Formulas for propellers in yaw and charts on the side-force derivative

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Title:
Formulas for propellers in yaw and charts on the side-force derivative
Series Title:
NACA WR
Alternate Title:
NACA wartime reports
Physical Description:
15 p., 7 leaves : ill. ; 28 cm.
Language:
English
Creator:
Ribner, H. S ( Herbert S. ), 1913-
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 )
Yawing (Aerodynamics)   ( lcsh )
Aeronautics -- Research   ( lcsh )
Genre:
federal government publication   ( marcgt )
bibliography   ( marcgt )
technical report   ( marcgt )
non-fiction   ( marcgt )

Notes

Summary:
Summary: General formulas are given for propellers for the rate of change of side-force coefficient with angle of yaw and for the rate of change of pitching-moment coefficient with angle of yaw. Charts of the side-force derivative are given for two propellers of different plan form. The charts cover solidities of two to six blades and single and dual rotation. The blade angles range from 15° or 20° to 60°. The equations, and the charts computed from the equations, are based on an unpublished analysis, which incorporates factors not adequately covered in previously published work and gives good agreement with experiment over a wide range of operating conditions. A study of the equations indicates that they are consistent with the following physical interpretation: In developing side force, the propeller acts like a fin of which the area is the projected side area of the propeller, the effective aspect ratio is of the order of 8, and the effective dynamic pressure is roughly that at the propeller disk as augmented by the inflow. The variation of the inflow velocity, for a fixed-pitch propeller, accounts for most of the variation of side force with advance-diameter ratio. The charts may be applied to obtain the rate of change of normal-force coefficient with angle of attack of the axis of rotation if proper account is taken of the upwash or downwash from the wing.
Bibliography:
Includes bibliographic references (p. 15).
Statement of Responsibility:
by Herbert S. Ribner.
General Note:
"Originally issued May 1943 as Advance Restricted Report 3E19."
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 - 003805575
oclc - 123958447
System ID:
AA00009448:00001


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Full Text


A R No. 3E19


NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS





WA RTIME 'li RE PORT
ORIGINALLY ISSUED
May 1913 as
Advance Restricted Report 3E19

FORMULAS FOR PROPELLERS IN YAW AND CHARTS
OF .THE SIDE-FORCE DERIVATIVE
By Herbert S. Ribner


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 217











NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS


ADVANCE RESTRICTED REPORT


FORMULAS FOR PROPELLERS IN YAW A1UD CHARTS

OF THE SIDE-FORCE DERIVATIVE

By Herbert S. Ribner


SUMMARY


General formulas are given for propellers for the
rate of change of side-force coefficient with angle of
yaw and for the rate of change of pitching-moment coef-
ficient with angle of yaw. Charts of the side-force de-
rivative are given for two propellers of different plan
form. The charts cover solidities of two to six blades
and single and dual rotation. The blade angles range
frcm 150 or 200 to 60.

The equations, and the charts computed from the equa-
tions, are based on an unpublished analysis, which incor-
porates factors not adequately covered in previously pub-
lished work and gives good agreement with experiment over
a wide range of operating conditions. A study of the
equations indicates that they are consistent with the fol-
lowing physical interpretation: In developing side force,
the propeller acts like a fin of which the area is the
projected side area of the propeller, the effective aspect
ratio is of the order of 8, and the effective dynamic
pressure is roughly that at the propeller disk as augmented
by the inflow. The variation of the inflow velocity, for
a fixed-pitch propeller, accounts for most of the varia-
tion of side force with advance-diameter ratio,

The charts may be applied to obtain the rate of change
of normal-force coefficient with angle of attack of the
axis of rotation if proper account is taken of the upwash
or downwash from the wing.


INTRODUCT I 01O


There has been a need in stability analyses for a
systematic series of charts for the estimation of the rate













of chanJe of propeller side force '..ith angle of yaw. Al-
tho..l -she fort.ula developed by Harris and GlO;uert in
re'erenc-s 1 .and 2 and -iscussed in reference 3, which
e::nrcssez the side force in yaw in terms of coefficients
for the .rnyaiied propeller, is fairly satisfactory, there
h-- been r.o a.dequate formula based pr im-rily on the
gemctr: of the propeller blades. An unpublished arelysis
has resulted in sach a formula. The basic assumptions
are sinilar to tAhore of the --orte.: theory for the unin-
clined .:orel.ier 'Ier. the Goldstein correction for finite
na-iuer o blr.Jes i. oi:i ited. Co'nP-.rison with a number
of e:oer 'i.nt c.l results -.as indicated that the accuracy.
of '-10 erce.:t obtain aoe 1:; the analyt icE-.l 'ethod i-s of
.i or-er obti-ri.ed uy the uncorrected vurtex theor,- for
the "an'clineil proel Ie-r'.

