Wind-tunnel vibration tests of a four-blade single-rotating pusher propeller


Material Information

Wind-tunnel vibration tests of a four-blade single-rotating pusher propeller
Series Title:
Alternate Title:
NACA wartime reports
Physical Description:
13 p., 11 leaves : ill. ; 28 cm.
Miller, Mason F
Langley Aeronautical Laboratory
United States -- National Advisory Committee for Aeronautics
Langley Memorial Aeronautical Laboratory
Place of Publication:
Langley Field, VA
Publication Date:


Subjects / Keywords:
Airplanes -- Wings -- Testing   ( lcsh )
Propellers, Aerial   ( lcsh )
Aerodynamics -- Research   ( lcsh )
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )


Summary: Vibration tests of a four-blade single-rotating propeller operating in a simulated pusher condition were performed because the combination of wake and downwash behind a wing was expected to provide serious excitation for reactionless vibrations of propellers with four or more blades. The tests were conducted in the LMAL 16-foot high-speed tunnel with a wing mounted at thrust-axis level ahead of the propeller; the blade sections at three-fourths the propeller radius operated at approximately twice their chords behind the trailing edge of the tapered wing at their closet position. Measurements of propeller vibratory stress were made for various airspeeds, engine speeds, and engine powers.
Includes bibliographic references (p. 13).
Statement of Responsibility:
by Mason F. Miller.
General Note:
"Originally issued June 1943 as Advance Restricted Report 3F24."
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."

Record Information

Source Institution:
University of Florida
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
aleph - 003806481
oclc - 124077221
System ID:

Full Text

fr'kfr L- 1" 3:.-:-.. .. ABE Do. 3F24

..' ... .


June 1943 as N
Adv ance restricted Report 3F24

By Mear F. Miller

Langley Memorial Aeronautical laboratory
Langley Field, Va.
PO. BOX 117011

Blo uttfpera ( originaLt isned to provide rapid distribution of
*Hi: grouse .p requiring them for the war Cart. They were pre-
eele1 sata, en.w uaclaslftel.. Some of tebse reports were ndt tech-
So"der "pe general distribntion.



D'OAl:VC, Ai-nSThICIQ DJ i.'.P0.-T



Bv i-ason F. diller


Vibration tests of a f our-bl.d.e sinle-rotating pro-
peller operating in E sinul--ted pus}-er condition were
performed because the c.-.tL iatntion of .-,ke -nd downvash
behind a wing vas expected to provide serious excitation
for reactionless vibrations of pro.',ellers, ',-ith f cu.r or
more blades. The tests i ere cond.ucteA in the L t.-L 16-foot
high-speed tunnel ,' a ',,in.- mounted at thrust-axis level
ahead of the propeller; the blede sections at three-
fourths the propeller r.!dius oper. ted .t apn)rovi:aiately
twice their chords behind Ith..' tr.ilinr- edge of the tapered
wing at their closest position,. e asure-ents of propeller
vibratory stress 'ere made for various airspeeds. engine
speeds, and enoRine .owers.

The vwae behind thp iinr; supplied serious excitation
for an Ped-ewise reactionless vibr;.ticn of the propeller
at a frequency of tvice the propeller speed; the resulting
vibratory stress increased cD:siderbl ly with airspeed but
was practically independent of engine brtike mean effective
pressure for constant airspeeds. i!.e effect of downwash
upon the reactionlr: 's vibrat.on-was very small; changing
the angle of att.cK-: of the ,,in. from L to 3.90 produced
no detectable increaEse of dorn\wasn excitation and little
increase of woke ex'.citatior, A siuiultted full-span split
flap on the lower surface of the winr, greatly increased
the vibratory stress and prohibited the running of tests
over thp stress pe.-- at airspeeds higher than 140 miles
per hour.

FD flatwise resctionless vibration was detected,
probably because the airspeeds were low for most of the
critical engia-p speeds and because the harmonic components
of wake excit: tion were small.


