Experimental and Analytical Studies of a Model Helicopter Rotor in

Experimental and Analytical Studies of a Model Helicopter Rotor in

USAAVRADCOM TR- 81- A- 23
NASA Technical Memorandum'81232
.
>
!NASA-Td-81222)
EXPBBIbBU1AL AUD A I A L Y T I C A L
STUDIES OF A MODEL BBLICOPTBB
(IAS-)
6 1 p HC A O 4 / f l P
iioeon
A01
11 HOVER
CSCL O l A
Unclas
63/32
08413
Experimental and Analytical Studies
of a Model Helicopter Rotor in Hover
F. X. Caradonna and C. Tung
September 1981
Nat~onalAeronautics and
Space Admlnlstrat~on
Un~tedStates Army
Aviation Research
and Development
Command
- 4 .
--
NASA Technical Memorandum 81232
USAAVRAOCOM TR-81-A-
23
Experimentaland Analytical Studies
of a Model Helicopter Rotor in Hover
F. X. Caradonna
C. Tung, Aeromechanics Laboratory
AVRADCOM Research and Technology Laboratories
A~nesResearch Center, Moffett Field, California
1Jn1IedStates Army
Aviallon Research and
Development Command
St LOUIS.Mlssour~63166
EXPERIMENTAL AND ANALYTICAL STUDIBS OF A XODBL HELICOPTER ROTOR IN HOVER
F. X. Caradonna and C. Tung
Aeromechanics Laboratory
U.S. Amy Research and Technology L a b o r a t o r i e s (AVRADCOH)
The present study is a benchmark test t o a i d t h e development of v a r i o u s r o t o r
performance codes. The study involves simultaneous blade p r e s s u r e measurements and
t i p v o r t e x surveys. Measurements were made f o r a wide range of t i p Mach numbers
i n c l u d i n g t h e t r a n s o n i c flow regime. The measured t i p v o r t e x s t r e n g t h and geometry
permit ef feccive blade loading p r e d i c t i o n s when used as i n p u t t o a p r e s c r i b e d wake
l i f t i n g s u r f a c e code
I t is a l s o shown t h a t w i t h proper inflow and boundary l a y e r
modeling, t h e s u p e r c r i t i c a l flow regime may be a c c u r a t e l y predicted.
SYMBOLS
A
r a t i o of vortex c i r c u l a t i o n t o maximum blade-bound c i r c u l a t i o n
aspect r a t i o
Ck s e c t i o n a l l i f t c o e f f i c i e n t
d
r a d i a l d i s t a n c e from a v o r t e x t o a flow-f i e l d p o i n t
R
radius of t h e r o t o r blade
r
r a d i a l d i s t a n c e from t h e r o t o r c e n t e r of r o t a t i o n
Vi
vortex-induced v e l o c i t y
VR
r e s i d u a l v e l i ~ c i t yi n t h e wake
y
r/R, nondimensional r a d i a l coordinate
z
a x i a l d i s t a n c e from r o t o r
r o t a t i o n a l speed
Y
azimuthal angle measured from t h e p o i n t of b l a d e overhead passage
YV
vortex age, t h e azimuth angle, Y, when v o r t e x s t r i k e s t h e probe
*Presented a t the S i x t h European R o t o r c r a f t and Powered L i f t A i r c r a f t Forum,
September 16-19, 1980, B r i s t o l , England.
1.
INTRODUCTION
The p a s t two decades have s e e n a c o n t i n u i n g development of methods t o p r e d i c t
r o t o r hover performance w i t h i n c r e a s i n g accuracy. These methods i n c l u d e l i f t i n g l i n e
( r e f s . 1-3), l i f t i n g s u r f a c e ( r e f s . 4-6). and f i n i t e d i f f e r e n c e ( r e f . 7) methods.
P r a c t i c a l l y speaking, none of t h e s e methods is s e l f - c o n t a i n e d ; t h e y a l l r e q u i r e t h e
s p e c i f i c a t i o n o f e m p i r i c a l l y o b t a i n e d wake d a t a ( s t r e n g t h and geometry) i n o r d e r t o
have a c o r r e c t downwash d i s t r i b u t i o n . I n e v i t a b l y , t h e development o f t h e s e codes
becomes a t u n i n g p r o c e s s i n which i t is determined j u s t how d e t a i l e d and a c c u r a t e a
wake d e s c r i p t i o n must be. T h i s s t a g e of code development p l a c e s g r e a t r e l i a n c e on
t h e a v a i l a b l e body of experimental r o t o r d a t a .
The a v a i l a b l e r o t o r d a t a i n c l u d e a s i z e a b l e number o f tests where d e t a i l e d b l a d e
l o a d i n g i s o b t a i n e d u s i n g s u r f a c e p r e s s u r e t r a n s d u c e r s ( r e f s 8-1 1) , and mre r e c e n t l y
by laser d o p p l e r v e l o c i m e t r y ( r e f s . 12-14).
There is a l s o a number of tests i n which
t h e r o t o r wake geometry i s d e f i n e d by flow v i s u a l i z a t i o n t e c h n i q u e s ( r e f s . 3 and 5)
f o r a wide v a r i e t y of b l a d e c o n f i g u r a t i o n s . Of t h e v a r i o u s wake s t u d i e s , o n l y
Boatwright ( r e f . 15) and Cook ( r e f . 16) made d e t a i l e d i n v e s t i g a t i o n s of t h e wake flow
s t r u c t u r e s . Cook's work is e s p e c i a l l y s i g n i f i c a n t i n t h a t he was a b l e t o measure t h e
s t r e n g t h of t h e t i p v o r t e x by a c u r v e - f i t t i n g t e c h n i q u e u s i n g hot-wire d a t a . However,
t h e r e seem t o be no u s e a b l e d a t a i n t h e l i t e r a t u r e i n which simultaneous b l a d e load
d i s t r i b u t i o n and wake measurements a r e made.
.
I t i s t h e ~ n t e n t i o nof t h e p r e s e n t s t u d y t o h e l p f i l l t h i s gap i n tile l i t e r a t u r e .
T h i s paper w i l l d e s c r i b e t h e experimental set-up i n which s t e a d y b l a d e p r e s s u r e s were
obtained using hub-mounted t r a n s d u c e r s and t i p v o r t i c e s were measured u s i n g Cook's
technique. The d a t a o b t a i n e d a r e f o r u n s t a l l e d flow ranging from t h e low s u b s o n i c t o
t r a n s o n i c c o n d i t i o n s . I t is shown h e r e i n t h a t t h e measured wake geometry d i f f e r s
s i g n i f i c a n t l y from p r c v i o u s l y published low-aspect-ratio d a t a ( r e f . 5). T h i s d i f f e r ence i s r e f l e c t e d i n a n i n a b i l i t y t o c o r r e c t l y p r e d i c t t h e measured b l a d e l o a d i n g
( u s i n g Summa's p r e s c r i b e d waki? l i f t i n g s u r f a c e code ( r e f . 6 ) ) when t h i s c l a s s i c a l wake
geometry is used.
2.
THE EXPERIMENT
The d a t a p r e s e n t e d i n t h i s paper were gathered i n t h e Army Aeromechanics Laborat o r y ' s hover t e s t f a c i l i t y , a l a r g e chamber w i t h s p e c i a l d u c t i n g designed t o e l i m i n a t e
room r e c i r c a l a t i o n . The r o t o r , s i t u a t e d i n t h e c e n t e r of t h e chamber, w a s mounted on
a t a l l column c o n t a i n i n g t h e d r i v e s h a f t ( f i g . 1 ) . The r o t o r employed two c a n t i l e v e r mounted, nlanually a d j u s t a b l e b l a d e s w i t h h a l f d e g r e e precone. These b l a d e s used a n
NXCA 0012 p r o f i l e and were untwisted and untapered. An a s p e c t r a t i o of 6 was chosen
i n o r d e r t o maximize Reynolds Number and a v a i l a b l e i n s t r u m e n t a t i o n space. The b l a d e s
were grooved t o accommodate 60 p r e s s u r e t u b e s each. These t u b e s connect t o a s p e c i a l
c l u s t e r of t h r e e 4888 Scanivalves ( u s i n g Statham PA 856-15 t r a n s d u c e r s ) d r i v e n by one
SS5-48 s o l e n o i d d r i v e mounted i n t h e r o t o r hub. T h i s arrangement p e r m i t s an ample
number of p o r t s f o r f i v e measurement l o c a t i o n s - t h r e e r a d i a l l o c a t i o n s on each b l a d e ,
with one l o c a t i o n b e i n g i d e n t i c a l on b o t h b l a d e s f o r comparison purposes. The
Scanivalve s t e p p e r motor was a c t u a t e d by a d i g i t a l d a t a system which acquired t h e
d a t a , computed t h e c e n t r i f u g a l p r e s s u r e d r o p s , and d i s p l a y e d t h e f i n a l p r e s s u r e
d i s t r i b i i t i o n . A f t e r manually a d j u s t i n g t h e two b l a d e s , t h e p r e s s u r e d a t a was a l s o
used t o check t h e e q u a l i t y of l o a d i n g s . The p r e s s u r e d a t a a t t h e 0.8 R r a d i a l s t a t i o n
a r e compared f o r t h e two b l a d e s i n f i g u r e 2. No s i g n i f i c a n t d i f f e r e n c e s i n t h e
..
.
,
loadings were seen f o r any o p e r a t i n g conditions. ( ~ d d i t i o m li n d i c a t i o n of this
loading e q u a l i t y is t h a t no c o n s i s t e n t d i f f e r e n c e i n t h e hro shed v o r t i c e s was
found.) The r e s u l t i n g pressure d i s t r i b u t i o n s f o r c o l l e c t i v e p i t c h r e t t i q p of So,
8'. and 12' a r e shown i n f i g u r e s 3, 4, and 5. These and o t h e r p r e s s u r e d i s t r i b u t i o n s
a r e tabulated i n appendix A. It is seen i n f i g u r e s 3, 4, and 5 t h a t t h e inboard
pressure d i s t r i b u t i o n s a r e only s l i g h t l y a f f e c t e d by r o t o r speed. However, t h e
outboard s e c t i o n s show conside:.lble p r e s s u r e a l . t e r a t i o n and shock development as t h e
t i p Mach number approaches near s o n i c values. O v e r a l l , however, t h e spanwise load
d i s t r i b u t i o n (obtained by p r e s s u r e i n t e g r a t i o n ) is ranarkably l i t t l e a f f e c t e d by t i p
Mach number ( f i g . 6 ) . I n a d d i t i o n , t h e t i p preesures were compared w i t h those of
reference 11 and a r e seen i n f i g u r e 7 t o b e n e a r l y i d e n t i c a l .
Wake d a t a were acquired w i t h a traverse-mounted DISA SSP01 hot-wire probe mounted
beneath t h e r o t o r . The probe was o r i e n t e d with the wire being tangent t o t h e r o t o r
t i p path. This permits measurement of t h e magnitude of t h e v o r t e x induced v e l o c i t y
when the remainder of the r o t o r downwash is properly accounted f o r . I t a l s o
excluded t h e e f f e c t of a x i a l v e l o c i t y on t h e induced v e l o c i t y measurement. Dzta from
the wire a r e acquired a t v a r i o u s p o i n t s along t h e t i p v o r t e x t r a j e c t o r i e s and can give
bcth the t i p vortex geometry and s t r e n g t h . One problem w i t h t h i s approach is t h a t t h e
vr --tex t r a j e c t o r y is not steady and t h e probe l o c a t i o n (which is chosen by an on-thespot d e c i s i o n a s t o where the number of v o r t e x core " h i t s " is maximized) c o n t a i n s some
a s yet undetermined e r r o r . The r e s u l t i n g d a t a stream has considerable v a r i a b i l i t y .
However, i n o r d e r t o be c e r t a i n of t h e vortex l o c a t i o n , t h e only acceptable d a t a a r e
chose where t h e v o r t e x core a c t u a l l y h i t s the prcbe. I n t h e d i g i t i z a t i o n process
(done o f f - l i n e a t a reduced tape speed), t h e above-mentioned d a t a system was coded t o
look f o r and accept only those d a t a which showed t h e c h a r a c t e r i s t i c s i g n a l d i p
(wherein the m i r ~ i m u mv e l o c i t y i s very c l o s e t o the vortex t r a n s l a t i o n speed) which
i n d i c a t e s a probe-vortex s t r i k e . This titrns out t o be a very small percentage of t h e
t o t a l mount of d a t a a c t u a l l y recorded. A t y p i c a l hot-wire t r a c e d i s p l a y i n g t h e
above-mentioned v a r i a b i l i t y i s shown i n f i g u r e 8.
3.
HOT WIRE DATA ANALYSIS
The idea of t h e c u r r e n t d a t a a n a l y s i s i s t h a t a t i p v o r t e x should look l i k e an
i n f i n i t e l i n e vortex t o a s u f f i c i e n t l y c l o s e probe. Unfortunatly, t h e probe meas u r c s not only t h e v e l o c i t y induced by the v o r t e x a t hand, V i , but a l s o t h a t induced
by thc blade and the remainder of t h e wake system a s w e l l , VR. The problem i n analyzi n g the probe d a t a i s , then, how t o s e p a r a t e t h i s r e s i d u a l v e l o c i t y , VR, from the
immediate vortcx-induced v e l o c i t y , Vi.
Cook ( r e f . 16) handled t h i s problem by assumi n g t h a t the r e s i d u a l v e l o c i t y was constant and given by t h e t r a n s l a t i o n v e l o c i t y of
t h e t i p vortex. Ht! then was a b l e t o find t h e v o r t e x s t r e n g t h by a f i t t i n g process.
This s t r e n g t h was found t o be f a r l e s s than t h e computed maximum blade bound c i r c u l a t i o n of the s i n g l e , f u l l - s c a l e blade used i n t h a t t e s t . I t was a l s o found t h a t t h e
v o r t i c e s measured were d i s t i n c t l y n o n c l a s s i c a l i n t h a t they contained a l a r g e rotat i o n a l region o u t s i d e of the viscnus core. In what follows, we s h a l l use a process
very s i m i l a r to Cook's i n analyzing wake d a t a .
F i r s t consideration i s given t o t h e v o r t e x t r a j e c t o r i e s . Figure 9 shows t h e
.luial and r a d i a l components of t h e vortex t r a j e c t o r i e s f o r a p i t c h s e t t i n g of 8'.
'Chi5 f i g u r e gives d a t a f o r a wide range of r o t o r speeds, and i t i s apparent t h a t t h e
t r a j e c t o r y is e s s e n t i a l l y independent of t i p speed
even i n t o t h e t r a n s o n i c r e g h e .
