Considerations of wake-excited vibratory stress in a pusher propeller

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Title:
Considerations of wake-excited vibratory stress in a pusher propeller
Alternate Title:
NACA wartime reports
Physical Description:
18, 4 p. : ill. ; 28 cm.
Language:
English
Creator:
Corson, Blake W
Miller, Mason F
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Publisher:
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:

Subjects

Subjects / Keywords:
Propellers, Aerial   ( lcsh )
Wakes (Aerodynamics)   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: An equation based on simple blade-element theory and the assumption of a fixed wake pattern is derived and fitted to available data to show the first-order relation between the parameters of propeller operation and the intensity of the wake-excited periodic force acting on the blades of a pusher propeller. The derived equation indicates that the intensity of the wake-excited periodic force is directly proportional to air density, to airspeed, to rotational speed, and to propeller-disk area. The derived equation indicates that the effect of power coefficient upon the intensity of the wake-excited periodic force is small. In normal operation the vibratory force decreases with increased power coefficient. If a pusher propeller is used as a brake, increasing the power coefficient will increase the vibratory force. For geometrically similar pusher propellers, a propeller of large diameter will, in general, experience less wake-excited vibratory stress than a propeller of smaller diameter. Limited experimental data indicate that the wake-excited vibratory stress in a propeller increases with the drag of the body producing the wake.
Bibliography:
Includes bibliographic references (p. 17).
Statement of Responsibility:
Blake W. Corson, Jr., and Mason F. Miller.
General Note:
"Report no. L-146."
General Note:
"Originally issued February 1944 as Advance Confidential Report L4B28."
General Note:
"Report date February 1944."
General Note:
"NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of advance research results to an authorized group requiring them for the war effort. They were previously held under a security status but are now unclassified. Some of these reports were not technically edited. All have been reproduced without change in order to expedite general distribution."

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University of Florida
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All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003605293
oclc - 71121859
System ID:
AA00009396:00001


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Full Text


ACR No. L4B28


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WARTI'IME REPORT
ORIGINALLY ISSUED
February 1944 as
Advance Confidential Report L4B28

CONSIDERATIONS OF WAKE-EXCITED VIBRATORY STRESS
IN A PUSHER PROPELLER
By Blake W. Corson, Jr., and Mason F. Miller


Langley Memorial Aeronautical
Langley Field, Va.


Laboratory


WASHINGTON


NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of
advance research results to an authorized group requiring them for the war effort. They were pre-
viously held under a security status but are now unclassified. Some of these reports were not tech-
nically edited. All have been reproduced without change In order to expedite general distribution.
L 146

DOCUMENTS DEPARTMENT





































Digitized by the Internet Archive
in 2011 with funding from
University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation


http://www.archive.org/details/considerationsof001ang









NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS

AD' U:ICE COlTFIDEII'TITL REPORT i10. L4B2&

COiMSIDERATIO IS OF VAKE-EXCITEL VIBR.ATO-RY STRESS

II! A FUSHER PROPELLER

By Blake VW. Corson, Jr., and Mason F. Miller


SUt:ARY


An equation based on simple blade-element theory and
the assunrtion of a fixed wake pattern is derived and
fitted to available data to show the first-order relation
between the parameters of propeller operation and the in-
tensity of the wake-excited periodic force acting on the
blades of a pusher propeller. The derived equation in-
dicates that the intensity; of the wak:e-e:tclted periodic
force is directly proportiornal to air density, to airspeed,
to rotational ?feeid, and to propeller-disk] area.

The derived equation indicates that the effect of
power coefficient upon the intensity of the wlake-excited
periodic force is snall. In normal operation the vibra-
tory force decreases with increasing power coefficient.
If a pusher propeller is used as a brake, increasing the
power coefficirrnt will increase the vibratory force.

For geometrically similar pusher propellers, a pro-
peller of lar'e diaTneter will, in general experience
less wake-excited vibratory stress than a propeller of
smaller diameter.