The operation of a single-rotating propeller with
four or more blades behind the wing has created ?ome
concern because of the expectation that the combination
of wake and downwash might supply serious excitation for
a reactionless typa of vibration. Because roactionloss
vibrations of a single-rotating propollor may occur at
all frequencies other than 1, kB, and kB 1 times the
propeller spood where k is any integer and B is the
number of blades, it is observed that the propeller must
have more than three blades to vibrate in a reactionless
manner (reference 1). A propeller vibration is reaction-
less if the vibratory motions of the blades are such that
the vibratory bonding moments and the vibratory forces of
the several blades cancel each other at the propeller
shift; consequently, reactionless vibrations occur only
with aerodynamic excitation and are not possessed of
engine damping. It was believed that with no engine
darping the vibratory stresses caused by the wake and the
downwash behind a wing could be unsatisfactorily high,
inasmuch as the vibratory strcssos would be limited only
by aeroiynamic damping, by hysteresis damping of the
propeller blades, and by damping produced by notion of the
blade shanks in their hub sockets,

Tests were conducted in the LMAL 16-foot high-speed
tunnel with a wing mounted at thrust-axis level ahead of
a four-blale single-rotating propeller. Measurements of
propeller vibrator. stress were made for various airspoods,
engine powers, and conditions of the wing for the complete
engine-speed rango, Most of the testing, was done, however,
within the limited range of engine speed for which a prom-
inont reactionless vibration occurred,

Menbers of the staff of Hamilton Standard Propellers,
Division of United Aircraft Corporation, collaborated in
conducting the tests and analyzing the records,


The singlo-rotating propeller tested is described as

Type . Hamilton Standard hydrom.rtic
Material . . luIiLu alloy
Number of blades . our
Diameter . 1? feet C inches
Blade design . . 6487-12
Hub design . . 24D53

The propeller was driven by a Pratt & .'hitney R-2800
engine geared 16:9 and mounted on rubber mounts in a full-
scale stub-wing nacelle. The engine-propeller-nacelle
combination is shown in figure 1.

The rusher condition was simulated by mounting a
wing at thrust-axis level anh?ad of the four-blade propel-
ler. The wing, which has an .-CA low-dreg airfoil sec-
tion, was inverted merely of convenience, this
way of mounting having bpen desirable for conducting: the
vibration tests reported in reference 2. Figure 1 shows
tho wing counted aherd of the propeller to sinul.ate the
pusher condition. The dimensions of the vin% and the
location of the wing with respect to the propeller for the
wing set at an angle of attack a, of jO are shown in fig-
ure 2. The ,,ing '-as located in such a %'ay that the blade
sections rt three-fourths the propeller radius operated
nt appro-ri rmtely tuice their chords behind tan trailing
edge of the tr-pered wing. The, simulated split flap used
for one of the tests is shown in figure .2 In order that
thr simulated flap would be attached to the rear spar of
the wing, it waes somewhat forward of the usual flIp posi-

Oscillograph records of propeller vibratory strain
were obtained br a method fully described in reference 2.

Electrical strain grges i--ere nount d longitudinally
on all the blades at the shanks and nepr the tips. The
gages were mounted on the ca".bered that is, the front -
sides of the blades (fig. 7). Because the maximum stress
of a blade surface for a given propeller radius is at
maximum blndp thickness for a flatrise vibration, the tip
gages were mounted to measure stresses at Laximum blade
thicknesses. So9e :eg.?s were mounted on the wing.

The strain gages on the propeller were connected to
a slip-ring device, which in turn was connected to volt-
age amplifiers. The strain-gage resistances varied with
the strains to produce fluctuating voltages the alternat-
ing components of which were applied to the amplifiers.


The gages were calibrated in such a way that there was a
known relationship between the alternating voltages and
the strain variations.

The alternating-voltage outputs of the amplifiers
were applied to oscillograph elements of a recording
oscillograph, and strain variations were recorded on pho-
tographic paper. There were 12 amplifiers and 12 oscil-
lograph elements; one of the channels was used for record-
ing a timing wave on the photographic paper. The timing
wave consisted in periodic impulses occurring each time
a given cylinder fired. These impulse records were
obtained by proper connection from a spark-plug lead to
an osaillograph element. The purpose of having a timi,.g
wave representing engine speed is to express the frequen-
cies of vibration in terms of either engine speed or pro-
peller speed, in order that the cause of the vibration
can be determined. A direct record of propeller speed
would have been jrst as suitable. (See reference 2.)

