The object of this report, the last of a series of four on propeller design, is to describe a simple method for determining whether the strength of a propeller of a standard form is sufficient for safe operation. An approximate method of stress analysis is also given

Weick, Fred E

English

NASA Technical Reports Server

3H
_E_HICICAL NOTES
NATIONAL ADVISORY C0_ITTEE FOR AERONAUTICS
No. 238
PROPELLER DESIGN
A SI},_PLE },CETHOD FOR DETEP_,CIN!NG THE STRENGTH OF PRO_ELLEP_ - IV
J
By Fred __'_. Weick
Langley I{emorial Aeronautical Laboratory .-
Washington
June, 1926
J
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AS MUCH INFORMATION AS POSSIBLE.
By Fred -. "7oic-::.
_ll ..... .'a,
Tke ob_ece o2 this reno:'t _:.:e _ -_
- , _a;_u o_::a series of fc,ar on
propeller .ie_ign, is :o describe a sin]:Se :';ethod for deterL_in-
""._" ," =_-'_'" the -ren<'th of a nronelq .... of _ o+'_-"'_"rS for::: isl_._, .Tzle_,_:._= so
s_=ff" _" _ for _oxl._c_L.c <.'lc_tho_l of s ross
_u=eno safe o-peratiol-i. _{K apT)-_ -".. ...=
::z'_alTsis is slso !i:iv_n.
intrc&_ction
.<:uer a oro_.d, ler i_as %een ,._,,:,-'_(-'z,=.,c_.;_'--o ::,_es certa:n_ aero-
dynamic req<iremcnts it is often C_esirc_ to know ::bother it
has su-._icient :_trez_.....ro c.....
_ .,,:.:.. _ sa_17e ov)er':t_io_. ,r,_= _TGS
.... ,_ - -._ act _,_r,%oe 3G S
analys4s of a r_ro_eller is a,. complex and laborious process, ane
-=_:"_'_' u.sod in rout" :"tlle a_opl°oxi_<lL!tOm..._,_ ..... ln_ da_l p-.:",o"k,. _are noses-
sarily inaccurate.
in this reoort a simole relation is _i',_.. . for _.._etcr.:_,inin@:
whether any p_:omo_ller of s __,ndaro. Nsvv i'orr._,is sufficiently
stron S for it_ oartioular _,-_%_in_7 _ *" ....._-r_.]ulr_:: _.... _ The :,,__et hod
used can be adzpted to any family of propellers of one Tot:era!
I
A_)roxima!:e St tess &na!ysis
_.._.ce _,.pe_ ¢_ forces s_ct on <ro_jeller i<!ades:
] C 0-2 t " _ .....
_. rlz __s ]_ forces,
3. Gyrosconio forces.
The :_ciual stresses are of a very co:no_icqt::d _÷_,_',_ but
{n routine <.csi:Tn v;ork o:o_s _._,_:e _fope]iers o_ui_, tho t',-;o
most important necd be con'_idereC:
!. U-aifo_ <sns:-ie strcss .,_c.e to centrifu_l forces.
_<, • .,.:"._x_.._u_.-_'_....tcnsi!c stress causca by bending due to
the lift 31' the mirfoi!.
_he o' Sea _"
- .=,_res cue _o ccntrifu_! force ,::ill be oonsiderod
first. The centrifuT&]_ force a,ctir_ on any p,iven particle in
•the propeller is re_resented bY the equation C.F. = '_ w2 r,
where _! is t'_-"" n,: v.:eiTht of v,he pa.rtis!e, T _S the accelera-
tion due to <'rav 4_-, -" the _,_ , _ _s a:_Eular velocity in radians -oer
" - " _.._C_I .second, and r is the czsta_ce of the particle *'"", the center
of rotation. :: rcvo_u__cns ]9er it;rote, _.._ an-
a +v L0 beo014est_7_= r VC!oci
_D
"T
CO ano. t:_.e _,..:_.._.tiontakes tho
q1_, " .