Limited experimental data indicate that the wake-
excited vibrator;y stress in a prop,'-ller increases with
the drag of the body prod:ucing- the "wake.


TITROD'UCTTOI'


With the increased consideration being given to the
use of pusher propellers there has arisen a concern over
the magnitude of the periodic stresses peculiar to this
type of propeller. A pusher propeller usually operates
in the wake of some other part of the airplane, such as
the wing, engine mount, or tail surface. As the








NACA ACR No. L4328


propeller rotates, each blade passes alternately from a
region where the slipstream axial velocity is practically
the same as the velocity of the free air stream into the
wake region, where the axial velocity may be considerably
reduced. When a blade passes through the wake, the
blade sections experience an increase in angle of attack
and a slight decrease in dynamic pressure; the aerody-
namic load on the blade thus changes periodically. The
type of motion with which the propeller will vibrate may
depend upon several factors, two of which are the number
of blades and the location of the propeller relative to
the wake, The response as measured by the stress pro-
duced in a blade depends upon the deflection shape of
the blade as well as upon the intensity of the exciting
force.

The vibratory stress in a four-blade single-rotating
propeller operating in the wake of a wing has been meas-
ured in the LMAL 16-foot high-speed tunnel and the re-
sults of the tests have been reported in reference 1.
In that report no detailed study was made of the influence
of the aerodynamic conditions of operation upon the pro-
peller vibratory stress.

The purpose of the present report is to derive a
simple expression that will show the first-order effects
of airspeed, rotational speed, propeller characteristics,
propeller size, and wake size upon the periodic force
which excites vibrations in a propeller operating in the
wake of a wing. If an atter.pt is made to account for
all obvious effects of the propeller and wake upon each
other, the problem becomes involved if not unr.anaaeable.
In order to maintain simplicity of the final expression,
it was necessary to make several assumptions, v:hich will
be discussed herein.


ASSUMPTIONS


The problem of estimating the variation of the
periodic aerodynamic load on the blade of a propeller
operating in a wake is limited here, first, to a parti-
cular type of propeller installation and, second, to
operating conditions for which the induced velocities
are negligibly small. The installation being con-
sidered is a pusher propeller located behind a wing with
the axis of rotation centered in the profile of the wake
CGIFIThjTTIAL


CONFIDENTIAL









IrACA AC'. : 1. I.4E?: C IiUFILD i'riAL 3


of the winT. It is a.s.suie. that the i."ropFell er disk is
lar-c e-ouh to extend beyo'n- the vinr rvake into the
urisstuirbed -ir s.tream. Thle J inc- dr-.g coefficient i!7
assa'm-ed to be constant vit'h Cirspteed; this assu.rption
inplies. a fi.xd :.:e pattern v..it the result that at a
liven ,,S1int nr, thrF wc,:e thr- vel-.eit .: defect will lvwa;ys
be proport'on-al to the a irse,-d. A dia 'ra:ri showivrnr a
typical distribu i:onr of velocirt- in rc.e wviake.: of a wing
is presented ini fir'l.lr- 1. (Se- ref-r'er-nce i.)

In order to pstin'-ate the firs t-d3ej'er nr-r-lodic change
of the pero,_y-;na-iae load on r proreller blade due to
intermittei tt change in a-.il -8 vel -it:-, .siimllr blade-
element theory (rf'ere ce .) is ... I umnd to be adequate.
The effect of t-hei chan' s in 9xal vel.cit upon the
blade-:ction dr'E-ic charac teistr i c_. I: reg!7rted a! nPeg i-
gible. Blao.e-sc tio lift, t.herc or e, i3 the only f.-orce
considered, in the Iblad'r-elcmenrt ana ly' -s.