All the amplifiers were calibrated simultaneously
at intervals during the test by applying a known alter-
nating voltage tc their input terminals. The amplitudes
of the resulting oscillograph traces were measured after
the tests, and a definite relationship between oscillo-
graph amplitudes and amplifier input voltages was thereby
obtained Bach inch of amplitude on the photographic
paper therefore represented a known amplitude' of strain
on a propeller blade. Stress values were determined by
multiplying strs'n values by the modulus of elasticity
for aluminum.

The static natural frequencies of reactionlees pro-
peller vibrations with Hamilton Standard 6487-12 blades
were predetermined by weasurement and are shown in the
following table:

S, Trequency
ode I (cpe)

r 16.7
S! 70,2
Flatwise i 137.8
S 230,5

Edgewise 45.8



The four-blc.d propll--.r, r sting on its hub wLich .rns
unre strained, was -xcit'd eit one of tnh- blsde ti.)s with
an rllctricnl ePcitr of varietile frpqu'rncy. It w s con-
sidered n.ot n,'cessa.ry to restrain thr hub b-'cuius. for a
renctionless vibration, the vibratory ins- .rom'nts and
vibratory forcr-s of th four bl-.dr~, cnnc,1 Pich oth-r at
the hub. From a low frnqu-ncy, th"- rxciter f'r.-qu .ncy wns
gradually incr-peed; wh'-n th=- various r-.'. ctionl-ss vibr--
tions appPrnd thr- frPqu'rnci, s w. r accurRat-ly dntc-r-
min-d. Oscillogrnph records of strain wrcr t'k p:n, using
electrical strain ganges for pickups; th' frnqurncies of
strain variation appearing on th'st r-cords were d,'tfr-
mined accurnt'ly by comparing th'an with the traces pro-
ducrd by an accurately calibrated, Plectrically excited
tuning fork. Frequrnci,.s for th" first five flatwise,
modes and thp first '*dVwise mode we-re dctrfrmined, B4c:ause
the present report denls principnilly with reactionlcss
vibrations, th" method of det;-rnmining static natural frT-
quencins of nonreactionlnes vibrations is not discussed
herein. A mor, co! upl- t discussion of the. mr'thods of
measuring static natural frequenci-s of a propr-llo.r is
.riven in rnfnrenc- 2.

A propollrr vibration is terr.r- flatwise if the
vibratory motions of th,- blade s.,ctions are primarily
perpendicular to the blade chords; whereas an edgewise
propeller vibr-tion is one with th- vibratory motions of
the blade sections primarily along th- blade chords. Some
flatwise motion generally exists near the blade tips dur-
ing edgewise resonance because of the coupling supplied
by the blade twist.

Centrifugal correction factors were applied to th--
static natural freocuencies of reactionless vibration in
accordance ,ith the accepted formula, which is 7xplsined
in referenrc .': ,

f = foC + End (1)


f natural frequency at a givr.n propellor speed

fo static natural frequency

n propeller speed


K a constant for a given mode of a given propeller

The method of predicting engine speeds for. reaction-
less vibrations of frequencies 2n and 6n is shown in
figure 4. The values of K used for figure 4 are as fol-
1 ows :

First flatwise mode . . 1.7
Second flatwise mode . 5.6
'irst edrewise mode . 1.12

The critical engine speeds are those at which the straight
lines intersect the lines representing natural frequencies.
Onlyv the first and the s-cond flatwise modes and the first
edgewise mode are considered for figure 4 because, within
the engine operating speeds, the straight lines represent-
ing frequencies of 2n and 6n do not intersect the
natural-frequency lines for the higher modes. The reac-
tionless vibration having a fr-quency of 2n is of most
importance and the reactionis-es vibration of frequency 6n
is also of interest. xcitations having frequencies
higher than 6n were expected to be negligible.

The teet conditions are given in the followi-ng table:

In ine bmpp Airspeed Ingine speed
(lb/sq in.) (mph) (rpm)

n&le of attack, C0

1CO I- 15 to 280 900 to 3850
150 1, to 2 1250 to 2850
I :CO i 1250 to 2860 of attack, 3.90
S ----- --------

150 ) 100 to 185 2i 400 to 2850
2- ---- 'I

ngle cf attack, Co; simulated split flap on wing

15C0 100 to I15 2400 to 2850
L C --------



Sizable excitation forces for reacticnless propel-
ler vibrations are expected if the propeller operates in
the wake and downwash region behind a wing. Although
nonreactionless vibrations having other excitations are
also important, they are outside the scope of the present

In accordance with the result of an analysis show-
ing that reactionless vibrations can occur for all fre-
quencies other than 1, kB, and kBDt 1 times the pro-
peller speed, a propeller must have more than three blades
to vibrate in a reactionless manner, nn' a reactionless
vibration of a four-blade propeller can occur for frequen-
cies of 2n, 6n, 10n, 14n (reference 1). It may
be noted that a reactionless vibration can occur at a fre-
quency of 2n for propellers with four or more blades.