Flgr~re9 together with f i g u r e 6 suggests t h a t t h e nonlinear t r a n s o n i c flow on the
b l n d c has l i t t l e e f f e c t on t h e f a r - f i e l d induced flow as long a s t h e l o c a l l i f t is
-
not g r e a t l y a l t e r e d . Also p l o t t e d on t h i s f i g u r e i s t h e v o r t e x t r a j e c t o r y given by
Kocurek's wake-fitting formula f o r r o t o r s i n f r e e a i r . Although t h e a x i a l component
of t h e t r a j e c t o r y compares w e l l with Kocurek's formula, t h e r e appears t o b e a g r e a t e r
discrepancy i n t h e c o n t r a c t i o n than can be explained by measurement e r r o r . The v o r t a x
t r a j e c t o r i e s f o r p i t c h s e t t i n g s ranging from 5 O t o 12' a r e given i n figure 10,
The present aim i n analyzing t h e r o t o r wake is only t o f i n d t h e v o r t e x s t r e n g t h
and not a complete d e s c r i p t i o n of t h e s t r u c t u r e . This s t r e n g t h w i l l be found by
f i t t i n g t h e wake d a t a t o t h e v e l o c i t i e s obtained from an a p p r o p r i a t e combination of
i n v i s c i d , two-dimensional v o r t i c e s . The v e l o c i t y from one such v o r t e x i s given by
where t h e s t r e n g t h of the v o r t e x i s described by A, t h e r a t i o of t h e v o r t e x c i r c u l a t i o n t o t h e maximum bound c i r c u l a t i o n of t h e blade. (This could be determined by t h e
pressure d a t a because t h e c i r c u l a t i o n peak i s not very s h a r p and is q u i t e c l o s e t o
the t a p l o c a t i o n . ) To accomplish t h i s f i t t i n g , i t is f i r s t necessary t o convert t h e
s p a t i a l l y dependent equation (1) i n t o a time-dependent expression, a s t h e vor ex d a t a
a r e time-based, Assuming t h a t A i s constant (which seems t o be t r u e w i t h i n reasona b l e e r r o r bounds), t h e conversion t o a time-dependent function is accomplished by
expressing d a s a function of time using t h e v o r t e x t r a j e c t o r y d a t a of f i g u r e 9.
The next s t e p i s t h e d e t e r n i n a t i o n of the r e s i d u a l v e l o c i t y , VR, which must be vect o r i a l l y added t o Vi before a comparison can be made with t h e probe d a t a . We have
done t h i s i n two d i f f e r e n t ways:
1 ) The first way t o determine V R involves very young v o r t i c e s (about 50" o l d ) .
For t h e s e i t was assumed t h a t VR was given by the v o r t e x t r a j e c t o r i e s ( f i g . 9). The
f i t t i n g process always commenced when t h e vortex core h i t t h e probe and ended when t h e
following blade passed over; t h i s assured t h e simplest p o s s i b l e flow f i e l d , a s t h e r e
would be v o r t i c e s on only one s i d e o f t h e probe and minimal i ~ f l u e n c eof v o r t e x s h e e t s
and blade bound v o r t i c i t y . Figure 11 shows some t y p i c a l con ~ r i s o n sof probe d a t a with
t h e f i t t i n g expression. This f i g u r e shows the v o r t e x velocity-time t r a c e s f o r p i t c h
s e t t i n g s of 8' and 1 2 " . I t i s seen here t h a t t h e f i t t i n g curve provides a good match
t o the d a t a o u t s i d e of the immediate core region. Furthermore, t h e vortex s t r e n g t h
is very c l o s e t o t h e maximum blade bound c i r c u l a t i o n .
2) A second means t o determine VR was required i n analyzing o l d e r v o r t i c e s
(about 210" o l d ) . The flow i s more complex i n t h i s c a s e , a s t h e probe always l i e s
between two v o r t i c e s i n the f i t t i n g region, and the expression f o r t h e vortex-induced
v e l o c i t y i s correspondingly complicated. In f a c t , V i f o r t h i s case was determined
using t h r e e v o r t i c e s - one outboard of t h e probe and two inboard. Again, t h e d a t a
were f i t f o r t h e time period between a probe-vortex s t r i k e and the subsequent blade
passage. It was found t h a t with VR determined by the v o r t e x t r a j e c t o r y d a t a , i t was
trot p o s s i b l e t o o b t a i n a good f i t of t h e c l a s s i c a l v o r t e x expression t o t t ~ ewake d a t a .
Instead, w e found t h a t a b e t t e r value f o r VR was found by w e of t h e minimum mebsured v e l o c i t y between two v o r t i c e s . A t t h i s p o i n t , t h e vortex-induced v e l o c i t y is
:.mall, but not zero (due t o the d i f f e r i n g instantaneous t r a n s l a t i o n v e l o c i t i e s of t h e
t h r e e v o r t i c e s ) . The minimal induced v e l o c i t y i s c a l c u l a t e d (assuming some value of
A) and s u b t r a c t e d flom t h e minimum measured i n t e r v o r t e x v e l o c i t y t o o b t a i n 1 ' ~ . This
t a s k was rendcred q u i t e simple by t h e f a c t t h a t the r a d i a l component of t h e s e veloci t i e s t u r n s out t o be very small ( t h i s was checked by c a l c u l a t i o n s and measurements
with a second probe). Since t h e two methods above do not give t h e same value f o r t h e
r e s i d u a l v e l o c i t y , i t is c l e a r t h a t VR i s not a constant i n t h i s case. We assume,
w
,.
.\
however, t h a t i t changes s u f f i c i e n t l y slowly t o render t h e f i t t i n g proceee meaningf u l . I n f a c t , t h e r e s u l t s thus obtained a r e c o n e i s t e n t w i t h t h e young v o r t e x d a t a .
Figure 12 shows some t y p i c a l comparisons of t h e o l d e r v o r t e x d a t a w i t h t h e f i t t i n g
expressions. T h i s f i g u r e shows t h e f i t t i n g s f o r p i t c h s e t t i n g s of S o , 8'. and 12'.
It is seen t h a t t h e 8' and 12' cases show v o r t e x s t r e n g t h s which match t h e maximum
blade-bound v o r t i c i t y very w e l l . A t 5' p i t c h , however, t h e s t r e n g t h is seen t o b e
considerably smaller.
It seems from t h e above d a t a , which a r e taken at a low r o t o r speed, t h a t t h e t i p
Although
v o r t e x develops i t s f u l l s t r e n g t h very e a r l y i n l i f e (mainly b e f o r e 50').
t h e r e is a f a i r amount of v a r i a b i l i t y between vortices, it is r a t h e r s t r i k l n g t h a t
very many v o r t i c e s c l o s e l y approach a c l a s s i c a l Rankine v o r t e x i n appearance. Furthermore, t h e v o r t i c e s (except f o r t h e So c a s e ) seem t o c o n t a i n a l l of t h e blade
c i r c u l a t i o n . This v o r t e x s t r e n g t h and s t r u c t u r e d i f f e r s markedly from t h e r e s u l t
obtained by Cook and probably r e f l e c t s t h e considerable d i f f e r e n c e s i n b l a d e geome t r i e s . A s r o t o r t i p speed i n c r e a s e s ( f i g . 13). however, t h e r e appears t o be an
i n c r e a s i n g d e p a r t u r e from t h e Rankine v o r t e x appearance. Nevertheless, t h e nondimens i o n a l v o r t e x s t r e n g t h seems unaffected by t i p speed.
4.
COMPARISON OF THEORY AND EXPERIMENT
I n order t o i n t e g r a t e t h e present wake and loading d a t a i n t o a b e l i e v a b l e whole,
e have
i t i s necessary t o be a b l e t o reproduce t h e blade loading computationally. W
chosen t o do t h i s u s i n g A.M. I. ' s l i f t i n g s u r f a c z code ( r e f . 6 ) . T h i s i s a very
f l e x i b l e , compressible, l i f t i n g s u r f a c e code which can handle e i t h e r prescribed o r
f r e e wakes.
I n i t i a l e f f o r t s t o compute t h e b l a d e loading were done u s i n g t h e Kocurek wake
geometry ( r e f . 5 ) . The r e s u l t i n g computed t h r u s t c o e f f i c i e n t was t o o high by about
20%. The next s t e p was t o compute t h e loading u s i n g t h e measured v o r t e x l o c a t i o n s and
s t r e n g t h . Figure 14 shows a comparison of t h e measured and computed loading using t h e
measured v o r t e x parameters f o r a c o l l e c t i v e p i t c h of 8' ( t h e t r a j e c t o r y is given by
f i g . 9 and we choose A = 1.0). The comparison is now considerably improved and t h e
t h r u s t c o e f f i c i e n t i s overpredicted by l e s s than 5%. I n view of t h e previously mentioned u n c e r t a i n t i e s i n t h e v o r t e x t r a j e c t o r y measurements, t h e s e computations were
a l s o performed with t h e e n t i r e v o r t e x t r a j e c t o r y perturbed such t h a t a t Y = 180°,
the a x i a l and r a d i a l p e r t u r b a t i o n s were t0.025 R. The r e s u l t s derived from a l l
p o s s i b l e conbinations of t h e s e a x i a l and r a d i a l changes f i l l t h e shaded a r e a i n
f i g u r e 14. That t h e above measured and computed r e s u l t s a r e roughly centered on t h i s
shaded region i n d i c a t e s t h a t f o r t h i s c a s e t h e measured t r a j e c t o r i e s a r e f a i r l y accur a t e . However, t h e b e s t comparison w i t h t h e measured loading occurs when t h e v o r t e x
r a d i a l l o c a t i o n ( a t Y = 180') is increased ( t h a t i s , t h e c o n t r a c t i o n is decreased)
by 0.025 R. The i d e n t i c a l s i t u a t i o n was found t o occur i n computations of t h e 12"
p i t c h cases; t h a t i s , t h e b e s t comparison occurred when t h e r a d i a l v o r t e x l o c a t i o n
was increased by 0.025 R over t h e measured value ( f i g . 15). For t h e 5' c o l l e c t i v e p i t c h c a s e , t h e s i t u a t i o n was a l i t t l e d i f f e r e n t i n t h a t a reasonable comparison of
computation and loading d a t a could not be made u n t i l t h e v o r t e x s t r e n g t h was reduced
t3 A = 0.75.
I n t h i s c a s e , t h e v o r t i c i t y which would otherwise have been i n t h e t i p
vortex was now included i n t h e v o r t e x s h e e t model. (For a complete d e s c r i p t i o c )f
the assumed v o r t e x sheet model s e e r e f . 6.) T h i s r e s u l t is c o n s i s t e n t with t h e measured v o r t e x s t r e n g t h and g i v e s t h e comparison shown i n f i g u r e 16.
f
The previous comparisons have been made a t low t i p dach numberr. The l i f t i n g
s u r f a c e code used should be a p p l i c a b l e t o p r e d i c t t h e e p a a s i e e m d chordwira l o a d i n 8
up t o t h e o n s e t of s u p e r c r i t i c a l flair. Beyond t h i r p o i n t , l i n e a r a e r o d p n r r i c r are
not a p p l i c a b l e on t h e blade and a more complete flow d e s c r i p t i o n is r e q u i t e d . AD a
preliminary e v a l u a t i o n of t h e high-rpeed flow d a t a , two-dimensional computations were
made of t h e flow a t t h e 80%r a d i a l s t a t i o n . This was done w i n g H o l e t ' s f u l l - p o t e n t i a l
code ( r e f . 17). I n o r d e r t o perform t h i s computation, an a n g l e of a t t a c l r i a required.
Since t h e region of supersonic flow is l o c a l i t e d ( i . e . , l i m i t e d t o t h e i a n e d i a t e
v i c i n i t y of t h e upper blade s u r f a c e ) , i t should be p o s s i b l e t o f i n d t h e awle o f a t t a c k
u s i n g t h e l i n e a r l i f t i n g s u r f a c e code. Of course, the l i f t i n g s u r f a c e code require.
t h e measured v o r t e x l o c a t i o n and s t r e n g t h as awntioned previously. With t h e a n g l e of
a t t a c k obtained thereby, t h e Holst code produced t h e r e e u l t s shown i n f i g u r e 17. T h i s
f i g u r e shows two ccmputed r e s u l t s - an i n v i a c i d r e s u l t and one w i t h a v i s c o u s rampboundary l a y e r model ( r e f . 18). It i s seen t h a t a shock-boundary l a y e r i n t e r a c t i o n
model is very necessary and i n t h i s c a s e very e f f e c t i v e .
5.
CONCLUDING REMARKS
The present study was intended a s a benchmark t o a i d i n t h e development of hasrrr
performance codes. The g o a l was eo o b t a i n s i m l t a n e o u s measurements of blade loail
d i s t r i b u t i o n and t i p vortex geometry and s t r e n g t h u s i n g f a i r l y standard techniqries.
I n s p i t e of some u n c e r t a i n t i e s (due mainly t o wake unsteadiness), l i f t i n g s u r f a c e
computations show t h a t t h e p r e s e n t measured loads and wake measurements are generally
consiscent w i t h each o t h e r .
The main conclusions from t h j s study a r e :
1. The Cook vortex measurement technique seems t o be q u i t e e f f v c t l v e Ic7r t w bladed r o t o r s .
2 . A t low r o t o r speeds, an untwisted, untapered, double-blade4 rot:~l;-prcriuces
t i p v o r t i c e s which can c l o s e l y resemble a c l a s s i c a f . Rankine vortex. % s c r t ~ i~oi r t h e
~ U D bound
lowest p i t c h s e t t i n g s , t h i s v o r t e x s t r e n g t h c l o s e l y approaches t h e ; I I P T ~ ~blade
c i r c u l a t i o n . A t higher ti; speeds, t h e i n n e r v o r t e x s t r u c t u r e appear? ?r:creasingly
n o n c l a s s i c a l ; however, t h e s t r e n g t h i s u n a l t e r e d .
3. I t is not p o s s i b l e t o p r e d i c t t h e blade-spanwise-load d?..itr' i6:.t:.f~n without
accurate vortex l o c a t i o n and s t r e n g t h d a t a . The present meaaurA v o l i , ( u l o c ~ t i o n
d a t a were s i g n i f i c a n t l y d i f f e r e n t ( f o r p r e s e n t l y unknown re.ss<iru+
:rorLtbc~r'li;ssical
d a t a i n the l i t e r a t u r e . However, t h e s e measurements were sr..o?a:;ei?s;S',e io obtaining
a reasonable comparison of theor- and experiment.
4 . For t h e present r o t o r
found t o have no e f f e c t on t h e
t o r i e s . The chordwise loading
only be simulated by nonlinear
l a y e r interaction model.
and speed range t e s t e d , r :e Q R S ~ : ' o f i'ar.do LC LOW was
spanwise loading d i s t r burio:: jrld rlw vc., t;lx crrrjecis profoundly a l t e r e d t y elit7 C Y ~ ; :: ' -7.' and can
aerodynamic techniya*:.a uhf: ,' = * ? , ! v s, ,;~oc.kboundary
.
% .
+
I_
ACKNOWLEDGMENTS
This work represents the contributions of many excellent people. We would like
to extend our thanks to W. D. Vann (Ft. Eustis Directorate, U.S. Army Applied Technology Laboratory) and H. Jones (U.S. Army Research and Technoloey Laboratories) who
were instrumental in initiating our computational studies. Special acknowledgment is
due to Georgene Laub who tirelessly and ably assisted in the running of the test.
Thanks also to M. Summa (Applied Mechanics, Inc.) who wrote the lifting surface code
i,ind assisted us in running it; S. C. Lee (University of Missouri) and T. L. Holst
i h e s Research Center) who provided us with the finite difference computations.
REFERENCES
1.
Crimi, P.: Theoretical Prediction of the Flow in the Wake of a Hovering Rotor.
