nasa-cr-201062 development and testing of airfoils for ...1.5 test section instrumentation and...
TRANSCRIPT
NASA-CR-201062
Development and Testing of Airfoils
for High-Altitude Aircraft
Final Report
for the Period
September 1, 1994 - May 31, 1996
,f
Submitted to:
Attn:
Technical Monitors:
NASA Dryden Flight Research Center
Steven Yee, Grants Officer
Contract Management Branch/XAA
MS D1044
Edwards, CA 93523-0273
Robert Geenen, Al Bowers
Fluid and Flight Mechanics Branch/XRA
MS D2033
Submitted by:
Grants Officer:
Principal Investigator:
Department of Aeronautics and Astronautics
Massachusetts Institute of Technology
Cambridge, MA 02139
Ms. Charlotte Morse
(617) 253-3529
Associate Professor Mark Drela
(617) 253-0067
June 1996
https://ntrs.nasa.gov/search.jsp?R=19960050516 2020-02-24T03:54:34+00:00Z
1 Completed Work
Essentially all the work proposed in the proposal has been completed or adequately
addressed. Additional work on heat-exchanger aerodynamics not in the original pro-
posal was also conceived and executed with the agreement of the Technical Monitor.
A summary of the specific tasks accomplished is given below. The corresponding
detailed results have been transmitted to Dryden personnel via e-mail as soon as
they became available. All e-mail transmissions have been saved, and the key ones
are given in the Appendices, along with relevant plots, figures, and papers which were
generated.
1.1 Airfoil design
The Apex-16 airfoil was designed specifically for the APEX test vehicle. It is in-
tended to be representative of airfoils required for lighweight aircraft operating at
extreme altitudes, which is the primary research objective for the APEX program.
In the course of designing this airfoil, Fairly extensive studies were made over the
Mach number and Reynolds number ranges of interest. Also considered were the
airfoil thickness, pitching moment, and off-design behavior. Limited use was made
of the optimization driver LINDOP [1] to fine-tune the final design and resolve the
numerous conflicting requirements. Appendix B shows the Apex-16 airfoil geometry,
coordinates, and computed performance polars.
1.2 Study of airfoil constraints on pullout maneuver
The maximum ceihng parameter M2CL value achievable by the Apex-16 airfoil (or any
airfoil for that matter) was found to be a strong constraint on the pullout maneuver.
It was concluded that if data is to be acquired in level flight, then some sort of lift
augmentation would be required, since any airfoil has little or no excess-hft capability
at its ceiling condition (by definition). A workable aiternative approach which was
identified is to use wing lift to achieve pullout, but then acquire data in windup turns
to achieve the target CL.
1.3 Selection of tail airfoils
Several candidate airfoils for the tail were examined. The primary goal was pre-
dictable behavior at low Reynolds numbers, and good tolerance to flap deflections.
The NACA 1410 and 2410 airfoils (inverted) were identified as good candidates.
1.4 Examination of wing twist
A number of issues related to wing twist were examined. These included: simplicity,
obtaining a uniform local cL across the test section, obtaining a high overall CLm,,_
for the pullout, avoiding tip stall. Both washin and washout options were examined
computationally. In the end it was decided that a simple flat wing was a reasonable
compromise between all the requirements, and allowed the use of one mold for both
wing halves -- a significant cost saving.
1.5 Test section instrumentation and layout
It was decided that the instrumentation for the test section would consist of surface
pressure taps, wake rakes, surface-mounted microphones, and skin-friction gauges.
Using multiple wake rakes was deemed desirable to verify spanwise uniformity, but
was found to be too demanding of the limited data bandwidth available. Using a
single wake rake mounted on a mechanical traverse was rejected due to weight and
complexity. It was decided to use a single fixed wake rake for accurate measurement of
the wake momentum defect, and multiple integrating rakes to verify spanwise unifor-
mity. Several test section layouts were designed, with varying degrees of compactness.
One of these was selected by Dryden personnel for use on APEX.
The wake rake was designed specifically to capture the wakes anticipated at test
altitudes. A design guide for the integrating rakes was also prepared. The layouts
and design guide are attached as Appendices B and C.
1.6 Integrated airfoil/heat-exchanger tests
A modest wind tunnel test was performed for an integrated airfoil/heat-exchanger
configuration, which is currently on Aurora's Theseus aircraft. Although not directly
related to the APEX tests, the aerodynamics of heat exchangers has been identified as
a crucial aspect of designing high-altitude aircraft, and hence is relevant to the ERAST
program. The computational studies and tunnel tests have proven the validity of
integrating the heat exchanger with the wing airfoil to achieve surprisingly low drag
levels at low Reynolds numbers. The results have already appeared in the Jan-Feb
'96 issue of the Journal of Aircraft [2]. This paper is attached as Appendix D.
References
[1] M. Drela. Design and optimization method for multi-element airfoils. AIAA Paper
93-0969, Feb 1993.
[2] M. Drela. Aerodynamics of heat exchangers for high-altitude aircraft. Journal of
Aircraft, 33(2), Mar-Apt 1996.
6 in
0.3 in. I
m
m
m
m
m
m
m
5
4
2
-1
-2
-3
airfoil baseline
APEX Drag Rake LayoutFull size
Mark Drela12 Dec 95
4.8 in
m
m
m
m
m
m
- 5
4
3
2
-1
-2
in
airfoil baseline
APEX Integrating Rake LayoutFull Size
Mark Drela19 Jan 96
°°°°°°.o°°°'+°°°°°
o°o°°°°
. . ....... Stanton tubes
• _.• m
°°°°°+.° o°°°°.°°°°°°'°°*°°°°°"
°°.°°'°°
,:;_'o Microphones
"*_. °
• •. 'O°oooo+Ooo_+,.
".. 0
°°°.°°.+o°.°,°°° °°°°°°°°'
........ "Pressure pl)rts
°°°'
o.-°°o
°°°o
°°°-°"
°°°°°
support sting
integrating rake
support sting
wake rakerake statics
APEX Instrumentation Layout
(proposed)Mark Drela7 Feb 96
support sting
Stanlontubes
.., ..,.• Microphones0
• O00eO00000 • • _
Pressure ports
°.o"
, support sting
integrating rake
support sting (lightweight)
wake rakerake statics
support sting
1,1,,I,,,,1''1
APEX Instrumentation Layout II
(proposed)
Mark Drela9 Feb 96
Stantontubes
"'Y"_'-L• Microphones
°°@°eOo°@°@ • °
°°°°o°° °°o° °oo_o.°°'°'_°°°°°°°"'°°°
oo•o** • • • • • • • *oo*•oo_.*o* * • • • •
Pressure ports
m
.°°°,
support sting
integrating rake
support sting (lightweight)
wake rakerake statics
support sting
APEX Instrumentation Layout III
(proposed)
Mark Drela9 Feb 96
Appendix C: Integrating Rake Design Document
7
Integrating Rake DesignMark Drela, MIT Aero & Astro
10 Dec 95
Ue _.