T c ar ( a, vel o-- cd in the anal'-sis 2.nd given
herein: has been usced to prep re a series of charts giving
tv c ra';e of :.-an'Je of s ic'e-force c efficient v'ith angle
of ;a-r ,.-- a fTr.ict Lni, o' the '.; vance-di.ia peter ratio V/nD;
t e blm.dc au ;le an% soiait' : ;.re :,aram t-crs; the c'.arts
c:-'-cr both si.:..-le ::ri. dual rotation.. 2he cor.putations
", -c YCe'.O for'. two repre pent-"..ive urope-ilers, the Hamilton
St.-nd-r-. 153-6 and the 1?ACGA 10-S30 -045. 0 ier.ns are given
fori i:ntar olating -'cr )ther nrpopellers.-

I.- crd.er to n:.ke the present report coa.lete in it-
seo f a-'.'. to .iLI-e tLe charts r..ore i-telli'g ble, formulas
for the side-fores and itching-mo.-ent derivatives are
given ne the ov.tst wit h a n e::ple.n:.t'ry- text. The other
pro:el.r t :' il i-; der-vtiv-e w'ith respect to yaw-r are
z ?o.

Tor: the -urpose cf e:.:politin- the publication of the
chart the &erivation of t'e formulas has been onitted
from tuhc recent p."per. There is irclu-led herein, howe--er,
a 7ran'i that oho'-;s a co.'T'r.ri-on of the theoretical values
:ith the e.xerimental dfata of Lesley, Worleof, and Uloy
(rCfer.nce 4).


S YI3C LS


.ic for-:u],as of the present repcrz refer to a system
of boi:- %:::es. For single-rotatin, propellers, the origin
is 2t t.e intersection o-" the axis of rotation and the












plane of rotation; for dual-r:tat ing propeller the
origin is on the axis of rotation halfway between the
plans of rotation of the front and rear propellertc.
The X s.:is is coincident with the axis of rotation and
is directed forward; the Y a:xis is directed to the richt;
and the axis is directed dowa-nward. The syr:.iols are
defined ac follows:

D oron-ellor diameter

R tin radius

r rali.s to anr,' l'la e element

SI disk en ( /'4 )

x f action of ti r a CLius (r/'R)

::o mi i:.i. fraction of tin radius a..t 'i.1ic shan.: blaAe
:.ecti c :.s levelo i li- takenn as 0.3)

z rati c of sr. inuier ra-.,iius to ti, radius

B -n. .bcr of blr.1Les

b bla.'.e section chord
4B 1
Co s "-idit :- t 0.75R L| [R


br 1.iA:l e a.:ple to zerr-lii't chord

0 b!.clade arc.-le to refez-er.cu chord., measured a.t 0.75R
st at i r., de re-ss

p .-.ou.etric : itch

S anzlc of ;.'ar, radians

a-i an,;.c. of attack of thrust a-::is radians


7 free-stream velocity

q frec-stroeam d:-namic pressure (1/? p7V)


a inflow factor












Va -xial velocity at propeller disk [V(1 + a)]
Lr + ]

r-at (1 + a) + (1 + 2a)I
f(,) qr-factor (1 + a) (+2a2
SiL 1 + (1 + 2a)2 J

Cr. thrust coefficient (thrust/pnD4 )

Tc thrust coefficient (thrust/pVY2D or CT/3J)

n rotational si-e.i, revolutions per second

J ; c'an ce-d ia.n t cr rat!i (V/nD)

S'effective ahxlix angle

t in L[ Va,/(rnr slipstream rotational velocity)

e *ide "zrce ( o ., : -es

S..: -.i force

i. T i tc-'. nr.j n'ent (b ody a xe's)

C-.v,, side---fcrce Occrivrative: rate of change of eide-force
coofticiet with angle of yaw [( IF/o',/q ']

Cul.., *.it. Linr.-morient O.erivative: ra-,e of nh ngce of
ni'.chin --r- omeint coefficicnt with angle of ya-r
[ ( q3: / ') /q qDS' ]

mo "-er i,-:c slo e of section lift curve per radian
( el".' en Z-'. C 0.95 T .,r)

r, .-inn cr f'ict cr

ka ride ash f ctor

K cr nst2..t in the souaticn for ks

i :.idco--irea index

A L. ofin.d by, opuatioin (2a) (zero for dual-rotating
pr opcllors )

I ir .tegral defined by equation (2b)












13 integral defined by equation (2c)

m defined, by- equation (Sa)

Su.bzcr i-ut s:

0.7E.- measured at the 0.75R station (: = 0.75)


F ORIUJLAS

.-teo cof Chan-es of S ide-Fc'rce Coefficient with Anile

o" Yauw for Dual-Rottin3 Prop cller


Th n .at-1.re of the ic rA'.1r.s 2or tihe. si :ie-for cc die-
ri-.'.ti...es ..: a i. sir.-.lcr to present tLe formula for
the !c L.:.i-rot. in- fro eJ l o l r first t. Fo- a AT.a 1-rot -.t iin
prIpc. e r ':r, the. sid.c- for cc :feri vat e is

S---. :^ (,
C:" 1q' I + ha,71i(


vr 1- E r c

the r i er factor :.; 1 .

the s id. e .azh factor 0.4

the i.. fl w f...ctor a = ( + ST.,,n 1) /2


the q.-factor f(a) 1 + n)a[(l + ) + a + )] ,a)
1 + (1 + 2 +2,


the- s,:liit:" :.t 0.7532 a = ,--

1
the 3i.:L--..ra ind.e:: I = /4 mo / ( b/b .75R) in PC, li


and. 1, f(.i), --s, and kha :'re discus?e'i in detail later.












