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8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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N O T I C E
THIS DOCUMENT HAS BEEN REPRODUCED FROM
MICROFICHE. ALTHOUGH IT IS RECOGNIZED THAT
CERTAIN PORTIONS ARE ILLEGIBLE, IT IS BEING RELEASED
IN THE INTEREST OF MAKING AVAILABLE AS MUCH
INFORMATION AS POSSIBLE
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'
EPARTMENT OF
MECHANICAL ^ AEROSPACE
ENGINEERING
(NASA-C8-1627541 AERODXNAlIIC-STRUCTURAL
80-17061
ANALYSIS OF DO AL BLADED HELICOPTER SYSTEIiS
Final Technical Report (tlissouri Univ.
-Rolla.) 46 p HC A03
/ SF A01
SCL OiC 63/05 471035
I N A L T E C H N I C A L R E P O R T
AERODYNAMIC-STRUCTURAL ANALYSIS OF
DUAL BLADED HELICOPTER SYSTEMS
NASA AMES NSG-2375
BY
BRUCE
P.
SELBERG
_
.
D ON AL D L. CRONIN
^^"^^^" "''^''^
KAMRAN ROKHSAZ
`
c
^
JOHN
R.
DYKMAN
R^'CS^ FPC^^.
^,
S^ `
4a
`` ^
Li
^^ `p^
FEBRUARY
19HO
U N IVER SITY O F M ISSO U R I - R O LLA
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. .
AERODYNAMIC-STRUCTURAL ANALYSIS OF
DUAL BLADED HELICOPTER SYSTEMS
Aerodynamic Analysis
Bruce P. Selberg
amran Rokhsaz
ssociate Professor
raduate Research As:i^tant
Structural Analysis
Donald L. Cronin
ohn R. Dylan
arla J. Yager
Professor
esearch Assistant Research Assistant
February 1980
Department of Mechanical and Aerospace Engineering
University of Missouri-Rolla
Rolla, MO
5401
8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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^{
^,
THIS DOCUMENT SHOULD NOT BE CONStDERED AS AN OPEN PUBLICATION IN THAT IT CON-
TAINS PROPRIETARY INFORMATION THAT HAS BEEN FILED IN A PATENT DISCLOSURE
^-
^^
i
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I
SUtrQrIARY
The a e r o d y n a m i c a n a l y s i s i n d i c a te d s i gn i f s c a n t powe r s a vi n gs fo r the bi r o to r
over the monorotor fc
r St ^ 1.0, Ga ^ 0.26 and either De ^ -4 d egrees or De ^ -b de-
grees. These sav ing s occu red for all th ree rot or radii at De ^ -6 deg rees and for
t h e sev ent een and twent y feet radii at De = -
4
degrees. When these results are con-
-
idered with th e st ru ct u ral analysis which indicat es th at for bot h th e sev ent een and
, -
ou rt een feet cases, where th e birot or and mo norot or are of equal weig h t s, th e biro-
. ,
or def lect ions are of th e same gene ral mag nit u de as th e monorot or with one tip con-
nect ion between th e birot or blade s. The tip connect ion is required becau se of th e
.
u nev en loads on th e upp er and lower rot ors and th e sensit iv it y of th e aerodynamics
to d e c a l a ge a n gl e a n d ga p.
more opt imiz ed st ru ct u ral syst em in which th e blade weig ht is redu ced mig h t
mov e th e blade radiu s of th e birot or closer to 14 feet case. In th is area th e bi-
rot or wou ld weig h less while st ill exhib iting th e imp rov ed aer odynamics for St
s
1.0,
Ga 0.26, and De
s
-
6
d e g r e e s . W h i l e i t i s r e a l i z e d t h a t t h e e n c l o s e d a n a l y s i s h a s
not achieved the optimal aerodynamic struc tural birotor conf figuration it has demon-
st rat ed birot or feasib ilit y in th at th e birot or syst em c an op erat e with sub st ant ial
required power savings with no weight penalty or with substantial weight savings for
the s a m e r equi r e d powe r a s the s i n gl e r o to r.
3
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` - - -
AERQDYKAPIIC SiJAQL4RY
An analytical study was undertaken to assess the aerodynamic fea sibility of the
birot^^r blade concept. The study investigated:
. Inviscid flow field about dual bladed rotor.
. Boundary layer separation on the rotors.
^}
3.
Three dimensional induced drag calculations.
4.
Rotor thrust and power required.
The aerodynamic study led to the following conclusions:
-
. The best aerodynamic res ults for the dual rotor occurred for a blad e stagger
of one chord length, a blade gap o f twenty six percent of the chord length,
nd an angle of attack between the two blades of -6 degreea.
j
^. For blade placement ; i.e. stagger -St, gap -Ga, ar^i decal age angle -De, that
gave the improved aerodynamic results, the boundary layer separated further
back on the dual blades than for the single bladed rotor.
3.
The delayed separation over the dual bladed rotor sy stems results in a lower
pressure and viscous drag than for the single blade.
4.
The induced drag and, hence, induced torque is lower for the dual rotor sy-
stem than the single rotor system when decalage angles are -4 and -6 degrees.
5.
The dual rotor at a Ga 0.26, St 1.0, and De -6 degrees requires signi-
f i c a n t l y low er p ow er lev e l s t h a n t h e si n g l e rot o r. T h e du a l rot o r at t h e
same gap and stagg er, but with De -4 degrees , also requires lower power
lev els.
6.
The dual rotor at a Ga 0.33, St = 1.0, Pe g
-4 degrees and -6 d^^rees re-
quires lower power levels than the single rotor.