Fr' all condi -ions undEr wh'.c the pro-eller blade
sections e:r-:-t l:it, t]' ir.tain a c-nse 'l:nt induced
air flow ha'-in 7 both 9.: l9.1 :ad tr lonrF vr'in city co l-
ponenlts at the pro.: eller. Ait s i ed -.li: .:v- the tale-off
arnd ,li.imb r-ance the in uced a:-ri-- velDc ity, is vei-" small
in co,'?,r-i.son with the .'orw..d s'e d. For n stefrl d c.:n-
dition r f nor-i-ral operation th i v -.'.o2 it-Le? induced at
various station ns E.loni the pIop,:eiler bltiadJ can be esti-
mated by th- :rocec'ur. given- in reference 4. Thi-s pro-
cedu-e, however, crnnrot be appliej F sat p.ile'.ent because
the p ,orell r oi-,rc tes a ith uInsr -, dy lift. IWhen the
rotating propellers blade trtve rP-Fs tnhe voi:er, the blade
sections exert a -.reitter lift, 'viich creat.-s an increase
in the induced vloci t:. 'T-E inrtan.aleoulC change in1
lift exerted ty tile p'i:ellec- blade secti ns during their
passar-e th h r u the w...-e is l~ ss than Ji t- be e::p ected
from the correspondin i charr-e in an&le ,.f Ifttack, because
developr.ent of the circulation -.n unsteady lift lags
behind the .nfgle-of-artack chanc-e (reference ) A rom-
prehensive trearc:ient -.i thi:h i-.ro')I?-m 'mivo ld I'r-quir-e such
specific as-uniptions concernin- the shape of the wake and
the distribution and regniu-le of th; velocSt:y induced at
the propeller that an:r solution obtained would be neither
simple nor reneral. 'The straightforward apprroach Fer-
mitted by the usr- of ir'.pl'7 blade-clement thcory and the
assumption of a fixed wa'ke pattern justifies the conse-
quent slight loss of accuracy.


CCT i r DEnTT I AL








1'AC:1. ACR :o. L4B28


SYMBOLS


V airspeed and slipstream axial velocity at pro-
peller disk, feet per second or miles per hour
(assumed identical in this analysis)

VR resultant velocity of air relative to any blade
element, feet per second

n propeller rotational speed, revolutions per
second

D diameter of propeller, feet

J advance ratio (V/nD)

R propeller tip radius, feet

r radius to any blade element, feet

x fraction of tip radius (r/R)

b chord of any blade element, feet

8 blade angle of any blade element measured from
zero-lift direction, radians

effective helix angle for any blade element,

radians (tan T- -

a angle of attack of any blade element, radians
(e -)

aw angle of attack of wing

L lift, pounds dL

Lc coefficient of differential lift nD4

CL lift coefficient

CL mean lift coefficient, effective over entire
blade
dCL
m = =- 5.7 (approx.)


CO NTDENTI AL


CONFJDEi- TOTAL









TACA ACi lo. L42. -LFIT'ITT .L 5


T thru?.t (propell er-s'iaft tens on' pounds

4 tor'quP, fo.t-r.po'urds

P po;we:r, f.oqt-pou:id? p T'r second

p densi;-ty f crir, .rl'.s per c'ulic foot

C' tL.rr. coefficient (T/pn D

Cp power coe:ffccient (Ppn'E'')

T.) propeller eff' irnce:.

B nrujrbe- of bla-cs of a zinc proPel rr

C0 C2, C7 con.tan.'tc.

Su1- script:

0.7Fi ;.L 0.7,


DE RIlVAl'TCI F EQ'TIO;- FCR E:CITIT; FORE


For a pro pellx'o operlatinv, in theft vaake of an airfoil
at thr..st-a::i- level a ::-elation cetv"een 'ritratory ex-
citirr7 force an. t'he pa1-ar:etcrs of r'opeller operation
car be derive- d by;r I'.rst expressn,' the f forcee on a pro-
peller blade elempont. Tl-.e lift f.-o.rce on a propeller
blade element of dl fferentiai radial length (fir. 2) is


cL = ApV, -:.CL dr (1)