Side-area index I.- The product aI. is pro-

portional to the area projected by the blades on a plane
through the propeller axis. This area may be called the
projected side area of the propeller. The significant
factor I has been termed "the side-area index"; a
is the solidity at the 0.75R station. In equation (1),
.ai 1 is always small in comparison with unity, with
the result that CyI- is approximately proportional to
olI and hence to the projected side area of the pro-
peller. The factor 1/(l + 1kaaIi) may be regarded as
a correction for aspect ratio.

If graphical integration is inconvenient, the side-
area irC..e:: 1 mnay be evaluated quite siri.ply and with
su-fficicnt accuracy by Gausst rule for appro::imate inte-
-r-tion (roifrence 5), which ordinarily requires fewer
ordin-.zte thon Simpsonts rule for the same accuracy.
DIetailz -re .;given in the appendix.

h e --2 ctor f( l).- By the definition cf a, the
e:-orescicn 7(1 + a) is the axial wind velocity at the
ro ell er dsc'-:. Accordingly, (1 + a)-o is the dynamic
nre's-ure at the propeller disk. The value of f(a)q is
on'ly rli'htl;- le.-, tha. (l + a) 'q for o.derate inflows.
Eouatir- (1) sho'r- therefore, that the side force for a
-iven ri.-le cf .v-.- is rcughlly proportional to the dynamic
Tpresu.ire at the .r'rpeli.er disk as augmented by the inflow.
A chart of the vo.riatiinn of f(a) with Tc is given in
f i zur- 1.

Si,,Lenncr factor k .- If the propeller is provided
-:ith a .spiincr in coimbinction with a liquid-cooled na-
celle, t,,e (ircunferen.ial component of the side wind due
co ya'; is c:.nsid.erabl-- increased inr the region of the
olade C:. :-:G. Th.is circumstance increases the side force
by- a f.:.ctcr I-s ,hichi is closely: given by

S (i2 C::s/x)2 (b/bo.75R)sin Po dx
o .
.. = 1 + C('Ib)

(b/bo0.s7R)sin 0o dx
zo











where xs is the ratio of the spinner radius to the tip
radius and. X is a constant which is ai.ro:.:in ...tel- 0,90
for a nacelle finenecs ratio of 6 and 1.00 for a fineness
ratio of infinity. For the spinners of .prcse.t--da;," usage,
ks is of the order of 1.14 0.04.

A sia.ilar effect undoubtedly occurs *-hen spinners
are used. with air-cooled nacelles, but the es t iration of
kg is more difficult. It is recomuendeC. that the factor
1.16 be usec..

Si.-evash factor :.-.- TheC reduction of side force
due to th'e sidietash of the sl ip.strean i3 acco-..nt e for
b.- t he s i c'ewash] factor !:q and by the deviati on of
f(a) fr'oj the value (I + a):'. The accurate cw:prezs ion
for o :a is

,I (b/b o .75- 5) s' i-" 3o c1'-':/"
/(: + a: _

r C(_o---i b) .
4 +rl (!1 + La)('/b, ip w]E

L./ (- c ): 1 1- c, : j

Tho efff ct is ar.nalo :-os to the r edu.?t ion f wing lift b."
do'n.ash. An .ver e 7a-l-o.e o:f is 5 '.

Se -i. tre accur" c :: nd l..- To the degree in
which c: 'r prisonn with e:-is t ing ex:neri ne t s e3 .',lishes
tae Bcciracy about ;10 ;ercernt of the side-force
formulas, it is suf.icie-tl. :'ccur- te- to use the mean
-ral-ie 0.-' for :--a ard', fr-.- the u aucl si",e sroin-er
(::3 = 0.14,), 1.14 frr 2 :..

Ph':- ical irnterriet action of troeller in :-a...- A
st'i;.- ecuations (1) a n. d (2) in li ht .:f the discussion
of the s id.e-area inC.e-: I1 anc the Q-f-actor f(a), with
data for erre entat -i.- propellers, sho-.'s t hat the equa-
tionz ?re consistent with the following physical inter-
pretrtio c'i: In-, develop. ini siid force in -'a..,, T'.e propeller
acts li.c a fin of hi ch the area is the ;roj ected side
are- of the propeller. (_he rc jected side area is the
area tro.'ectel I:.- the blaO.es on a pl-ne through the a:-is
of r ta?.tin e. -'or t'o or one blo de, this :rea -:aries ,*ith
Pzim.th; but the te-.:t refers to the average value, ..,hich












is given to a close approximation by one-half the number
of blades ties the area projected by a single blade on a
plans containing the blade center line and the axis of
rotation.) This equivalent fin may with small error be
regarded as situated in the inflow at the propeller disk
3-nd subject to the corresponding augmented dynamic pres-
sure. T2he variation of inflow velocity therefore accounts
for Liort of the variation of nide force with advance-
diamneter ratio, for a fir:ed-pitch propeller.