7.
As a result of the lift of the upper a nd lower dual rotors bein g different
nd the sensitivity of the results to proper gap and decal age angles, it will
_
e necessary to tie the two rotors together at the tips with a possible adds-
=
ion tie at the position of the second bendi ng moment.
4^
4
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^_ .
. .
AERODYNAMIC-STRUCTURAL ANALYSIS OF DUAL BLADED HELICOPTER SYSTEMS
An aerodynamic-structural analysis was carried out for dual bladed and single
bladed helicopter rotor
systet;a,
At y p i c a l b i r o t o r c o n f i g u r a t i o n , a s i t w o u l d b e
mounted, is shown in figure 1. The upper and lower blades maintain this same posi--
^
ion relative to one another as they rotate . An end view of the blades are sh own
in figure 2. The distance one blade is ahead of the ot her is called stagger i n per-
#
ent of chord, 5t, with a positive stagger indicating the upper blade is forward of
- -
t^e lower blade. The gap, in percent of chord, is desi gnated Ga. The angle of at-
tack between the two blades is called decalag e angle, De, and is negative when the
extended chord lines intersect in front of the two blade elements . The aerodynamic
^
tructural analysis considered the hover mode of operation and all dual bladed sy-
stems were chosen to have the s ame lifting area as the single bladed system. In
addition aspect ratio of the single bladed rotor was selected as 20 and each aero-
dynamic birotor blade was selected such that they had the same aspect ratio as the
single rotor. Three different diameter birotor combinations were chosen to assess
aerodynamic and stru ctural performance, 28, 37, and 40 feet in diame ter. A constant
chord NACA 0012 airfoil section with an 8 degree lin ear twist was selected for all
calculations. The blades had an airfoil sec tion form 0.25R to R where R is the
blade radius from the hub of rotation. Rotor tip velocity for all cases was 600
feet per second. The blade sizes along with the mode of operation are shown in
Table 1.
AERODYNAMIC ANALYSIS
The analysis level can most easily be discussed with respect to four main areas
which are listed below:
1.
Inviscid flow field analysis to investigate aerodynamic characteristics for
various dual rotor blade placement combinations with respect to blade stag-
ger, gap, and angle of a ttack between the two blades.
2.
Boundary layer separation point analysis and subsequent viscous and pressure
drag analysis.
=
. Induced drag calculation for the three dimensional dual and single rotor sy-
stem.
4, Compilation and integration of the above to predic t Chrtist and power require-
ments.
5
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.
^
.
^
.
^
^
,
-
^
^
.
6
^
~ ~~~_~ . - _ ~- . - _~- -, .__..~ ---~ _=_.. - _ ~,_ - _, . ,-~- ;
-~ _
~~r
~_--
^
--
^
^
~
^
^
.
.
^
L
^
8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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i
1
4 1
t
W
v
i
7
8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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_ ^ ^ _ -
-
ma
y.
n
r - -
_- -
ABLE
1
AIRFOIL CHARACTERISTICS
A 0012 const nt cho rd blade
A
8 degree li near twist from 0 .25R to R
Rotor tip speed - 600 feat per second
Single rotor blade dimensions
iameter w
40 feet
chord
feet
s
Dual rotor blade dimensions
Case I
^ s
iameter 28
eet
hord
1.415 feet
Case II
diameter 37
eet
^
hord
.175 feet
Case III
diameter ^ 40
eet
chord
1.0 f oot
nviscid A:^alysis
Nenadovitch 1
who did extensive computatio ns and tests with two element airfo ils
btained aerodynamic impro vements for the two element case over the single element
-
a s e on l y in a n a r r ow ra n g e of S t , G a, an d D e. Th is reg i o n w as w h en S t
s
1 . 0 ,
Ga ^ .33 to
.
66,
and De -3 to - 6
d e g r e e s. Fo r ga ps gr e a t e r tha n o n e , n e ga t i v e
z 6
taggers, or for positive decalage angles the two element aerodynamic chara cteris-
tics were degraded with respect to the single ele ment.
, . ^
aplace's equation of the stream function was solved using a f inite difference
p p r o a c h in a C art e s i a n co o r d i n a t e sy s t e m. P res s u r e di s t r i b u t i o n re s u l t s f o r t h e
NACA 0012 airfoil se ction were com pared with those o f Raj
2 , Eppler
3
, and G.-.abedian^
4_
to validate the numerica l technique with agreement being excellent.
The inviscid computational analysis was carried out in this narrow region of
S t , G a, an d D e w h er e N ea d o v i t c h f ou n d ae r o d y n a m i c imp r o v e m e n t s. F ig u r e 3 is t h e
pressure coeff icient, Cp, distribution for the upper and lower elements for a St 1.0,
+
a 0.26, and De -4 degrees for the lower airfoil at a geometric angle of attack
8
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^-
----
UPPFR AIRFOIL OF A
T
VYO AIRFOIL SY STEM
NACA
0012 , S t
= 1 . 0 G o = o . 2 s
e
,1
1
0
------
INGLE' AIRFOIL
^
,
ACA 00 12 , ^s4
rt
^
,_
1
rti
_ yr - r . .... r .r ...
..' .
p
^^.O
--
/C
/.0
----
LO^f
R
A1 RFOlL OF A
T
V^O AIRFOIL SY STE'r l
NACA 0012 , a=a
n
'
0 ` '
^--- SINGLE A1RFD/L
^'^-.__
ACA 0 0 /2 , a=4
-..