.he propeller is divi&ed _n-to staticns usually soaced ei-
_ _ ..n(_io :cadius) apart along the __.._....- zus.ther 6 in. or 15 per ,_,.,u,. ,. -
_- _ _ _s q i-r_. ;_ r_._ia] leucth a_ each stat'c_.,Considering oe_t.,_o ........ - --
the :_._eit:ht V._ of c-_ch.._,ectior, becomes W : Aw, where A is
N.A.C.A. Technical l_ote No. ?$8 r-
_ __ ion squa cs a_dth_.._crosc section_i area of _h,_ _e_ i.._'_ re i_Rch ._
i3  .o-x it7of the matari i pounds per cubic iron. T .c
C@_q _.......... c ..... TCO 8, o <; =Trmn
W
) °_t
dr _ o, , 60 ./
a "_i.0_ --m't,l_o_ l_O0_'_l ccntrlfuga! force at s n7 station will L@
-.- r Ar-- _,:_ *-LJ ,. £ ,, _" j
r << ', C,O ,,
In practice this "_ = ..... -"in _c:_ration is _'-_"" _ oon-p ..... orm_,. __ra_hioa !1 _,. _ne
trifuA-_l force i(C'F') i_< ca!culatod for each aection _nd
_L r
plot _.....:.<._.%_a_inst the ra_i_zs of tke station, and a cu_rc i:._clr_wn
h. o_,"-_ _ •,n ._o Doir_ts . vis. Then the tezsl ccntrii'uga! forco
-at cecn k_..c_zos_ ,.,rillbe rcprcsonto,i by the area under the cur_-c
from. +'_, tin _:o._:iusof *_" ropc]ilS to _l'.cradius of the sta-
tion. The tensile stress in each sect, o_ ms obtained by livid-
in T the tot_! centr__fusa! force for t?.o s_ation by the :tree of
the oection, or S. - v.F.
The above computations for all of the stntions of a nro_oc! -
Tho staticns, b!adc
wiiths b, _._ the uToer_ and ].cwcr csmocrs i_U %nd hL,. s_rc
obsnincd from the propclicr layout or de_,i%T._.
various sections arc then comnutcd h., ._.r'__._,.._o_oof ' c_rtformula
A ]=': ?l . 7 £_ .... n '
I_ _--]i_' is a,r,aooroximooto fo:..._.ular.-hich iF; corroot :-.zo::_,n
N.A.C.A. Technical i:otc hTo. 233 4
practical limits for the R._..F. 6 (modified) airfoil section
used in propeller work.
_hc i ,,,_._, is a c-N._-'_'ion of the tensile stress duc
to C Y. for il_ 3-foot station of th ,_ _ropcNer F_ivcn in _'_
N - 1750
r :-- 36 in. = _ ft
b = 7.63 in.
h U -- . _7
k L = 0
I. A = .74 b h
74 x 7 _= • .?.__ (.,_7 + O)
_'.23 s,q in.T.: } - • •
S. Ar -- Z 23 × :_ _II@ _ in 3
2 r5. .d (C.F.)= Ar : /2 : :: : A_ x .105 _x2_ x l,::O_
dr g < 60 / " 32.2 k 60 /
_0 _ !! = _. per :.n. ra&ius.= 108 Ar --: .L_c x 6.4 !2,380 i'_:
4. St _ C.F. _. _.12._L_bZq__ " (oianimetered) = 4140 lb /sq. in.A ,%. S S "
In bending, the irene!let acts a_ a cantilever beam. The
load on the beam is --'_ .
___.en as the, lift of the airfoil only, no
other aerodynamic forces being considered. The load, then, is
proportional to P CL AV _, vr!::ere p is the density of the air
s - .e_o_ CL is the abso-in rams units (which may be taken as _,_,_o._,
Q
' ") -_ C,N.._.O.A. Technical Note No. _,-_., $
lute lift _.,o_=-'icient of o_:e _irfoil. A is. the ,%irYoil aroa, and
V is the vcqoc _-" relati,,c to the r_ir The _,0_ "- "" _
_ ,_j ......... e is dzJ_._el into
].-foot " -_ _'_lJi. aS •
The lift-0or foot of radii.it i,s divan by
where b is the: blade width in f_ot, and V r
/J
P CL b (V/_)_
2
,.7!3C _ "of ._he blade section with resT)act to th@ air in feet per _o.a_,
rNh 2
2 - -or (V r = (V' + (2 is t,:,£_,'ol.ocity of _hc plane60 /
in feat per second plus an emD_'mc,,._ in._zn,:_factor, or
V' = V (i + j S), -rhcrc 8 is t.h_ slip.