The wak- behind a wing may result in a serious reac-
tionless vibration of a propeller with four or more
blades if the frequency of pecitation 2n is equal to
a natural frequency far a reactionless vibration. Each
blade of the propeller passes through two low-velocity
regions per revolution. The periodic change of forward
velocity with respect to each blade causes a periodic
change of angle of attack of each bla.e. Periodic forces
therefore act upon the blades to produce a propeller
vibration at a frequency of 2n. The effect of a change
of forward velocity acting upon the propeller blades is
shown in figure 5. The greater force occur for the
lower forward velocity because of the greater angle of
attack. The decrease in mognitade of resultant velocity
Ri, however, eli htly offsets the effect of the change
of the angle of attack. T--pical total-presnure and
static-pressure variations in the wake region are shown
in figure 6.

The excitation provided by the wake is not sinusoidal,
and excitaticn? at frequencies thrt are harmonics of 2n
therefore e:ist. These haracnic components, however, are
smaller than thp fundurmental component. The excitation
having a frequency of 4n r'ill not excite a react:oaless
vibration of a four-blade propeller. Although an excita-
tion having a frequency of 6n can produce a reactionless

vibration, the third harmonic component of wnke excitation
is expected to be quite sm:-ll and to give little trouble.
Higher harmonics of wake excitation erp expected to be

A reactionless vibration having a frequency of 6n
car. be first, a second, or a higher mode, depending upon
th, propeller speed. The hisghst mode that can be obtained
with this frequency of 6n depends upon the upper limit
of propeller speed, the natural frequencies of the modes,
an$ the increase of natural frequencies of the modes with
propeller speed. (See refer :.ces 2 and 3.) For modes of
vibration higher than the first mode, the vibratory vploc-
ity of some parts of tha blade is 18O out of phase with
that at other parts of the blade (see fig. 7); and, with
the. excitation acting in the same sence over the entire
blQan length, some parts of thp blade absorb energy from
the excitation, while the remaining parts dissipate energy.
If a renctioninss vibration of frequency 6n appeared at
a relatively high propeller speed, it would be one of the
higher modes and th-reforA subject to thp cancelation
effect. The car.celation effect is somewhat decreased,
however, because an excitation acting near a blade tip is
morn, effective than the same x.citation acting near the
blade sh-,nk.

Thn. pr's-nc of downwash behind a wing is *-xpoct-d
to supply excitation for o prop ller vibration at a fr.--
qu'ncy of In, .ns shown in fi-ure 8. Th- doi&ward compo-
nent of vlncity in the plen of thr propeller disk in-
crmF.s.:s the eangle of attack of a proprllror bladc. during
on--half revolution of th- propcll-r and creasesss this
angic during the r-.maining on.-half revolution. This
periodic change of anglo of attack of the blades causes
periodic force to act on th' blades and th.rrforo results
in a propeller vibration at a frequ,-ncy of In. Also, the
r-sultant v.-locity Va of th, air with respect to the
blacr.s is variabl- -'ith the sam, frequency as thr angle
of attack and aids thl o'riodic change of anglt of attack
to oroduc-? thr vibration. Th. vibration at a fr,'qn ocy
of In .'xcitcd by th." down'-' Jh is not reactionloss but,
if it occurs simultanr.ousl: with the rsactionl.ess vibra-
tion., is -xp,-cted to increase t -.- er-riouisnrs of the reac-
tionless vibration yxcitrd by th,- wak.',

Incresling th enangl of attack -if a wing,-s an
incrrnse of down'-.,sh angle and, as a result, a vibration
-xcitcd by downwesh would b- oxpectcd to b;.comif mor-, pro-

nounced. Although the wake behind a wing follows the
downwash, the change of magnitude and shape of a wake
profile is sm.-.l for a change of angle of attack less
than about 50. (See reference 4.) A relatively smill
change of wing angle of attack is therefore expected to
produce little chan-e of a propeller vibration excited
by the wake.