If the coefficient If differential lift is defined as

dL
dx.
Lc (2)
pn2D4

equation (1) can be. put into the forti


L =s b L ec2p
c --xrDCLE sAL
C D'.F T DE:IT I AL








6 COT 'DE'iTTAL NACA ACR No. L4B28


The change in coefficient of differential lift caused by
a differential change in forward velocity is



dLc T2bx2 ( dCL d
C- T4 (sec2 dC + CL sec2) (3)
dV 4D (V dV


The lift coefficient may be expressed as the product
of the lift-curve slope and the difference between blade'
angle and helix angle; that is,

CL = ma
=-3 e -


If the blade angle is assumed not to change with rapid
changes in axial velocity,


L -m -- (4)
dV dV

By performing the operations of equation (3) and using
equation (4), there is obtained


c = b2 m sec2 + C,(2 sec2 tan (5)
dV 4D dV dV


By figure 2,
V
tan =
TrxnD

from which

sec2 dg 1
s dV TxnD

These relations when substituted in equation (5) yield

dL_ b (2vc
SdL= D 2C mlxnD)
dV nFIDE3 TAL
CO FIDE!.TIAL









ACA. ACE l,. L4E2.. CiFIDP 'TIAL


w hic _h, from equ. at o ( )., :..v s


d() 4 ('CL dx m lnD-, rx (c)


The int-egr ri.:,n e.: q.'v.tion I'.) .. ..ie-s the following
relation be teen the lch&i.e in lift cln the entire pr'o-









within bracik*:ts, the one 2nt in1in 2r will, in y.renral,
beller iade c.nd c r son It t" e other an is.:. ili t rellc a-
\ **O-L -,, n '/ d(







tion between -'-L E i : -J. do s n.t e::i;t, Out equ ati i (7)
csn be s ir" pli ied with sr..iil losI of accurs;: by; u.si:n! a
mean v-n lie of lift c .o: fic, et -T rle rd.'rd es ef'fe -
tire and co:intant Elonr.' the l:..lde. In referee nce C Loci:
shows ti-a.t th, t.hr'ust -,effici t en ti_ o V r.opeilleri can be
compute'd. 'WitI: f;,i-r ac'I.rac-r f'roi an e ler.e enta thrust c,.ef-
ficient, st x = -.' y- usirg i:}-e inte rating f.t.ctor
r/4. deriul ationr. b's-d on the u.se of thi" fsact:.l" is
given in the ap per:n i.:, \ ich s;ho,' ." an c i.. rc ::'" .r'iate rela-
tion between the eif'ec iVe lift t ceff c lt and the oo-
pelle: opera atin t ch rac, t e "li ics.


CL CLrO.-F

f I C e (s:)

r ().D ,R /"T + 4.'4


'oIhenn a men va lue of lift coefficient is used, tro in-
terr al s ht ,-, 1 tht deed nly the eoety of the propeller
blade remain in equation (7). For a ,i'.,en blade design
these in-tea:rals ar1_ coiins.tanta and i may: be evaluated graphi-
cally from the relDtio1ns


CO-FI IDEITT IAL








NACA ACR No. L4B28


1.0 b
C1 = D dx
0.2

1.0 b

C2 = bx dx
0.2


When the constants C1 and C2 and the F::x;ession for
mean lift coefficient (equation (8)) are substituted in
equation (7), there results


SpnD3 [ 64 Cl CTJ I
dL- mC2 dV
4 _
B ).7R \ + 4.84



The assumption of a fixed wake pattern permits the
concept that the velocity defect at a given point in the
wake is always proportional to the airspeed; thus

AV = -C3V (9)

This definition is used herein without regard to the
ratio of blade width to wake thickness. Further con-
sideration of the effect of wake size upon the vibratory
exciting force is given under "Discussion." By re-
garding dL and dV as finite increments and using
equation (9), the intensity of the propeller-blade vibra-
tory exciting force is expressed as


AL = 3n m64 Cl CTJ V (10)
4AL = C mC2 2B .( b
oD .7R + 484

The substitution of an average lift coefficient
(equation (8)) in equation (7) provides a means of ex-
pressinr the steady operating condition of the propeller
in terms of customary parameters. The effect of dis-
tribution of lift increment along the blade upon the


COFITDE; ITIAL


CONFIDENTIAL








IIACA ACE HIo. L4B2'3


wake-excited propeller vibration depends upon the blade-
deflection shape. For a given trpe of blade deflection
the vibratory force should be governed by equation (10).