-_
-,
C o.o
---
--. - __ .... . . . _ .._ . ,
P
-
^ . _
^
^^
O
1.0
Figure ?
9
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_
_____a_=
rte-_
- - -s -__
_
. y
of 4 deg rees. Superimp osed is th e pressu re dist rib u t ion for a sing le airf oil ele -
ment at 4 degree geom etric angle of attack. Even though the upper airfoil is a-. a
sero geomet ric ang le of att ack with resp ect to th e freest rsam vsioeit y
v sct or it
has
a
pressure disti^ibutian and hence a lift that corresponds to approximately 4 de-
g ree ang le of att ack. The resu lt ing lif t vsct os on th e upp er airf oil is thu s rot at ed
^ ^
iving an effective thrust or negative drag with respect to the direction of nation.
The loner airf oil has a Cp dist rib u t ion slig h t ly less th an th e 4 deg ree sing le air-
oil case. The net resu lt for th e comb ined two elemen t s is small ch ang es i n tot al
lif t coef f icient along with a neg at iv e indu ced two dimensional drag coe f f icient ,
CD z i
. At an 8 deg ree geome t ric ang le of att ack a simi lar dist rib u t ion is s h ows in
figure 4. Again the upper airfoil, due t o the f
] aw int eract ion, is act ing lik e a
single airfoil at a angle of attack greater than
$ degree even though the geaaetsic
ng le of att ack is only 4 deg rees. Alth oug h th e lower airf oil has a Cp dist rib u t ion
orresponding only to a four degree angle of attack the total lift coefficient stays
nearly th e same while th e indu ced two dimensional drag coef f icientCD
2i is aignif i-
cant and benef ic ial. Figu re 5 shows th e indu ced two dimensiona l drag coef f icient as
a fu nct ion of lif t coef f icient for dif f erent decala g e ang les. Both th e
- 4 and 6 de
g ree decalag e cases d emonst rat e good imp rov ement s at all an g les of att ack while th e
De ^ -2 degree case only gives a negative induced drag at
low
lif t coef f icient s. Fig-
ure 6 illustra tes the effect of gap for the - 4 and - 6 degree decalag e cases, Both de-
calag e cases demonst rat e th at th e hig h est neg at iv e indu ced drag coef f icient lev els are
btained for the narro west gap investigated with improvements falli ng off as the gap
increases . Gap s of less th an 0.26 cou ld not be obt ain ed becau se th e aub mat rix of
^
ach ding
s flow field wou ld ov erlap cau sing nu merical comp u t at ional prob lems. Far
the De ^ ^4 degree case at Ga ^ 0.26 the effects of stagger w e r e
investigated. These
are shown in figure 7. Again the St ^ 1.0 case dem c^r
:
Etrates the best results.
Boundary Analysis and Sep arat ion
. ,
A sep arat ion and viscou s flow analysis aft er E. Truck enb rodt
5
was used to pre-
diet sep arat ion point s and th e viscou s ,drag ov er th e sing le and du al element cases.
Figure 8 shows separation points results on the upper surface of the upper airf oil as
a fu nct ion of x/c and De in comp ar ison with th e sing le r ot or. For St ^ 1.0, and
Ga - 0.26 th e sing le rot or sep ara t es bef ore th e birot or in al l inst ances. The lower
rot or does not hav e any sig nif icant sep arat ion ov er eit h er it s upp er or l ower su rf ace
and i
^ not sh own. The sep arat ion prob lems which do hap p en for th e sing le rot or o ceu r
when C > 0.6. Thus the differences b etween the birotor and single ro tor will be
i^
more pronounced for bl ades with either a larger geometric twist than 8 degrees or f or
_
0
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_ -_
^^. _ _
`
3
.0
---
NACA O 0 2
PPER
A JRFOlL OF A
t
^
'^^ 'YO
AiR
FO /L SYST E 11
^
t=
/, 0 , G
o
= 0.26 ; ^^,="4
^ ^
_
^
----- SINGLE AlRFOL
- 1 ,0 ,,
A CA 001 2 ,
a =
8
-
-
1
^
~ ' ^
1`
/ / ^ - _
V
^^.
. . . . . , .
--
:
I. O
. f
.
/C
^
i
.
. 0
----- L O
y
Y E R
A I
RFOIL OF A
T1
'YO A/RF41L SYSTEA^
NACA O0/2 ,
Q's8
$r=
l.0,
Go
=
0.26 , ,De -q.
-I .D
^ .
- ----
i l Y G
LE
A IRFOIL
_
ACA 0012 , a=4
a
i
^/c
.0
FigurN 4
17.
8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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_a__.
.00s
k l
U
,
004
w
U
,002
4
Cp
23
4
N
-002
w
v
O -004
..
S
t= t.00
Go= 0 2 6
l^ D Q
=-2
p
D e
,^-fie
o D e = ^ 6
. 4
.6
8
.0
-os
Figure 5
iz
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_
._
..__:;
___
:_
-r .. _
e
n _
-
e__
-
==_ ..=ar.
x
^
_
__
-
.
E
F
^.
s^ = i o
=^ ^
^ . 0 0 4
v a
4
De=^6o
^
t
G
v
G
o
w
D
2 6
^ .26
v
.002
.33
. Q
33
c^
^
O .46
^ .46
4
Cfl2i
o
_2
o
s
8
cv
.002
P
W
-:004
a
:oos.
a
s -
ooa
^ }
Figure 6
; -
i
3
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^_
^
i
Q
^ ,
9
i
W
v
w
0
U
^ I
j
v
Q
:002
N
i
t
st
:004
U
C3
ti^
rOO^
Ga 0.26
Da =-4
o st=o .7s
V St=0.86
O
S
t
=1.40
Q
S^-
1112
0
Y.4
6 LOC
Figure 7
14
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-- .^
--
^:
^.