CAI. Report No. BI-1994-S-1 and No. BB-19944-2, Cornell Aeronautical Laboratory, Inc., Buffalo, N. Y., Sept. 1965.
2.
Landgrebe, A. J.: An Analytical and Experimental Investigation of Helicopter
Rotor Hover Performance and Wake Geometry Characteristics. USAAMRDL Technical
Report 71-24, Eustis Directorate, U.S. Army Air Mobility Research and Development Laboratory, Fort Eustis, Va., June 1971.
3.
Landgrebe, A. J. ; Moffett, R. ; and Clark, D.: Aerodynamics Technology for
Advanced Rotorcraft, Part 1. J. American Helicopter Soc., vol. 22, no. 2,
Apr. 1977.
4.
Johnson, W.: A Lifting Surface Solution for Vortex I~ducedAirloads and Its
Application to Rotary Wing Airloads Calculations. Massachusetts Institute
of Technology, Aeroelastic and Structures Research Laboratory, TR 153-2,
Apr. 1970.
5.
Kocurek, J. D.; and Tangler, J. L.: A Prescribed Wake Lifting Surface Hover
Performhnce Analysis. Presented at the 32nd Annusl National Forum of the
American Helicopter Society, preprint 1001, May 1976.
6. Summa, J. M.; and Clark, D. R.: A Lifting-Surface Method for Hover/Climb Loads.
Presented at the 35th Annual F o r m of the American Helicopter Society,
Washington, D. C., preprint 79-1, May 1979.
7.
Caradonna, F. X . : The Transonic Flow on a Helicopter Rotor.
Stanford U., Stanford, Calif., March 1978.
Ph.D. Thesis,
8. Rabbott, J. P., Jr.: Static-Thrust Measurements of the Aerodynamic Loading on
a Helicopter Rotor Blade. NACA TN 3688, Langley Aeronautical Laboratory,
National Advisory Committee for Aeronautics, Langley Field, Va., Feb. 1956.
9. Scheiman, J.; and Kelley, H. L. : Comparison of Flight-Measured Helicopter
Rotor-Blade Chordwise Pressure Distributions with Static Two-Dimensional
Airfoil Characteristics. NASA TN D-3936, 1967,
10. Brotherhood, P.; and Young, C.: The Heaeurement and Interpretation of Rotor
Blade Pressures and Loads on a Puma Helicopter in Flight. Pferented at the
Fifth European Rotorcraft and Powered Lift Mrcraft F o M ~ , Amtardam,
The Netherlands, Sept, 1979.
K, R,; and 8-r,
H. L.: Surfbca Preerure
11, Gray, R. B.; McHahon, H. M.; Sh.noyr
Measurements at Two Tipe of a Model Helicopter Rotor in Hover. NASA CP-3281,
May 1980.
12.
Sullivan, J. P.: Experimental Investigation of Vortex Ringe and Helicopter Rotor
Wakes Using a Laser Doppler Velocimeter. D. S, Diaeertation, Massachusetts
Institute of Technology, June 1973.
13.
Bsllard, J. D.; Orloff, K. L.; and Luebs, A. B.: Effect of Tip Shape on Blade
Loading Characteristics. Presented at the 35th Annual N~tionalForum of the
American Helicopter Society, Washington, D. C., preprint 79-1, May 1979.
14. Landgrebe, A. J.; and Johnson, B. V.: Mearurements of Model Helicopter Rotor
Flow Velocities with a Laser Doppler Velocimeter. Tech. Note, J. American
Helicopter Soc., vol. 19, no. 2, July 1974.
15.
Boatwright. D. W.: Measurement of Velocity Component in the Wake of a Full Scale
Helicopter Rotor in Hover. USAAMRDL TR 72-33, Aug. 1972.
16.
Cook, C. V.:
17.
Holst, T. L.: A Fast, Conservative Algorithm for Solving the Transonic FullPotential Equation. AIAA Paper 79-1456, July 1979.
The Structure of Rotor Blade Tip Vortex.
AGARD CP-111, Sept, 1972.
18. Lee, S. C.: Effect of Turbulent Roundary Layer on Transonic Flows.
Report, NASA Interchange Number NCA24R450-001, Aug. 1979.
Preliminary
..........-..-...
---
ORIGINAL PAGE IS
OF POOR QUAtITY
:1 I
0
a
WWWLuWWWWWWuJWWWWW
*hQbOP.NP7qPFJb739h>m
* N h h O b 7 M s * * m 0 0 h a ' *
eoh~a3-0mw.r-(o.r-wa,n.o
w-Ml9t'JI'Jf9rlNMd-W~mm
*
4
0
w 0 0 0 0 0 - - ~
0 C C C 0 0 0 0 0
.
I
LI
+++++
I
I I I
WWWWWWWWW
m*mb.-lO-O.b7*Cbb 3 m P , b > L - C
m h b - o m r - . m a
dCJmMi'Jr.hd*
........
I '.
0 0 0 ~ ~ 0 0 0 0 0
I
.'
................
O O O O O C O O O O O O O O O O O O
Irl..,...........
.
0 0 ' 0 ' 6 0 i? n
?
0
ago*:
0 0 0 0 0 0 0
"'!
+ + + + + + I
WWWWWWW
rQb>hr-'che 0
I r r m a 0 s ~ 0 . r r
.
.
0
1
00000'
, + + + I
WWWWW
m-mm*
a - w r ~ h
< .....
*)*(Yrccc
hcncu-n
ooooa
"'
-cn..
8
d
--.
*d
r
\
&
8 0P+ 0:+O0+0O+0O+08+001+0. rI0r10(
d wwwwwwwww
3 ~ 0 C O O Q 0 0 0 O C O O ~ *
O d O O O O O Q O O O O O O O O
1 I
++++++++++*+++
wwwwwwwwwwwwwwww
n c
P
0+
* F
d e n m o 9 b > m
P ~ M Q M
.0b3VOh-hM
J ~ ? Q I P I ~ P
~ i m m m b 7 m ~ ~ ~ ~ ~ ~ c
de.W3no
~ N P ~ N ~ ~ ~ - ?
G
............
+
U
l4
*
q
0
=,
#
u
................
0 0 0 0 Q 0 0 0 0 0 0 0 0 0 0 0
O h g . t c b d M 7 M
o o n r d m y , p y ?
! + + + + + + + + + + + + + + I l l
UJWuJWWUWWWWWWUJWWwWW
r
4
r
~
~
~
?
aN O
t ~ oO
.
dP.CJCIb>F4rrPId.10.-O.f
l>O--OS
b P m M l 1 3 b 3 P * S t v O t r . a 4 h b D h
W M K t P P q P P t 9 M m N N H d h W .
.
.
.
.
.
.
.
.
.
.
.
.
I
.
.
.
++++++. I I
q W
WWWWLUWWW
0
~
I
~C D ~~I
~ .o
O )~
P F I S~
~PIW
f
b7.Oh1.rOOW0.d
FI
MD.RO-4PIO.O
1 . r r ( ~ I r ) ( U ~ O D C J ~0
< .........
.
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
.
'
d W q - e O M P ~ S O L t 7 N h N b 7 m O h
O O O O r c l - r ~ ~ C I m M ~ P L n 9 h O D C D
M
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
...................
)
0
dOPODC'rhChD.0
0 0 - ( v Q V ) 9 b 6
0 0 0 0 0 0 0 0 0
~
+ + - + + + + - I - +
I +
I
+ + +
I
I
W
+
H
O
C
J
V
~
O
O
~
~
O
D
~ . r ~ . - ~ ~ c n c ~ rr .\ r.hr r 1 1 . r m - ~ n m a
I
::
w
3
O d q h e - m P . 4~3b-ICJCOb390
a o 0 0 e - - r ~ r t n n + m r o b a
l4
\
-
-
C
O
O
O
~
-
~
C.1 C QJ P 0
rC,
P
~ 49hCJPChrJ9F.
W * U D H ~ C J O . O M
-OODMqP,M-c,-
.........
OI=,OOO~>OOO
O
~
r)
w
-2
o
I
.................
oooooooo*oooooooo
2
- C 4 - - r c r Q ~ P C
G o ~ . 4 ~ I m b - J b *
.........
000,00,00
-
N
<
$ O C t . O C ~ O 5 C T O . - L O U O @ - 00Ci.30
I
:.
--+-+++*+++++
?
W W W ~ W W W W ~
0
I
w
+
b
. .
d
J
&
n.
- 0
~ I
~
z
I
a
)P
~
.................
~ o o ~ o o o o o o o ~ o o o o o
bl
::
C
N .
c,
. .
-. . . . . . . . . .
o ~ o o o o o o o ~ o ~ o ~ o + -
"5:.0
w
~
O
u
I.
~
0
0 0 0 0 0 0 0 C 0
I
I
1
0.
3
I
1 . r 3 0 ~ 2 ~ 0 0 ~ 0 ~ ~ 0 ~ 3 ~C . o. oI 0dC ~ - - @
oI C O O O C Q ? O G
C 3 Q 3 0 0 0 0 0 0 0 6 0 0 0 0 0 0
+ I
n
,
ooo,eoeoo
U
n
Irl
e
Q
- ......
3NhCUWSmo.m0.-?0***0
0 0 0 - ~ ~ t v N m m * M S - a h *
- .-
X
.........
0 0 3 0 0 0 0 0 C ,
I
1
. . . .
\
d
-CL..ISPC.)P~DCT
S
Oc ~ o r r o . ( ~ - r 2
o ( *u ~
T
OL7dOP16-4P
hC.lMPIC.(MMF-Pd
b
0 0 0 0 0 0 0 0 0 0 0 0 0 ~ @ ~
-
8
C
=
q
d
w
\
LC
+++++++
I
~ ~ W W W
0
b7 CI 9
r ~ ~ r . ~ . - ~ r - ~ * ~ m n ~ . o n n 8
(OP?OPnOh9CD0C4h(uW
C J P I P P ~ ~ ~ P J ~ ~ P I H - S
UIWWWWWWLL
3.
& C F - - O Q ) C h *i
oc
I ~ ~ ~ O C , Q I F , P I ~
rn
131F)*LFIOWO.o
u > r ~ m n r n c ~ - *
C O O O C ~ C O 0 0 0 0 0 0 0
0 0 U 0 0 3 0 d
I
ri
.O ?I P 9
C+
C'l Q
':' l CO
............-.
~ - ~ s o n e - n ~ n ~ . ~
O O ~ H - N N ~ ~ P I I > . O ~ O )
..............
O O O O O O O O O O O O O C
C,
w
~
-
n
o
........
0
.. . . . . . . .
a
O~-.QDOQD~P\O.
O O ~ I Y M I r ~ L ~ h
f30000000
3 C O O a .
- 0 O C O S - 4
vl
0 0 C O O e h C J O O ~ S O O I
3 3 C 3 0 0 C
"?
++++++
l
W W W W W L ~ W
0;)nc)bjo-u
e a t o r . u o m
OhpIb-~FIPr"lh
4rIWV1fl1.rW
o
4
."....
I
+
&
OOCOc'OO
OCOC#O
+ + + + I
w w w w w
c* " 2M Ze 9E
.....
0
z
Y
d W C d d W
0
OOOClO
B
1
2
O ~ ~ I S ~ D P )
Q0LF)O.Y)
U GC~CICO
0.r..
l4
QO..(tv190D
. * * * . . .
0000000
00000
,
14
0
J
11
~
.
a
0:
0
8
a
.%
(1
Q
-
~ 0 0 0 0 0 0 0 3 C 0 0 0 0 * ~
C O O C O O O r ( *
0 0 0 0 0 0 0 0 0 0 r 00000
+ + + + + + + + + + - r + - r +
I I
W W W W W W W W W W W W W W W W
0 W W W W W a W W W
V J W + ~ ~ P J ~ ~ W ~ T O & W ~ I I ~ O m m ~ 1 n - r ~ a ~ ~ o n ~ n ~ 8o n ~
O9d9b-JdOOhmdD.VJOMC(
I'JldO-OctYIO
- ~ Y I ~ W ~ M M N N ~ ~ - I * h h?
l*lr)hl-1-19d
\I *
0
C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~
0
? zzrz:r:tP,..
a
* . . . * . * * . , * . . * .
:::g:z:%.
.
.
I
m
W
* - * * . * * * *
000000000
I
I'
0 ~ 3 b m 1 n ~ r n ~ m 0 - ~ 0 - @ - 9 o
CIOOW.-*CyCIMVJ*n9*ho
. . - . . * * * * * . - * * * *
0000000000000000
.
.
*
OhS-rD.rrn*Y)
0 0 ~ N ~ n O
h
r r r r r r . . ,
0 0 0 0 0 0 0 0 ~
- .
..- . . * . . .
. * . . * . . . . * * . . * . * *
.
<
..
*
.
*
.
*
*
*
*
I
.
.
0000000000000
000000
+ + A + +
I
12
m
.
Ill
0
3 ~ e 0 0 0 0 0 0 0 0 3 S 0 0 + 0 0 0 3 0 0 0 0 0 ~
0 0 0 0 0 C O
+ 1
1 I
W W W W W W U W W W W W W W W W W
r t t > - 9 ~ . ( ~ 1 0
P . ~ - ~ I - ( V L O Q J Q D
r v C N 0 0 h b ' ? b ? O h c n ~ r h N
\-4b>P>hCOCb S m
b > e 1 0 @>P
1
++++. +++ +++++
*
8
.................
b > d b > t b > b > b W t r n m m \ Y N - h *
3 0 0 3 0 6 3 3 @ 0 0 0 0 0 0 0 0
I
"?
Q
I
11
).I
- 0 Q C C C . 0 0 C 0 0 0 3
+ + + + . * + I
w w w w w w w
9 U N b - J 9 - *
...RFh
r.C,(il
....-..
OhfiIb-W.1lW
-4MWrnP4-)..)
~ 3 0 0 C 3 0 C .
I
2
@rnCVOh(cM
O. .Qo -. N
. .' .C 9 m
0 9 0 0 0 3 0
L
l
w w w w w w w w w
-?'4m-m-ome
h N - l n r 9 0 h P
* 9 * 0 3 m * 9 *
n-mrCIN-4Sb>m
W W W W W W W W W
-0.ab00.mODh0
C U W * k ~ O . Y h I V *
a 3 ~ 0 . ~ r n V . 0 0 - - 0
*
C;
a
<
L,
~ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 - ' - ' 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0
I + + + + + + + + + r + + + + t l l
WWWWWWWWWWWWWWWWWW
d d N * ~ F 1 N = m * b Q b 7 * 6 N h S
I
*
q
0
I
L,
~
o
O
C
6
0
0
~
-
~ ~ 0 0 0 0 0 0 0
+ + + + + + + I 1
WWWWWWWWW
=-**wY)QDo*
b ? m s s o c u r h *
m**hSO.mmbNnmcu.--meJ
*..".".
7 ' 3 0 0 0 Q O C . 0
O O C O O O * - *
000900000
+ + + + + + I
I I
WWWWWWWWW
O.Oh*FJ*rn@h
b ? * ~ h r h - O O
.+ .NcP( )Y
Yw
) bn
>e
dQ
J D
- ~
O.O~ h
.........