DISCUSSIo T


General.- The expression for the magnitude of the
vibratory exciting force (equation (10)) shows the rela-
tion between aero.dynamnic excitin:i force and dimensions.
If the quantities in the brackets are disregarded, the
force is proportional to air density p, to an area DL,
and to the square of velocity having the components rota-
tional speed nD and airspeed V. Of the terms within
the brackets, mnC2 determines the greaterr part of the
exciting force that is due to the increased angle of at-
tack of the blade sections within the wake. The term
that includes C7J. represents the change in force due
to the decreased d-c'namic pressure within the wake
(equation (Z)). Actually the t r-i involving CrJ
(equal to Cprj) is relatively s;iall g.Ind minimizes the
effect of rLnC2 Sn the range of normal operation.
Retention of the term CTJ is desirable, however, be-
cause, if the propeller is used as a brake, the thrust
coefficient becomes negative and the effect of the
quantities within the bracket? are additive; the result
is that, other conditions being equal, greater vibratory
forces are experienced.

Effect of wal'- size.- In deriving equation (10) no
effort was made to account for the effect of variation
of propeller location downstream from the trailing edge
of the wing nor of the wake thickness. The assumption
of a fixed wake pattern permitted the statement that the
ratio of wake-velocit" defect to airspeed is constant
(equation (9)). It is known that the wake pattern
(velocity profile) in a given winfg wake changes with
distance downstream from the wing (reference 2). Close
behind the wing the wake is thin and the velocity defect
is intense; farther downstream the wake is thicker and
the velocity defect is reduced. Both wake profiles
represent the same mormentum loss, and the velocity de-
fect integrated across the wake is approximately the
same at all stations within a distance of several wing
chords behind the wing. As the downstream location of


COrIFIDENTIAL


COU FIDE1TTIAL








'T.iCA ACR No. L4B28


the propeller is changed, the time required for a blade
section to traverse the wake changes in'inverse propor-
tion to the velocity defect and therefore inversely as
the exciting-force intensity. The vibratory exciting
impulse, which is the product of force and time, remains
constant. Although vibratory stress in the wing struc-
ture may be considerably affected by downstream location
of the propeller, it is probable that the wake-excited
vibratory stress in the propeller is very little affected.

li1 data are available that show directly the effect
of wake size but the vibratory stress in the propeller
blade shank measured at constant airspeed, rotational
speed, and power varied directly with estimated wing drag
with and without flap (reference 1). 'These limited data,
as well as dimensional analysis, indicate that the con-
stant C3 and therefore wake-excited vibratory stress
in a pusher propeller are proportional to the-profile
drag of the iing producing the wake.

Effect of propeller dianeter.- In -r:-eral, pusher
propellers of l.ar .' t:. ill. experience less wake-
excited vibrator': stress than propellers of small di-
ameter. Consider the following cases:

Case 1. '..o pusher-propeller installations of dif-
ferent size but geometrically similar with respect to '
propeller, wing, and wake dimensions operate at the same
airspeed and with the same rotational tip speed. Equa-
tion (10) indicates an exciting load proportional'to. D2,
If a blade is regarded as a beam, the unit bending load
increases, directly with D and the bending moment at a
given station therefore increases as D3. The section
modulus at any station also increases as D3. The wake-
excited stress would therefore be the same for both pro-
pellers for a given mode of vibration if the two resonant
conditions occurred at the same rotational tip speed.
Because the propeller rotational speed is inversely pro-
portional to D, as is also the static vibration fre-
quency for a given mode, the resonant condition for the
two propellers would occur at the same rotational tip
speed if the vibratory frequency did not change with
rotational speed. V' .:he the effect of centrifugal force
on the resonant frequency of the blade is considered
(reference 7), it is seen that resonance will occur for
the propeller of large diameter at a lower rotational
tip speed than for the smaller propeller and therefore,
by equation (10), the vibrator. stress will be less.
COiTFIDE. TIAL