¢
I
(y)
1Ay
Z
d_T____.___
II rhi
I_I[ LIIII
Figure 1: Integrating rake layout and dimensions
1 Basic Relations
An integrating rake consists of an array of pitot tubes all feeding into a common reservoir,
as shown in Figure 1. Assuming that the static pressure across the entire wake is constant
and equal to the edge value pe, the wake velocity profile u(y) will produce a y-dependent
total pressure seen by the tubes:
po(y) = ½Pu2(y) + pe (1)1 2
= _Pu2(Y) + Pooo _pu_ (2)
The non-uniform po(y) will produce a mass flow rh_ in the i'th tube. Assuming fully-
developed Poiseuille flow in each tube, this mass flow is proportional to the driving pressure
difference po - p,, where Pr is the reservoir pressure to be measured.
_r d4
rhl - 128 ve (Po, - P,.) (3)
At steady-state, all the tube mass flows must add up to zero, and if all the tubes have
the same diameter d and length 2, the pressure differences must add up to zero as well.
N
Era, = 0 (4)i----1
N(po,- ;,) = 0 (5)
i=1
Substituting for Poi in terms of the local velocity ui, and multiplying by the presumed-
constant tube spacing Ay, we get
N1 2 - _pue+ po_- p,) ay = o (6)
i=1
N
E (e_ - p_) Ay = 2(po_- p_)L (7)i=1
whereN
L = _Ay NAy (8)i----1
is simply the height of the N-tube rake as shown in Figure 1.
The lefthand side summation in equation (7) is seen to be a midpoint-rule integration for
the momentum+mass defect
pu_(o+ _') - f(pu_ - pu2(y))dy (9)
_(pu_- pu_)Ay, (10)
so that with the constant tube spacing Ay, the final result is
p_(0+_*) _ 2(po_-p_)L (11)
or 0+_* __ po_-p, L (12)po o_- P_
For the most accurate measurement of 0 + g*, it is clearly best to reference the reservoir and
local-static pressure transducers to the freestream total pressure Poo_, so that po_-p_ and
Poo.-P_ are direct measurements with no bias uncertainties.
2 Near-wake Corrections
Note that the integrating rake does not give the momentum thickness in isolation. If the
measurements are to be used to support or validate drag calculations, this causes few prob-
lems, since the measured sum 0 + g* can simply be compared with the corresponding sum
from the calculation. If the goal is absolute drag measurement, then it will be necessary to
estimate the shape parameter H = 5*/0 to deduce the isolated 0. This can be done fairly
accurately if only the minimum velocity in the wake is known.
Umin = min (_ee)(13)
Measuringthis will typically requirea separatetotal pressuretube placed sufficiently closeto the wake centerhne.
Assuming the minimum velocity is known, a wake velocity profile is then quite closely
approximated by the Coles cosine profile
1[u(y) _ Um_n+ (1 -- Cmln)_ 1- cos _ ; -5 <_y <__5 (14)Ue
where _ is the wake half-thickness. From the definitions of 5* and 0, we have
5" = 1 - - ey = (1 - u=_15 (151Ite
= dy = (1-Umin)_ - (1--Vml,) 2_ (16)
1
H = 1 - 3(1 - Um_,) (17)
and the isolated momentum thickness then follows immediately from the measured 8 + 5* .
_+_*e _ (18)
H+I
The above results also apply to moderately assymetric wakes (such as the one sketched in
Figure 1) since each wake half above and below the velocity minimum is still accurately
represented by the Coles profile.
Both Umi_ and H quickly approach unity downstream, making their measurement or
estimation less and less critical. Ideally, the rake should be moved downstream until it just
captures the entire wake, but in practice the wake thickness and location are somewhat
uncertain, and some conservatism will be required.
However the shape parameter is estimated_ a correction will still need to be apphed to
the resulting momentum thickness if ue/u_ at the rake is not unity, as is usually the case.
The true profile drag/span is simply the ultimate momentum defect
D' = pu_e_ (19)
where 8_ is the momentum thickness very far downstream. The evolution of the momentum
thickness in the wake is given by the yon Karman integral momentum equation
1 dO 1 du_
O dx - -(H + 2)---- (20)u_ dx
which can be integrated from the rake position to far downstream if a unique function H(ue)
is assumed. The particular empirical assumption
(21)H-1 \ H--1 ]_k¢
results in the well-known Squire-Young formula.
_¢_: 8rake((Ue)rake)(H'ak_+5)/2uo_ (22)
3
3 Design Requirements
In light of the assumptions made in the derivation of relation (12), the following requirements
must be met for the result to be valid.
1. The flow in the tubes is fully-developed Poiseuille fow.
2. The flow in each tube has negligible dynamic pressure.
3. The static pressure at the tip of each tube is the local total pressure Po(Y) •
4. The pressure in the reservoir is uniform.
5. The tubes all have the same length l, diameter d, and spacing Ay.
Requirement 1 is equivalent to stating that the profile-development entrance length for
each tube must be very small compared to the tube's length. This gives the requirement
rh_>> (23)
4_/z
d puo_dor e >> (24)
16 #
which makes the worst-case assumption that po_ - p, "_ pu2/2, corresponding to the entire
rake being immersed in a massive separated wake. In any case, it should be possible to meet
the Poiseuille-flow requirement without too much difficulty by using sufficiently fine tubes.
The only drawbacks of excessively-fine tubes are fragility, and possibly an excessive settling
time.
Requirements 2 and 3 are essentially equivalent, since negligible dynamic pressure in the
tube automatically imphes that the static pressure at the tip is nearly the full total pressure.
The requirement is
rh_<< u_ (25)
um¢,,= p_r(d/2) 2
1 du_d
or 64 l u << 1 (26)
which turns out to be essentially the same as Requirement 1.
Requirement 4 means that the dynamic pressures in the reservoir must be negligible
compared to the pressure drops across the tubes. With the dynamic pressures in the tubes
already being negligible, this additional requirement is met by making the cross-sectional
area of the reservoir larger than all the tube areas put together. With D being the reservoir
diameter, the requirement is
D _ >> N d _ (27)
which can be very easily met in practice. On the other hand, an excessively-large reservoir
is undesirable, since it will increase the settling time.
A design parameter which still must be selected is the appropriate overall height L.
Clearly, this needs to be sufficiently large to capture the entire wake. However, making
it much larger than the wake width is undesirable,sinceincreasingL will proportionately
reduce the magnitude of the pressure signal po_ - pr, giving reduced accuracy. It is perfectly
acceptable to build an oversize rake, and cap any tubes which fall well above or below the
wake in order to improve accuracy.
The remaining design parameter is the total number of tubes N. This only influences
the accuracy of the midpoint summation approximation to the transverse profile integral.
Twenty tubes should be sufficient for typical featureless wake profiles. If the wake thickness is
expected to be significantly narrower than the rake height L, more tubes may be appropriate.
4 Compressibility Effects
If quantitative results are to be obtained from the integrating rake, corrections to the above
relations may be necessary if the freestream Mach number is appreciable. The exact relation
for the pitot total pressure is given by any of the standard isentropic formulas, e.g.
-r
po(y) = Pe (1 + _M2(y)) "_-_ = Pe 1 2h-_y)]
For adiabatic flows at near-unity Prandtl numbers, the stagnation enthalpy can be assumed
to be nearly constant across the wake and equal to its freestream value.
1 u_ ( x:_IM2 _ho(y) "_ hooo = 7_1 M_ 1+ 2 oo]
(29)
Combining this with the second isentropic formula above gives
Pe _--1 M2 1 -- (30)
which is the relation which would be used with a conventional rake to determine the velocity
profile from the measured total-pressure profile and the local static pressure p_.