The use of a split flap on a wing is expected to
broaden and strengthen the wake (reference 4) and thereby
considerably increase the propeller vibratory stress
occurring at a frequency of 2n. A split flap on the
lower surface of a wing also directs the air downward be-
hind the wing and is expected to increase the excitation
at a frequency of In.

For constant airspeed and propeller speed, the pro-
peller vibrations excited by the wake and the downwash
behind a wing would be expected to be less affected by
the engine brake mean effective pressure than those pro-
peller vibrations excited by the engine.

The trailing edge of a wing may possibly vibrate
because cf aerodynamic excitation supplied by a propeller
operating close behind it, if its natural frequency is
equal to the frequency of excitation (reference 2). The
frequency of importance is En; each blade passes the
closer part of the trailing edge once per propeller revo-
lut i on.


The results of the present test are present! in fig-
urps 9 to 12. Thp stress peaks are labeled with vibration
frequencies in terms of propeller speed n and engine
seed N for example, 2n and 4-.1-. The stress peaks
of the curves representing total vibratory stress have
more than one frequency component, and the frequency com-
ponents are given in order of importance. Some of the
stress curves are given only for a frequency of 2n; these
stresses were measured with a wave analyzer.

A prominent propeller vibration having a frequency
of 2n appeared at an engine speed between 2780 rpm and
284C rpm. (See fig. 9.) This vibration was evidently
edgewise, inasmuch as the first mode of edgewise vibration
at a frequency of 2n was predicted for an engine speed
of 288C rpm (fig. 4). The engine-speed prediction was

somewhat high but is considered good, any prediction with-
in 50 rpm being satisfactory for test purposes. The
curves of figure 9 are plotted for the leading-edge posi-
tion of the shank for two reasons: (1) For an edgewise
vibration, the stresses at the shank are maximum at the
leading edge and 1800 around the shank from the leading
Pdge, as discussed in reference 2 (the leading-edge posi-
tion is in line with the leading edge at approximately the
42-in. station of the blade); and (2) For a first mode of
vibration, the maximum stress along a blade is near the
propeller hub because stress depends upon c/p, where c
is the perpendicular distance from the neutral axis to
the extreme fiber and p is the radi-us of curvature of
the neutral axis.

The effect of airspeed upon the vibratory stress for
the edgewise vibration appearing at an engine speed of
2820 rpm is shown in figure 9. These curves demonstrate
that the vibratory stress increased with airspeed. Part
of the total vibratory stress was produced by engine exci-
tation, as evidenced by the frequencies 4 ., IN, and

The effect of engine brake mean effective pressure
upon the vibratory stress is shown in figure 9. The vi-
bratory stresses having frequencies of 2n change only
slightly with brake mean effective pressure for a given
airspeed; the very slight variation can be due to experi-
mental error. The vibratory stress of frequency 2n
would be expected to be practically independent of brake
mean effective pressure, as previously discussed; however,
if the total vibratory stress is composed of some engine-
excited components, some engine damping exists that may
vary, with brake mea-n effective pressure to produce such
slight variations of stress as found in figure 9. At
first glance, the bottom curves seem to vary considerably
with engine brake mean effective pressure, but it must'be
noLiced that the curves are plotted for slightly differ-
ent airsneeds.

The downwnsh behind the ving should provide excita-
tion at a frequency of In. 'ith a win.- angle of attack
of 0, traces of vibrations iavin a frequency of In
worn found for an airspeed of 2PG miles per hour, but no
indication of the frequency In appeared at the lower
airspeeds. (See fig. 9.) The effect of downwash upon
the total vibratory stress at the engine speed of 28920 rpm
is small, probably because a frequency of in at this

engine spe-ed is not a natural frequency of propeller
vibration and because the downwash Is limited in a con-
strict-d air stream of 16-foot diameter.

Changing the angle of aGtack of tnr win- from 0 to
3.90 produced little increase of propeller vibratory
stress. (Se. fig. 10.) This result shows that thp wake
and thn downwash behind the wing were affected little by
the angle change. Because the pres-nc- of the tunnel
wall is believed to have limited the downwash, the loca-
tion of th- wake would be exp cted to charge only slightly
when the wing angle of attack is increased 3.9. In
accordance with reference 4, a change of 3.90 in th- wing
angle of attack should produce very little change of the
magnitude and the shap- of a wake profile.