The lift par unit radius L, is calculated for each sty-
tion and plotted a_rai_st _..e radius of the _ ' _"
manner :_,s for centrifu_ml force. ,hz_. _;ives a qoad cu_,,o for
the ore Dollar as shovm in _ 8 The shear -t an-.: point is "ivan
R
_ : z._ the a ea under _'_by tke oqua%ion Fs / L dr, which "_ r ,_nt_los,d
r
cuz-_c a.nd is _ound '_" - h_ a,_r_p_.c 117. The v%lucs of F s at each o,-_
tion are tken plotted in like manner, _ivin C ._zsbea, r curve (Fi:S. 5).
ft
The bcn_J.i_ :uoment at an)- point is I.' = f S dr, which __s _n,_
r
area under the she_,r eu_rc. The maximum tensile stress S t at
each station is then calculated by means of the relation St _ _[Yt! '
_<here I is the le_st momcnt of inertia of the section mad Yt
is _ " _ _o_.e dzst_nce from .+.ha ncutra_ axis to the outermost fiber on
the v..'orkiny face. The nou_ra_ axis for the least moment of incr-
tie runs throu[:h the c.f_. of tke section <_nd is assumed prrallol
to _'_- _ {,._e ;. .... _._ cads
_ cord of _ irfoi]., m,:is _s not s%rictly _e o._ I
to vary s!i[:ht errors. The positions of the c.g.'s of sins!e and
double _ " " ,_c.<_ocred R.,_.F.6 (modified) _irfoi!s are sbotvn in Fi.-'. O.
mhe._ _c_st moment of inert"zc, I is _<ivcn a_proximato!y._. _ by
I : ........_a_"_,_ b ha for _....._-in_::_._--l-_cLml-ercd section, and
I = .o_-72 b (9 U + _m) _ "-L!2 b % hL (h u + _-h)
#or ,z double cambered section.
_ _ _e to bonding ar _s sho:_L for _]._The ca loul_ions of ot .... ]
of the stations of the pro?oiler in tke second part of Table i.
For she o-moot s_ tmon the ca]cu!stions in detail are as fo].-
_ 0'75 :
= .416 h : .416 × ._7 : .257 it.
= 047 ° 1_ ha : {54-72 × 7 65 × <_Ca : 067 ir_ 4
• ;_, . . . -,_,1 , .- _o
S I : .067 : -,o', in a
Yt •237
4-°
S_rY 2w x _ × ].mii_O
• - .. = -. : _'rA i'_./fSO0.60 o0"' " .....
5e L>£'r__-",h = F_<_2 : 5r,<: :Dr',60 / ......" .... ' ........
5. V' 158.5 (i + ½ S) = '::_ >' : =o_ 4 ft., scc.= ._,_. 5 1.0@4 , ,_o. /
7. (Vr) _ : (v')_ __._' a w60rz'J_/ = ,jo,°_-_,70 + .303, _..O = c.._-,_,_-00.
8. b (ft.) = 7.@_____55= .6_<7 {t.
• 12 -
9. CL = .SIO (from desi6_ data).
19. L nor ft. = PC L b (Vr) _ _ .076 x .510 x .657 ×
2 z_ o X
• £a
II.
}" 8S8,9C0 = _o.= F_ Ib
_ _ 2550 (from ?£raoh) = 8500 lb./sq.in.
St -- I = ._o_S°_ ' _
The total _wre3s for l h, c :,"ot_ -, { _:_ ....
. s' _o_, -s ,,;i_ SLi_l O£ Lke oc__tr!i-
17 "7"] 7 "t r ..... e_q_d b
-----.............. endi_ C stress, or,
_ou,J.._ St = C r''c_%t.) + % (oe:ld..j ,1180 4- _.q _ lOt _ = . .... _,_,_ --: 18,':-& it./
sq. in.
