison between Calculated andExperimental Results. T.R. No. 487, N.A.C.A. , 1934.

3. Sur les Fossibilit&s ae vitesse e! de rayon dlactiondes gyroplanes. Communication & llAcad6mie des Sci-ences, May 25, 1936.

-7-. SUr le rendement de propulsion d-es oiseaux par batt$mentsde leaurs ailes. Comptes Rendus ~ llAcademie desSciences. June 23, 1924. Vol. 178, p. 2238.


35/56

.c1

z=.

r---------- - --- ......____ 9 meters .,,_____ .,I

~


36/56

M.A.C.A.Teohnieal Memorandum lVo.816 Figs .

.

a.4

. . . .

Figure 4 The gyroplane of 1907

.- -.. .-. .-


37/56

,, +2q=~ /!m J=A%S+3

%s =l T D2 h / 4q=u 0.888h q=AY/TDI II I Curve I inclination,,

Curve II,a 1 II IIIII ..

I

!I

t

,!,

.40Mean blade inclina-n

.25 .50 .75 1.00 tion in ~ of pitch-h = solidityratio. diameter ratio.

i?igure 3.- Test data obtained in 1907 with.the balance, Fig.2.

lard~ .E(n(1isDP.

(->7


38/56

I.A.C.A. WOMioal kfIO~IO. 816

i... . ..- ,

,. .,., .:.

~iguro 6.- 1935 q rperimental ~roplane.

_ _ _


39/56

N.A.C.A. Technical Memorandum No. F16

x- . -

// d~ Y= 21n

I

$

IiI1

1It

III

1

~---------- --$/

/

\\\

/

\

I

I

I

1//

l//~

----- -,-_----- -

\ \\ \ \

\ \\ Articulations

I ..-

/B///Vq .

Figure 7.- Distributionregion for a

and advancing at spetidV.

of speed and reversed-velocitypropeller revolving at rate n


40/56

N.A.C.A. Technical Memorandum No. 816

.U=%,g = o.688ufio I experimental curves% .

II theoretical curves for ~=~:

U4= 0.000142~o(l+l/N)+O. &3)3 (CXO= 0.015)

4.0 -iT- i -]

..+-..-t

4+&~~~i

3.6 [ ,-- -- - *

i

// /-

3.2 ;1-{7:_/~

(T

2.8 -1 L.- .

I

/

I

L-r

-lt ..

2.4 ,

-l_.+1

-1-.-L

1 L.&.pJ-

--t--t--+ 4/--~ .7 1II -1-i !1( ! I I i.

1+.111111 Iii!! il~li I I ! I I I I I I I

1--11.[11 1/

2 . 0 ,+., ~ I I I I I I II 1 A

+tt+i+

0l=H?4+L.J__l._LL_lLLl_J.__l.i_!).q lL-J...L._!_o .(32 .04 .06 .OF .10 .12 .14 .16

ho

Figure 8.- Lifting quality qand inherent quality u of blades of totalarea s plotted against solidity ratio ho s(near ground6=.1). I-ii/4


41/56

X. A.. . 4 . Technical !tilsmora.ndum o.816

----- ho= 0.068, hr= 0.015, 1T=4

ho= 0.07, hr= 0.015; N=6

7.2

6.8

6.4

6,0

5.6

A

--w-t+ t-t--tl-l

o .4 .8 1.2 1.6 2.0 2.4 2.F3V/nD

Fig.9

N=6

N=4blades

Figure 9.- Gyroplane.- Effsctive aspect ratiohof a blade.


42/56

N.A.C.A. Technical iiemorandumITo.816 Fig. 10

Propeller flatwise in the wind - tested

inE,iffe-lind tunn~l.

Relative pitch: 0.55, ho = 0.14 (2 blades)

ho = 0.28 (4 blades)

1 0 0 CL z4 bladesho = 0.28

-==&:-ti---i- - , ++. -L-WI-&7

t 1 :-++-+

100 Uz.2blzdesho = 0.14

100 @2 blades

o .4 .8 1.2 1.6 2.0 2.4 2.E!v / n D

Iigurti0.- Theorctical curves for lift coefficients

a~d hors.epowor.The dots represent tests.


43/56

N.A.C.A. Technical Memorandum No. 816 Fig. 11

--- --- ho = 0.068 hr =0.015 Cxo=0.011 w=l.5 N=4 $=~2,000

ho = 0 . 0 ? o - 1 r = 0 0 1 5 c XO.0.009 ~=1.5 N=6 ~ 15,000

I /

I !

3.6

2.P

z

l o o o f l

O. P 1.2 1.6 2.0 2.4 k.eV/nil

u=z &4

1 0 0 a z

Figure 11.- (lyroplane.ift and newer coefficients.