Just outside the wake, where u(y) = ue, the total pressure is the same as the freestream
total pressure, which implies
-- = _-XM_ 1- u_'_]'-i (31)u ]J
This gives an alternative form for the total pressure profile
Po(Y) = Poo_
1*/-1
(32)
5
which then replacesthe equivalent incompressibleform (2). A second-orderTaylor seriesfor equation (32) about M2_o= 0 conveniently recovers the incompressible form, but with afirst-order Mach number correction.
+ O(M ) (33)
(34)
Equation (34) truncates the Taylor series, and also drops terms which are O [(u2e- u2)2] ,
which is justifiable for a typical small-defect wake profile.
An additional effect of compressibility will be to produce a non-uniform kinematic viscos-
ity profile across the wake. This will affect the tube mass flows rhi, which are still given by
relation (3), but u must now be replaced by the local kinematic stagnation viscosity Uo(y).
Assuming that the dynamic viscosity varies as # _,- T b _ h b results in
ue #e Po
Uo #o Pe
u2 y, lZ=!M2 1 - 1 + 1
_ho] p, ho 1 + ZZ!M2 1 + _-3-M22 _ 2
which is suitably approximated by its Taylor series.
u_ _ 1+ zz--1-M2 [ )u_-_2uo(y) 2 oo -(b + 1 +
M_ u.-"_ 1 + x:!2 -b u2
Z u:(y)] O(M_)'7 1u 1 +
2 u:(y)"7 Ue--
3'-1 u_
(35)
The viscosity exponent b can be estimated from the accurate Sutherland's viscosity law
( T _ 3/2 Too + Ts#(T) = poo k_--_] T + Ts
; Ts = llO°K
(36)
by matching its logarithmic derivative at the freestream condition.
b __
T d#l 3 1
-_[oo - 2 l + Ts/Too
(37)
_ ._.y._3'--1
(38)
(39)
The rake tube mass flow relation (3) now becomes
(hi - _r d 4 u¢ (Poi - P, )128 u_g Uo_
and the zero net mass flow condition (5) is
N
i=1 l]°i
N
or Z (po - po,) =/=1 l]oi
0
N
(po= - p, -- Ay.= l"o i
(40)
(41)
(42)
The summationon the righthand side produces
2
-- Z:AM2 ue - b L - _z_ (Ok -4-_ (43)i=1 l]°i oo
where Ok and _ are the kinematic thicknesses defined with the density profile omitted.
e_ + _ = 1 - _ dy (44)
Substituting the total pressure approximation (34) into equation (42) produces
[ )]Z tie Pooo--poo(u_-u_)-- I+_-M_ -1 Ay = 2(poo o-p,.)_ ve Ay (45)
which then reduces to the compressible equivalent of equation (12)
-_-l_x-(Ok+ 6_)] } (46)
where the higher powers of M_ and (u_2 - u2) 2 have been neglected as before. An exphcit if
somewhat imposing expression for the kinematic momentum+displacement thickness then
follows.
2
_+ _M_ -_(_ -b)Ok+5 k = 2 p°_ - p_ u2 P_ L oo (47)
._u_ _-i ["_(_ -b) - 1]+ _o_- p_Po_ u_ 1 + _ [u_ Po_
Again, the natural reference pressure for the reservoir transducer is clearly po. The ratio
of static/dynamic pressure in the equation above can of course be replaced by the Mach
numberp_ 1
poou_ 7M_
which is itself obtained from the total/static pressure ratio.
velocity ratio follows from equation (31)
(48)
The local edge/freestream
]2 2u_ - 1 - 1 (49)u_ (7-1-)M_
7
Appendix D: Journal of Aircraft Paper
Appendix A: Record of technical exchange via email
C"¢
)'-I
t::lr.,..1
tn
),.n
o,
o
,i.....i
l::l
g¢)
¢_,
!7
¢.
v
.%, q;
g_
i
_,, <:
_;: o7
r_ .... ,',
r_inc_
;11,_,
u, '%
cs •
7,,_ c. ¢, I_[v ,r- _,,
rr7 <I;'_ :L "v:
•.U) -_ '.
a_ ,T -.
m _4 S {!_ (11
,r...4
i...4
,-4
ill
i-.i-,..4
Ill
)--I
-,...I
(II
¢)
),¢¢)
lal
I11
lal0
®
N
t_
i'i
:_ ,i -r
rV <,
r;]_ ' {i_ .... a
i -_ ,i,
i_=,_;;_' _:! ;_ r'7I_;_" -- ..
_T, m
' _ _ _ c)
, .a _ '
................................ :!:g
)q8
{iI ¢I >: H 1., ,-_ _ ._ ao _ :.
>:2 n._ "g7 "=;'<.H {) a2 _ r} "
._ ._ .'. _ <t) _ _ ;4 .z_ <_ cs o
g
:-:X
.:4_J3,.o 3:
': ' d_
r_ _ L_
¢I 11,
'_, :" i} o;
= _ :'2
,-I
[,,-iI¢1
.o
I,,tl
O
,-I
®
[,-0
ii ,'_q ,_: .C ,
" •!i'?_ _ _'_S ,n )_ :
:i i' 'i! ii L_" , _:ml
:N 'T1 r, rtl
,S r,l .i '_i'
"'_ _' ,L,'
, .7_ ,_ ,]:, '_ ):
,) rA ," r_ m ,:, .,_
,J
_'_'_ _ i 2=_"'-:
_i_
b9
r:
*i
C
@ :J
,, ?r_
_,_
_, .'j .5
_, :.
c _
,N
ii r:,,,, b
:) >: ,_i -
_ G ,.J.., ,q _ •
.... .o O
_/Jf_S SI2
rt,
...... d "d
.... 21_I_ _ _.2_,"f
,i ,:?8 _'L;'_ _ ,_ _d,,_,,-,
rt"
--, @
%_
u,
q, .
_H[:!,
m @r,
,, iii
A
¢,-Ii-I
®
,-I
g)
0
®
®
:7
i'i
;i
i'i
Sr_
C
_ _ _ O _ _ _ _ r_ _
..... 7_-_SC',:1¢1
.'i
i
_f
c: _4
@ C
c
@
....... ii
l.r)
3 ,:: 2 ii <" ii T E 3,
0 ._i-_-_ _L; ri _i]
_, ,_ _ _' ,_,_ ,
H
.... _ _! _#'_
o o ,, ,y, A: ._: ,il
._
i
J:,,
o ,_, •
c u,_
r_ c ,:: "
....c o
- rn .... ,1
1,1"I
,-4,-4
,-4
-H
-H
0
I-I
o).i-)
illi-'1
I-I
I00
14®ill
I.,i10
.:_ ._, I ,_ &m,, , i
,, i ,,, :,go
NI
r,
,,,,_ _ ............
,-,_ ,.4=3 °_=_ ..... .,_@ @ :,', :" 0
o_':_ _,_._ _._ _ g .......... . :., u] t" "" '
OD
v-I
l=l
!.i'l
,10
ltl,e
0
,-I
®
_L
'd
!:i::!
d
v
.4[:ll,-_l:'
if,H
El
'TIE
m"
d;.:L
c_11
e:
rJ iv
,:) r_, ,_
_l] r' z Ll C'_ l][
oi
m " d.... _ _ _,_ "" _], _ _ _}_ _: _
,u ll)._: tq .