000000000
I
.,,
'
I
- ~-
0 - 0 0 0 C 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0 ~ 9 0 0
r l + + + + + + + + + + + + + + l
WWWWWWWWWWWWWWWWW
o
m
m
o
o
~
~
~
~
r
~
m
YmnTP4m-NaI*-m-emmI-J
Cc8Sdb7b?hl\&m*nanhOb>-b>unb~b~b>rnnnmm--rn
n
.................
30000000000004000
I I
I
'
~
o
m - 0 0 0 0 0 3 ~
0 0 0 0 ~ 0 O
t I
1
WWWWWWWWW
0 m
b?P
~
n I O+D * h Q + P J *
**0).II**N1')W
*.rb-I*TrnPJd*
1mmw*.rmcu-hl
8
,
0
++++++
.........
000000030
I
I
0
ORIGINAL PAGE IS
OF POOR QUALITY
a
0:
,
Q
\
~ 0 3 3 0 0 0 0 9 0 0 0 0 0 * r c
0 0 0 C 0 0 0 0 0 0
+ + + + + + + + + + + +
w W W w W W L u W w W
n f i h ~ o r n m c h r n
d f i N b ? h ~ ~ +
. . 1 W q M N 9 h b * I
~ N Q 9 O L i )
X
0 0 0 0 0 0
+ + I
I
W W W W w w
. r r F 1 O o D
~ N d 9 Q h N h
O . h t h ( V - ~
w m ~ N N N ~
0
C)
$
0
,
.(
*
>
~
~
b
*
~
2*
h
3
01
0
I
@
*
z
0
=*
I
an
T
a
O b S Q W d M w r )
O O
.
O - J N ~ ~ F
0
I ~ ~ ~ ,
000000000
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~
~ 0 0 ~ 0 C e 0 0 0 0 3 0 0 = - - - ' - '
0,
E O 5 ~ O O O @ O O O O o ~ o o ~ o
I + +
+ + + + + + + + + * + I l l
w w w L . , W W W W W W W W W W W W W W
r ~ ~ 1 9 d r r o o o - m 9 n . c w d * b m m
0
q ~ g o w 9 9 9 9 l 9 - t 9 O P ( h ~ N O
mdbabOOb19mhP(CYP)mr)bIF)h
p , n r n + m d 9 b 3 - r w W t 9 ~ N ~ ~ N P I \
b
000000000000000000
I
I
. ,
O O O C O C
000300000
l l I
~
,
a
.................
~
n
~
a
~
m
~
-
s
~
b
~
~
(
h
~ O O O - - - J N I V C J M M Q P ? ~ ~ ( D ~
. . - . * . * . * . . * . * - * . *
000000000000000000
f
0
+
W
h
- 0 = 0 0 0 3 0 3 C = 0 3 3 0 0 0 C C 0 0 0 0 C C 0 0 0 0 C C
I + + + + + + + - + + + + + + ;
W Y Y W ~ W W W L L I W Y W W U Y i . l
d W 9 P m ~ W 9 N O N O N O . W t \
ODh9.7Cm~Ir,~ro-ru~*cr,ll7ru
u 3 9 9 W * O C ' J h R m N h d9kx-IIil
2
y
a
. . . . . . . . . . . . . . . . . J*
~
2
*,
0
0
,
n r r u y - , b , o + r , b , m ~ n n ~ ~ - r ~
0 0 0 0 0 0 3 0 * 0 0 0 O 0 0 0 0
I
I
I
e
4
V)
- N N N - l h W * b >
N
hdhO.hh*b'I(r
rrN.rrnN-0.db
. * r . - . r r *
000000000
I
1
~
b
O
.
0
d p g b > q q C J r -
0
0 0 0 0 0 3 0 0 0
0
-
. , i ~ W W k ! ~ W W W W W W L u
~~r:cr..nr-~ccn~-rr;mcm
m - r w a o b > n w m r n s d b
h o ~ ~ - m ~ i ) n w . r m - r
~ ( ~ 3 ~ n n - r ~ . r m m r c c c u - -
d
-
.
.
-
.
.
.
.
.
.
.
.
.
.
-.
k
9
=t
.........
0
.
-
L
3 = 3 C 2 C . C 0 3 = ' 0 O 3
e a ~ o o c . a = , c o o a o
0
0
( U d O . j O C C 0 ~
0 0 0 0 0 0 0 0 0
1 I , , + + + + :
W U Y W W W W W W
hdCDdT)-II\h'o
hncob>hqmb?h
bh03rnQJdVN-
a0
-
3 0 0 0 0 0 0 3 3 0 0 0 0 0 0 0 0
r)
0
P> T n@ o
n hs O . 6 0
O ~ N ( b 7 ‘ 1 9 h F
. * r * . r . 00000003
O ~ ~ h * r C I ~ - ~ O ( i ) P r 3 9 5 ~ ~ C)@ ~ " 4 . - O ~ V e , \ - T C
C ' ~ O O O ~ ~ t ~ J f i F J ~ . r l i , l i , ~ h O I
OO-@F4?9MP\O.
I
~
W h
O
Wl W
dm
W aW, h
Wm
WwWc W
u
u
-.
*
rg
~
? ++++++
bl
Y
3
e
&
. r . r . * . . *
O O O O O O O O Q
I
<l4 . . . . . . . . .
i
.
+++++++
-JOP(QbrcPab?
a~ O
h~n w * c u h ) - o l u
............
OtVhNll>Of9O.PlmWOd**O
~ o o H ~ - N N ~ ~ Q w ~
o . * r - . - . r . . r * * - *
000000000
I I
W W W W W W w W W
ob3rmhwm\F)O
, ~ ) ~ b ' , n o ~ * n
O O O 0 O O C O O O O O O ~ ~ ~
I
I
\
)(
O Q O O O t 3 O - J ~
.
.
a
-
.
a
*
.
-
0 0 @ 3 0 @ Q O O
-ooooocc.-
ap
ooooc?oc.
rq ~I o
-++++++ :
0
- .........
+ - - A + * + + + - + + r +
M
.............
),
W W W W W W W * ; i l
~ > ~ ~ ~ C D ~ Q . C I * T
~
Q
O
P
J
~
O
S ~ ~ O L ~ ) O . O . Q - Jrn
3
OD\~)NI~J.~ICI~;N~-~
C
3 3 ' 3 0 0 0 C 3 C
0 3 0 0 0 3 3 0 0 0 0 0 0
I
r ~ + o b - ~ o . m m m * ~ e ~ - ~ m
O O d d - J N N I 9 m T b 3 9 h
> .............
'
?
0
'
C)
OOP\CD~DQJ.-PIO.
OJOO-JN?9b>li)I\
-
. .
C I C C 3 ~
0 0 0 0 0
g
+++,
0
+ + + + + + I
W W W W W W W
90---4r10;)
h O 0 3 - 4 r ) U
QJObrrU1-09
O..tP.tC.I-9
-,
-.
* .......
*
\
3 0 0 3 0 3 C
I
\
.
* ...........
0 0 0 0 0 0 C I 0 0
0000000000000
000300.3 0 0 0 0 0 C
.
o n c c o h t s m
O O - l N ~ * a ,
.......
2*
0000000
15
1
W W W W W
e ~ m c u h
&.19?9W*
C l d h Q S
CIP(vdb7
.
.
r
.
-
3 0 3 3 0
e
'
P)
r)
0
3
P O O D - ~ ?
.....
oI'1-radD
0 0 0 0 0
a
0
~
~
~
g
d
h N
w ~
- - F
* N O O N C O N h a * - I h f
9 0 n h n 9 . c a p a p ~ b . l
m ~ ~ h d m w ~ * ~ b
I S O * b > t ~ r ) N N N
= ............
I
b
u
C; 0w 9whwOwN wO wO wD w
6r)
l
o m m
> d f 9 m
~ ~ f
I
LI
000000000000000'0
................
r
n
~
~
h
*U
--
2
Y
8
..................
C
3 0 0 0 0 0 0 0 0 0 0 0 0 ~ 0 0 ~ ~
I
. r . . r . - - r r . r r . r r . .
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ~
~
O
0
Y
'
,
*1
\
r
r
e
~
C
0
0
0
0
0
0
0
0
0
0
0
-0003000300000000
+++++++++++++
+ I
-
0 0 C 0 0 0 - - ( U ' ~
+ + + r +I +
I I .
W W W W W W W W W
9*-**9w(YCY
o(rdm~~>curcrnfi
00.hCEW94n0)
m-*m(Y.-aprcO-
.........
rZ)
0
-
M
000000000
.........
~
~
CII
0
.O
000000000
I
I I
rr(rQOOb>h0.0.0
0.0
N T I
>
d h 0.
~
*
O
O
o
002000000
O
O
l A+++,+
l
W W ' r l W W W W W W
r‘lr)OMh(V-O(V
- d h m + h W m m
*mrnr)hdCUdQ
~ m w b > - r w ~ - m
~
I
I
v
d
a
.................
8 \
a
*(
P
0 0 C , 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I
.........
--
V
A
l
I
w W W W W W W W W W W W W W W W W
M9dCCYhb>b>,')h9dmr)rrNCY
*b>WNQ=hNOOMn-*-lb>W
b.@(D90.0CVhMb>-b-a0.wWOD9
b>b~i)b>b>\~)**n,nm+nctm-or
I
r
0
0
O h . 4 2 0 d P l * O
OO*Nmb>*hQD
000000000
- m 3 9 0 m h d ' 9 0 b > N h N h > m O h
d~;O~rc-C.(CVmmQWMshmw
n
CL
*
-
I
\
000000000
000000000
?
0
LI
V,
)(
0000000000000000
.
tOb~rc*0.13rCI
(DCU(rWNd-hD
1
1
OFIhNb>*r9*F9C*O-l**0
o o o ~ - r c ~ ~ m m
0
0
t h n m m a o n z
.a . . . . . . . * .
2
I
u
ooooooo-n
- ~ o o o e o o o o o o o o ~ ~o~~~~~~~~~~~~~~
+ + + + + + + + + + + + & + I
I
wwwwwuwwwwwwwwww
I
)r
h
C'l
9
.........
0
000000000
0
I
I
I
C
28t
Q
P
sd
'
11
b
.................
~ - 0 h b ~ 1 h - ~ 0 b 3 ~ 0 9 r i 9 0
f i ~ ~ r o o - - ~ ~ m m - t n ~ * h o -
u
\
O
d
+ + + + & + + + & + + + + I
W W L J ~ + ~ W W W W W W W W ~ W
[email protected]>-9daWOW9*
OhNhhQI*0.**,')b>')*
* * t C Y O h 3 r c N ( Y ~ . Q N m
~ * w b - n n r * * n m ~ w - s
0 3 0 0 0 0 0 C
C;
L ~ W W W W W W W
hb>'46*WO*
9 Q D 0 . M h ~ r c n
Sb>ODlhQDP)h
I
..............
~ o o ~ o ~ o . - l
3
3
,++++++
........
n N t - m ~ ( ~ m
I
...........
t \ 9 6 b > * ~ * n t s s ~ d m 0
* r - N W m r 9 e b > S h Q
00000000000000
-
I?
0
8
0
OhQICDOdhD.
00-C.lrnb'llC)h
n
0 O O O O O O O
-,
~
"?
+ + + + + + I
0
I
a
-mwvm-b>
.
.
.
I
.
%
)r
.
' ~ 0 0 0 0 r 3 0
v
\
)(
0
'P)
0
0
-
-.
O O C O -
W W W W W W W
* * O . O ~ . e o .
0Q)WMrcNil-l
0 @ 4 0 9 b > V
.
,Y
........
U
I
~ 0 0 3 0
0000000
'
0000*000
00000000000000
= ::.
.........
000000000
000c?0000000000000
~ O O = ~ ~ C d 0 3 O C
C . , 4 0 0 0 0 0 c ? 0 ( > 0 0 C ~ 0
- N - W Q Q h Q O
o o - - w n ~ r > h ~ .
.
O r , r l 9 f ~ OM
.......
2
00-CYT*OD
0000@03
0 0 0 0 0
+ + + + I
W W W W W
I\CEO-N
~ . r r m h - t
- O b > N V
NYCY-P)
0
O O O C O
G
.....
*Ob-l-C?.b>
QC4-900
.....
C O O 0 0
16
Q)
0
t
a
0
0
@
Y
8
6
+ + + + + + + + + + + + + + I
I
w W W L u W W W W L u W W L u W W W W
~ * ( O r ( ~ L . ) C O O j C Y t \ l b
W J 4 9 h h P > Q 9 h ~ r 4 m C ? b
~ ( X I G Q O ~ Y * W ~ W T
-v-*F h - o b ? n n ~ ~ ~ c r
7
>
,
(
'
O I N * ~
h b 3 W
~ ~ - - C O O
- r c g P
..............
\
b
,
O
C
~
~
C
.
1 * ~ c ~
.
C OI
~ d~O O
~O O C~
~
r So
0 0 0 3 3 C
~
O
~
~ O~O ~
) + + + * + I
I I
I
W ~ ~ ~ 0
" .JW U W W W L u W ~ ~ d
P3N.OhliiF>OhEOno.*n*(*
r-.
c v m ~ o . ~ * * . r O .
Q 1 * r O ~ ~ Q *
4.4
OS
c CD
.ShOU)
o Q ~ ~ U ~ - Q D N C
~ . l~a U
~. -O
c
i l P * ~ ~ ~ m ~ < * ~~ v - v ~ c J - ~ L ~ ~ u .
Q
O O O O O O c 0 00 0 0 ~ Q O O c ' O
d
I
I
I
~
m~mo.Gewaw*Li)'
N ~ b > O F ) % O U l O
+ ~ P ) ~ c J ~ Q ~ .
~ t ' J M Q b > 9 Q l
~
~
o
~
~
o
c
1
;
O
C
q
W
.
2
O
-
O
O
=',
~
O
C
~
C
O
~
O
O
O
O
O
O
O
O
.
O
h
5 ~ 3 ~ C 3 3 ~ 3 @ @ 0 0 0 C O "
- - C C . O S C 0 . 0 C 0 0 0 c 4 0 0 0
1
u
*
h - d O * b > D W Q & d f Q b > r r b : V
k
.........
~ 0 0 6 0 0 4 0 3 0
+ I + + + + + + + r + + + + + + I
01
.........
U ~ ODO ~
dc.I+rb>.C,hO
c ~ ~ , c . o ~ - . - N c J P ) P I * P L ~ ~ ~\
~
O
3
--
ds*Qb>'lhQ-O-O
- u ! p g 3 M h d 9 C b > N h c J b - W c h
* .......*.........*
u
'-
0
.........
.. . . . . . . . . . . . .
h
Q
0
000000000
3
~
0
0
0
0
6
C
3
C
O
++++++++++ 1 I
? W+ +W * W+ +
W ~ W W W W r J W W ~
0
......... .
-,
h
O P ~ ~ C ' I ~ ~ @ ~ > V . ; ~ V . Q C J ~ Q - G* h~ 9 Q h @ M * b ?
o e - m ~ n * h m
OoO.crc-FIh(r)rnrrr,s.c,fi*
4 0 0 0 0 0 0 0 0 0 0 0 0 * ~ ~ " '
OI
J
W
b 3W
- 0W0 0W W9 W
NW
OW
W Ll U
x
M C O o s + 9 - C u b
4
P3
1 ~( \- Q
r W
. rQ
* amD N
OW
( Oh* r& ~
1
I
* ................