COF IDENTICAL









HACA ACR Hio. L4B2 C


Case 2. On a given airplane a change iL. rade front
a pusher propeller- o.f all dria.i ter to a siii; lar pro-
peller of larger d.ameter. The rvtstial tip -peed and
airspeed are the same for both propellers. This case
is identical \.ith case 1 except that the ratio of alk:e
area to slipctrean cross-sectional area at the ,propeller
disk i rerdued. For tis eason as well as for the
reason -iven in case 1 the vibratory excitinrr frrce and
consequently the stress will be less for a pusher pro-
peller of large diameter than for a srill propeller.

Compre.s-ibility effect.- The nom.o-ess iblitl of air
affects the propellrr *ibratory, excitinF force only to
thE extent hat ttlt affect- the b<,lede-s-ct ion airf-il
characteristics aid the viinr wake.:-. The quantity n
within the brackets of equation (10) increase.C with
blade-secti on ooeratinr Nach nLrmb',r and produces a cor-
respondrin, increa-e in the thrust coefficient CT. The
net effect is an increase in excitir.- force due to corn-
preFsibilit-, with an increase in either rotational tip
speed or airlspeed. This in cre 'a in ec:.ctinr force is
in addition to the direct effect of the rotational tip
speed or air:peed indicated b- equation (10). In
general, airplanes do not operat- at such hiph airspeeds
that 5ing r- draF (".al:e size) is much affected bt comipr.es-
sibility' however in some cases propeller vibratory stress
may be influenced b'y the effect of comrpressibility on the
wing drag. tjirpl.ar.es having win:- sections with a thick-
ness ratio of 2c to S2 i-,ercent m.r:ay operate at hiah alti-
tude at a value of iach number clote to the critical
value (0. t 0 to r the w:2 1n. It would be possible
in a shallow dive- -o exceed the critical M['ach nurinb-r and
thereby to increase the v;inC drac an. in turn the pro-
peller vibratory qtres-.

Excitat ion f req ueny. rIn t ornrin through one revo-
lution; each blai e of a pusher aroi.ell-r operating in
the wae wa of a vwinc located at thrust-a::-s level receives
two rwake-excited impulse. M i'r .iode of propeller vlbra-
tion ha. in. a resonant frequency o"f 2n ray- be excited by
the wake. because the waake region through which the
propeller operates rma-y be quite sharply defined, the
excitation will contain harmonics of the frequency 2n.
The harmonic components, however, are Hf relatively
small importance according to the tests of references 1
and 8. Although previous tests reference 9) indicate
that it is possible to produce a second mode of vibra-
tion with aerodynamic excitation, the first modes of


COIVFIDE"ITIAL


C0:F FIDEiIT IAL









NACA ACR No. L4B28


vibration occur most frequently with such excitation
(references 1, 8, and 9); therefore primary interest is
in the vibrations that have a frequency of 2n.


APPLICATION OP EXCITIiG-FORCE EQUATION TO !71.STURD DATA


Apparatus and methods.- During the tests reported
in reference 1 Th-: propeller operated behind a wing
mounted at thrust-axis level (fig. 3). The plane of
the propeller disk was located about 23 percent of the
wing chord behind the trailing edge, or ap'roxiirately
2 blade chords (at the 0.75P) behind the wing trailing
edge. The wing wes tapered and had NACA low-drag sec-
tions. A simulated full-span split flap was attached
to the win. for some of the tests, .'he propeller was
driven by a Pratt & 7:..tney R-2800 enline mounted in a
nacelle and supported in the wind tunnel separately from
the wing. The single-rotating propeller was a Hamilton
Standard hy';'ro-.tic of 12-foot diameter, which had four
aluminum-alloy blades of design 6-' 7-12 used in a hub
of design 24D50. The propeller rotated at nine-sixteenths'
of the engine speed.