"'"._,.e:__ i _e _act that t,h_ bl,%dcs __-+ to some extent _:_
practice is adde _ _,_e• ..., . to the original complex nature of the " :- _o_-'o_.
it :'¢i_I readily be seen that no c'reat de_rce of accuracy car, ".-_
exoecLed[ rom tLJs analysis i+ d_c_ ho,,:ever, _ive o:,_.0_.._.ive
fi_Ires, if a propeller which is kno_. to ha.re suf_icjent
strensth lor saJ?e o_cration is analTzed for stresses, and -.,be
ca!culatcd stresses of sim__lar propc!iers do not exceed the
maxim__m _'7-,,'_..+ed.._._._._.,value of ,..otrc,_s,. for the icroven nrope!!cr,.
. s" b iderca . othey may "._:so c cons " sere /or tri:zl ±lickts Sine_ the
stre-.ses :In ....
_geo:,euricstly simiT.sr propellers opeTatin£ at =Lc
same V vary i.,_ a certain clef into'so man_er, 4.e., as 0z,_
,a ]q, •square of ._..etip s_ced, z¢ is only necessary to keep bclow a
.... 3 ..t. 4.- 4prod_oto_:_.incd _i_ speoA _o k,.-.;pthe stres:_,.es boiow 9, certain
- .ivalue When tn_ AR and CR are _:u.r__-
• .{.d, however, cliff croft
values of %he ti D.....,_."op,_ are require& to 0reduce the same ,_tress
An Equagion for Determining Role.tire Stren_th.
it was known from. ex_0crienco that a !0-foot oak propc!ler
of low pitch herin{ an AR cf G and a CR of I, could be
safely operated on a:-: airplane ,,rhich had an f:.P.Li, of !.730 at
maximum horizontal shoed _inc _ f;-,.:_ s÷re<_ses are lower +'o-- cr,o-
pe!!crs of hi_her pigch a!i other fee%ors ...o,r._inzn_.constant,
Ii'.A.C.A. Technical Note No. 8S8 8
the above case was taken as -m consemJative standard by v:hich
to jud_.e the strength of other oro_ellers. The stress was cal-
culated for the case of tk_s !C,-foot propc!icr of AR-= 6 and
CR = I b_: means of the system given in this report. Assm_.ing
that the propeller turned 1750 R.P. "'_ -__:. at the maximum horizo._oal
speed of the airplane, the ni[.hest stress found was 3268 lb./
sq. in.
To find a relation Letweer_
may be t_.._e_ a_ m cc.nst:_nt tlmcs
CI<_ AR, a_d tip soeod (which
i,_) for a constant value of
stress, calculations wore made for several standard propc!Iozs
having di±_ferent values of AR and CR. The value of _TD _vcs
then found st v:hich the stress of 3268 Ib./sq.in. <vas obtained
in each case• The results were plotted as s"_ovm in Figs. 4
and 5. Cons ",_l,_erln'-_3 the cuz_es as strai<ht lines the follo',:_ing
very s£mple equation can bc derived:
CR : n-,_':_ ICD + 3 AR 4 3
This is called the "._on:-_t,:_nt,_res,_ Formula." for if the
CR is of the correct value to just equal tb3 right-Dmnd side
of the equation, the maximum stress will be constant for all
standard Navy oak propcl!ors, if the CR is larger than nec-
essary, the stresses will be lo_:er; but if the CR is s,_'ller
than that indicated as nece,csary by the formula, the stresses
,-,ill be hi_her than _he safe standard•
It sometimes happens that with a particular combination
_".A.C._. Tcchnica! Note No. £38 9
of ensine, airplane, ::nd nropeller, vibrations occur rhich may
cause %ho propeller "to Jail even thouTh calculations indicatc
that the sSrens.-:.h __s ,_ufficient. This can :;sual.!T be foretold
in m wooden Rronc!ler bT e:<ccssive flutter.
Conclus ions
OwiuT to the -_ -_- tb ....
_a,,u ,_:_u evon u.._e, "qost complete and 7aius-
.u _ " . ,._ _ -. .. _ -1 ._T cuakln_ _-_*_o-_q4or _ll&_ _ _,. _- tru.:.,_ a__._=, _es are inaccura.te bcc, aus_ of dis-
tortion a._6 ncn-unifoi'mit7 of m_teri:_! in wsodcn_ronei!ers,
simclc reintion such _s the ore dcscriLed i.u this note is .son-
sidercd a satisfactory strength _b_k for :prcpe!Icrs of sire_" °
form. Its simglic -'_- _ ..... __'-'" _,_...._ it a usc-h-I
- _-..,Ta-::_ ,_, oe of ...._.!ication -_'"_- -
tool in the ha.n:fis of a _ropcl]er dcsijncr.