\
O d O Q O O O O O
+ + + + + + + I
3 0 0 0 0 0 C r O O
0 0 0 0 e 0 C 0 0 0 0 0 0 0 ~ 0
I
e c ~ o O O O - ' ~
I
1
++++++
1
W L U U W L ~ W U J W W
- 4 9 C h i 0 0 . 0 0 0 ~ - 0
a-ti~a;sco'lhvq~
aVCr-thC'ITTPJP)
03
+
by
3
0
.........
C30033C.33c~
OD
01
-.-.- z$i;z
- -
Q
N
w - u
Q)
.. .-,c .
s,g..;t;z:
$ ;
+-&+,--**-&--.>+
6
,
a
\
b
W
W
~
i
i
r
~
u
~
.;s:zggg:
+ + + + + 3 . -
1
~
L
L
PIP. 9 9 r , , , 3 *
\>.oh . a h *
T U b - F b > 0 \ ' 1 + 9 V J b - N C C
~ ~ n m ~ c o . r ~ r n m
C I Q b3b3li-J o T P m P ? C J d r S
..............
i
h
~
~
~
r
C J . O c > b > O 1 P ~ O . ~ ~ Q ~ ~ r ! O
O O - ~ ~ ~ * ( U N P ? V I ~ I , ~ * ~ ( D
..............
0
(I
a
+
r
;
~
r
.
L;,
a
*
\
C b ~ ~ 0 0 C 0 0 0 0 @ 0 0 0
?
L
d~ ;*-i wMw.r~ j a*
i i : ~
' E ‘ J C ~ M S YO f - A
@
- a v e ~ a ~ . w ~ ~ *n
0
.........
o o o o a o o ~
2
........
; - o o c Q c ~
C S 3 C -
-
O S O C C O O
. 0 6 0
? C- +C +
+ :
0
s + + + r + ,
,
a
W W W W W L U W
14
.
a rn W In V, W
C . c W h E L i . ~ U
oco~~,s~ri,.rw
- ~ ) Q V I P J - W
.
a
,
.
0
3hUOfi(D-4h*
CQ-P(P)U>Mh
c30000500
-
.
"4
b > a ~ . r * ) N r V * )
0 0 3 0 Q 0 0 C r 0 0 0 0 0 0
.
d
C=
I
\
h
.
3 O O C O O C
1
2
Lh
0mCY9hO.I-l
OO*rIW.(LW
.......
2*
0 0 0 0 0 0 0
17
-
CJ
L-J 0 H lo?
d @ . O & *
P I f 14. r -7
m
CC.GOC
@
buwwww
m h h h 4
.....
o b 7 u n
oN.t.OaD
c
d
w
.....
e.0000
ma
U
~
8
V
1
N - N W W W I U *
r w).r
LI
v
-1-
C DA* *0\U
; NCh. )L* qh .l M
0 - * N W W W
e
........
L
mmmmmmm
-1'1
mmmmmmmm o
1 I
Q O O O O O O f 0
0
r r r h l w ~ ~
O r Q D U O r W * S
a
w
r
m r d ~ r O ~ ' l r - h )
a w 9 9 9 * w v r 4
u
n;
mmmmmmmmm
++++++ I +
I
I
0 0 3 0 3 3 0 0 0 0 0 0 0 3 0 0 0
.................
W L I - W
* r V W
U N O C
r W h W
N W
~ f
O r
9 4
U P I L ' l L f i L q * * * W *
O J W W O I U O O S & *
* q - A W V * U U U A W
8 9 * * 9 & P A & * I b 2
,
l
%
P
8
mmmmmmmmmmmmmmmmm?
I
I + + + + + + + + + + + + + + + +
0 0 0 0 0 0 0 0 0
- 0 O O O O O - 0
.........
0 0 0 0 0 0 3 0000000000
9 0 0 0 0 0 0 0 4 0 0 0 0 0 0 3 0
.
600000000
W W ~ ~ W N N
o.L~+*QD*a*O.
~~L'IW-NNWI
L10c'l(10PoObaW
I
.
- *
8
.
..................
000000000000000000
P
~
~
A L S - N W N W W I J . Q L ' I L e * o . O
mmmmmmmmm
++++
I I I
I +
000003000
m
e
a
r
u
~
~
m
~
~
I
~
2
O
?
mmmmmmmmmmmmmmmmmrn
W O U U W I O ' O V I I W O W O 3 ~ N & 8
I U ~ L ~ O ~ N ~ ~ ~ O * ~ W U
~
w
~
I l l + + + + + + + + + + + + + + +
000000000000000000
W - r O O O O O O O O O O O O O C O
w . - r O O O O U O
r
O
N
~
c
c
i
+
3
I
000000000
.
.
.
.
.
.
.
.
I
* r r r r , ~ h ) r C O
O O N ~ Q D W h ) O $ .
0irlIUSh)h)UPO
,+U9NU90W *
mmmmmmmmm
I
r(
8
*
+ + + + + + + + ,o
00000000(9
~ 0 0 0 0 0 0 0 0
0 - 0 0 0 3 - - -
-. . . . . . . . .
~ 0 0 0 C t 0 0 0
,
+ I++++ l l I
W WWWWWWWW
P h10rrP)OMLs>9
*rlO''lFP,O0.
IV e d m a v o . - 8 L - .
C" b e l r . I - d o . * C l
0 00000000
I
g
b N t 0 0 4 d - H
O
+ IC+0 +O+=+O O
I o OI
o ' w w w w w w w w w
I
t'JP9r(b30.aC.E13
- p o w b r r m w r >
0 3 0 . m r l h d ~ Q P J
P)O.NPJHH9-b> '
< .........
bd
6
I
w
0 0 0 0 0 0 0 0 0
1 I
I
WWWWWWWWW
cyrrO.Qr.ICIm*CO
o
m u s r n ~ h ~ - h
.-4hs00..00drJ
C4 0. C1
.
U
r
l-1 i-4
a
d
K
i
t'J
hatmmHP.0.
0 0 - ~ m n n h
0
0
.
-
.
.
*
.
.
0 0 0 0 0 0 ~ 0
d 00000cc
?
0 0 0 0 C 3 0
+ + + + + + I
WWWWWWW
P rJWerr(G0
s'rP1>PEUo.
a
*ocna;.onq
0. L i ) v m r . j d -
0
I
u
"?
0
I
- 2,
e--
-
d ,
3 0 0 3 0 '
1 + + 1 I
WWWWW
hQ.rCD-Q
hb3-OW
b3wOP C
.....
.......
dNrlI3.m
O * C I O O
0 6 0 0 C C O
I
0
*
.....
7
' 0 b> 6 b>
0Cl.rdOI
ooooo
O - O C ~ o o r ( ~ H
a
b7
?
C( O
h *W
)%
( .- Q
J U
D -~t (NOr Y
. ~
PJ
~ (
.-
~ 0 0 0 0 0 4 0 0
.3
U
+++++++++++++++
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
++++
I
l l l
WWWWWWWWW
-hYlmhmmclnO
b
O O O C O O @ O o 0 O C o C = - ~ ~
0 0 0 0 G ; 0 0 0 0 0 0 0 e C C C O
l 1 l
WWWWWWWWWWWWWWWWWW
b 7 - d d ~ . . N ~ b > n h e m * d * a ~ C ' J . O g W T O U T Q 9 ~ 9 V * d N 9
0. P * b 7 ~ d m N m m m m n O d h b > P J
+
0.
*
........
I
Chg~g.rcr3PLFI
0* 0* d. .c -~. m
n 9 h m
- * .
000000000
- -. .
1
O r r 0 0 r C I O ~ N d .
O 0 0 ~ O O c . C o
l + + * + I
a
I
+
.. . . . . . . . .
I
a
~ h ~ 0 3 0 ~ O . ~ b ' ,
-9OObt9-1Irb-l
ri
OPb>LOh-r.PJT
v3
. t r c ~ ( ~ c l c l * r n h
0 0 0 3 0 0 C 0 0
I I
I
I
?l
.-
'C
dQQ(DIFlhD.0.0
3 d 0 0 0 0 0 ~ ~
0 3 0 6 0 Z O O C =
I + + + + +
I i
WWWWWWWWW
0 u p m n a o ~ ~ > m n
2 +
8
9 h Q O 9 C J O O V
*mmm-mMrJ9
h ~ . ~ n r n r ~ c c h m
M
--.
.........
3 O C . 0 0 0 0 0 0
I I
I
(C
s
#
0 0 0 3 o C ~ - C
0 W 0 0 C c . 0 0 0
+
+ + + + + + I
I
W W W W W Y W W W
. r M N h O D . h a D o .
C U
o
~ hC ~hP W
Y gd DO~ DO dJ h
~ l r W4
.........
1 m--P1Ncc9FI\
LC 0 0 0 0 0 0 0 3 0
I
I
I
.-
-
H8-46.Ccl
C 0 0 0 0 '
1 + 1
I
I
W W W W W
hlnS0.h
-0wLF)O.-
m.09nm
9 d h r e O
I
ORIGIMAE PA= IS
Of POOR QUALlTV
rg
T
0
II
.=
w 0 6 0 0 0 0 d N
- O O O O C O O O O O ~ C ~ O ~ -
0 0 0 0 0 0 0 0 0 C 0 0 0 0 0 0
+ + + + + + + + + + + + + + I
1
W W W W W W W W W W W W W ' r ' W W
~ r r g r ~ w ~ ~ ~ r l n m
M ~ > D
~ 1 h l * h h l 0 0 0 h c P . E
30.
. ~ o - ~ . m r ! r n - t ~ n c r r e n n c- N .
- . r s m m ~ ~ > ~ m n r r c c w - - ::+
0 C C 0 0 0
+ + + + + + + I
0 W W W W W W
s ~ ~ m ~ ~
8
C
h h~C O
* O. *C. IIY. )Yh ,= O
0:
v
r
8
0
8
I
O C V h w n Q . M O . r , 0 . r O r c O * s O
3 0 0 d 4 d \ ~ r ~ m m + 1 r , - . f r - ~
2*
~
~
~
~
^
~
~
3
6
3
0 0 ~ 0 0 0 0 0 0 0 0 0 0 0 0
Z ; i + + + + + - + + + + + + I
1 1
L U W W W W W W W W W W W W W W W W W
o
?
(
V
'
000000000000000000
....
. .
a
.
M
0 0 0 0 0 0 0 0 0
'
0
C
+
W
0
(P
..................
3 = 3 = 3 C G 3 0 0 C O S 2 - C 0 3 0 ~ 0 C 0 3 0 0 0 0 G 0 C
s + + + + + + + + + + + + + I I
W ~ W u W W W W W W W W W W W W
.................
*, *
I
a
.
' ....--........... 4
0
*
\
2
-
~
>
"
~ ~ ~ f l & i i * i ' L u W W W W W W ' ~ W
r- , PJ
?.i
I\ Q P. O. O. Li) I,- O
,
~ c h C O 9 d 3 4 O ' X , r . O
~ ~ ( ~ m ~ - ~ r . ~ m r n ~ c
- r s a b ? ~ i ) ~ ~ > . r ~ n n ~ - - l i ,
..............
r
~ - O O ~ ~ O . ~ O . F J * T C I ~ ~ O
3 0 - - 1 ~ ( ~ ~ 1 m m . r n 9 h 0 0
II
b
M
~ d 0 3 0 3 c 4 -
r
r
.
.. . . . . . . .
CC
0 0 0 0 0 0 0 C
I
3
*
2
0.
4
4
Ohmmm-h*
........
OO-PJmV1b')h
-0300
3 0 0 0 C
I + + + I
W W W W W
( D O P . P 9
b-Jb-JT03
.. " "
r ~ r o o - ~ . r . o
i c ~r~1-4 t-4 r. L> 9
t-1
.........
r n r n i r ) 9 S * P ~ 9
8
o m - hIJ>rnWO
~ ~1
s m ~ . ~ . ; n o n m n
h a ~ m n n ~ d h l
0b00'03++++++
O O O O O G C
l
U Y W W W W W
t ' ~ 6 9 r r c @ , - 8 0
0 b-J b? C
Q
I
00000000
.. . . . . . .
I
I
+ I + + + + + ,
= . 0 0 0 0 0 0 C , 0 0 0 0 c ~ o ~
..............
M
- . C C ? e o o 2c.
:
0 LurrlWWWul:ri&
~
I
0 0 0 0 0 0 0 0 0 0 0 0 0 0
S
I
0 0 0 0 0 0 0 0 0
2I(
e.
..-
.........
00000C‘00000000000
O
3
0 0 0 0 0 0 0 0 C
- r J m Q Q V h P C I
CIO--PJ~~~-J'I&
C
rl
O . ~ * ~ ~ -d
,
I O n h
O ~ ~ P ~ * ~ h ~ T O b > r ~ 0 9 b ' l 9 0
OOCCI3-.-CJNMP1-?MLn9hCh
~
h
..r
> - C 3 0 0 0 - -
0 0 0 0 3 0 0 ~ 3 0 0 0 0 0 0 3 0 e
C
r?
........
v ~ ~ ~ I , ~ Q ~ o ~ H u ~ ~ c I . s 1w *~ F DJ O~ . QC .$
& ' J 9 l ~ ~ d o ~ W ~ ~ P P . 3 ~ O D V @0 3 b 7 r i S * L F
v d % Q h ~ h ~ ~ ) ( ~ , 1 * > 4 m r n c u " * P
-..<::c.c.e.
< > ; 3 3 C C G 3 3 = ""? +i- +j- <
++*++++-++++
, 9 m 1 \.
S
+ t ++tr+l 1
y ?
"
o w W W W W W W W i r i
b 0 h U - l . r ) C h C h ~ J
h i i l - T O . c U O ~ I 9 P J O - * 4 9 Q h a
I
'
.
000000000000000000
"
>
000000000
: I
1. . I
W
d
a
Q
t.
@( U +
Pr @~J [ U~- M~
( U .~
5PL
vV)MP)(Ydh.(V(*.
-.fQODVlhO.0.0
O O r N Q I f J S h O .
*a *
LC
N +
- C~ OC O ~
o O ~N ~
3 0 0 0 0 0 0 0 0
+ I + + + +
I I I
W W W W W W W W W
v
h
y
CO
@ r ' 9 P Q O M h d S O m N h N b l m O P
O O O o - ~ ~ N F J m m ~ 1 b > s h m L 4
J
Y
.........
.
* .........
C
0.
0
000000000
0 ~ ~ ~ I ~ v J - ~ ~ o . O D ~ O - I W O ~ 8? ( ' O
V hn-lb?hQPhb>
<* . . . . . . . . . . . . . . . . . .
a3
,
01
-
a
r.
O h S Q D - M - n
oO-rrmbIr,.ohm
r ~ m w o p w ~ . - r m ~ ~ ) ~ o . - n h m s0n h 9 n n o - b r 9 . 0 ~ 0
~ ~ V J @ ~ O ~ > I ~ ~ P ~
LUICI9hmmhOPPr9mNPJ-Sh9
'-
.
000000000
.. . . . . . . . . . . . .
0
I
.........
.................