D
i ["
_7 .. ".
rl:, _ 177[.: ,, .
?' '< 72 _:'; <<
• _ il *o *_ r/ $ ,_ L, _, _ II ,_ i_ "61 0.I
:X_,':7,<'_l:
,.4 J;
[!if _
_ _ i:_!_
"T3 _: rt_ Ill
-H
®
Ill
0I-I
_p
elIll
}-I
N
O0
Id
, I;l_
ml
-1 _; , • i ,t _ re
<<,
Y:
rtl tD
r<
'<
rl
,]l _ _o
• . c, ....
?:I ,__ '
.)/_@ rl,.el ":_1 ,_
0i-I
0'1!-I
i.n('_,I
i,
o
;i
XI
7Z:: :-L:
<,_,;I_l !I!
_r'
!i_ i_ rL_
"_ _ii•, ,_ ci
r m
- ,'m
:j q, , t ' .... ,_..... _ ,'_I_ _.L: .: q: [,i
L :< " _:
..... _'V ,1 _ ,:, '_ !:b
i ,i, .... i_ '_1 ;:i '_J
z. _ c:
_' i_ :
E...q
...... _ _ _-_ _>
:b ',
,-4
_4
Iio14
@
®
14
14
®
N
9q
'TI m Ip
,L) _: q7 r,
_.'___ :4._
,L, .rlS . '
2 ,!_g" C:itr,fz •f
._[?'::(,:
,i, [,o ,_
: ,_1 ,3J
r_ _
.,H
2. c _
{: ;-
v . ,L' _ '
,) >: m c H .H q.,
. _ U_rJ TI1[, •' p _ uc, _' i
ii
ii
._q ii
.i
S
rll r_
C_
i
%O
O_
O_
r_
u')
lJ
p.,..
oo
0
a)
X
,_: :J
,i ,i_
",, !%7' T ':'
',. i 'T'C. _ BR
..... @ _ .,,
CI ,, '_
..... _,,_ _
q! L_ I!
f:r-*
c_ :-i
• _, .c_
K q .... t2 ....... _2 ri!, -_ t.: r._ ,_,
@ .T,
m c .H ): N 'r3
_'_,i_i ., _, . : .... _ _ _
Ch •o o '.'
.._ c.
LIg " ........
,i
-r,i
m
-e,t
N
oh
®.I.a
®
N
N
®
::::1
N
::::1
L>; _:,
[_ rll i:: :<
;. _ '_ ,3,1(lJ ..AO 13 _, _ rU
c o
i,-I
1,0
0'I
121
I,,I"I
o,
e_
0
,i-I
l:l
®
7,
r_ ,i:,
c _ - _ _ _i
'i] - ,,
o7 ,[ :<
= .,i 44 ._4 • 4
c_
.. _W' [I :Ll
. , 0"J
_ _.::_ ._ L
:. ,_ _
.r_
i_' _ _ __
o
z:
g_
i,,rn _,
m
0 ..
,_ .C;.
r]
,_ [,q
?: tu _ ,, ,, _, <,, ,,
gr, , ;
:, }-
[7. . .
_ .,4 ,_ _.: _
._ _ _ ,_ _ _,
[P, r_ uq :[i ?: _ _ ,
2 _ ....
,--4
i,-I
r-.l
ill
r-I
iii
-r-I
I)
011
r_
0
®
_J
r_
17
t-
_; _+ ; "i__
.....
0 :' @
io J o m
'"7_ g ®2• _ _
:_ _ '_ .... !.:
._ ¢_
.,--+ . oJ
_._,__,
• .u
_,___ ....
_ _ :_. _.w U_
'-' _o °_:; ,7:4 ::i,,
.L.
I,O
G_
,H
C,,ioo
ol
O
,,H
I:1
O
r_ c _ ,i_,
...._i_ _*,,_X :__N _ a_ uq _'J
..... ?: LI'21
L_
L, _: i;
u,,; •
,o ,D /4 [ -m T_; _' u, , a
u_
" i{a...... -.:.... _ _, ,_......
(1:,
.,q I ._
rv @
._ o _
[ii_ c) *J ._ ol ,)
._ tr, ¢0 u,, • ,1, ,i I
H
-,.4
®
,,..4
-H
®
t_
0
bl
®..0
iii,l-.-I
¢l
I,-I
'1:1
III
bl
l,,.
:::i
I.iUl
:::i
I!l
@,c._J
"e
,11a:
.<
In
•_ ,77
x]
ii tJ
iJ @ _'
,, s fi
r,
:':":".*: 7 y:i,,:,_,,_ ,[: F+ ?:
,. _ _z :.:
:_m
,1] ,11 o
,. g'" i'a._ 2
_ _:_r,_ ._ -_ _' "
._,_,_ _,_x::_.a
!!! ....
>1
u, tn
@
2 ul
_
i_rg
• o o
o c @ '_
_._2C2 ,s2
O 'U "'_
r _ q)
_,u ac: t) _e) g_
>_ ..-io ,% _ o o ,::<o .
La ..q re] _ iX *a *_i'
.C
_ _"_ _ _ S _
L,:
.4 ','I
-.4 '"
._._ __ :'.4_ '_ '_ ' " ':" _ _ '_'' "
E
J,
Z
-1, _]7
,t: 7
'- ,_, {1) o
J, '_1 'i'
, _ ,-4 vq . u7
V) r_ g_ .u ;.,
_: ,1, _--,_ _: .5 ._-r__
_-:_,_.__:'t......._._,_,_ _#__ , .__._._
........... _.,_ ._ _,_) _
..,_ _._ _,_ _ :.......
.,-I
d,
,-I
,-I
r-t-,4
"%.
,-I
-,'-I
_J
m
la,
0
I'4
®
14
,l::l%.
m
bl
m
Zl
14
m
14 • ,:_i E_ _ r'n
_7 _ 'T1 C
,o - A
_q 0 .< ao o o _,
rr_ ,L, c u
..... "2 _.....
',, ,_ {-4 o '_3 o _ "
c_ ',i: :-: _ ',< c
,, a •. c_,
T 7:7 :i,2 _{'_:,Z' ::_:
?: m m r) ,_ .o, • :<
am q; _1
rs, ._) c ,J o :<
= < ....
O
,k
'T1
0
@
C
_., L,
Eq _ _i
r_
<
h,
o ?......i-t
,rl,,,$ ,;,:.i 7,
cA
• m_
If:, _ _J <I .C
:j ,lq ;, • .t5 _U _ _ C_ C_
r_, rh
:,, < <_
5qc . m] _'}
i:!,,u _ :.i q)
H r:l [
;: i=.,t,
.... _ _ _
$ _1.2X
-H
I1
-H
®
®
0
_J
®
N
W
I
01 :, '
,,: Li _' =' :I_
,_1 <i
q ?]
" L[{
_' _' ,: ,: :', r_ :.: _,_
7.r_ m
,7: .__:_ %i/
[<
r-
o, _ ? &,_ A C u_ ¢1
_+L_ h (._ •
_,_ _ .,.