^
_
. w
1.0
^
INGLE
~
O T O R
W
8
U
W
Q -
0 26
V
D,^ - 4
. 2
4 De=-sp
.2 46
.0
X/C
.^
Figure 8
w
5
8/10/2019 Analisis de Estructura Dinamica Para Helicopteros
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^_
t h e 8 deg ree case considered but at hig h er ang les of att ack , i.e. from 12 degrees Co
4 deg rees inst ead of from 8 deg rees to 0 deg rees or 9 deg rees to 1 deg ree as consid-
ered herein. The birot or is not se p arat ing sig nif icant ly ev en for C1 as hig h as 1.2
for St ^ 1.0, De ^ -4 deg rees and -6 deg re es and for all gap e considered . Figu re 9
sh ows th at as gap increases th e birot or mov es in th e direct ion of th e sing le rot or
alt h ou g h not ra p idly. Figu re 10 sh ows th e eff ec t of st ag g er. Except for St ^ 0.76
the separation point does not demonstrate any trend s or move signif scantly.
It was anticipate d that viscous and pressure dra g after separation would be ^=:.-
cu lat ed. Howev er, du e to comp u t at ional prob lems in pred ict ing th e pressu re drag af-
ter separation , the viscous and pressure drag were obtaine d from two dimensional 3a;;^
fo r a s i n gl e r o to r at the s a m e C
1
. Thus the be n e fi ts fr o m the l a te r s e pa r a ti o n c c e
t h e birot or do not app ear in th ese final th ru st-power required cu rv es. When th ese
correct ions are app lied, th e birot or will hav e ev en lower power required resu lt s and
hi ghe r l i ft r e s ul ts tha n tho s e r e po r te d Her e i n.
Three Dimensional Indu ced Drag
Finit e asp ect rat io rot or indu ced drag calcu lat ions were made using th e classi-
cal vort ex filament analysi s. This analysis was app lied between 0.25R and R since
t h e analysis is symmet ric with resp ect to th e hub. Figu re 11 sh ows indu ced torque
resu lt s for a St = 1.0, Ga 0.26 as a fu nct ion of decala g e ang le and ro t or radiu s.
Except for th e -2 deg rees decalag e ang le th e indu ced torque for th e birot or is less
t h an th e sing le rot or. While variat ions du e to rot or radi u s are small th ere is a
sig nif icant variat ion in indu ced torque with resp ect to decalag e a ng le with th e -6
deg ree decala g e ang le hav ing th e least in du ced torque. Some of^ t h e indu ced torque
t h at occu rs as th e decalag e an g le get s more neg at iv e is prob ab ly du e to th e lower
r o to r l i ft tha t exits at the s e d e c a l a ge a n gl e s.
Thrust and Power
When th e sect ional C
i
s are int eg rat ed ov er R, as well as th e sect ional valu es
of
CD Zi'
CD
v iscou s' CDindu ced we get th ru st an d required power. Figu re 12 shows th e
required power versu s th ru st as a fu nct ion of decalag e ang le at a St ^ 1.0 and a
Ga = 0.26 for th e th ree birot or and m onorot or radii . As wou ld hav e been expect ed
from the previou s results, the De -2 degrees case requires birotor p ower that is
essent ially th e same as th at of th e monoro t or. Howev er th e -4 deg rees and -6 deg rees
decalag e cases sh ow sig nif icant ly lower required Bower lev els th an far th e sing le ro-
t o r c a s e . W h e n t h e - 6 d e g r e e s d e c a l a g e a n g l e r e s u l t s a r e
linearally extrapolated to
^#
6
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.
Y
I.0
t^
_
^
v
r/
.6
J
. 4
. 2
ms .
_, -- >.^__ .: ^-
.
_ _ . _ s., -^ _ _,
_ - _ - _
_.- .___ _ _ _
_ _ _ '
` ` __, - _ -` ;_ _ __
_ .^_ _z = __ ,
_ _ .__ .^___ ,
--
^
_
_____
-
.z
^
s
s
.a
/c
Figure 9
-
17
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.
i .
t
I
O
^
^ n
3
3
9
^-
LU
U
W
U
^
J
i.^
.6
.4
C^
__ __
_
__ __ -ff-_ .. _ _ _
__a
._ __
"> __-__
_
_
Ga = 0 . 2 6
D 4
SIPICLE
R O T O R
a S
t
= 0 .76
o S
t =
0.88
A S=J.00
Q S t= 1 . J2
.2
4
6
^{/ C
Figure 10
. 8
.0
18
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soo
J
^
400
O T O R
_
j
OD
^
t
^ I.O
G
a = 0.2 6
200
w
ROTOR RADIUS = 14 ft.
.
RoroR
RADIUS
^
7
ft.
o
oo
^
ROTOR RADIUS = 2 o f t.
_ I
2
3
4
5
S
DECALAG.^
A3'lGL
De
o
Figure 11
i
Y
1
19
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4
0
`
s
t
=^. o
G =0.26
O ^
/
o
4NOROTOR
d
,
w
t^
p
e
^
2 0 .
^
lr
^^e
= 4
^
^
^
p
e
=
6
^ R
-- . --
,Rodius=14.15 Ft.
^
Ro diuJ= l7 Ft,
o
^'
^
o diu^ =20 Ft .