' 0 0 0 0 0 0 0 0 0 0 0 ~ >
00 , 3
I
I
j
0 0 G
W W W
~
.CI.~T.~
o e r ~ n n ~ n . . r c ( ~
8
ol
b-
*
~ S C O C C ~ 3 3
V
-
tl
P > " P ~ P J ~ M
ChWZIJ-Pl
r(
C ~ . 3 O ( S C
e:
I
C'rCIC1OhO.m
O O - F I Q 9 D
* ........
0
2
0000060
POb?')D.V)
O N " 4 O J
.....
4
0
00000
--23
- -
.
--
.- .--
-
.-- ----
-
\I*
rr Q
U
n
C 0
o c.- r
....
.hO.*O
'09bO.
;too0
I
I
9 ~ 0 0 0 0 0 0 0 0 0 0 0 0 ~ ~
0cJ00000000000000
O r r O O O O O - H
+++.++++++++++ I
b: W+ +
W W W W W W W W W ~ W W W W W
o
I
d
90.09
)r
QOMOm9h@Y)-l@V)*nl''*
Y-alhSMQMrJmW(U:yfi
\
L(
O C Q 3 3 0 3 0 0 0 0 0 0 0 0 0
I
2CthrJb73W@19+*3-I@*6
c ~ ~ . ~ ~ ~ r l ~ ~ . ( m n
< ................
.
r
n
OI
=
8
..................
- - - O . a , h 9 * O L F ) Q M P I P ) C J - - h h l
0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 9
. . . . . . ' .
C(
hl
v
W
0
#d
U
a
V)
a
d r . > . r ~ 9
C ! ~
~
000000000
I
I I
O-
.........
w
3
@
C.4
0 .
~ P P O ) I F 1 2 @ @ 0
~ ) ~ ~ o .
.........
~ -*
h0 0 j l l r ~ h
C ~ L ~ P ) O ~
..................
L
o ~0r0 . +a No P
o ~ ~ ~ ~ ~ > - ~ - ~ r ~ t ~ n c r o n
r n
0 0 O O O C ~ Q ~ O
0 3 5 3 0 3 3 0 0 3 r > 0 0 0 0 0 0 0
- .................
C1
I
~ O O F l 0 N 9 P J d r J b 7 i f l 0 ~ h ~ 0
(
. - r C - r n r n , ~ . o ~ ~ o r n n n r ~ - -
;r;
.'
.
r.1,
0
I
I
I
+
3
+++
W
V W
~ (W OW . W~ W
~ W
- I~ (~ V
4PI*il3PIC\1~13
~)ODPY)~C.ISD.~(
QNQ~M+-~.PCV
.,.,.. . . -. . . . . . . . .
..............:...
I
w
L3
m
0 0 ~ 0 0 0 - 1 d 000000000
*.+I
l
I
mOJCIhe~mb>dsM9c~9C1OOD
a
CL
4
3
6, C
W
-lil>c+OQ * a m a * - m M O a d a M
* N d m h 9 h * O O P 1 N P O . F ( h O h T
~ d 3 U ~ b m * d 9 C + . ' T 0 9 9 N N h 7
.
0 0 0 0 0 0 0 ~ 0
I I
.ii 0. 0- 0 0 0 C ) 0 0 0
. r r - l - 1 . O O Q 0 3 0 0 0 0 0 0 0 0 ~ - I
.
Cl
......... .
0 0 0 0 0 0 0 0 0 0
g 3
+0
+0
+0
+0
+0
+0
+0
++
+++++++ I I
w w w w w w w w w w w w w w w w w w
C
,,
.........
obaMd-I-In(Dn
Oh**@-rJPV)
s 0h O
* OdC4rl.IV19~
*
l4 0 0 3 ~ 0 0 0 0 0 0 0 0 0 0 0 ~ ~
I
(U6.0rtrr00.9h
0.
L O O D ~ V ) ~ M - I * O D0.
- - .. . . . . . . . . . . . .
LI
wwwwwwwww
h O b S l 9 ~ 0 1 ~ f l m m
w ~ , ~ c I o ~ . P ~ . ~ ~ J - ~ o o D ~ ~ 8+ *m - l r u n n r u o ~ ~ r u
.-r.icr-rq-rr.~.z
C3Cd-r'JP3b>*B
.........
O ~ . * ~ 3 0 ~ 0 3 0 0 0 C 0 0 r r *
0 0 C ~ > 0 0 0 0 3
0 3 L 3 0 0 0 3 0 C 3 0 C C
c 3 O O O O C 1 3 ~
00
1
eU
+ - + C c f + + + + + + + +
0
I
pl
\
0
I
u W i u u l u i & W i i i W W w u W u
b--4~3daJODQJ>r.J.Ur)Wr3F
-+++++*
1
W W U W U W L J W
MCJCO~ 3 - ~ i . 0
-.. . . . . . . .
TOCClil>*;CJ0+9IiJ*NNh
~ P I ~ ' ~ ~ K J * . J ~ ~ I O D ~ F ( * - O ~ ~1
ChCOh99UJWJPI?C!P)P)4N-I
Lc
C ~ ~ 0 0 0 0 0 0 0 0 0 0 Q
..............
~ ~ O I D O ) C I O . N ~
Mlb7 m O @ 9 4 M
O
D
b
3
~
P
I
:1
'
3
d
~
0000003r'.
~ m~
3
I
i
c
I
2
r.1 d C* Ln0.
O O H -
m9.P) 0 . V N d r ) O
..............
-
~
J
M
~
M
Q
U
0 0 3 5 3 0 0 0 0 0 0 6 0 0
0 0000 3 0
0 O O O d O O
*++++++
? W
W W W W W W .
0
rl ~ @ V . P J O . ~
=
8
Lc
*
~
~
~
2'
?
0
~
-
0 0 0 0 3
-
I * + + W W W W W
= .....
I
'
Q ~ . C ? . Q T
COJQ)L)il>'
I,-, M .4 *J. \?\
Clt-13
A
L.
ILl
?i
d
(r
o c:a-aor.
I
U
........
3 0 3 C 0 0 0 0
40060.
MP)O.Cl*OUCr)
b T l I > - ~ I d O
b l z ~ b - J * C ~ M
" ' *
~
OhCOODQ)dh*
O a r r ~ n v , ~ r .
9 I r , ? J * l h O r)
3 S . d i 4 T . O Q )
0
r . . . . . . .
ooocoao
3
0 C- 0
QOM9.Ln
.....
OrJv-4m
4
v
O O G C C
L
25.
-
- .
d
0 ~ 0 0 0 0 0 0 0 0 0 0 0 0 0 ~
0000000000000000
X +++++++++++++++ 1
0 W W W W W W W W W W W W W W W w
1
01
G
9 9 N - d Q Y 1 Y ) O . O O . O . ~ h * ) ~
~ . ~ b h m m @ a ~ n ~ m O s * * )
h-OOWMY)99-mO)V)O.~m
.............
.+ ~
b
-
D
~
-
~
~
Q
P
~
w
Nb *- a~- - -~. d ~
@-nN
................
--
@C'IhWb6Wmt9F-Q04**0
OOOd.rcrJFI(Yr3P)bM99hO.
o
0
%
. '. .
OI
C
.:
,:
I
-
_.
.
.,, .:
- r l P 9 0 m h 4 9 0 0 C 4 b N U 3 9 0 h
O O O o r c ~ ~ C ~ ( Y ~
\ O *D 5)
x
3 0 0 0 0 0 3 0 0 0 0 0 3 0 0 ~ > 0 0
..................
-
I
h
3
0
a
3
3a
w
w
\
n
+ r + - + + + + + + + + + + + + I
.................
O
O
~
~
O
O
-
C
~
J
C
J
P
)
0 C 0 0 3 0 C , 0 3 0 0 0 3 c . 0 0 C
C)
Pi
-
r'l
000000000
I
1,. 1. . . . . ... . . .. . . . . . . . . . . . . .
..
.*
.........
[email protected]
o o - m * m * n *
€at0000000
...
Y
W W W W W W W W L ~ W W W r J W W W W
o . ~ - * P ) ~ D L ~ ~ , o I ~ ~ c ( o . - ~ o ) I > *
n o m m n ~ s b m * a n m b > ~ ~ r h
.p - o h ~ 9 r c P h a Q a 3 + 9 3 d n
r ! ~ . . - ( ~ ~ ~ ~ ~ a n ~ ~ n n
< .................
~
-.
84
r'l
*
.........
0 0 - 0 0 0 0 * ~
8
~
W W W W W W W W W
o c o n n * * a a O
oOD-0.117yIdv~o.
* . ~ Q o o . o . ~ - - ( M
~
ID,RO.--I-QN
- -
*
oD
!
" ..........
h
*1
3 0 0 0 0 0 0 0 ~ 0 0 0 0 C 0 I
0 0
z m
t
-
00+0000000000000C 3 0 3 0 0 0 0 0 0 00000'>0
OD
~c
~
.-
r.m----mcvn
. .;,
'.
'.
.
U
\
000000000
+ + + + + + I I I
I kt3.h.OCY~r)-O.hl
hCClQD09hODQ)-hOe*NY)h*.-r
- I ~ O O ~ Q D - N ~ O P J ~ * ) ~ ~ C S h~ O~h ~n F 1 e 9 n
0 0 0 0 0 0 0 0 0 0 0 0 0 0 C 0 0 0
4
0 O
~
~OOOO@w-'
0
0
+ ?-"?Qi~h,P"yy:piy~~t~
))
P
0
-
. .-
wwwwwwwww
W
- t q - n n - o ~ ~ ~ ~ o o m n m o 4,
9 mrc~)rt*bhw-
8
0
W
0 0 . . ) ( ~ m n 9 h m
000000000
~ r c ~ ~ 0 0 0 0 0 0 0 0 0
003000000000000000
+++++++++++++++ I I
q +
~ W W W W W W W W W W W ~ W W W W
(rl
. . . . . . . - ..
O'h9TO.d*)*b'I
*
pl
y
000000000
t I
0000000000000000
?
W W W W W W W W L u
S Y ) P W h h N W M
M M O N ~ M ~ . P J C S
ONP9*&\@-9QD
c .........
N
O O O C O G O O O O O O O O Q O
I
2
M O O O O M r (
9
f
T
r
OD
"!
0 ~ 0 0 0 0 0 0 0
I t
I
" . N * Q P T h P O
:
< ......... o~cooco*o=.4
~
~O O
~ *~
- R~
P Y@
UJhO.
OD
I
0 3 3 3 0 0 0 0 0 0 0 0 0 0
U
m
,
0
.(
\
b
+ + + + + + - + A ? + + + +
W W W W W
3 0. r . m t
r . r r r ~
W ~ . C O .
W W W u W W W W W
9 h \i7 CJ n CJ .r C . I ~
o m n m o ~ u l n n ~ o
* ) Q D O O D Q ~ O N ~ O
..............
0 . ~ 1 ~ * 9 n n . r r > n m ~ - 00000000000000
< o.o.-.- .- .m .~ .i (.m. .r -., .~ .n .~ h ~ ~
m a o b 7 0 . n e n c ~ r r ~ - m o
00000000000900
.
- 0 0 0 C O ~
!g 00
+0
I +
0+0
+0
*.0
+ 0I ~
, mnnoo*mn@
-. . . . . . . . .
0
O N O S P ~ ~ ~ O M
In
O D Y ~ O ~ D O d
~
b
0 0 0 0 0 0 0
++++.++I
QDC(NCY--~CM
QD
~ 0 0 0 0 0 0 0
-Y
I
I
2.CO.~.OQ.DM.WC.O.VD.-~.~ ~O .Y
~
. -
c r o o e - .
?
0
8
00000'
, + + + I
~ n w r n r ~ .
p(
om*r3CV
r h r u * ~ W
.....
0 0 0 0 0
I
0
-.
W
.
IbIYWWW
IhQ.mO
\
)r
*
)
00000000
0 0 0 0 0 0 ~ ~
?
W W W W W W W W
....
In
X
"r
P0ITlO.Y)
3mw-ow
oooer,.
, l J
U
~
0
0
0
0
C
I
O
-
oooooooyy
++++++ l
w
6, w w w w w w w w
I
~
~
0
h
0 0 0 0 0 0 0 0 0
0
< .........
oooorr
-. . . . .
0 0 0 0 0
I
W W W W W
++++
0
MNrlrlP,
00
I
++++++
W W W W W W
k') 0. .o
h3.r
OD--
ho.0
-rnr;locua,
. . . .r!. .
a m 9
b-1
rc
300 0 0 0
I
3 mc4 9 f . V.
P)'
.......
O O ~ ( u 7 9 a 2
O O O O C O O
(q
amli)Q(II
03
b> m b7
0uIQ)c'P
0 0 0 0 0
0 0 0 3 0 0
0 0 0 3 0 0
0
1
.3
b > h n m & r c N M N
.rQC4FIOOMb>OD
~ * O P c b > C U h P O
h ( U r l d - r c b h W
0 0 ~ 0 0 0 0 . - J 0 0 o 0 0 0 0 0 0
+ + I
+ + + + I
I
W W W W W W W W W
~'rh0.n.4V-IODOOD
m m - r o ~ n e ~ r r 9 I D h h O O N L n l i )
Li)MO.rlNr4.-J-O9'J
.........
O O Q O O O ( 3 c . ~
I
I
I
'3.
~ ~c- iOo
o
Oo
'O
oOoMo. -oI F
o(
+
I + + + + I
I I
WWWWWWWWlrl
, ho
e
mer n
4 o* +
n~*o*- h
r c r
1.
..........
~ommhw-F(b>b
MODrC-ddhm-4
000000000
I
I
I= I . . . . . . . . . . . . . . . . . .
u
M m ~ * o m h . - l 9 O b > m bNk>rnOh
o o . o o ~ ~ - ( ~ ~ ~ r n n ~ r v , s h m m
O O O O O O C O O O O O O O O O O O
O dobe-001~
0 0000000
I
1
+
+++++
W w w w w w w w
O * - O h Y l * *
0. h N h * - O 0. O O d 0 ' n N O
IO r n e J F I - l r i r a
000000-
",+ + + + + +
0000000
6
0
3
,,
l
WWWWWWW
* m m n n r t h
bm~b>mo.-
9r990.W.lhb
mOD9CTM-r\
.......
0 0 000.30
I
IiI
0
WWWWW
mmhr\*
In-m-OD
O
dN
- hH
hh
C rE4
.
0 - - 0 0 0 0 0 0 0 0 0 0 0 ~ ~
.
.
(
+ +++++++++++++
+
-
o o o o o o o o o o o o o o o o ~.
C;
I
*
W W
n
b O
o ~
W W W W W W
n c m n h n M O ) Q D ~ ~ +
~ l h & ? ~
W W W
m m b
. ~ ~ - ~ ) d
W W
> o
( ~ N
g d
I I
W W W
o s a
( Y N O .
g l b >
...............
n
*
I
C
j S0 ?O
*
o ~ d ~ ~ o O C O 0 ~ o o o o 6 ~
~ d
000000000000030000
I I
++++++++++++++++
q W
W W W W W W W W W W W W W W W W W
- ..................
h
~
~
w
b
~
~
r
n
-
-
m
~
~
-
m
m.
0 0 0 0 C ~ C
ohar+c(nrn
C Y h N k > O . n O . F ~ O . W 0 4 s d O
3 O O I M - I C ~ N ~ % C ~ P ) ~ > ~ ~ ~ O .
0 300000000000000
0
.........