The effective aspect ratio of the projected side area
is of t::e orde-r of two-thirds the geometric aspect ratio
with :.'.:-. rotation. The effective aspect ratio is much
lss 'it; single tlan ',ith dual rotation; the smaller as-
pect ratio accounts for a. reduction in the side force,
which for thia ix-ulade Eamilton Standa-'d propeller $155-6
varies 2roc. 4 percent at P = 550 to 21 percent at P = 15O
A aieanr volue of t_.a effective aspect ratio for single- and
dual-rot :.t in; propellers of present-day usage is 8.


Rate of Chance of Side-Force Coefficient with Angle

of Yaw for Single-Rotating Propeller

For a cincle-rotating propeller, the oide-force
der iva-c ive is

OY/, kgf( a)a I
Cy, = (-)
S q' Ii/(I t) + kali .I


The defiT'tiona of equation (1) still apply and


6 = (2a)
C(l + I13)


\,h er e


12 = mo (b/bo.75R 'os P xdx (b)


= 2 m --- xedx (2c)
4 0 bo.70R sin
x*












A family of approxirinate curves of I are given in fig-
ure 2 a f-unctions of V/nD, 'ith the solidiL. cr a 2s the
parameter. -he curves are applicable for bla'ic-an.gle
settings at a,. given value of V/nD in the r -,ne in which1
the bla.i"es are not stalled. The data cf _i u:ure 2 w.:ere
cor a.uteCL for z- definite propeller, Hairilton S L ndard 315.5-6,
but ray be app-lied. to an- other pi-opel lor ';itl- neglig ible
err-or in Cy .... The variation of 2a/n with T is

given in figure 3.

The term L is pos-itive over the o1rer ,t ing range of
the pro..peller i 1 fli lht n:;. i. r ou .-!..- ,:- c-t enth n Ic 0
Co 0,-r.rizco of'i 0 ,.; .''n ( 2 ) for sin .- l e rot:. ti .i i t. P, eo. .-
tion (1) for ".u 1 ation s o'r t. nt t;.e cif .Jt of -r osi-
ti'-e A c a r 'd :ti'.'o i .-I thL1t is, a .in -"e-

rot ati ... .rore-ler-r *:-.re- i :ncos less s i.e f e ce in :'a''
than. the co'ros-r on .i.. .u:. -:o at in. p: .eller.

_he red-a:ct. ion 1 .n ci.e .c ce in. y-a.': :can.hec 24 ,c.rce, cs
fo-" I .' v -' Lde n.',l:.: it :verare i. 15 or c- "t. The re-
duiction i, c-:',la in ;. : : ,v t. t LAt C B ... Ltry- of
disk lo:'. ; i.r' i ch or 1: in'l1-: t' at '., rorcller pro-
duces t.ic pit. c h i nr::, ..: i t du .: to ;,'' al ind.c es a co0-
po nent o 1 i tI rei. o e t,.- eff I the rr.sle a
of :.-,'... For .' .l--r.trti" rop..=1l r- t -.erC is no re-
sul .ant n.;-. .., L tr, bo cc.'.:s the '.' .. Atrios of th.e ,i"k
loa in ,3 of t>e two ec t ons cr' so g is .C.sc :'. s -Z to cora-
pen'. nat c.


Rat e of C-a n e- of Pit .. C .h iL .en::

.'it:. An l. e of ..',

For (: ,',ual--:'ot it. r r ler, the it ch in .o;.:nt
derivati-i.' is a--.ro i...it e]'' _e o for tho r,' .s; n prev iously
menti on .. For .. sin '1c-r-C.t.at n ;r-'ope'ller this der ivi.-
tivo is given by1


C., ++ (5)
S qD'St 1 + tk. ( It A1)


w here the ..c it. ive si, is to b t-: ei f :or '. ri ?. t-h r. d
propeller ".:*..'- t .he n '. -.tiv.: si for .' leoft-!l-andi propeller.












The definitions previously givon are applicable here and


cl2 + 2J 2a
M = 3(a)
2( 1 + a 13



SIDS-FORCE CHARTS


Forr:.ulas (1) and (2) have been used to compute a
series of charts of the side-force derivative


Cyz, = qS'


This .derivative, oth 3ar.rise interpreted, is approximately
twice the area of an equivalent fin of average aspect
ratio cdiviCLoci b' the disk .area.

Each ch-rt 6;ivcs the variation of Cyi with V/nD
for a. ranLe cf blade *v..rla and aTplies to a. definite
solidity. There is a series of charts for each of two
blade f'c.r s. UOn. bl--..-Le forn is a conv cnional type,
Hamilttcr Standard 31lb5-E, with a plan form almost syr.mnct-
rical about the M.,aximum chor(, .rhich is at approximately
the 0.6CR czrtion. The other blede form, iTACA 10-3062-045,
has a wi:l., al.7ost 'n.ifor.i chordi out to th'.- 0.75?. station
and i rou-inrid tip section. The u.lan for.us and. itch
dictrit.t ions for the two propellers -re shown in figure 4.

armilto n Stantclrd _pro-oullr 3155-6.- The charts of
fi-..rc.s 5 to 9 arpl-- to Hanilton Standard propeller 3155-6.
Fi,'arcz 3, 6, 7, an,-. 8 are for the two-, three-, four-,
arl .'i:-bOCLCe sir. gl-rotatin F pror pellors, respectively.
"Figtr o 9 i. for ; si-:-blade dual-rotating propoller. The
solidity a varies from 0.061 for the two-blarde propeller
to 0.182 for the :i%-:-blade prouellers.