1
, _
-
'
^^
^000
o00
o0o
T N R V S ;
b
Figure 12
20
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- -_-,__-
--
- -
--
z--------
-^
---__---=-
-__ ----
--=
- -
r
he same thrust levels as those of the sin gle rotor the required power levels are
st ill sig nif icant ly b elow t h ose of t h e sing le rot or. Th is is t ru e f or all t h ree
birotor radi i conside red. In figure 13 the same power required thrust curve are
_
hown except for a Ga 0.33. The same general trends occurs as for the Ga 0.26
case except the required power levels are slightly higher for the birotor cases.
^ ,
ig u re 1 4 ag ain illu st rat es p ower requ ired v ersu s t h ru st t rends excep t f or a Ca 0.4 6.
However, except for the -6 degrees decala ge case the required power levels are of
the same or higher than the single roto r. A linear extrapola tion of the -6 degrees
^ `
esults yields lower required power only fvr the 40 feet and 34 feet diameter blades .
In figure 15 the results for stagger are sho^m. For a Ga = 0.26 and De 4 degrees
^
he stagger is varied from 0.76 to 1.12. The St 1.0 yields the best results fol
lowed b y St = 1.12, St = 0.88, and f inally St 0.76.
ue to the sensitivity of the required power results to both gap and decala ge
angle it is necess ary that spacers attac h the upper and lower rotor together. This
is required because the upper and lower rotors are carrying significantl y different
loads when the rotors are positio ned for the best power required results. The struc-
tural analysis ind icates that with one tie at the tip of the rotor blades the change
in decalage angle is insigni f icant while the change in 'gap is acceptable for the 17
f oot rot or b lades. Two t ies, one at t h e t ip and t h e ot h er at t h e second b ending mo-
ment p rodu ced insig nif icant ch ang es in b ot h g ap and decalag e ang le. Th e added drag
these ties would cause can be minimized by cove ring the tie with an airfoil section
that is free to rotate and align itself with the incomin g flow.
21
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^.. .,
^
_
-- __- _-.
g-
_ __
_
x
t =1. o
,, '
= 0.33
^
/
NI DNOROTOR
^
o
Q = 2
^ i
t
C^
^
^
--" ' -- ' Radius = l4.1 ,^ F1 '.
L^
-----
Radius= 7 Ft.
e
^------- Rad
us
s
20
Ft.
uu
s
P ^
/^
^^^
_ _
^
o 0 0
o o 0
voo
T H
}^JJST
b
Figure 13
22
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P
^ '
^ P
/ ^^
^'
/ A ' ' ,
:Q
i .
i .
`
1
^,
t
= i.o
o
^ aas
4
'
o N O R
OroR
^V
= . o ^
D e
=2
o
D
e
=
ad
D
e
c -
_ w
otor
" _ -'" Rodius
i
`^ l5 Ft.
2
_ _ _ _ Rotor ^ ^ ? Ft.
w
odiu
T
ar
P
R
otor
=20^'t.
^ n
- ^
odiva
w
0
Q .
S000
000
000
THRUST ^ ^
Figure 14
23
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1 O
,.
^
^^
^^
3
i
t
L . .Y
P
p
.^
a
:^
T.
. ,.. _
^-
G a
= 0.26
Dwwp
t
^ .o .
o S
t
= l.12
e
^
't
= 0
es
n S t = 0.76
- - - - - - RADIUS
3
14 .13 f t.
-- `
RADIUS =1 ? ft.
'--'
'- RADIUS =20 f t.
j
^
0
PR
3
0
o ^
loo0
000
000
THRUST T 1 b
Figure h5
24
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STRUCTURAL SU^tARY
An analytical study was undertaken to assess the structural feasibil ity
of the birotor helicopter blade concept.
The study focused on two aspects of structural performance:
1.
Response of a representative birotor to loading characterizing
a steady-state hover.
2.
Natural frequencies of a representative birotor.
o order to evaluate birotor structural perfot^oance, birotor br.havior
was compared to that of a baseline s ingle blade. Criteria for birotor
structural feasibility included:
1.
Blade
otresse
for the birotor do not exceed values consis tent
with current aerospace practice as exemplified by stres ses in
the baseline blade.
2.
Hub loads produced by the birotor do not exceed values consistent
with current aerospace practice as exemplified by loads pro duced
by the baseline blade.
^ ^
. S ig n i fi c a n t nat u r a l f r equ e n c i e s of t h e b i r o t o r f a l l g e n e r a l l y in
the neighborhood of significant natural frequencies of the baseline
blade.
`
he study led to the following conclusions:
1.
The birotor is in theory a dynamicall y balanced configuration.
True balance may, therefore, be achieved by the add ition of small
c o r r e c t i o n w eig h t s. St ab i l i t y an d co n t r o l p r o b l e m s f o r t h i s
configuration are, therefore, not anticipated.
2.
The birotor without structural spacers between blades is n ot a
3 feasible configuration. One spacer connecting blade tips produces
acceptable structural performance and may be acceptable aerodynam-
ical ly. Two spac^.r; -- a
p
e conneeting blade tips and one connecting
- blades near the eeco
^u .
. r'_'
hp
bending anti
p
ode -- lead to deflections
in steady
-
state ho^^er which aze acceptable from the aerodynamic stand -
point.
__
5
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^
^
ce__
`
3 .ocal hub loads for the birotor are higher than those for ':ie
baseline single blade.
s a consequence of non-zero stagger, the
individual blade center of mass will be either forward or aft of
the radial axis along which the blades will interface with the
hub.
entrifugal loading, therefore, leads to transverse shear
and in-plane bending stresses which must be reacted at the hub.