Q 0 0
I
I
- ................
*
O M O O b * O ) h I n
6MQDd*h)Ob>F)O
r d d N ~ r r Q ) P - -
~
0 0 0 3 0 ~ 0 0 0 0 0 0 0 0 0 0
I
O
m o-dc-rno-
1
)
++++
I
I
W W W W W W W W W
C;
~
-@QOOO-@dd
~
b
;
......
d N m b 3 . 0 h 0
O O C 0 0 3 0
-
0
0
~
0
0
.
.
0 0 0 0 0 0 0 0 ~
++++++ I I
90.
0 W W W W W W W W W
> ~~ ws ~ c ~ ~ ) . a h * b > m
I r ) ~ > e ~ ~ m n n ~ n . o n c u n n . r w n I~ b > m e r , o o r u h ~ t f i
m m n ~ o n o o m m s ~ n h s o m n
- h w c u m ~ l o ~ . h
.
I @ . ~ d . ( ~ e ~ h h b 7 + m m ~ - c ( - r ~
h N ~ e 4 d ~ h r r I b >
< .........
Q Q C , O O O O O O O O O C ~ O O O O O
O O Q O O O O C ~ O
t
n
0
E
xu
w
a
3
Pa
-y
$* g 2
*
Q
C
3
I.
*
4
.
4.
Q
m
8
0 0 3 0 0 0 0 0 0 ~ 0 0 0 0 0 0 0 0
0
~
~
~
~
~
~
0
0
0
30t.03003033300000
a
M
~
y
W W W W W W W W W W W L L ~ W W W W W
C h ~ 9 0 O . h b > - O T t - 4 U l ~ N O h O . O
"
C,06000000
~ ~
0 0 09 0
0 0 ~0 0
0 0M
0
, + + + + + , + + + * + + + + + I
a?
:
4
N
~
~
~
u
a
o
~
T
O
.
~
~ Uh
o
a
d ( ~ - o . m m ( O b d ~ . P . r P ) t ~ ~ . -w
~
.................
~
tf
3 r s r \ + P l h ~ . r , , : . L i l C 1 O d L > O 3
O O O Q O ~ - ? I ~ \ ~ P >b >* u > 9 h 0 .
* 3. 0. 0. 0. .0 .3 .~ .~.o.o.c.o. o. o. o. .o o o
'?
0
I
1(
M
4
t C C 2 6 O C @ O 3 0 3 0 C 3 3 C 3 0 3 0 0 0 3 0 0 0
N
~ W W i ) W W L i W W ; Y W w W W W
rlI\OhCJ*.r:)r'lmEh.-r4haD
9 - P > 3 0 W ~ ~ h h C u ~ @ F I
*~.r~nri,=**53h0-.(~~
~ . ~ ) m h ~ l i ) b > * m n m ~ r r h
..............
!PI
.c. o
0.m
I* r ~ ) w.r N-. m 0
..............
O
O
M
L;)
-
(
-
~
J
~
~
P
)
Q
~
0
- P I - Q P P - 7 3
O O M M C ~ ~ L ~ J ~ O .
.........
OD
0-0'3033.0 3 C O C T a O O
0
I
1(
W W W W W W W W
O - P I . O O ~ Fb
ODQQC.ccrdli)O
O h m b 7 N h 4 P 4
O.NNh)NM&P)
C' 27
3 0 3 0 0 0 C 3
0
\
-Ll
+++++
-.
......-.
~
~
O
D
r4
- ........
*,
O O * P J ~ ~ > F , > ~
3 0 0 0 0 0 0 3
-6
WLLiWWWWW
CI .rc?CDOb>M
3
h a d r u V M O
LFJ'CO.OLI>*~CJL(
pl
+ - L - t + + + +
I
c>eo*.rmoo
i4-I
M
3
I
i
~ h r n m m ~ h *
~
0 0 0 0 0 0 0
c'. 0 0 0 0 3 0
.I
rl
I
3 3 0 0 0 0 0 0 Q 0 0 0 0 0
?
.........
e00oooooa
'?
+ C . + + + + + + + + & + + I
3? 9* h ~ O I 9 N ~ . l W Q
Lilm-eINrI.-.Ov
t
0 0 0 0 0 3 0 0 6 0 0 0 0 0
2
1
O C 0 3 0 0 0 0
1
1
+ + + + + * + I
W W W W W W W W W
Plb>ilP90.+9C4aO
, *?
' ~ ~ . r m * r u ~ a . r ~ ~ . m m m n ~ - v h m ~ ~ e r n . ~ * r n n * h
2
4 0
4
X
I
.
-. - . . . . . . . .
~ M P ~ O ~ h ~ S O O N h N b > ~ O M hw Q Q D b > h O O 0
C O O ~ . - U - N F I P I M ~ * I F I . O ~ C O ~ ~ U O Q - C I * M 9 h C I
q
O
C
I
0
...................
.
U
I
' . * " '
0 6 0 0 3 0 0
0.0
1;
0'3000:
! + + + I
Y W W W W
-lh e T b 7
r>mo.rn
Y ~ > E
9 C 1 w .-by
.....
h
1Q
1-
~
.i.4
'4
?6c',CC1
1
3 rnCU9hO.m
.......
U
0 OHPAt.dOD
M
0 000000
\
C)
\
I(
i
*Ob>&b>
3 ~ l l f
.....
> C O O C
~
a
~
a
0
4
29
~
~
0 wwwwwwwww
91Y00.0tn0.9
8 mN9d-I-OQI01
.
M-L>-'OCuOD.
.-ctwmm-rcbrd
I C IO
*
q
0
I
9
C
0
+
W
c
. . 4 ~ . . l ~ ~ d 0 0 0 0 0 0 0 0 0 - ' C C , 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ + + + + + + + + + + + + + + I
WWWWW.JsC:+ W W W W W W W W W '
* * b m v ~ v . ~ - - N 0 0 F ( 0 ~ 0 0
~ > ' I Q o o ~ ~ w M w F ( N ( v e* ~ ~ ~
b?-t4NF(fldM-*M=WhSOON
F . - ~ - , ~ ~ ( O . ~ T ' C ~ ) * : P J . * ~ ~ W R
W W W W W W W W
w r 0 c t ~ ~ 0 . r
h-rc*mC)wO
.....
.-cf.*b9
O O O O Q
L
1
0
2
0
8
a
.
%
&
O m 6 0 0 0 0 00000000
+ r +++++ t
W W W W W u r W W
QaIStmSctCV
[email protected](O.F(flNh
x
9
........
m ~ . * o n q ~ m m
h
OD@NCUIYrrrt
(Y
O O O Q C O O O
0
0
I
h m m a ~ h *
<* O'??Y?"i'lvi":
O O O O O O C O
.-
'q
Ifl
W W W W W W W
* O O . C 9 3 9
0
I
CbrnmsotnQD
C
bI
-
- 0 0 0 - ,
O C O O O
l + + + i
W W W W W
NQOMD.
(ilPCDa,P
OhCJdlr?
9' N* P" d*+ ' 0
3 0 0 3 0
k?
-
'
0
%
?r
3
I
U
*
I
0fQN9hPm
.......
O o - N w 9 m
ooooooo
-
. .*..f.. .
QO(r.DY1
U 0 r4
Q)
*
\
0 0 0 0 0
4
U
* - v 0 0 0 0 c t ~
0 0 0 0 0 0 0 0 0 '
+
I
+++++
1
I
W W W W W W W W W
M h w - I 9 * 0 * 0
[email protected]
* S ( Y h N * + t 9 *
" L l ) N l U ( U - ~ * N
.........
ooooooooc
I
I
.
-
'I0 I
000000r(H"
000000000
, + + + + + I
1 I
W W W L U W W W W W
( \ ( h * 0 9 0 h d Q
e*)o*hmY)nn
- 4 h r n S W T d t F ) b
,-'.FJ-(Y(Y~Ph(Lil
. * - . - a * . .
0 0 0 0 0 0 0 C \ 0
i*
2
" r'1-tQf
W P
PC'
.........
0 3 - * ~ n l i , h ~
, G 0 * 0 0 3 . 3 S
OhIDmCD-h@
0 0 - r d ~ m 3 n h
........
0 0 0 0 0 0 0 0
-
-
0 e 0 0 0 C ~
0000000
- @ O O *
I
W W W W W W W
W h c ) b
I . r + +I
W W W W W
-oQull>9
++++++
\i,rnI.h.lhN
*03*mli)om
.......
0 0 0 0 C ~ ~
.>>
4qq@(i)
4hc.30
. . . .4
a)ccsli)r?c.ro.
G3
C 3.30030
.?eOeo
I
rl
r.14
X,
-3
?I
0
I
Orn(ubF*m
OOr*Cblr90D
7@rnVlI'i
O t J T * Q
O C C 3.200
eoaoc;
.......
.....
el
u
-
O d r * d d d r c . . l 0 0 0 0 0 0 0 - N r c
000000000000000000
C + + + r + + + + + + + + + + - I
I I
W W W W W W W W W W W W W W W W W W
-u+rq~--csnnedm+-q
0 0 0 0 0 0 - ~ ~
000000000
++++++I
1 1
W W W W W W W W
6. W
O t * T * ) S h Q D O
o n ~ ~ ~ ~ n e ~ ~ n o s m I
@ a ow m
n m en o m c u m
M O O O ~ W N ~ Q N ~ P ) O ~ ~ m
~ h ~O O
- l Q N Y ) O
9.44..lM-d..l*QmmMNdhm*
hNrcNCYMQIrch
. * . * . * . . -
* * * * - * * * * - . * * . * * . *
:,~0000000
O O O O O O O O O C O O O O O O O O
I
I
d O O r c H .
0 0 0 0 0
6
a
C
1 + + I
I
w w w w w
m n m - r l
m k n d w
Ob')**rn
.....
QDol-o..r
3 0 0 0 0
I
U
\
n
1.1-.
~ n c u +* m~
.*....
ooooooo
u
O O - N * 9 Q i
- .
32
.roYI*u>
..
O(VPQ0D
C O O O C
'TI
I
I
I
1
I
,
,
rn
I
8
I
I
I
I
I
4
--
!
~ 3 ~ - . 4 ~ - 0 0 0 0 0 0 0 0 - d
3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
I + r + + + + + + + + + +
l l+ +
LJ J W W W W W W W W W W W W W W W W
rl h 3 0 l O O h 9 d M b 7 9 d n L D m O
D h n d . - h - m m m P 4 P . - a S P h
iD m ' 4 - 4 - 0 0 - m h O - r I n h 9 ~
t\ b 7 - - a - d . 4 a 9 1 b > P m N - ' b h
o o o ~ o o o + -
<~ 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0
1
I
0 0 0 0 C 3 0 0 0
I I
I
I3
.................
0 0 0 0 0 0 0 0 0
I I
WWWWWWWWW
riPaDmD.tl7.4-0.
@ ? h 1 4 C m C J 9 0
FJSVlr3*hb7**
b7rJ~NCJN-'Ob>
+++++++
.........
G
-,
I
I
I
I
*
<
*
.-
I
I
0 0 0 0 0 0 d
0 0 0 0 0 0 0
0 0 0 rc
d..
mm-JO).-*m
0 0 0 0 0
+ + + I
I
WWWWW
rJOPOD9
-*m*ofiC*
Ob9h-P@m
0. LD Q l i l r n - a
-*.-a-
0 9 0 rJm
d W . 4 P M
0 0 d 0 3 C C
O O O O O
I
++++++
I
WWWWWWW
.......
IL
.....
WWWWWWWWW
P M9)3'D9*0-h
hl d d h t Q P . l h i U S O .
*
q
0
I
C
LC
0 6 0 0 0 ~ - d ~ ~ 0 0 0 0 d d ~ d
000030000000000000
+ + + + + + + + + + + + + + I I I I
WWWWWWWWWWWWWWWWWW
w
F n b M * O O P . 3 9 f ' 9 ~ m h w w - '
O. V I S N Q h 0 P . m
n - . r ~ w . r ~ . r h h i ~ ~ . ~ m ~ o ~ r n ~~ r )- . e . m n w n h
m h t P h 0 3 d - d t m h N m O S m
..................
*
wwwwwwww
mhmQ)*ddM-r(rlmnd*S(YMO.
3 0 0 0 0 3 0 0 0 C 0 0 0 0 0 0 0 0
I
I
.....
'rOY)O.b>
ONQSID
C O O C O
-
~ O * ) r c d r c r c d d
000000000
C; + w +W lW IW I WI WI WI
*
I
\
)1
u
%
?
WI W
z,
rcFIo~(DmV)ODNm
C I I O O . h h M h O *
~ * u ~ O 9 O C a V I
..1N-l9hh9P(U
3
.........
V) '
0
* 0 C I 0 0 0 0 C 0
I I
~ h - O W W d D P V I
o q ~ C V M b > 9 h O D
.......
boooooooo
0 0 0 4 . - d ~ P . ~
00'0030000
+ + + I t
I
l
l
I
0.W U J W W W W W W W
m O b 7 n N O - * P
I P)o~Qa'Nb>CDC*l
Y * ~ @ n n b > h b ?
%
O:Tyy:'4-yCI'y
L?
~ 0 0 0 0 9 0 0 0
' 1 1
I I
3
0
.
- * v m b > n + e c
........
'2
Y
,,,,,,,,,,
3 ' 0 1 C4
.
4 4 CC iPP
W W ~ W W W u W W W
torno-womrrrn
I
LC
LC
3
a
-&
Wb>m..I+r)dHq)
C-J
.........
0
I
0
I
0 0
I I
0
@
~
. .
0
I
G
0
4 < ...........
+ P J d ? . r Y h C r O
C 0 4 * c 4 M b > h O -
0 c . 3 0 0 0 C ~ C I 0
00
2
0
,
= o r c d d O * r
. ; 6 0 0 0 0 C 3
+ + I
I I + I I
l L I W W W W W W ~ ~
o n c( r.4 h w b-.
-
-,
o
TwFI-dOmP
~ r I ~ M 0 0
@ h ( V 5 * - I P b *
........
0
1
ri)
~
P
'
Li)
s
3 0 0 3 0 0 C > c '
I I
I
0 h m m m - 1 x 0 .
4 4 4 d.C l.r ) L.C.) l r.> h.
0 0 0 3 0 0 0 0
0
~
0
G
0
0
0
C 3 0 C 3 0 0
+ + + + + + I
W W W W W W W
Vl .O PJ "I r b? a
-
L T J S T P ) C ~ ~ . . ~ I
I-'P' .'L P r
.. C.
M
.
x, v:
rr
_
.
.
I
.
* ' t l
.
w
. - C-.
-
,
G r r r r r r c
0 0 0 00"
" ' + I I I I
6
I
w
w w w w
11'1 f i .o ,\ 0
r)
Y:
.'
P h E - d
.P.dcrG@.
e. .w.I..irs. .
PI
LC
.
U
\
T
rr
3OC.C.G
C.
*Ob>O.y)
oc4903
B4
. - . a *
U
~ 0 0 0 0 0
A
. .-.