"_ _ _ -_
.-, ,_,_ _ _,-i
_ C ,_J Nm .m <i ?,
%1 .G q) rr, ,_
o ,_ u) . +
._ _._
_D r i
(:
71 ,J
_ bq
kL _ _
_q
sJ -
rd .,q ,
ql
_' _ r_ I _ _ _'
•_ Lq U r_,
....... _ _ b__,, i:1
i,,o
0'1(_
T-I
1::1
I'q
eo
I.n
oe
0
,H
O_
[-i
L: _
._ :_ _ _ _, _'_ _ _ < _ _1__
_ _ _ _1_ _ ,_ _ _,
• , _ o @ ,2 N
r
-8 N f...... ii .... :N .... .< ' "
_sr_
. @
?, ..... # ...... _N ? __@ c _ q, r; K, .c _l ".1 .
_,,_,?' ,_._S_ S!:,"
rn _ r_ @ _j U __ _ Lil
0 @
_,:_i
m m
•q _ N .J :, o -
F
9 _ .... " 4'
G
@q_
H @ @ r
, -_ o ,i_
r,
r_
S .....• .H ,,
_ ._i_ _'
r ,_ c _J
,-I
,--I
iii
,-I-,,-I
iii
II)
,-I
-,-I
®
®
III
I0
0
14
¢)
4-)
ill
1,4
'I::I
III
14
III
14
:-:_.._.... _ ®_I _ _ _ _ .....
,:_ ,_, _ _ .
.... I:L8 ..........
@
• o.c ""
@
H._ _ _ C_ -
• _ ':'_ ,:, _;q @ _ ,u o c
@
i
t
'1' E_
,o
• ,:, A o_
• A
• _ u5
_ ,:, N r-i ,3_
o ',_' m _ ,:,
_,; .., _ rl [7J S its{ [2 :]',
@ ,J,: ,J:
.,._ @ . >: • r,n _J o (1:,
.... ,-_: i _,_"_
N _n " @
, _ C r _ :_: I { : D :.,
,_i]',_: ..Gl:?:f.:
if,
_4
r_
m' 2_
O
rl:'
:<
%1 O
' F:
< S !_: %:2
_ .. :x. [[! r, rL ._ m :]I
o-, c, ,J o .c. _ _ ,
_-__?_,_ '__ m m
'_ _
C.
,C
;)r,
C
m
C
O •
L9 ,_ rl: _: Ip
rl: .,J n] ., ,r_ u_
.J
.o, [. ] _ i.,r_ _ m
_ ,_2 C C
[<
T_ ?: - q< C _ ri_ ri_ C
2
I'-I
,--I
1II
,--I
-,-I
-i-I .m
0 [) (1,
. _:r_ i__
i1, L_ T_ L9 iLJ
C
%1 r,
.C
bn :_
H
N4 _,_4
c] _ IIi[I gJ II
,, ,,, .
-* m
R _ ?,:2
G]
• -I ' q:
L' _ aa '
i
'T_ _ E,-< ,J m
C',I
,i-I
I:=1
IP,I
It
O
,-I
I:I
i.:,
_LI r_l ill
mm:
.......... _,7 _: ,_ LI_'_
hl'/
<.
u,r"
hl
<l, {_ ,,
H , :, H _] <,'
'7
c:
H ._ (II C
G, .+.L,
L: • :J H (lI A_
P]
i
(::
7
o
FJ ilI
d.
,-4
®
®
oN
N
N
hl<' E:u:, rn
" S&
_ r_
• C '_i
:.<'I L_ '_ :,! r:i
..........:.2]A ,5 L: " 'i_ !
,< r: ,< ....
c m¢i] [i_ "< .c
._ _ _g _,
m
_J
'T_ m
_l _ [: rU e)]
:i m ', ii
ii [7 [Q _z, H
;7,
off _L_,_ IiI +_ ._ _ _ -_ II _ I: _L: iTi
c _: D _ o c e2 e : _G
•_ ID _ G1 _, :< .H 'il) C '_! _9 C H
, Q:, _ r ) < _lI _ ,, m (i) C
_] IU
_I_'_
r-, _
o"J _ xc
Co2 :._
N C,_J
,i,c: 2
q_ [J <)
._ rr,
;4s4
cq
l:1
it)
_J
1.1"1io
0
l:l
it
r'
_. _,.._ =._ _. Z,_, 4.." 4.."-_ hl e.1. ._,L: _ ._] .... _ *'_4 " u < _ _
._' n+ _. - . ' _." ,TJ _ _ ,_
..:', ,7. :':" " '_' _ ......... ,_ -__'_' "_t!r_ i, ¢, _, .,_ _. ,:, m _n _ _ :,
K:5
:7<; ....
< £:': _, '_
,r_ ._ _ _ _ .._ moo
-_ .. ',_;.. <<:7.. _',_ {_}<__ _ ,,,7_
m >. :_: _m , < ,.
S
O O T1 • ',.,
G -
_ C 0.1 .
rd q_ kS4 _ _ ()
i
dit 2
-l-I .. rs,
< ee_
r_
o " _i _! ?".... L: , d # <,t
,<
® ,_:I '_'...... :,] 5 <' < _,
_,'_i :'. :_ _ d
c,, _ r14 ',',! .... : ,.':_ _: _ ......
.... <_
k,
,q
-1L9
_t:!
" _ _d
'T1
m
_, _ 4 _=
tn (}
r_ _
_4 _ ql 7 q_
kq'Y _ # _ * '_' <::
r.D ,,LI_ '.
.,d m c,_ ,,-t 14_ _d ill _i
b
• A
<;.( ,,_ r'_ - r3 '0
r_r::
,1)
<1 C.
cJ ".
C
_ o •
,:
E ra zJ _2_ _ -_
..d :, ,_ _D
2b. c,_ ....C
0
,-I
I:::1
oe
0
,-'i
i::I
T" C i!1 :;J ,.J ,
._ i:1 ._ :_ _ ._
'u
_J
,, m ?:
C1
'_' _ _ ',i _ <J
,:u
,J
.cQ):. ,a c) m _ c _
L_ m
151
...._:' _ _ ::i
u, .J
..... g_
,:_ 7,] '_ ,_
._ _: • , _ ;:.... _ .... ;:.,
rl:, '- o _ • m ._ ._4 _._ _ _ s d _ _
Gl -_ L, .
r_
®
-,_ _ _ _ :_
0 :: ,* rl, ri) C. _ q_
N
I,..i
L_ :., ul roT. (7, '_'
LJ,[-
$
(,
_ o
"-: ,4 41 C c ,_ ,, ,[) ,x: ._ ._)
, _: =y "' ,_ _ 2,• . H
o, =
,p .. _TI
r_ "• eq e_
CO ,--t C
..<'l _ < . :._7:',
,i; °'
m r- :-: m
# %_', ,......., ,i h _:
_ ._<g 7 ,.:,_ 7/>'<4:,L
_, [:_ '_ <I- _ '_...q i
rl, i
,.-I
i::::1
1.1"1
oo
oo
0
,I-"l
la:1
I'a
k:
_ iil
,_, { _: ::i
¢1 _ a:
ql
rrJ _ ¢_ .H
7" _0
£
L, L: ,--+ -_
A A :-: F-' r _ ,.