The experimental data consisted in oscillograph and
wave-analyzer records of strain, "L' .ch were converted to
stress; electrical strain gages were used for pickups.
The stress deterninations are believed to be accurate to
within 5 percent. The method and accuracy of strain
recordings are explained in more detail in reference 9.
The strain-gage circuits were completed through a com-
mutator in front of the propeller. Leads from the
commutator were supported by a steel cable 3/8 inch in
diameter stretched across the wind tunnel just behind the
wing. The propeller operated in the combined wake of
the wing and the cable.

Tests and results.- The propeller-blade vibratory
stress ,.,..s ;.IE s.e during tests in which the rotational
speed was held constant at the resonant speed and in
which engine torque, and therefore power coefficient, was
held constant. Only the airspeed was varied during a
run. threee runs were made with different constant values
of power coefficient. An edgewise reactionless vibra-
tion was encountered, which produced maximum stresses
near the blade shank.


COGrFILEITIAL


CC T 12IDETIAL









iACA ACR i!o. L4B23


If darrping is assuiued to be constant, the vibratory
s ress for a Riiven prerEller isP proportional to the
exciting force AL for an:y ,iven resonant frequency.
In a strict snsnse, the dumping changes when LAL c.,an5es
for example, a changFe in ai,'rspeed V would be accor.-
ranied tb ch-,anges in aer',dyn-Lsic da .pinr and r:echnical
hyster.--ls d-arpin1. In the application of equation (10)
to the available test data, however, it ir as umed that,
within the acc.,'racy of the equation and of the vibrator:y-
stress I-Ieasurer ents, the cha:in:e inr thIe dar.pin-. iS siw:all.
For constant damcpin:', the pro-ell].r v ibrat ry S, tres: under
the conditions of the tests should have increased directly
as the airspeed increased. A sli.;ht effect o.f power
coefficient mirfht lia"e been ex pected but, because Cp ]
is practically constant in cL'h operation r- tranpe, this ef-
fect would be ver;.r small. The results of the stress
measurements are 1iven in table I and are shown graphi-
cally in figure 4, in wl'hich vibrat. 'r stress at the pro-
peller blade shank is plotted against air-peed. The
straight-line variation of stress -:.ith airspeed required
by equation (10) has been fitted to the data front refer-
ence 1 by the rnethod of least s.quares, and the arreerent
is reasonably good. There was no consistent variation
of vibrator:. stress with povwcr coefficient.

A fewi additional measurements of prop:elle-r-blade
vibratory stress were ,made after a simulated split flap
was attached to the ",in- ahead of the propeller. The
deflected flap caused such a great increase in the vibra-
tory, stress that, 1.'hen the airspeed was increased above
150 miles per hour, the "ibratory stress became dangerous.
The stress increase produced 'by tlh deflet'. td flap is
attributed solely to the increase in wing- dra" and not to
the downwash associated with the cihane in fwing lift;
this conclusion is based upon the test results of refer-
ence 1, which show that increasing the angle of attack of
the winz from '0 to J.90 produced practically no increase
of vibratory stress at a frequency of n. There are
available only two :-ets of test data t~ wh;ch wake-
excited vibratory stores: may Le correlated with the drag
of the body prodiucinr the wake. These data taken from
reference 1 are rre'sented in figure 5, .wh-ich shows vibra-
tor-y stress of frequency L'n measured a- the blade
shank. The draz coefficient based on wing area was com-
puted from the combined estimated drag of the wing and
electrical-lead support cable.


CO ITFIDETII" TAL


C, ITFIDEIIT AL









NACA ACR No. L4B28


COI;CLUSIONS


The derived equation that shows the first-order
relation between the intensity of the wake-excited peri-
odic force acting on a propeller blade and the parameters
of propeller operation and limited experimental data in-
dicate the following conclusions:

1. The intensity of the wake-excited periodic force
acting on the blade of a propeller operating in the wake
of a wing varies directly with air density, airspeed,
rotational speed, and propeller-disk area.