A 1 i-'uid-cocled nacelle of fineness ratio 6 was as-
sumcc 3d.id th..: 'pinn-er diameter ,,'as taken as 0.164 tires
the ipropellci dian-meter ia determining the cpinner factor
ks. The .avera:c v.lue of ks, which depends slightly on
the blaJ.c--.nle setting, in about 1.125. This value
sig.ifi''s that, on the average, 12.5 percent has been added
to the ":aiL.cs which would oe obtainoc in the absence of a
Dinfr. or .













The vrl.uos cf V c used in thi compu't:tt ions were
obtained from figurco 24 and :36 of r. f rence for the
250 r .i-d 450 blade '.ingle s and *'r erc int erpolat ei. for the
cthur Ll._s.e -:.lc.s ..ith tho aid of fiYrurc 15 o: re cr-
ence 7.

17 ACA ro- llzcr 1'0-0g2?-045.- The chrrts of figures
10 to 1' ijpply to :iACA C .ropcll.r IC-:-.06-0.' Figures 1Z ,
11, :':1. 1 rrc. 'or i... '..'--, t.ruee-, .r.'1. fou--blade sinr: l,-
rotatin; ro' l.'. r3, r s-ect i-'el- -Fit ,'irc 13 is for a
si x-blade du-l -rot .o ir. pror. ll er. The sol i'it a varies
fron- 0.032. for the t.,o-.- LC.'L :,ro ell-r tc, C,.Q -7 for ti:o
si x-- ac'. a. : C c-p ( 11 .:r.

The sp in.lcr-na? .l1 r'opCort io '..0c t -:c. t .
as or EL|.. Ito:-. t c- '. .rd ro.e ic I b. :-- .. .. r rr e-
spond.rg- : r c -:r -:tlr..c ."o the spinner factor i 1. 15.

:?.-C r '1U..S of C ... -ti .ip.t.' t i. '
obt.-i'.ncd -'ro i nyp.1 i- 'C. r -p 0t-.c tjl. ..'-.-' r T.C
tihrcc--bl:.di- :'i: :-' t -..t: T o:c11 r' T '.' :'.-.. c 'cre
ext:-a. ol-it '.,C for fa c';,r L1i.cL s ..::. f o: :.r 1 u es a.c '.
for -:.-.1 rG t otaQc :,L n r. ith t-, aidr o ffi.-res "4 2.3 of
refcrc nce It i .liyecl t, .t the crz'c r C i .7 C L,

intr'cUi.c d c i ,- o rr ord i-- t.. eC: .-a',ola-,t 1 .r0 i thin h i
or 3 lc: .'" .t.

C,.in.-:'- o0 .'! ,,i it i r::. 'im : t.- i ;Lr : .'4 :'.r son t ,'he
va" .tion of Li-c I; i..-f o.'cc J0. r .v -": 'it> .1.vai.c.-
dia;ct er r-.tio for t1 c t o--I'la c :'o.c]. 0-or ell r of reCfcr-
en.. -1. C'rv .:. co: c...t ]. fr .. t f or. ul 2 f t,-.c. ar ; c nt
reCnor-t nP C lott ,i '.1'. t'.tc ,-2 .. r-1 n. "t. al .r-.lu,..

7nt -ar: latii n :- bl..' si:... ..:ce sol _l it; .- hc
comp-it 4i ns S o' t o rt, w ithi t L'c usr.al ran b .l O tI'int
has -. relativcl.- r i'-]. .ffcct o: C--. Th-e t '-'-r c i.'o uV -Lt

par- mc t 3 r : c li it;., J.-. ., ? t 0. 75 .nd plan f orrm,
0f or .'::c ,/-T. "'. c rt. i Cr i-- a J. fcr;:' m":;
be i.t r :.ol".t i .:->.-.l?. frcr. thL. c rnr tc.'. '- ric or v .ir ia-
tious of a clil. a ..n. : ". ti C r. --10 P3.

The tte.- na. t i. 0o C.. for lan fCrC. between

thooc of z.::. i Iton Stan.n r '.'a ro ellcr 3155-6. ca.n.1. 1'ACA
pron.llir; 10-33062-0.'1'5 w ou.ld bc l:-" cc d to re uire a
cLo.tb1. c rr 3 t on c .; for id ity, ': ?.u :. e T' t.,














propcll-es are not ch..ar ted at the same soliditios, and
a s econ.i oie for planr fo-m,. A simpler proccd-:.rc results
fro:.. t:e following considerations:

Fo *: g;.-ecn solidit,,, it is found that The pl-n form
of 'he i'ACA propell,:r 10-3062-045 yields about 13 percent
C. r:o i. fo- co thai- ,eas the plan for-i of t': 3 Ha.amilton
St..>.c '' e llr 1i.,-- at the s-rmc V/nrD. The factor
1.1. hol-'::L u rTin i 2 or 3 percent ncar the linc of zero
thrut -1theo.'th the error incrC cases to about 6 percent at
lo'.. v/.D --'. i. ? thr'. s To this acc-tracy the s ide-
force oc: fic cr. r fo.r .r, ron:i .e of a Iiven ::lan form
a-:.. soli.-.ty a = 0,091, for c:.am"plL, coul07 bu est l.i-ated
fre:,. t o a = 0.O'1 ch..r.t of hkr.1 ilon S end r.rd propellor
S1i ,-G b') co ..:ri: th .rive.i plan Lc-:n. 'r ith te plan forms
of c.. It cn rT.Lan d*.r- 5153-6 .and :IA3A 1--03Cj2-045 propellers
in fi.' 4 .'n in r c-asi. the or inat eos fromn tec chart by
tLL c :.. :':* p'i,. r ct.io:-, of 1 per ccrnt. In mra.: inm the plan-
f--rr. co:., .: -: *n, r-.t .' t cho-iu rl be iveS-n ;:'e root zec-
t. i, F.1. t b., L .1 ,. I" the sol .iity a d c not ccrre--
Sn Ir. r tt-.t i-" .:. of the carts, tuo charts of c-iffereut
solilit t o te s i.:e roell r may be inter:.. olted. liinearly.

Ui" o)_f ,- r for :rcpellcrs irn Ditch.- T.he charts
.ith '' C .. L ti t C : 'cr :';- can bc ae ed to obtain the
r"ate :- :...- : ". of n,.rin" :'or, :it, an le of tta :k of
t'.rr .. is, .f ti' c "-iLt. once of the uiw t on "he argle of
flo', ..'t t c' ~Jrop iller i.; included. The o ,'. ,sh. can be
t .-.en i.to : ,ccu.:'t if e -'..ellcr i in 'rc rt of the
'i br.-,, by- r.1 r ipl.,'ur t'e val!u of Cy, o'. interpreted
1- 7/1
'.s -Ct b' 1 rlus the r.te oa change with

:--l.: -' rt -ac!- of t z. `..7le of u i wa: sh induced at the pro-
p- 11 r :; t : vi.i If the .r.. cp ll r is e",:' ni the wing,
t4-.* c tr C iulJ. .0 1 m:.r.us the rate of chan'cngc with an-le
of' ?.at'.':L of r,-:c :-. U-1 of dDwrnwash ,ina-uced at" the rro-oller
b:- .fh.. :.:. .


c'27L-I CLD IiC- ?.r :.?.KS


',"at i. s for pro P sellers in i'a n.* n.c'. charter of the
i.- '.. c '. rivat ive d .r.ve been givon herOei focr single-
3:1 -r ::-..:in; r opel?.lers in r.mr.s of a :side-aroa index
.. ..--. :... ressure factor '. icn is f. f action of the











13


inflow f-.ctor. The ctud;,, of t'..? cou.aati onrs inrd.icat ues
that they are cons intent .ith the ifollo-ring phricl
int rmr-ctation: In CeovoCoping sidjr forco, tho. rjro-',ller
a.cts li!:c a .fir of vhich the .ar e is the ,r ojcct'. cd .-.ide
aroa of tl-e propeller, th,. effocti-c aspe-ct. -:ntio .is .of
theo order of and the cfecct iv'. d-. ai'.a!. ic ri-.r cs re is
roughly that Pt th,, iroprlle:C Lis. ..s -r mcit cd. b:' thc
inflow. The .rn iat ion of the inflo..,, veloc i for fix od-
pitch propell r, acco..nt? for i, ost of the va-.i- t ion of s .id
force with. :.d c co-. iamo ter r-tio.


Langle' i: nmor ial A r o: .ia-..t .cal Labo:-'tc'r:,
.Ta. i ar.al Ad' i ior:- C ri.m t uc :.'o -r Ae ron.u, i cs,
Lanrl.oy io11- V a.



LPPZ"-D IX


Ga.u0.s ruleo for .ppror :imc t c iI.t creation r.a be
exprce s.s b:." r.h e nationion



f(;:)dx i1(-.1) + fP ;(::2) + .+ Fn (-
0

.rhor c o :'-n .. r. 'o c :... r1. I to .PT
are C -. .ss coefficients. For t:r.- Interaln i t,.,: pr cs,-nt
reopo rt, i'.- or.ir t s c ~r '.. ':.'.l rc. cuafi %.rnt to c-.er cr-
ir.o withinn 1 p.rc' t. For x ta.c:.c :-3 0.2 arn

X.'n+ 1 :.kc:n as 1, the :-. proprlite v lu.es arc'


xi = 0.208 PI = 0.0%[

:-, = 0.C85 P, = I0..i

X:- = 0.600 P- = 0.220

X4 = 0.815 P = 0.191


:: = 0.983


P, = 0 .0"5













1
As -.r. ox :iy.le, th,.: iz:tcr.a1l
"o


(b/bo.?75.)sin Po d:


which o rzc'.rs ir_ I my bc c-.-r..1uatcd as


( o/.D .) a (b/D)o.,c9
.. --.----- J +0.191-....... sin 0oo3=5
,O /`. coo. ) (o D/ 3 .n h
-i-o7R 0. ?r- "


' b / o0 .6oo0?.