4 .
lthough blade loads for the birotor are higher than for the base-
line single blade, maximum blade stresses are similar, since the
centrifugal loading described above is reacted by portions of the
blade structure which are typically lightly loaded by aerodynamics.
5 .
ignificant natural frequencies for the birotor configuration are
generally in the range of significant natural frequencies for the
baseline blade.
he more complicated birotor structure leads to
more modal activity in this range ai.3 significant coupling of
in- and out-of-plane bending, and torsion.
In summary, although detailed blade and hub design were beyond the scope
of the study, the work done lead s the writer to cone Lade that, in s pite of
higher loads described above, the birotor concept is structurally feasible.
Soc^e redesign of the blade structure may be required to efficiently
react transverse shear and in-plane bending.
he hub will, moreover,
require additional structure to react birotor loads.
erodynamic perfor-
mance may be traded-off (by reducing blade stagger) to reduce loads and the
consequent need for added structure.
The birotor concept is, additionally, attractive to the dynamicist
since added latitude for tailoring natural frequencies and associated mode
shapes is afforded by varying the location, stiffness, and end conditions
of the structural spacers needed for a feasible birotor design.
27
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I
I
I
I
I
Table I -- Properties for Baseline Blade
f
^
,^
---
,
o.
I
sB
Material: Stainless, E - 28 x 10
6
, G ^ 12.5 x 10
6p si
^.
rea . 5.39 in2
I
y y
3.89 in4
I
.63 in4
zz
I
8.94 in4
xx
includes factor to account for warping of,non-circular cross-sections.
r
28
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.-
:
3
i
s
Table II -- Properties for Birotor Blade
ti
-^
Material: Stainless, E
8 x 10 6 , G
3
12.5 x 10
6
p si
17' birotor
Area
.19 in2
I
9.06 in4
YY
I
.941 in4
zz
I
xx
.84 in
14' birotor
Area
.70 in2
I
3.53 in4
I
.16 in4
zz
I
.746 in4
xx
includes factor to account for warping of non-circu]ar cross-sections.
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f .
Hover Loads
D ur i n g t h e ae r o d y n a m i c p o r t i o n of t h i s st u d y , ae r o d y n a m i c lo a d s rep r e s e n t i n g
a steady-state hover condition were develope d for the blades described in the
previous section. These loads are given in Fig. 16 for the ba seline blade,
and are exemplified for a birotor
(
17' case) in Figs . 17 and Fig. 18.
The given aerodynamic loads were combine d with gravity loading and
centrifugal loading corres ponding to a blade tip speed of 6 00 f t/sec. in
order to develop the results de scribed below.
Composite hub loads, i.e., loads due to a single bas eline blad e or to a
^ e
air of birotoc blades are summ arized in Table III. Six birotor cases were
investigated.
The one -t i e b i r o t o r ca s e s in c o r p o r a t e a si n g l e st r u c t ur a l sp a c e r co n n e c t i n g
_
he tips of the biro tor blades. The two-tie birotor case inco rporates a tip
s p a c e r an d a sp a c e r at rou g h l y t h e se c o n d in
-
p l a n e b e n d i n g ant i
p
ode. The
m u l t i-t i e ca s e in c o r p o r a t e s a t ot a l of ni n e sp a c e r s p o s i t i o n e d at ev e r y ot h e r
m o d e l n o d e po i n t (
approximately 2 feet apart).
, -
The unique loading produced by birotor oper ation is represen ted in
Table III by the torque directed along the blade , T x
. Thi s i s a gy r o s c o p i c
torque developed as a cons equence of the fact that the ro
* .
or spin axis is
n o t pa r a l l e l to a s y m m e t r y ax i s o f a bi r o t o r bl a d e pa i r.
(
The opposed blade
pair produces an equal and opposite gyroscopi c torque so that gyroscopi cs
are reacted entire ly within the hub assembly.)
The study requirement that birotor tip speed be equal to baseline blad e
t i p sp e e d le a d s t o a h ig h e r sp i n rat e f o r t h e b i r o t o r , an d , t h e r e f o r e , t o
a proportionally higher birotor axial force, Fx.
The higher lift, F
y
, seen for the 17' birotor leads a s a consequence to
a higher tangential tor que, T
z
. It is worth noting that thi s torque component
i n c r e a s e s le s s t h a n p r o p o r t i o n a l l y w ith F
y
when the 17' birotor and baseli ne
blade are compared.
Worst case local hub loads, that is, worst case loads at a theoretical
individual blade
-
hub interface , are summarized in Table IV. Clearly seen is
the significant influe nce of spacers on the in-plane bending torque, T
y
, and
the out
-
of-plane bending torque, Tz.
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t4
^
O
N
..
' O
^ O
w
Q
O
^
O
m
w
N O
^o
^,
^
^o
,,
w
i
t
^^^ -
U -
1N3i^0
j lhldtV^tQ0^3^y
V
O
N
-
.
NO
p
r
^q -
30 ^
0 .^
l t^dAl^ oo
?^3d
d010^1N3^
31
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i
r
^_
^ -
t t
Q
j
O
-
N
-
O
t
^ qf
-ui
--
Al3f'VOpy
o r w d n r^ c a o ^ 3 d
d
O
...
h
a
a
.^
w
Q
d
m
O
W
N
o
t
^q^ - . o^o .^
r^udnr^oo^3d ^d
aro^.te^^
32
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^ q 1 - u 1
1J^3S^Oyy
J^l
bJy^100^3 'b '
c ^ U
o
^
w
d.