The simulate-d split flap on the lo'.,ar surface of
the wing greatly increased the propeller vibratory stress
at a frequency of 2n. (Sea fig. 11.) This increase of
stress is attributed to the strengthening and th" broad-
ening of th.- wake. Although the pr sence of the simulated
split flap was also expected to cause a vibration of fre-
quency In, no such vibration was detected. l'ith the
use of the simulated split flap, however, complete re-
sponse curves wrr- not obtain-'d for airsp-eds higher than
140 miles per hour, because of the dangerously high
stresses anticipated.

Figure 12 is a stress curve covering the entire
engine-speed range. Although a flatwis-" vibration hav-
ing a frequency of 2n was predicted for an engine speed
of 1150 rpm (fig. 4), no such vibration was detected,
probably because the airspeed at the critical engine speed
was only 21 miles per hour. In practice, the velocity of
the air with respect to either thp wing or pusher propel-
ler would be low for an engine speed of 1150 rpm. During
the test the result of which are presented in figure 12,
the cement bonding the gagos to the blades softened some-
what. The actual magnitudes of the stresses are there-
fore approximate, but th" frequencies are correct and
provide a reliable indication that no vibration having a
frequency of 2n was present.

Neither a flatwise nor an edgewise vibration having
a frequency of 6n was detected (fig. 12). Figure 4
shows that the critical engine speeds for vibrations hav-
ing a frequency of 6n are 300 rpm, 830 rpm, and 1350
rpm. Of these cases, only the second flatwise vibration

occurring at an engine speed of 1350 rpm would be expected,
because the first critical speed is below the operating
range and because th n.airspeed is low for the second crit-
ical speed. The fact that no vibration having a frequency
of 6n was detected near the blade tips for an airspeed
of about 110 mil s per hour and an engine speed of 1350
rum indicates that the third harmonic component of wake
'xcitntion was small.

The,- stress curves of figures 9, 10, and 11 show that
the reactionless vibration of frequency 2n excited by
the wake is serious. The vibratory stresses considerably
*'xceedcd +250C pounds per square inch for the shanks.
Inasmuch as propellers with more than four blades are also
subject to roactionless vibrations at a frequency of 2n,
the wake is expected to provide serious excitation for
edppwise reactionless vibrations of propellers with four
or more blades.

.-o vibration of the wing was detected that could be
attributed to aerodynamic excitation provided by the pro-
pn l. r.


Th.: results of vibration tests with a wing mounted
at thrust-axis level ahead of F four-blade single-rotating
propnllpr to simulate a pusher condition in a constricted
air strAam of 16-foot diameter indicate the following

1. The wake behind the wing supplied serious exci-
tation at a frequency of twice the propeller speed for
an edgewise reactionless vibration of the four-blade pro-
pr, 11er.

2. The vibratory stress for the rerctionless vibra-
tion increased considerably with airspeed, but was prac-
tically independent of engine brake moan effective pres-
sure for constant airspeeds.

3. The effect t of downwash upon the serious reaction-
lIss vibration was very small. Changing the angle of
attack of the wing from 0o to 3.9o produced no detectable
increase of downwash excitation and little increase of
wake excitation.

4. A simulated full-span split flap attached to the
wing greatly increased the excitation and prhobitnd the
running of tests over tho stress peak at airspeeds higher
than 140 miles per hour.

5. Agreement between the predicted and the measured
value of engine si>eed for the reactionless vibration was

6. No flatwise reactionless "ibration was detected,
probably because the airspeeds were low for most of the
critical engine speeds and because the harmonic compo-
nents of wake excitation r'ere small.

Langley Memorial Aeronautical Laboratory,
National Advisory Commnittee for Aeronautics,
Langley Field, Va..


1. Kearns, Charles '. : rngin'e-Airecrew Vibrations.
Aircraft Zncincrrirn-, vol. XIII, no. 150, Aug.
1941, pp. 211-21.

2. Miiller, Mason F.: Wind-Tunnel Vibration Tests of
Dual-Rotating Propellers. irACA AR-1 N. 311 ,

3. Theodorsen, T.: Propeller Vibrations and the Zffect
of the Centrifugal Force. SAIA T. N.. J11,

4. Silverstein, Abe, Katzoff, S., ane Bullivant, W.
Kenneth: Dowawash and '"lake behind Plain and
Flapped Airfoils. a0,Rep*. No, 61bl, 1939.