N.A.C._%. Tcchnical Note ice. 2S8 I0
Table I.
Stress Calc_:!at ions
for I0 ft. Dural_&::in ?repeller
II.P.H. = 10-1 R.P.'._. -- 1750 S = .188
C ent rifu_l.
O _ -
d(C.F.) = Ar w :i,/__,w[_ = Ar x .!03 ,< (2w x ].7o__: i09 Ar.
dr _ _ 60, 38.8 \ 60 I
Radius, in.
Radius, ft.
b, inches
h uoocr
!owor
Area, sq.in.
A r, i._l.a
C.F. lb.
IC_ - °
,_. F. Ib ./oq. zn.St A
4.5
3.33
o3
• 567
30.6
3305
o eO
I $82
48 4S
4.0 3.5
5.2...3 6.70
• 35 • 45
].55 ,3.23
G.t.? 93.6
7ooollo!1o
i
I
i
•5,[CO i 7640
2560 5485
t
[z6 i 3.D
 .ol
I
7.651 8.02
•57 •£8
3.2,3 4.0_
!!6.4 !21.8
125S0 !5190
!3380 19C50
4140 ,:860
24
2.0
8.02,
.Sd-
.'_ 99
,t"e
119,7
k:9aO
i eooo
r.:-,-:,,10
18
1.5
7.78
I. Ol
.08
6.87
l!S.O
iS300
32,300
g!50
12
1.0
6.75
1.19
.79
9.89
118.6
12800
38800
3_2,0
Ob_U
for 1C
.:_.#. n. :: 104
V' = I. 0C4 x
Table I (Cont.)
Ca].cu!mt ions
Tm _ r r 7 r-f'_ r-, _7"-,i 0<, = i___
Bonding
487 x V::
.:, • 169.4 ft./scc.
•09 6
•O? 0
0 9 _,
<; _J <.,
Jt
I
I/Yt
_,_rN _+/_
..... ,1. Lpl ____, ('3 "160
' 2wrN1 680600
k, GO/
(Vr) _ 707006
o .ob, ft. ._:7_.
CL abs. .4-50
L, lb./ft. 106.7
Shear, lb. 31.0
T" " _ I
_, In. lc. 96
- }_Yt
_t=T _ ,1-800
!b./sq. in. ,
I • i.I:6 } • ].87
0.'].06 0298Ii .0?3 •].54
i
1
i i
I
I
i 563.7 r£O
I
i . ¢s6
i
i
! _"; Fj
o'-r, ,
}
i i3,.9.9
i
i 92• 6
!
•_,23 0
j 6580
458 600
•:F58
•bOO
162.2,
l,:,!•6
""70D- J. <
7 6OO
.$37
• 0670
.2,33
55O
O, aO_
528900
• 637
•510
]26.5
,h a
,:,2_. 0
2350
8300
.:783 .550
• 1:1.90 .225
• 4tO .643
4_8 5(:27
t
I
i
,,o6:]f.O , _.c___....
•5'.[,? • £,88
•570 •C30
]O_.S 80.4
_81..4 330.6
C_7 ffh,f_ "'_ '-6"
_.JU [ 0 L:O
• 470
.455
o 68
._/ •
275
'75680
9oOO,q
•648
•760
53.7
3 _q=•6
77_0
8030
.960
2. !0!
2.!9
I !83
::9390
•594
.840
35.4
3.90.0
7 %04 r_
,I _ ,-7
._-OOtO
st
St (bend.)
St (total)
Total
I
] ,"82 i
. 2- ;.
!
i
48 O0
i
I
6287_
I
560 ': "_ _
ooc, O _c_00
9!,_0 11025
Stress
4140
8300
]_2440
486O
9100
13360
B2] 0 3].50
8850 8020
14060 13170
3920
"%0%',.)
8520
N.A.C A Technical i_,-,<__¢o 238 vic, i
rrl
"r|
©
r-_
(i)
C'I
O
['0
p
.H
40
C)
14000
12OOO
i0000
8OO0
8000
4000
2000
0
Fi _' !b.