T( F',o .O. 7


(b/:S )o .a,5R
0 + .1 sin s _'
I .coo-. (o c b/ r ;0 .815.5r
^..co^ ~ ~ .7 5.q8^ "'-'


S. o'-- r3,
sr O --0 S 32
E -/'-' oro .i.t o l I t



.i: :'az b':or. -1 t;o n -'"or Ii .iv Cl nt

b/ ". 7s:? i r co.':1.".:-io.:i .z t.3 p ra. t-o o .' u.. irng u/D
.C : c ., -::-foLnT "'_-"..i. bl .














R.L,;: .FLREL CES


1. H ra'iri R. G,: Fo-r.ir on a ro. cller L.:c to Sidj-
.i:.p. .. T. i:. 21o. 427, Erit -h A.C.A. 1918.

2. lC-Tlh rt r : The Staciliz,.- feriv"ti--.7 of .rn irsc'',
2 : ;. Io. 0'2, "i' t ish A.C.A. 19.

3. C-octt, En.r ; .. J r'. .Rss H. R.: E i'c- t of Pr-.pcll r
Opcrc.t :c orn t.:e Pitching icH'i, .nt o ." 3 in, --:l -zuc; inc
rionc l..-.ncs. I.: CA A.C.. i"-- i1 4).

4. LLZ1o::,, E. ". Worl :', C oo g '. nn-.-, t.ni :;'
Air Pron- .1 in Y.i. 0er. c. 7, _ACA, 1037.

5 ,',|.'<.: II-: : : '..' '_: ;n'l .a.,,".t'."t ...s 0of 7lu Lt ';--. .. .ic for
A i:-' r f:t't D es .-;',: .s, T. h R c.1' P .' C 1 '"! ,
r -. .v r- z,


6. ZE.nc:o.., J"c]- Q.: .'u E;'fuct of Pit,' onr Force ann.
-''-r nt Ch r*atcr i t ce r.' F-i. l-Sc : Pr oppl!."s
of Fi': Soli tic--. i7ACA A.R... Ju'o 1-^2.

7. Licr s-.n:: D vi1., .r.:1. } r Et.-", .: Tr ts cf TI
]..1 -.c- c.li :c.u.llc:." ",T.th l r' r' c'-.t Pi ch Distri-
t .. i r r -, rt "jl .' .. ,- 1- : G'' ?.c Fo. -5-,
1.2CA CS < U;.. 10. J













Fi.r-s. 1,2


I. .2 .4


I I A j II
S2..;1.?L._ _1 __ L I __ 0
6 !.,) 1. I.? 1. !.;. !.9 P.O


Figure 1.- V'ariation of j-fact.jr :(.a wit c T /n






1, ..... ....-- -


c2 -T-
I _

-_--- 1 -. ------------
4 ---t.. t -- --- -ft -






0 1- -- .. 5
I D
Fi e arati of 3 wi th '!/iD and solidity -. Appr-.imate
curves for blade -ant le e. t tines -t -*hi-h the bides
0 1 2


cur-ves for t.1aaenre ..... at tinss at vihizh the Una~es


NACA







NAl A


.5- --------------- ... --- -------- -

.4 -------- -.2 -- --- --

S.3 -1 t- / .

Si_- _-- -- ----






0 .2 .4 .1 .8 1.0 1.2 1.'! 1.? 1.8 2.0
T
Fiaeiue 3.- Variation of Pa/7r witt T T-. = CT / n .

I.2---_- -q- --- ....
-I I









.TACA propel ler lrj-7 .~ i 1


.. -, -- -. --- -?3 -3|,i 2
8 .. .. ... I1







I tI?
.2 *4 .- 8 1.0 1.1 1. I 2.0



Hait Standard propeller at 0.7| i
0 I I 0... .
-1 .27 r ---: 1-.
^ .6 _- -- 4#.---- _- --.--r- -... _--4-_ _



1- --/___; ..--. -_,., ,
'2. -tA m- ,-42-, .....L I.. ._ ,, .






Fi re 4. Plan f piti s 0-30 -04



San. a _ilto-. Stn rd .propellers..--- --
A JAAa propeller I13-5-r.2-05, .2c a.7to -.

.. H -- -4 '--i- .- A I---.-- l_ --



.1 .2 .3 .4 .' .7 .e .9 1.0

Figure 4.- Plan fr,.'s an,.i pitcd !i..t i -";t..).ofls )f i7ACi 10-30'2-043
an: 3ar.ilt.o0 Stani. rd. 31..:-" prope-llers.

























=;- I 3 16 at 0.7:,R

-- Line f z-ro thrust --

S 1.2P 1. ?.0


-.4 2. 3.2 S3.* 4.0


'./nD

Figure o.- Sile-force leriv'tti-e f.:- .ingle-r-totinz Fam'iilton St-nlard
pro-jllel r 315 -' ,itn spi.ne". Tw-, bl-iles, r, .,' .