,') {>e_, H
,,._ q, ,,J
_ :2 d
O ii i:<c_ ;4
+ c, LL re" r_
::I: i_2z rl _,_
,1 _ r_
, o_, _, _,
• o
0
ac, r_ r_ nl L_
*-, LC' '_ _'
.< C i <; rd
¢
on qq 411
a: C Ill <) i 1 T"
,1"'4
,¢
,""1
,"'1
III
1""4
iii
I..I
_>i '_..... _ :., <
:L, : rl, .r_ *_ ¢
e,;
¢
_t
_4
_4
C:
Z
d,
c_
'-,,x: t
24
H C
d_
¢ Z 7
,::_ ":;: # ::_i_':g :<0:0 [, '] m oh
f4..Y;g:i?_ '_t _:7?_% ,:,m7 2:_ _g :°
"_: . ¢.2
c . •,
H
H Q! H _ 0
I-I
I:::1
Ill
ii0
r,,,
,0
o
,I,,-i
I:Ig
;., ,, r}
:., .,_ _, '' rl:,
A: n, ,,
'T_ ,__ _:' '1' '1' :_,
ti"
C FI L: ,_ L,_
u_q_
...... V, _ _
¢' _ _'_ :i; -_ _
? . H ,_ ,,11
r¢ _. 'L I ,I al @ E e_
: • ,_i_,<....1'i
7 _ _..... _ _ ,_ ,__'N '_ _ '_ ,1_ _ C
D , _ - @ :.,-_ ,q .c
@ 0
r) _i q3@ @
re _._
Ln _2 _ bn @
:': _ _ >:_ ,_,,_ _
.... _ _ ...._ ...._'_ _ c _ _ o rr_ q_ ,__ __ ,_ .._° ._' _ :.:
:.... _it,_ _' ,,:_ ._ -x<
0"1
0'1
i-,,I
I--I
iii
i,-I
I-'t
",'4
III
®
N®
nliii
ifl
0
4.l
®
I'4
la
®
j _ r. _ _ . _ _ ._ r_
?:I !.i_' :i? _-__i:".... H .....
i
{,
(,)
'," *n
0 D_
:.,_ _
:':,_: _ _:' _ _; _;
o, _ @ . m
,_. cq
-g
•L: r,j _,H q,_,i: r.: _A '"
ql
- fi
@ "_,
[9 r_ _ ij_
_, '_ _ _, ,_,
_] rt, 0
._._: ,_ ,:. _ :.: _,r : ,'.] .:_ ,J
i =,N :.: _.... _,:':<
%O
Cr_
01
[.rl
o,
r_
Lrl
oo
0
Io
®
r_l LI r,.
r ±J ?: '_ :u r_ .u _L]
_' _ " 7 !,_
'L_
...... :i iL; I_' '_'_ :_' '_'
IX)
r-I
,-I
,-I
.,-I
,m
r-I
-,..I
®
@.e,
0
61
@_J
,-4
®1.4
1,4
i;'i:'
ii!i .... ....
•-._ _ _ _ _ o :..... ,_ , ._
Ln
,o
u-, (, u} Q_ .
..... :.,g ,,,?_
:.,, .< r, g ,_;L;L, .. rv, _4 _ er, ,,
=q , a q'_ = .:_.
'. .....: _ o ,c'r',,2
:..', O)• Jo c_ _o
£, :_ ._ cn .,_
o tnX: :._o
r_ 5
•_ _
• uq r_
':' _!_,_ _2 5 ....._2
_'5 r9
.L: mr. _ L} q}
Appendix B: Key figures and sketches
APEX 16
x
1 000000
0 996936
0 988795
0 977291 0
0 962745 0
0 946684 0
0 930138 00 913447 0
0 896699 0
0 879909 0
0 863091 0
0 846244 0
0 829370 0
0 812468 00 795546 0
0 778591 0
0 761610 0
0 744595 0
0 727557 0
0 710498 00 693423 0
0 676338 0
0 659238 0
0 642136 0
0 625022 0
0 607898 0
0 590773 0
0 573635 00 556493 0
0 539344 0
0 522184 0
0 505023 0
0 487855 0
0 470681 0
0 453510 00 436337 0
0 419174 0
0 402019 0
0 384874 00 367749 0
0 350641 0
0 333560 0
0 316510 0
0 299492 0
0 282523 0
0 265599 00 248739 0
0 231948 00 215238 0
Y0 002036
0 002939
0 005338
008683
012817
017254
021685026011
030208
034271
038196
041983
045629
049137
052501055724
058805061747
064550
067212069734
072110
074342
076424
078355
080136
081760
083229084542
085695
086690
087527
088202
088718
089073
089267
089299
089166088867
088400087762
086951
085961
084791
083434
081885
080140
078187076023
00
0
0
0
0
00
0
0
0
0
0
0
0
00
00
0
0
00
0
0
0
x
0 198625
0 182124
0 165761
0 1495570 133556
0 117799
0 102355
0 087310
0 0727850 058990
0 046262
0 035096 0
0 025944 0
0 018879 0
0 013576 0
0 009594 0
0 006567 0
0 004250 0
0 002489 00 001204 0
0 000381 0
0 000024 0
0 000089 -0
000556 -0
001466 -0
002906 -0004935 -0
007560 -0
010851 -0
015033 -0
020527 -0028026 -0
038406 -0052060 -0
068128 -0085370 -0
102840 -0
120161 -0
137275 -0154200 -0
170985 -0
187738 -0204639 -0
221631 -0
238067 -0
254021 -0269935 -0
286070 -0
302451 -0
Y0 073635
0 071014
0 068148
0 065024
0 061628
0 057944
0 0539560 049650
0 045017
0 0400880 034955
029839025057020836017218014109
011391
008957
006718
004607002575
000624
001269
003190
0O5O90
006846008327
009522010544
011514
012515013603
014821
016156017542
018957
020404
021923
023559025357
027355
029589
032060
034644
036998
038916040388
041481
042255
x y0 318997 -0 042742
000000000000000000
00
0
0
0
0
0
0
00
0
0
0
0
0
0
00
0
0
00
0
335659 -0352439 -0
369357 -0
386421 -0
403596 -0
420860 -0
438200 -0
455601 -0473059 -0
490567 -0
508116 -0
525706 -0
543327 -0
560976 -0
578654 -0
596354 -0614079 -0
631831 -0
649604 -0667405 -0
685216 -0
703005 -0
720758 -0738477 -0
756158 -0
773800 -0
791402 -0
808960 -0
826477 -0843943 -0
861354 -0
878696 -0
895951 -0
913086 -0
930043 -0
946688 -0
962660 -0
977023 -0988508 -0
996818 -0999998 -0
042958
042918
042645042174
041531040737
039812
038770
037626
036393035082
033703
032267
030780
029249
027682
026084024461
022820
021167
019511
017861
016229014622
013049
011521
010046
008636
007301
006051004901
003863
002958
002205
001634
001280
001176
001319001619
001946
002103
O_O_©C C_
•-a 0 J3°_-I
_C ro0 J o
L × ×
CE E E
ICO
X ---, COIII . •
[3_ 0"-) ('XJ13S
C)
000000000000
lall
IIIIIIII
ggggZZZZ
00000_0_
,i,i0000
IIIIIIII
ZZ_Z
0000000000000000
0000
IIIIIIII
XXXX
0
iiiiiiii'iiiiiiiiii'ill ' ' _' " ' _"-
> ..... i..... i : : _..... : ...... : ..... _ ..... .* - - I_D
0
(_D.""4
I
t.D
I I I
.....!......i.....i.....i-_-l......i.....i\--i .....i......i---,_-!.....!.....i......i.....