2. The magnitude of the power coefficient has a
very small effect upon the magnitude of the wake-excited
periodic force that causes vibrationn in a pusher pro-
peller. In normal operation, inc (easing the power coef-
ficient decreases the vibratory force. When the pro-
peller is used as a brake, increasing the power coeffi-
cient intensifies the periodic force.

3. For geometrically similar propellers, a pusher
propeller of large diameter will, in general, experience
less wake-excited vibratory stress than one of smaller
diameter.

4. The wake-excited vibratory stress in a propeller
increases with the drag of the body producing the wake.


CONFIDEIITIAL


CO=TFILZTIAL











IACA ACER lo. L4B23


CC!;FTDENTTAL


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NACA ACR No. L4B28


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C-TF ID3 4TIAL


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H:ACA &CF IH o. L4BEi'


1. Miller. a son F. : Wind ,i-Tunnel Vibrsti.nr Te'ts of
a Four-Blade Sincr-e-rottatinr Pushr r Propeller.
ARER io. 32'24, I :CA, Jue 194I .

2. C-oett, Harry J.: E:X:perPirlenltal Irn'estit-t tion of the
lIorner-tTun methodd for D- termining Fr.fl_ Di g.


3. v'eeic':, Fred E.: rcr'fllf't Pro 11:iler DE'-ign. McGlraw-
Hill Bcok Co., Inc., lO,

4. Locki, C. II. H., and .e-ntsan, F'. : Tbles. for Use ri
an Improved frethod cl -- r e3're .trip T'i -c. '. alc.-
lation. R. n: LI. 'o. 1 74, P .itish a...C., 19 .

E. Silver stein, ;-be, and .o--r, Upiur T.: eri-
nenital Ver'fi~atIion of thie -Ther. of :-cIllating
airfoils. Re,. !:o. t63 129 .

6. Lock, C. U. H..: A Gra ical Iet-od of Calculat.inr
the Perform-rance of an ,irscr-w. R. : I. No. 1849,
British A.R.C., 1.-.?.

7. Den Hartcg, J. P.: ;:ee-cnice.l VirF-It ion s. VcGraw-
Hill Book Co., Inc., 2d ed., 1.10.

S. For'sic'Av, J. FL., Squire, H. r., an. Bi.', F. J.:
Vibration of Propellers Due to .1on-U:iniform InfloC.
RFep. ITo. E.35 38, R..E,; ; pi"il 1 42.

9. 11ller, f'son F.: Win-d-Tnnel Vi'-ratiron Tests of
Dual-Rotating Propellers. ARR :"o. Till, !.ACa,
Sept. 1943..


C OIFI DEIT IAL


COCFIDEPTIAL






NACA ACR No. L4B28


TABLE I

VIBRATORY STRESS AT SHANK FOR FIRST

MODE OF TEGE'TSE, VIBRATION

LBlade design, Hamilton Standard 6487-12; aluminum-alloy
blades; no simulated split flap attached to wing; a,, O0


C D!'FDLE.'TTAL


Airspeed Vibratory stress
(mph) (lb/sq in.)

Power coefficient, 0.048

106 2800
185 5 3E 0
280 7050

Power coefficient, 0.072

142 3400
185 5500
280 6800

Power coefficient, 0.096

157 4100
185 5600
280 6700


CO1F IDENTIAL







NACA ACR No. L4B28


CONFIDENTIAL


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CONiFIDENTIAL






NACA ACR No. L4B28


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'Or!FIDErITI AL


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CONFIDENTIAL







UNtVERSITY OF FLORIDA
I 111~II III[ l11 iIlI
31262081032863


UNIVERSITY OF FLORIDA
DOCUMENTS DEPARTMENT
120 MARSTON SCIENCE LIBRARY
P.O. BOX 117011
GAINESVILLE, FL 326 1-70 f USA




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