44/56

I?..C..L.Technical ~iemorandumNo. 816 Fig. 12

I, ho = 0.068, h= = 0.015, Cxo = 0,011,

w =1.5, N = 4 blades, U/D2 = 1/2000

II, ho = 0.07, hr = 0.015, Cxo = 0.009,

w = 1.5, IT= 6 blades, (s/i12 1/15000

18

IT.-.. ....

16 4---T- -.

1: /; k

1-t

~ ---

+

-

14 --;+----I---- -- --

1.-.

y12. ..-,

+0.104

gyroplane

Figure 15.- Gyroplane of the future (0/lj2=1/15000)and zirpla~e of exceptional aerodynamic qualities.


48/56


Figure 16.-

ir;;~:tof me (CXO=O.018 ,h =8 ,&130, q=O.77)

. ., W, hp.

4?0011

o

\s

+& 2300 ~

-LL

II_-:\_.~ 900

~! 1500

1- -J

1 0 0I-

4 8 0

Gyroplane of the future and airplane of the sane weight.Power aosor~ed and quality q of gyroplane at 3000 m.

.


49/56

.

N.A.C.A. Technical kemorandurnNo.81~

W,h

3000

2800

2600

2400

22@o

2Go@ I

aerodynamic incidence giving Cz const.(u= 1.5)

l)=25 m. P= 15 tons

) 6= 0.74 (3000 m) 1I

400 - .

\.

0.4 .8 1.2 1.6 2.0 2.4 2.8

v.Parameter of translation,nD

C,kgm

18,000

16,000

14,000

12,000

10,000

?000

I-Its

3.5

3

2.5

2

1.5

Fig.17

Figure 17.

-.


50/56


B= 2?+ D, DiameterTz P,Total weight

----- - -ho = 0.068, hr = 0.015, cxo = ().011,

P = 1.5, N = 4, a/D2 = 1/2000

ho = 0.07, hr = 0.015, Cxo = 0.009,

U=l.5, N= 6, CT/D2= 1/15000

Figure 18.- Coefficient of propeller torque.


51/56

N.A.C.A. Technical Memorandum No. 816~z/y2 .p/5~2~2

.- -- ho = 0.068, hr =.0.015, Cxo.,..

N = 4 blade-s,

ho = 0.07,hr

N = 6 blades,

13/i)21/ 2000= Ools! Cxo =

c/D2 = 1/15000

4.4

4.0

3.6

3.2

2.8

2.4

2.9

1.6

1.2

.8

.4

0

=0.011, )J= 1.5

0.009, ~ = 1.5

Fig. 19

Pigure 19.. Lift coefficient.


52/56

.

N.A.C.A. Technical Memorandum No. P16

hO

- -- 0.0680.07

9

?

6

1000$3

5

4

3

2

1

0

Cxo

0 . 0 1 10.009

N

4 blades6 blades

hr ~

0.015 1.50.015,1.5

Fig. 20

lT-

D21/2,0001/15,000

m

Figure 20.- Fower coefficient.

. . G


53/56

.

N.A.C.A. Technical :~eniora.ndum ?o.816 Fig.21

,,

1 0 0 C Z

56

48

40

32

24

16

8

0

I ho= 0.068, hr= 0.015, CXO=O.Oil, ~= 1.5, N=4, ~=~022000

II hO= O.0~, hr= 0.015, CX.=0.009, ~= 1.5, N=6, ;2= J 150003 pCz

111 FrouJci~duced parabola Cx=~

T-1

/-111i

3 / 2Cx = ~

TT~ 2Figure 21.- Polar of gyroplane referred to area S=of swept disic. 4


54/56

Fige. Z3. 23.A.C.&. Teohnloal Memorandum No. 816

...

~. f

_

,. ,6

n I

I6)QOPUiNE MUl~ BREGUET

Design of a 3-engine t&phlbian gyro-plane.with retractable skids formingballonete and with a hull.Total weight:- 16,000 kg(35,273 lb.)Propel ler diameter(3 blades eaoh):-

25 m (82.02 ft.)Total blade area:-34 m (365.97 eq.ft.)Total maximum:-Power output at 3,000 m (9843 ft.):

3600 hp.00eed at 3,000 m :-

uaing 2900 hp.:500 km/h(311 m.p.h.w 2400 hp.:40011 [

249 82000 hp.:250 II 155 H 1

Hovering at 3,000 m ,power imput.2650hp

Figure 22. Gyroplane of tne future.

UPPER .,Cem , ,U..m,,.%

. . . . . . . . . . . .

-L .

, -

.-....... .:.,,

Figure 23. Gyroplane of the future.


55/56

,.,..

\

\. F/ .>

Figure 24.- A transatlanticgyropla~e.

.

w

&.


56/56

. .I

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1:.. .

q .4 ,.. .V

,.,

i+-->.+-----

Documents

37103422 the Gyroplane Its Principles and Its Possibilities by Louis Breguet