-,.
. ,
^
O
J
^
^`
^
^
V
^
O
N
1
^
O
O
. ^
: ^
^
o
c
0
o
^
.
^
w
c^
^
^r
o
g
r
^ ,
o
^qj --
^Q2^0^
^l^l^^^JA00^13^y
^JQ10^11fY3^
33
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--
__z_-_ -
_---
-
-
^.
^.
^_
Table III -- Composite Hub
Loads
}
^-
'^
X
Case
FZ
TX
y
Tz
X
y
(pounds)
(
inch
-
pounds)
Baseline
104000
10
0
1770
137000
All 17' cases
123000
020
0
12700
149000
All 14' cases
146000
40
0
28800
105000
34
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Table IV -- Worst Case Local Hub Loads
}
d
^.
Case
Fx
Fy
(pounds)
^ y
Baseline
104000 810
17' No tie
61000
690
17' One tie
6 4 0 0 0
600
^ ~
17' Two ti e
6 6 0 0 0
54 0
^ ;
17' Nine ti e
71000
620
. -
^ -
14' No tie
73000
58 0
. -
^
14' One tie
720A0
50 0
r -
^ .
{
{
^ }
35
x
F Z
Tx
Ty
TZ
(inch-pounds)
0
1770
0
137000
+4200
-770
+432000 96700
+26 00 2600
127000
(_gg000)
74600
+1800
3700
83000
67500
+ 650
k500
83000
58100
+7200
-1020
+620000
69000
+4500
5750
(166000)
53000
-
149000
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z,. _ ---
-
-_ R- - - = --
.^ _
The spacers are also seen to produce with increasi ng number a reduction
in tangential shear, F
z
and an increase in ra dially directed torque, Tx.
In Table V are aum.^arized, for the several birotor configurations,
worst case deflections of one birotor blade with respect to the other.
Inspection of this table revea ls why structural spacers ar e required. The
^ _
hange in gap for the untied l7' blades, for example, is roughly four
times the intended gap and the change in s tagger is roughly equal to the
i n t e n d e d st a g g e r. A ero d y n a m i c s wil l b e sev e r e l y inf l u e n c e d an d b l a d e
i m p a c t i n g se e m s a ce r t a i n t y. Th e si n g l e sp a c e r ca s e p r o d u c e s a w or st ca s e
change in gap of approximately 20X of gap for the 17' case and 14 x of gap
f o r t h e 14 ' ca s e. T h es e co n f i g u r a t i o n s ar e ac c e p t a b l e st r u c t u r a l l y an d ma y
e acceptable aero dynami cally. The 17' two spacer configuration appea rs
fully acceptable from both standpoints and additional spacer s offer no
great advantage.
^
orst case bla de stresses are exemplified in Table VI for the 17'
.
case. These strESSes were developed f or the cross
-
section properties illus-
trated in Tables I and II and are presented for comparative purpose s only.
Calculations are given i n the Appendix.
Worst case spacer loading is summarized in Table VII. Loading given
=
or the 17' two spacer case was employed to size a spacer in ord er to assess
t h e p ot e n t i a l ef f e c t s of sp a c e r s on b i r o t o r ae r o d y n a m i c s. T h e w or st ca s e
n
ormal stress will be approximately equal the sum of the stress due to bending
G -
I c
1)
and the stress due to axial loading
Q2 s A
2)
For a uniform circular cross-section of rad ius r, eqs. (1) and (2) may be
summed to yield
g
n
7854 r^
.1416 r^
3)
Given a working normal stress o f 50 ksi, and Table VII values for M
and P of 16900 inch
-
pounds and 2480 pounds respectively, eq. (3) may be
written in r
36
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_
_ ee^ .a
__
__
_
^
'
^
^
Table V ^Torst
Case Relative Deflection
^ .
Caee
D Gap
D Stagger
D i'wist
(inch) (inch)
(r)
17' No tie
17.6
16.7
0.004
17'
One tie 0.733
0.728
0.002
17' Two ti e
0.220
0.187
0.002
17' Nine ti e
0.200
0.050
0.001
3
14' No tie
13,6
7.3
.001
i
14' One tie
0.633
0.190
.004
^ -
^ -
. .
. -
37
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Table VI -- Worst Case Blad e Stresse s
Case
Normal Stress
Normal Stress
Bottom of Blade
leading edge
(ksi)
( i)
Baseline
61.9 ^O
17' No tie
iuv.
79.2
17' One ti e
87.1
37.7
^
17' Two ti e
81.4
32.2
17' Nine ti e
74.5
33.8
i4' No tie
7.6
11.2
14' One tie
3.2
9.2
38
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t
Table VII -- Borst Case Spacer Loads
Case
ending Moment
hear
xial
ar^ua
3
(inch-pounds)
pounds)
pounds)
inch-pounds)
plane 1 plane 2
plane 1
plane 2
17'
One tie
8300 2500
2700
31 0
1570 900
17'
I
Two tie
5900
4 6 0 0
2300
430
2480
220
17' Nine tic 10500
750
1400
100
50 0 170
14 '
One tie
110
10300
6 00
1050
2660
520
39
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r 3
- 0.01579 r - 0.43035 - 0
4)
Th e only real solu t ion t o eq. ( 4 ) is
r 0.7620 inch
It f ollows t h at t h e requ isit e sp acer h as a diamet er of rou g h ly an inch and
a half .
Dynamics
^ -
Modal analyai: wan p erf ormrd f o; t h e b aseline conf ig u rat ion and f or t h e
six birotor configurations described in previous sections.