3 4 5
in ft.
©H
©
2O
0 I S ¢ 5
Radius in ft.
Fig.8 Load curve;o..rca = shear;i sq.iu.= 80 lb.
/_%
N,A.C.A. Tecn_.,i, al ],,_ctaNo.8So Fi_;.S
gO0
550
SCO
_o0
,].]
H
_00
,r-I
d
©
150
I00
5O
0
Fig.3
....................i .. \ _.......................t .........................._..........b .......
....... _----'--k ...... 1............. i...... i........ I----
i i iI ' _ \ : t l
I J b _ I
t I , , \ } i i I
I i ! i } _ !
[ I , { \ _ ; ; I ....... i......
_, ...... _ ...... _.... q\ ................... _ ...... i ..........i i , ;\ _ i ;
I ! i ' !\ i _ , i
........ ] ...........J...........: ..... i .... I \_ _ L _ _
i
_ i ! I \i i ! i
......................... 4 ...... _ ......... ÷.........................................._'- _......
; ! I :
! ! ! \ i _ !
! ! r i _ \ i i
! _ \L ! I
............................... ,........._.......................-A-- 4 ..... ;............
\
.........................................................} , < V-
: i , I i I \ i i I
4 , \, I
........ ,_....... i ........ +........... t........ _........ _ .......... i....... k!...... _.......... t
! i _ i i i\ i j
........ ti ...... -}! ..................: [I.......... ]i......... !I...............[ .... _--T:........... i
} , i ! _"\ i
i _ i I \
l 4 < \ ! 4
; i I
! ' " .....i .................iX.....
I 2 S 4 5
Radius in ft.
Shear curve;_.rea = bending moment;l sq.in.=
50_12 = 600 in.lb.
j_
_r_.C.A. Tec::._:ica! );ote No.238
19000
18000
ND
17000
.8
, ! !
i i ,
.... i i
]
I ; b
' r i i !
! _ i t/ i
: t / !
; i ./'/' !
//-/' j,
i : i , /I ! i ........-I........
i / i i _ ':
I i ../_ _ ! i ;
' i //:" I
i /_ , i
: / i ! i
!
1 0 1 1 1 _ 1.3 1.,1
OR : _,_b:,r i'_,tio
Fig.4
20000
18090
ND
16000
14000
!_-.L,-7-OUof CR r_ith _D for c--,.+_,nt ot_ .....s. AR = 6
[ i --- F--'-
. : i : I [
i ! i , i ! l I
) I , i • 1 _ i I
i , ; i.......; ......t.......!.......I..........., ....
; _ _ i ; " t- ...... !............ _.......... _----- +_........
.................. .p . ............................ ................. ,
l _ i , t I
5
Fig.5
(; 7
AR = Aspect -_
Vari" _a,_,ion of AR with ND ffor constant stress. CR = !
N.A.C.A. T@chnica! Note No.238 Fig.6
-!{ax.cmmber = 1.0
_ _;/i i ih _i F---_-_ iL_.i_ i,z_<i ! J _I t , i_
_0 _41 _ ! __ I_ _i ' I- I I
• .........iT-1.... , j i
i©o II . • _1 C_ b9 _ I.O rO D'- CO OD
B lari_ widt'b,"(b)-- .........................
_____ _±._____I_____L_____.L ...... 1 .......
I,.Ta,vysta,nda, rd blade section. R.A,F.No.b modified, flat face.
_- Sin_le camoer t
._..tota,1 _eotion • _ ,._ ,
'/ 9 - ,_ - _- %q`-J-<SX_TT ,--._._ ,
" .........................'-...._ -_-7/_£ _. 'J___ _
_ ....... ,-_ f ' --:---,:_(:,},_ .......... _-__-_t--
-- -. 44,?.!; ..................... _ ..... c. _. lo':.,-e r ib
Double camber
Ar9% of upper section = .74 bh U
_._,..r = .74 bh L
_ - '_- ]_ .
• 9-.Lo,__.r]-X. 74bhu_.d16hLX 74bb.L
_ _ :416(h U_ hL)
x ; 74bhu+" ?4bh L -, _. .
Fig.6 c.c.and area of sections. )_


Propeller design IV : a simple method for determining the strength of propellers

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