.-


-- 1) '- at D.7 -- i
.... -- --1- -- 4- -- -4 -, --
" iiLe Jr zer. trust I



.8 1.2 1. 2.0 "'. 2." 3.2 3.6
-/'..


Figure r.- Siie-force Ierivative frr .zinale-rjtating Hrr.ilton Staniard
propeller 31j5-6 itn sinno-. Three? blades, ,G. ".'r l.


NACA


.1


4.0


Fis.. 5,A







NA:A 'i-s. A,P


Ix ,- -- ---. I _-
E- -e- : -,- ..t '



Cy __ .4. )






7/no
Fi,-ure 7.- iie-for:e t i-e ': r s le tt i t. Staniari
I prpeller -ljb-y wit .prLrner. r is, 0.321.

1 I I l I I 7I -
Pi~~re 7._ Siie-for~e i~ri~rati '.'e n~ i, e ra i -=m lo Sa tr

dWVFTllN 7l> t --- re.?a lis ,y .]


.3P
Zy


.4 1.2 1., ?.0 ,.. 7.. 3. 4.0

Figure B.- Sile-'.jrce teri'ati'.e for sinele-rotatine Hamilton Stanlarl
propeller 715-g witrn spinner. Six laies, -', ..12.








N..A- i.~7 *. ,- T

-- -- -t o -
.48- ----



A *o !o I
i I" r =





32 --
.2 -- ----- ---- --!








i' I < / ) I i Ii hI
.1T -- 1 --- H- --


.0.o L. / _L _L__ ___ __
.A 1 1. ?.) ^. -. ,. .
"D

?iiLr 3i.- 3 ,e-f r: e e o eriv ti r e t 'c,; i l-r t _-i t ilt -n St n ri.
p opi.ll r 713.-' vi '1! 3i r. 3 lai ". 1 .












0-- --- --- -- --- ---- --------- --






.4 1.2 1. .0 ?. .f .? .0


Pip-lre 19"'.- Siie- ',r.:e3 ieriati-re +",." si '.?l --rint tin. "..A. p,' ,pell.er
1J-3.2a.P?-6451 ', itr. sp]i'n : r. "w.' late-., ._, 0. =')8":.








NACA


.33 "-v -- -



.
I i. I I ,






.CY _-- .. .. ,_.- -, 4 ___ _
----- -a 4

























= /U Tat .7 .
.6 -Lir of ?.-rn --
.4 .8 i.3 1.5 .C, ?.8' ..2 J.6 4.0
Fig re 12.- Si.'il-f rc iriv,3ti-.- for 7.i 1.-r1tatn.i 1'.. prov'll'r

i2-.30,2-O0 ~.ithn spi-r r. F -.r, lais rT, 0.1 .
I6 ,y*.-. -'-T f rI.-.-. ~ "~.~ |




r -, ... ..x,--- ...... *--"-- ,- -- -
I 4V-- -- -T T- .=~ rz- I -:- -- ---
i "-" ---

I i i ;I ', i Q -i i t ,-

-- q-* -' -- ^ 7--- -." -


i ', I *Lr of ,"- rn I i 't-n:- I I I

-- 1. .5 'd -. .. .*. .
r iI

Fi=ig rc 12.- SiiL-f~rc.c iLrivgti':.' for iv.zl.-r':tatin,; \'.2A prooicllr
IJ-3O.2-J-5- with epinm.r. Fnur la s.3, .C, 0.If.


Fip-.. 11,17








NACA
1..


Fi,.s. 13,14


-. 1 .? ,'. i1 2.4 2. j 2 L.;
V/nD

Fijire 13.- tiic-forze iri'wattv- for I .'.l- .1 tat t.a i.A .. 1 .-or-l lr
I0-303 --,4 with s':': ci. -itx blaIts, a, 0.27.


4. j


*"- 7 2 ---- -7r .
-4 -- ,8 P ?.7.n i::pcri.n;tSl Calculated -1--
I '- ,
+ ":. -
F _l J __ L L ...... ,
S--- ----- ---
4'1 -


J.I

.....




.04" -,---- -, j- U T I
--1.0 1.i ,11 4 0
Figure 14.- com -arison of calclatci and v.-&cricantal Esiite-fcrce
derivativ._s for tv'_ -tlnlj r tcLl pr, Cp r.--, ur ar.
terminated, -ccpt for P = 1g.~-, vt poir.t hrc obvix;.s otalliir of
blad-cs occurs. Exp.:ri.ic tal dit- from re eronca 4.


<







r









Ei





UNIVERSITY OF FLORIDA

I r
3 111111262 111 10 6 5211111,111111.20



INERSIWY OF FLORIDA
DOC, UMEITS DEPARTMENT
20 MASON SCIENCE LIBRARY

)o MARS-TONno
P.0. BOX 117011 iU
GAW4ESVILL.F-, FL 32611-7Vil USA
GA..,.VIL..







E4






4'
Sii

.iKE.ii~ii

'Ib
J"



"Ii

y ..rii

"-w&Jg4


. .ui~l"'1




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