Th a model b eh av ior f or t h e b aseline b lade is st raig h t f orward and is
summarised in Table VIII.
Modal b eh av ior f or t h e 17' b irot or conf ig u rat ions is su mmarised in
Tab le IX. Modal b eh av ior f or t h e 1 4' b irot or is not inclu ded since i t
exposes nothing new.
An examination of Tables VIII and IX illustra tes that potentia lly
sig nif icant b irot or nat u ral f requ encies are not g reat ly dif f erent f rom
orresp onding b aseline b lade n at u ral f requ encies. Dynamic st ab ilit y and
cont rol p rob lems aniqu e t o t h e b irot or concep t will not b e p resent , at least ,
based upon this preliminar y view.
Th e addit ional comp lexit y of b irot or conf ig u rat ions su g g est s rou g h ly a
dou b ling of modes of v ib rat ion wit h in t h e f requ ency b and of int erest. Rou g h ly
h alf of t h ese modes dep end st rong ly on t h e sp ecif ics of sp acer desig n, locat ion,
and end condit ions. None of t h ese f act ors were inv est i;:
,
a*.ed during the present
st u dy. Spacers, wh ere emp loyed, were assu med t o b e rig idly eonnec t ed at
individual blade centroids.
Spacers,
-
oreou er, modif y symmet ry of t h e b lade conf ig u rat ion and t end,
-
herefore. to couple in-plane bending, out
-of-plane bending, and torsion.
The impact on helicopter flight stability and eontrol of incr@axed
modal active ity and modal coupling associated with the birotor configurati on
-
eserves further study.
40
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Table VIII -- Baseline Simp le Blade Modal Activi ty
Mode
requency(Hz)
Out-c^r
-
Plane Bending
1st
.74
2
nd
0.9
3
rd
0.4
In.-Plane Bending
is
t
.85
2n d
8.8
3r d
35.5
First Torsion
9.3
41
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Table IX -- 11'
Birutor Blade Modal Activity
i
Mode
Frequency(Hz)
No-tie
One-ti e Two-ti e
Nine-tie
In-plane Bending
1 St.38
6.69
6.93
7.91
3
(6.38) (27:5)
(coupled) (coupled)
^
nd
9.7
40.4
40.9
42.2
(39.7)
(coupled) (coupled)
(coupled)
3 rd
11.0
111.2 111.3
112.8
(111.0)
(coupled)
(coupled)
(coupled)
Out-of-Plane Bendin g
1 st
.4 2
1.51
1.57
1.73
(1.42)
(6.58)
(12.5) (22.4)
`
nd
.8 5
9.08
9.27
9.70
? ^
8.85)
(19.4)
(24.3)
(53.9)
3 rd
4.7 24.9
24.9
25.3
(24.7) (36.4)
(37.7)
(75.4)
First Torsion
9.7
87.2
100.8
141.2
(69.7)
(coupled)
(coupled)
(coupled)
Items in parentheses refer
to a mods roughly
c or re sp on di ng , g e ne r al l y
with blades out-of-phase.
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--
_
i
f-
Appendix
Stress Calculations
The text, Theory and_ Analysis of Flig h t Stru ct u res, prov ides th e equat ion
^
Mzlyy -
MyIYZ
Y) -
MyIzz - Mziyz (
z
)
11
-
-
xx A
I
YY
I
z
z
- Iyz2
yyizz -Iyz2
If twist is sufficie ntly small, Iyz
a
0, and
z -
^^
6=--
xx A IZ2 IYY
where
P axial load
My : torque ab ou t an axis perp endicu lar to th e
chord intersecting the elastic axis
Mz
: torque ab ou t an axis parallel to th e ch ord
int ersect ing th e elast ic axis
and where I
yv
and I
zz
are according ly def ined.
Sample Calct lation
For the 17' birator with one tie, Table IV gives
Fx
= P 64000 pounds
TY= M
y
127000 inch-pounds
T
z
=
t
z
= 74600 inch-pounds
Table II gives
Area = A = 3.19 inch2
I
yy
= 19.06 in ch4
I
0.941 inch4
zz
^2)
43
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^
On the bottom of the blade
y
1.4 4 i n c h ( 1.44
12 x 14.10/2),
P
z
a
0, and
^
a
64000 +
4600(1.44)
xx
.19941
Q = 87:1 ksi
_
x
^
t the leading edge of the blade of
y
, and z 2.65 inches (
.
188 x 14.10),
^
nd
= 64000 + 127000( 2.65)
6xx
.19
9.06
6 = 37.7 ksi
xx
s
e
i
4 +
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^P^_.
EFERENCES
1 .
enadovit ch, M., Recherches sur les Cellules Biplane Rig ides d'Enverqure
Tnf
ine, Publications Scientifiques et Techniques du Minister de L'Air,
Tnstitut Aerotechnique de Saint-Cyr, Paris, 1936.
_
.
ai, P. and Gray, R. B., Computat ion of Two-Dimens ional Potentia l Flow
Using Elementary Vortex Distribution, Journal of Aircraft, Vol. 15,
=
ctober 1978, pp. 698-700.
3.,4.
reule r, R. J., and Gregorek, G. M., An Evalua tion of Four Single Element
Air-foil Analytic Methods, General Aviation Design and Analysis Center,
The Ohio State Universit y.
S. Truckenbrodt, E., A Method of Quadrature for Calculation of the Laminar and
Turbulent Boundary Layer in Case of Plane and Rotationally Symmetric Flow,
NACA TM-1379, 1955.
i