.... . '. .... : .% _ _ _'.... .1_/...... ' ..... _ ..... " - - -_ _ ..... _ -_-"-- - -q- - - _, -i-'," ....
co
(.0
U
Od
0
Od
I
00
...... _............................... _........... < ..... ,,...... , .....
0 0 0 00 _ 0 If) i ' ' ', .....
lID I",, I"-• • • • ', , ' , ,, ....
0 0 0 0 ...... _.............................. L..... _ ..... ; ..... '....... [ .....
I |
I , |I '
I , :
.J
L)
' ' i ' '
',...... ,...... ',..... ': ..... _- ..... ',...... , ..... _ ..... i- ..... i ...... i ....
, , , , , , ,
0 l.f)
.. c;0
0
0
_ J/ x
CO
>
0")LIJ(./-)
: : :_-_-_..... : _ ...._i_I
000000000000
.all
IIIIIIII
ZZZZ
I_n
,r--i
I
f "_ , _ "., _ ,*
_ --_ _ _-
o _ d :';11SI I I
t
C) 0 C3 C) Ii i i i i i ' i i i io_o_ i._ i i i i; i i .i... i .
............................ ,_ ..... : .... c ...... _. ..... : ....
,, ,, ,, ,, ..... ! i _...... t ..... I...... i _! ..... i...... i..... _ .... ! ..... ! i...... i(I r_" _ (_ ', 1 : _ _ : ', , , *
_-_-_ .....i......;.....r _i....._......... :...., .....i............."::_.....i.....:_......_.....
..... ' ...... ' ..................... ' ..... ;q_ .... ' - ' ' • ' ,_s _'
oooo°°°° : : , ,_....: ,_,/o o o o ! _ _\ \ i i ",i i i i _'Z/oooo ' ' N/ : _-oooo ' \. . . s ' I .'//0_ co 0_ co _: | : : ", : ' .. ' f,/.
. : : : _ ' :_. _-, , ,
II II II II ' ' ........... _ ........................
(_ r'_- r_- f_- 0 0 0 0 ......
XXXX
o to o
i i
I ' ,
I ' :I
..... i ' '
J
0
L_
0
0
0
CO
0
I
I
0
0
0
0
U
x
d
0
x
0
__I
0
0 If') (:3
.-_ 0 (:3
c_ : : : _: : : : : : : i i...... :...... :..... , .... ,,<-._ ....... :..... ,...... : ..... :........... ! ..... : ..... .---_,._....
"-......::......_....._:--: ......::....._:.....).....i...... I?_...... i-iiiiiiiiiiiiiiill
0
_ U
fi-
Xt.D
0
0
0000_00000000_
ill| I
IIIIIIII
_uuu
ZZZZ
L_
0 (--) 0 "'1 II I
/I
0
CO
cO
(_ LF) C] U-) ....._.0 _ r "- r_ ............... - ............... i-- ,
.... _ i _ _ iIIIIIIII
Z_Z
00000000000000000000
II II II
XXX
IJJ I.LI l.IJ0._ O_ O-CE CE (I
Lidmr-
(_0
X
I,I13_rr
LIO
Od
0
OdI
I
C30
• ' '0 ' '
• . • . : : :
i il i i :, : i i: : ' '............ ia.... ! ..... :...... :, ......... : ..... i- : ..... : - : . . . • . . :
..........!1......_: , : ' ' ". . -_..........._-',.--:......_.....:....:.......i.....;................!I' ' I' " .... , ,
......................................................:: ::\-ii, ', i i .... , , ,
.X_,_ , ,, , ,'-. " .i"" _. o°_i i _ i i i "i"" : "/ r_
-_-I.....i.....i:,,-::.....::......I.....i.....}--;.<.'_....o o k----I--_--: ..... : ..... :-"a-_,"-:_--S_L--! ...... i.....
CO r_ r_ , _ _,-- --'-- --- J ', ', '
o o o o ................................................. "..... :...... :.....
| |
I ' 'iI I :I ,
.-d
(._)
0 LF) C3
- o o
X
0
o oo oc) o
£d
II II
n'- I12U U
z z
o oo o
6c;II II
EE (3Z:E :E
o oo oo oo oo oc) ood ,-,
II ii
w wn- n-
(_0(.0
XX
WW
no_
rrrr
ooo
II
n-u
z
oo
6
II
rr
00000Ln
II
Wrr
LO
X
W
O_
rr
O0 " : : ]_:|: _ % ; " ; ; Z_ : ; : :• .................. i ........ ,_ ..... %.._... : ..... , .................... _.; -- -.; -;.- _..._: _._.- -
i : . . " . _-,_ , . _ - ," T...T.,_ .-_"
: : : _...: ..... ............ :..... - ..... : ..... -..._ ...... :...........
.... s ,_r-_,_. .' : : _ _ % : ', ..
I
i
I I I
I o o
I _ ,_. (-_II o L_ o
I I I
i I
'|
/,/,'
/#
,!
• ' ._.'.I_._L ..... ,...... : ..... ; ..... '_..... :...... , ..... ; ..... ', ..... :...... '......
! ! \!' ! ! ! ! ! ! ! ! !
.....::......kl_!_' ::............!.....i.....::......::...........i.....::......::......i::,,........... :..... _-.\.:_-,-.. .......... _..... : ..... ....................... ! .......... ,; ....
i i\i'i i ' i i i : : / . : . ,:....._...._ \_',_............_....._....._......_......I....._....._....._I-_.....i\\'_ I ! ! i ! I ! ':" /
o: o .....::..........I....o _ _ : _ _, ";_____L... : __.L--_ : .: ....
,., w_ : ....... _ "T. .L,/ :. _-" o° o° o° i : i _--_-- i
I .......
I I :...... ,...... ' ..... " ..... '...... ' .... , ..... _ ..... ', ..... :...... '......
i I . ,j ...... ,
: . ; . . . ;
IZ) 0 Lr) 0
0
£D
UO
0
0
0
O0
(_0
Od
0
?
I
00
C3o
U
(Ei-
X
o
X
0
ooooo_ooo0o0oo0o_
=i..l
IIIIIIIIII
uu_uu
ZZZZZ
00000000_0
00000
tlt1111111
O00000000000000000000000000
Illlllllll
XXXXX
', ', i _',_ " ' " ......_ ...... i...... i _ (<"_. ."' .,.-:-'_:. : _ :-".....,_:: ............ ::..............._--..=:..... : _"_-
• - - _" - :-'-"_-'_'.,t_--" - _- - -"_"-• ......................: . ..:, : __..._. . .......i......I....""....._ __"_'_--_'-_: .....:'"....." .....:......:.....(Z')
"' i ! ;" " ' i_ ' t : : ! !.......i.....i.....!i:::i::::::.,.:::::::::::::::::::::::::::
,I
,iiE, ¢i
, ', Nix.
, .o
_ '.:\,._ o _
_\ ', .\ / _ --..i ...% •
:\ ._ ,_ ,_: : : ./ : : : : ,,:
:\ :\ : _".: : ," : : : : :,' :..... :_-: %, - : _-'.,_- ........ . ;._' - :..... '_..... :...... I..... : ..... :- / ..... :.....
!_ \ _'i ! i i i I ! :.'" i..... :..... ,X .... i .... _":............ ; ..... _ ..... ;...... :...... I ..... _ " - ; "_ ..... :.... _: .....