- --
.-.-
.-
.--
--
w ' * - M " 0 C 0 0 3 0 0 0 0 0 S G O O O c O O O O o O O O O O O
I'
WWWWWWWWWWWWWWWWW
0 d b - J - @ l N O r n 9 P m * * m * P o
h
-*++++++++++++++
u
rn-1name4~~*rnmern*nmoa
m O h r d w O r n r ~ F D
M O S O N c I *
- c . ~ w - - . - l ~ . m w n n ~ m n m ~ a
................. 3
D
00000000000000000
0 0 o-r,0.-8-Fl
0 0 00000'00
6
I
h
+ + + I I + l
I
W W w w w w w w
me4 - m - r n ( P - m
h
**
b
h
I
w
~
y y. y. ~. .o .o.o.o
?aQ.-l-*-avl:
I
I
00---.-.-I:.
?
0
8
\
-
3 0 C 0 0 1 > 0 0
+ + I
I I , I !
WWYWWWWW
0 - 4 0
C.1 [rr t-I
(t
~ , a , ~ n n m h m
. . . . . . .cu.
homrn+:.tn.a
~ ' C a~
J m.a~0
00000000
1
'I.
omr19hCbr9
,odm...
I
m
T c c h 3 M h h
I
o
~
~
~
ff
6
rtCIC(rtudcl-LV
0 0 0 0 0 0 0 0 0
+ + I 1 1 1 1 1 1
W W W W W W W W W
, ~mmnfinor.r\
.(
.
,or4mb-~a9-00.
rcOrnPIeJbr'v,cr
. . I ~ * ~ o P ~ T F ( ~
. * . * . * . * *
000000000
I
I
I f.1
W W W W W W W W W
CROor-JmmPSLn
.I1*o.o.o.03
r4l.
0
WL~Iwrr!wlLiwd
Q ~5, 0 h p i by LU
o
a, b
mr:
o- ,-- +r m~e c
wr . o
~ e a c
\
.E:
r;
........
0.Vb>-+w9.h-
0 0 0 0 0 C ~ 0 3
I
I
I
OhoJa)m.-Ih*
........
-.
-
co--.~nv,li,h
~
- -o o c o o o o
ow-+..
2
O O O O G '
+ I I 1 I
Y W W W W
.. . . . .
1
I
b,
'
U
W
P**tr)P
C 1 9 - 9 9
n
u3
f.hqU?rd
rZ)
G Q O C O
I
C.
vloaver
.....
.z
QOLnO-Li,
C C d W d Q )
00000
0'
I
8
d
,
.\
2W
*
(q
0
I
\
L ' o H O o d H r C @
O - ' - - ~ O C Q 0 3 0 0 C 0 0 0 3000000000000000
@
?
+ + + + + + + + + + + + + + + I
o
a
wwwwwwwwwuwwwwww
O O O O C O O O ~
wwwwuwwww
O W h N b 7 * I 9 O - f Q * Q 0 ~ 0 - 9 0
O G O . - o . - o ~ N C 4 ~ ~ W b > O 9 h ~
. . - . * * . . - - * * * - * -
0000000000000000
w r r d d d O C C ~ C O ~ f C 4 & w
t 3 C = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
+ T + + + + + : T + + * + + + + I
I
W I u L L W W W W i & l w L ' i l l W W W W W W W
rib h 7 Q M @ Q b l L i Q 9 S * h 9 0 9 M
b ? @ L i l Q h . f - C i T b 7 M 9 9 ( D m P b 0 .
9mh@hn~-'@~)b3i,mns>1r,ch
ddd-4.-lcCObI;)MPMml'lrc(DrJ~
.
r
.
.
-
r
-
.
*
.
-
.
*
.
*
.
-
.
-
m
w
O
w
I
b,
%
a
Y
U
U
h
W
0 0 0 C 0 C 0 0 0 0 0 0 0 3 0 0 0 0
0
W
0,0000000
*
*
.
a
*
-
-
-
*
---
C.-,..4+.4dWF~..4
y
L 0 0 0 0 0 0 C S
=
NOIiJt400PS99
L - J h h C U T d * T r
C1V)O.hLF)LFIOI-C
*k-,hSODli)M*
+ + I I ~ I : I I
0. & 4 U W W W W W W W
m
U
M
* . . . - . . . - . * a - . . . . .
In
Ob-QQC?-~MQB7
O O H C J ~ I ~ , O ~ T
-
d M ? T G C m h d b O b 3 ? , : h f < b 7 m O h
iJOC.CMdmCICbMmd*M9i\;O00
A
9
u
2-4
fi
0
b'l
a * * . - - - . -
0
C)000000ao
I
hl
a.
o . ? - ~ r . m ~ n o . ~ - 1 0 n e 4 m ~ o m m
o.o.ncro*mso
bhO-?UCIb>Ck3P9VJFlh00
OQbPdm@Oa3*
O I b U i ~ v , ~ b ~ k > M e ~pl ~ . -~o 9~9 . . . . 1 ~ . l ~ ~ C r O
~ ~ A d c l C D 9 k n Q . Z ~ ~ t ' ~ r ~ ~ %
- ' ~M ( r ( 0 4 W @ Q ) k n ~ I
. - * . . . . . * . * . - . . *
* . . * . * . . *
y
0000000000000000
O O O O C O O O O
I
I I
0 C G C 0 0 4 0 0 0 0 0 0 0 0 0 0 0
2
I'l
+ + , + + I
l
l
I
1
A.Y.fCali)b@cIG
0 0 4 f . l . r k - J 9 h *
*
.
a
*
.
-
*
-
-
0 0 0 0 0 0 0 0 0
0 0 U P ; 2 . 0 0 ~ "
,
*3
& r c
''.
d
U
0
a
e-4
bt
0
I
w
i~1
4
Cc
0
* ~ - h m m + m n m r ) m ~ 1 ~ ~ ~ 4 r t ~ . i o
w
,
0 3 G 3 0 0 0 0 0 0 0 C 0 0 0 0 0
I
%
td
ri,
-7
C
- . - - . . * * .0
6 0 0 0 0 0 3 0 0
I l l
I
b
Q
m
3 e e h w V ~ h d P C b > N 3 9 b > C 0
$
3
M r . J - 4 - r f
S T 3
* ~ ~ ~ ~ - - ~ ~ ? i n n r r r a - eo o
~ - -r p , ; l u , r x ~
. . - - a
I
.
,
.
.
.
-
*
.
.
.
.
-
~ O O C C . O 3 c ' o O C o O o O O O
d
m
* > ~ D M ~ ~ W > b > O C + C ~ J C 4 r h O
*
c,daoooocc~
?
=LI-:occ2
OOCGOOC,
++ I + + + + '
*
.
.
*
*
I
-
*
.
N
-
d
I
u
5
0
8
46
y
* - - = = c ? s ~ C C o : ; *
o r cosac,onscoeo
- ~ + r + i + + r ~ 4 + r + + l
~ W W W W o ~ W W ~ ~ W w w W
W i h i C ) ~ f l C C F . OC ? * 4 + @ 3 d
'~)r;---ococ-r..
-~a>i?u>n
Q ) ~ ~ \ 1 > ~ 9 C I d ~ ' c W Q d ~
dcdO.Qb99QTMk-J4CO
.
.
.
m
a
.
-
.
.
.
-
.
.
*
> c ~ 0 0 0 0 C O O o 0 0 0 0 *
<. o. o- .o.0* 0. o. .o*o- o o o 0.,.o . .
? 4 ~ 5 b - J @ I 9 & M ~ T C 4 d D O
o ~ - . - o d ~ r ~ r n n . r k n a p m
0
pb
4.
y
*
LriLuWWWWWi&l
0 P) 1s) O. C.1 @ k-J ',h
.r
SLi)QP)mCIo-l
O.VSc(-lc(~Q
?.J
O O O O C O O O
0
...-""
I
o
W
0 h O D a D Q ) d h O .
0o-~rnli)11>h
* . . * . - - -
00000000
-.
?
0
'
N
y
C b O O O C . 0
+++++++
?
0
-
L U ~ W W W W W
('1
0. .
r b-1 lh r?
"7 b-, b f i S* T 0
'2 3 LD P4O- P r O
L-1
r cc Q P) PI rr
=
I
*....-.
ooooooc
b
I
2*
...
0
0
.
-
0 0 0 3 0
+ I l l !
WWLL'WW
h 0 k? P- 0.
r3 k-J b? 0. 7
U 3 9 T 1
1
7
c?D.c~~->" . . *
C- o c,c. o
-. f*~.l .i .t ~. . n
Q P ) ~ J Q ~ @ - ~
O b H N Q 9 a D
Orlq-QG!
.
0 0 0 3 0 0 0
0 0 3 G 0
40
ii,
I
I
C---r,
C ~ 9 3 O S O
.c
o.L-,o~-v~o.-
A
4
,
I
-
m
'F
r.
t;'
. -
ORH31NAL PAGE IS
OF 'POOR QUALIW
C\
BLADE CONST RUCTtON
7.5ft
HUB-SCANIVALVE
ASSEMBLY
I
HOT W!RE WAgE
TRAVERSE
\
>
6 in.
143m)
,-
4
I
120 in.
(3.068rn3
, WAKE
EXHAUST
DUCT
4
'
Figure 1.- The model and experiments1 set-up.
UPPER SURFACE
UPPER SURFACE
LOWER SURFACE
I
I
0
.5
1.0
4
/
0
.5
1.o
0
xlc
xlc
52 = 1750 rpm
Mtip = 0.612
-1
.,.
UPPER SURFACE
R = 2500 rpm
Mtip = 0.877
R = 2250 rpm
Mtip = 0.794
-1
,/
UPPER SURFACE
UPPER SURFACE
LOWER SURFACE
C~
0
I
1
0
.5
xlc
1.0
0
.5
xlc
1.o
Figure 2.- Comparison of measured pressure distributions at r/8 = 0.8 from each
blade; collective pitch Bc = 8' (solid line = right blade, open symbol = left
blade).
figure 3.- Measured pressure distributions; collective pitch
8,
-
5'.
L
-------$2
= 1250 rpm
M T l p 0.439
CT '0.00459
---R
r/R = 0.80
= 1750 rpm
MTIP= 0.612
CT " 0.00455
-
= 2250 rpm
MTlp= 0.794
CT = 0.00462
5'2
.5
X/C
1.0
--- $2
= 2500 rpm
M ~ l p 0.877
=
CT = 0.00473
Figure 4 . - Measured pressure distributions; c o l l e c t i v e pitch
8,
-
8'.
L
---a
= 1250rpm
MTIP
0.00796
CT
-a
r/R = 0.80
-1750rpm
0.610
CT a 0.00807
-1
----
52
= 2279 rpm
MTIP' 0 ~ 7 9 ~
CT "0.00792
.5
x/c
-2
1.o
-
.
r/R = 0.68
r/R = 0.50
C~
-1
0
-
.5
x/c
1.o
xlc
Figure 5.- Measured pressure distributione; collective pitch
0,
12'.
TEST DATA, 8, = 8"
SZ = 1250 rpm, CT = 0.00460
0 !2 = 2050 rpm, CT = 0.00461
0 $2 = 2500 rpm, CT = 0.00464
REGION OF LOADING VARIATION
DUE TO RPM CHANGES
0
.4
.6
.8
RADIAL STATION, r/R
1.O
F i g u r e 6.- E f f e c t of r o t o r speed on blade span loading.
-
PRESENT TEST DATA,
0, = 12", MT QPe,r/R 496
0 GRAY'S TEST DATA,
Oc = 1l.So,MT = 4260. r/R = 0.966
PRESENT TEST DATA,
8, = 5 ,MT = 0.226, r/R = 0.96
0 GRAY'S TEST DATA,
Oc = 6.18', MT = 0.250, r/R = 0.966
x/c
Figure 7 . - Comparison of present r e s u l t s with s i n g l e blade t i p loading data.
\
4'
'VORTEX
(TOP VIEW)
PROBE-VORTEX CORE
INTERSECTION POINT
/
VOR1 EX SHEET
TRAJECTORY
I
Figure 8.- Typical wake probe data.
0
A
+
P:
--a
0
0
50
S2=650rpm
52 = 1250 rpm
52 = 2540,2414 rpm
52 = 2250 rpm
CURVE FIT OF PRESENT DATA
\
KOCUREK, TANGLER DATA, Cp0.0046
100
150
200
250
VORTEX AGE, JI,
300
350
400
4%
&g
-
Figure 9 . - Wake geometry measurements for various rotor speeds and comparison with
8".
c l a s s i c a l data; c o l l e c t i v e pitch Bc
0
50
100
150
200
VORTEX AGE, ,$
,
250
deg
300
350
Figure 10.- Wake geometry for various pitch settings.
Figure 1 1 . - Typical - ~ r t e xvelocity-time trace and 1/R curve f i t for various pitch
s e . t i n g a ; vortex age = 50' (nominal), fi = 1250 rpm.
Figure 12.- Typical vortex ve1ocit::-time trace and 1/R curve f i t for various ~ i t c ! .
s e t t i n g s ; vortex age = 200' (nominal), R = 1250 rpm.
Figure 13.
Typical velocity-time trace and 1/R curve fit for vartous rotor
50"-65'.
speeds; collective pitch Bc = 8'. vortex age QV
.5
TEST DATA 8, = 8", OR = 150 m/s (491 fpr), CT
-
MEASURED WAKE GEOMETRY, CT = 0.0048
CONTRACTION REDUCED
BY 0.025 R, CT = 0.0047
REGION OF Cp VARIATION DUE TO WAKE
GEOMETRY CHANGES
,
,
VORTEX
.4
-
0.0046
AM1 LIFTINGSURFACE THEORY
. .......:
'.I
_
.... . . .
u"
I--
5-
0
.3-
U.
&
8U
t-
J
J
a
z
9
-2
-
k
Y
V)
I
0
I
.2
I
I
.4
.6
RADIAL STATION, r1R
I
I
.8
1.O
Figure 1 4 . - E f f e c t of vortex p o s i t i o n on loading computation.
- ---
TEST DATA 6, = 12". QR = 150 mls (491 fps), CT = 0.079
A.M.I. CODE, USING MEASURED WAKE GEOMETRY, CT1 0.0083
A.M.I. CODE, VORTEX CONTRACTION REDUCED BY 0.025 R,
CT = 0.0080
/@I\
-
I
.3 1
0
I
.2
I
I
.4
.6
RADIAL STATION, r/R
\
1
.8
Figure 15.- Comparison of measured and computed loading.
J
TEST DATA, 6, = 5", a R = 150 mls (491 fps),
CT = 0.0021
MEASURED WAKE, A = 1.0, CT 0.0024
CONTRACTION REDUCED BY 0.02R
A = 1.0, CT = 0.0025
CONTRACTION REDUCED BY O.02R
A = 0.81, CT = 0.0023
-----
---...---
i
-
.2
Figurc 1b.-
.4
.6
RADIAL STATION, r/R
/-\
/
C
.8
Comparison of mec~sured a n d computcd l o a d l u g .
1.O
O
TEST DATA AT 0.8R MT = 0.877
a = 2.10° (FROM A M.I. CODE)
-1.0
C~
0--
FINITE DIFFERENCE
CODE,INVISCID
FINITE DIFFERENCE CODE
WITH VISCOUS EFFECT
-
[T. HOLSTI
0
Figure 17.- Comparison of measured and computed chordwise pressure distribution.