& N




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it ilap atracherd to iAly.






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Ci.,. 8


-*.... -.r-, :

-;"*_ ___i

-'1 .r1 o-' attac'..: for no d.r,-n.ashn
Minir,.um anl of at tac'- .cr *E-i.oltion
wit., duwnwasa
L.axiju.m. a:gle of attac.- per re.-;ol..tion
with Ai., 'i:^ash
St aGiu:n rad.i.:
1RotJ.t i', speel
Respective forwa.i .rel.,-itiea of air
R.,poucti'e reuiultza!.t vjlocities o:
bJa:e -le,,ent relative tj air

Fi.yure 8.- Ef'fect of do..:r.wash upr:: the an-le -f attack
and. reultant .elocit., f -r 3 blada element.



VRo='"*" '/- ;&








Fi. 9

000 ----.. ", 28, h
2 |- SOmh ________umh
'J Total vib-atrryj V, 185 mph
stress (oscill- [V 107-; bnep, 100 l./so in.
ograph data) -- V, 1-2P mphi bmeo, 150 lb/sa in.
Ol, 157, bmep, ?00 lb/so in.
7, '80 rDh
2n stress c.oc.- -,- 185 i:ph
Sponent (a';- 1 l ph; br.ep, 100 Ib/si in.
analyzer data) V, 142 mnh; brep, 150 lb/sri in.
V, 157 mr.oh;, 200 lb/6.o in.

,00 ...... .---.... --. T- 4 --.. ... -- -
S 1! / i !1 /I

,0 J' --------J -*--.--"-""-- 1 f = 2

." I

000' '

S. 1 .... I .
10 --/ 1 1 -i- .. iL -

Lihep, 10 l isa in 1 2 / 5n 2 U/so in.

"--i,-.-n- --- -S-
"-"r :' -------....---- ---.. .- .____ ...;_ .. t-. .. -_ -"r..._,_ ._ i __

;00 ?"O ?' ,0 2 .,0 2-fO P2800
Engine sp-eci, rpm

Fi zre 9.- Effect of airspJei and pon shan-- stress at l]adiing-
edge position.. 1) r, -no si.mulatei split flao on .;i:g.


MACA FiP. 3:)

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=1is,000 ,- = -- ---- --- ........ --- ---r- -
Total r.i ,r ,i'v cr s (acill:,a-"* h l.a.ta),
:.. ,."; V,134 r..: ---- .,3.0; V,18- mpn
--- -,0 0;,1.2 :...L -- r,,0; "7,165 , ---

2n str',-- co::.pc ent .wave-a:alzt-r L.Ita)
12,00O ,3. ,l.- :ph :. '; 7, 18 p; -
--- .0'; '$,1-.2,2 ph -- r,0 'T,1.5 :..h.

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so.,or.o|--- ---- U -- .- -- ,- .-.l --
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2-0 2 2 BtO 320 ?30 22"- 00 3200
E:. .z;i spe-:d, rp!..

Figure 10.- Iffict of .in- ar..le of atta: .:por. shank stress at
leading-edga position. Bra:-e ;.ean effecti-,v pressure,
150 pounds per souard inch.

Fig. 11


12,000 -' --*
*12,000 -- (i) Flap on wing (2) No flap

*10,000 --------
-o, oo --- -- -.. ...-- -- --- -- -- -

n I I
8g OO -soo -^ 1- -- y- -
Sf=2n1 ,1-!"
Ja ,_ _____ ---.-.-- --- ___-

' f=2n



2,000 .. ---. .........-- --
.000 ---

2-100 2800 3200 2400 2800 3 00
Engine speed, rpm

Figure 11.- Effect of simulated split flap upon shank stress at
leading-edze position. m = 00, bmep = 150 Ib/sq in.



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10C' l 18U' ... 2) 3000
En -.'i:r.L -'- ':, rpn

Figure 12.- Su munary c;ur-'. s of str.?s .*t 1?1 inches fro:.. tip. = 0;
no sirr.ulatu. split i'lp on '.inr; V, bclo-- 10 I ph.


=2,0 ,


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