: :\ :_ ¢, : : : : I : : : : _:..... :..... !..\._:._..:_ ........... ,...... :..... -.... ::...... _._r.'.:r.... ',..... :.,.... :_.,_..
: : _: \ _ "'-L-"" .... : : : / : : ": ://..... i...... i.... -_,---,,,-i,..... i...... i..... i ..... i...... i..... -I..... i ..... i..<-.i.... _.S-l.-
: : _, _:_ : : : : / : .< : I:1
' ' _,' 'r' - .. .... _ ' ;.
\ ... I,.-./i.....:_.....L.....::..........b._._ ..........IC_ 0 , _ .... -_,.._ . ,
o o o _ _ ', '. i f '. : ', ',0 0 0 0 0 ...... ." ...... _ .... ....... ._'--, ..... , .... ....... ,.....0 (_ 0 (_ 0 ' ' ' - ' ' ' '
i_ 0 0 0 0 00 0 0 0 0od _ LI_ ('0 Od
I I ,
' I , :I ' :I ,
..... i ..... _..... ,"..... i ............ _...... ; ..... '....... i .....
, ', ', ', ,, ',...... '...... _ ..... i- ..... ',............ ( ..... ': ..... ',...... ',.....
', ', ', ', i', ,, ,,
', ; ; ; i ', ', i
C3
X
d
0 I_D
0
0
d
0
OO
(..0
U
(M
0
i'M
-,.d.
I
00Od
C)C)
Ux
0
DO
_J
0
00
od
>
iii0o
..... :...... : ..... : _" " - -_- -:..... , _. -: ..... :...... I..... : ..... : ...... ,....
..... :...... :..... _..... ! ........... : ..... i ..... :...... :............... ,_..... :...... : .....
..... ....... . ..... : ..... ,,............ , ..... _ ..... ,...... ,........... 1.... ':l ..... '....... '......
0
l--X
LF)
C)
o o o(22) 0oo OO
II II II
I-- I-- I--
nr n 1 _r
u (-}
z z z
o o ou3 I.F; LOcO LO (_.0
dSg
II II II
n- rr (I
0 O00 0 00 0 00000 0 0I.C) O00d
II II II
iii1,111102 02 rr-
XXX
I, I LLI I.iJ0_0_13_
fT- n- c'r
LD
.--4
I
J
o
... j j_Sl
$3_"_"_I i
, ,_ ._. [ ;'- _.
_. = _. 1__-,,"--.o, o /io,
!
. il, . : . . .i,i I
...................... t--,.........i..... i.....!......i............i.....i.....i......i......, . , I I
J%
' ' ' _1
o o oo o o
. o o c)
If; co c_
!
I ,I' I
: : : i i i : .>.
, .... T"!" I-!
: ! ! ! | ! _/!_i,....;.....:.....',.....;.....-,--...:-,_.-'......:---i.-.-....
................ ...........'. ', ', ', '. i; ........... _..... _ ..... . ..... :............ ; ..... ; ..... ,,...... ,......
, , ,, ,.,, ,, ; ',- ..........._'...... _..... ',......'............_..... ':.....',......',......
, ', ' '',
,, ,, ', ', ' ', ' ' ',
(_0
LO
Od
0
::3'I
(_)
0
c_
r-_
_" X
CI
0 L_ 0
._.1
0
13o
>
w
...... 15 ......
.............................. ' ................ t ............... ' ..... _ ..... _ ..... :...... :.....
................. : ..... T.......... "_....... ;''" _ "-. ....
: : : i i ] i li li i :..... :...... , ..... _ ..... ,............ ,..... _ ..... ,...... ,.......... _ .... i_- .... ,...... ,.....
..... :...... :..... _..... :............ :..... i .................... __ ..... i...... i...... i..........i......:,..... :,..... ::................. _..... !......_.......... t_..... _....._......_.....
..... :...... :..... : ..... ! ........... i..... . ..... , ..... !..... , , , , _
---' U
¢,¢-I---
X
0
-G-
o o o
o o o
£d£
II II II
L_I _.1 LI
z z_
oOoo o o
II II II
r-c c12 r'r
000o o oo o oo o oo o oi._ ('0 od
ii II ii
L.iJ L.IJ tuJn'- rr" OC]
XXX
L_I L.LI I.J_lnO_O_(-I- _I n-
CD
L_F> "_ 0
(__.)
I I
oco
oI
k_" _L'""' /''). _.2/,"
""_--__._'...7_'lZ.;.
.- _ It,_--_7_C --<
O0
CO
od
0
od
I
' ; : , ' ,'% , ' , , ,..... :........................ _............ '_i .......... :...... ,........................ :.....
: : .... _ , : , ,
.... t Ii • ; '. '. '.
i i i : _1_i_._...:...... :........... i ......................... :...... i i i i i I i i '. '. '. :
! It............{I!I',:_.....::...........i.....t.....::......L,-:..... , , , , i t ' _. ' ._.',
......iI IIlIli.....: i :\.i, / ....: ..:-: : i : i i ,,i i i i/Z" _.
i...............i..... ...........
L.O
IJJ o o oo o ou_ 00 ¢_J
t
I ,I 'I
...... i ............................... i ..............................
......
, , i
0
J
U
00
if)
o(2D
o
o
0,-,--I
00o_
0
co
>
o o ooooo o 0
£gg
II II II
/-- }-- I--
U
zzz
oooLl)u')bO
Sdd11 II II
(I_ rr
0 O00 O00 O0O0 0
II II II
LU I.iJ LUrr" rr rr
XXX
IJ I._ I, I
(__. O_ O_(I rr t-r
........ i ' ' 'i
...... ,...... , ..... ,, ..... , ............ : ..... ,. ..... : ..... ,,............ _ ..... ; ..... ;...... ,,......
...... i..... i ..... i ..... i ........... i ..... i ..... i ..... i 'L ....... i ..... ._........... ..'_"
...... )...... !..... i ..... i .......... i ..... i ..... i ..... ' .... k,.._i ..... !...... i......
......i......i.....i.....i............i.....i.....i-...._..i ......
......................i................i.....i...........ic-!!i .................
_ _.1 0
I I
_ U
¢ri-
XLF}
0
0
0
0 (---)i
',,I I I
I
O3
LO
Od
C3
Od
,4,,,,.
I
i i i i i i i :_'...... !......!..... i ..... i ........... !..... !..... i ..... !. ____
', ', , , ,, ., ., .
...... ;...... i ..... ; ..... ',-............ :..... ; ..... ',...... ;......
,
: ; : ; ; ; ; ;., ,. ,
o o oo o oo o o
I
I ,I' I
0
.._..,, ..... ; ..... ,,...... ;......%,, ,, ,, ,
_; ', ,, ,,
-_- - : - -_-7 _----." ..... :...... 0
.... _._. _. i ..... :.. _. .:......i "<__'.J i
c_
L ........... _..... ; ..... L ..... :............ ; ..... L ............ :......
_ ............ ',..... _..... :...... '............. _ ..... ', ..... ;...... ,......, , : , : : , ,
, , , , , , ,
(3 L_ 0
S SI_D
.._1
(_.)
\\
i,i
U
t-r
U-n-
l--
Z
LU
U
rr
.J0.-
0
[
(_0
XW
El_
O:
00
II
m
nm
Ln__o
[:]ii
II
J
U
II
Ub
LO
d
b-Dn-8_
U
E:)
J
W
>
._1