Design and construction of a remote piloted flying wing

I !

I i

APPENDIX A

AERODYNAMICS

I t

L

i

i J

APPENDIX A1

The Eppler E325 Series Aerodynamic Data 5

Separafion b,:,_:'.e warning T. = boundary layer transffion ,_ upper surface S. I boundary layer separcfic_ v tower surface U. = upper surface L.- tower surface Re = 7x_O _ C_ -- 10_ 1 ...

L.Ox;b // / / ._-----_ C_ I ,'_ _. _ i "'/'./ I I ,/'" I_J _ r = _/ t I / ."

z z z / , , I / ." / , / /" /,/ 0.5- ////,/'/'/'"

,--_ _._ W,':., I

/1 it I I I, / I

.--_, ',\\ 0.5 xlc

_,,'_,,,J,, ""-, ":_ lO3_o 2,: L

:- (_:1 I .

_t ._.2_." q.''2". _. = l'',J",3S;_ C',_" c: .... 3:*" E 327, . . . . .

'" ,',e" S.'f::,_ -. =ccper sJr'ace .. = .2,',6r #...'13_ C ...... i -_ _.... _-.,___ .... ,., ,. f __ .... " ' '" _ ,c.J.

' " " " / ;C.

,- . '(' (_., C i ' 5Y - i 0.5 _ . . i P _|_ .b. ," - .-.¢. / _ _,I ,"

d' it

'. / -C:.05 +1 ', J_--

5 Z_.-'15 4t o ,_

- /[./c- :.og_.jv

':'-" ""-_.,, c. 20 T._ _ '( ,' '"c< 9,--"" x/'c 0.05 _tN.a_.. PAGtE m

t

i

Separation bubble wcrn[ng T.- boundary layer transit{o: ,-. upper surfcce S.- boundary [ayer seporat{or,

E 329

{ower surface 13.5_J, c- mo_. U. = upper surface L. - lower surface Re = 7x10-_ Ci 1.5x10 {

-___ ...... _

2.5x',0: ! 10 _, r = _.

. ,,,_1 c_,_, J l///- " , ,/ I /: l / C;.._ / ° / i /' ,'" 2 _, qll i , : / ,_ I.l.J. /s / / 0.5" i ;: t _',t: J Of . ...

; 1", "- , ^ £

APPENDIX A2

Lotus Spreadsheet for Drag and Lift Calculations

b AR C329= c327= c325= Stot4wng cg= 0.2455 13.6925 0.73 2.2098 6.689337 0.4148 0.3302 b= Cmac: Stot= Cmcg q= 0.3648 48.95320 0.3683 329 327 -0.05 0 0.05 0.550416 a.c.

i 0.290020

329 327 325 -0.051 -0.0024 O.O48 0.046 -0.00192 16.33333 13 9.666666 -0.052 -0.0O48 -0.053 -0.0072 0.044 -0.00457 x/c : 325 -0.O54 -0.0096 0.042 -0.41482 329 327 L 16.39850 -0.055 -0.012 0.04 -0.68975 -6.36652 2.097213 K S ratio : 327 325 0.048555 0.333333 0.247807 0.418859 CI: Cd: 329 327 325 329 327 325 alpha 0 0077 2 0 53 0 35 0.15 0 0086 0.008 0.27 0 0091 0.0085 0 0079 3 0 65 0 48 0.38 0 0094 0.0087 0 0081 4 0 73 0 56 0.0094 0 0085 5 0 86 0 65 0.45 0 0102 0 0108 0.01 0 0094 6 0 95 0 76 0.59 7 0.69 0 0115 0.0107 0 0101 1 03 0 87 L(ibf) L(N) )D tot (N)D (ibf) D (wing) D(e-plat )D(L-gear 13.42254 0 146024 0.036206 0.003362 0 423644 0 .095239 3.017521 17.82757 0 153626 0 438847 0 .098657 4.007816 20.95045 0 157945 D (duct) 0 447486 0 .100599 4.709871 0.105959 5. 527216 24.58616 0 169866 0.049093 0 471327 0.111373 6.402903 28.48139 0 181909 0 495413 0 520414 0.116994 7.165359 31.87295 0 194409 )D (duct) v(m/s) = v m/h)= D (wing) D(e-plat D(L-gear) q 48.95320 0 157945 0.036206 0 049093 0.003362 8 94 2O 25 76.48938 0 246789 0.056572 0 076708 0.005254 II 175 0.007566 13 41 3O 110.1447 0 355377 0.081464 0 110460 0.010298 15 645 35 149.9191 0 483708 0.110882 0 150348 0 631782 0.144825 0 196374 0.013451 17 88 4O 195.8128 0 799599 0.183295 0 248535 0.017024 20 115 45 247.8256 0.226290 0 306834 0.021018 22 35 50 305.9575 0 987159 0 371269 0.025431 24 585 55 370.2086 1 194462 0.273811 26 82 60 440.5788 1.421509 0.325858 0 441841 0.030266 O.51855O 0.035520 29 055 65 517.0682 1.668299 0.382430 599.6767 1.934832 0.443529 0 601395 0.041195 31 29 7O 75 688.4044 2.221108 0 509153 0 690377 0.047290 33 525 35 76 8O 783.2512 2.527128 0 579303 0 785496 0.053806 37 995 85 884.2172 2.852890 0 653979 0 886751 0.060742 40 23 90 991.3024 3.198396 0 733181 0 994143 0.068098 42 465 95 1104.506 3.563645 0 816908 1 107672 0.075875 44.7 I00 1223.830 3.948637 0 905161 I 227337 0.084072 D (induc ) D tot (N) D (ibf) L tot (N )L (ibf) L/D 0 315198 1 077883 0 242319 20.95045 4.709871 19.43665 0 492497 1 684193 0 378623 32.73508 7.359174 0 709197 C1 2 425238 0 545217 47.13852 10.59721 0 965295 3 301018 0 742101 64.16076 14.42398 0.586258 1 260794 4 311534 0 969276 83.80182 18.83948 1 595693 5 456785 1 226739 106.0616 23.84372 Cd 1 969991 1 514493 130.9403 0.030162 6 736772 29.43669 2.383690 8.151494 1.832537 158.4378 35.61840

i

I 2.836788 9.700952 2.180871 188.5540 42.38884 3.329286 11.38514 2.559494 221.2891 49.74802 3.861183 13.20407 2.968407 256.6430 57.69592 4.432481 15.15773 3.407611 294.6157 66.23257 5.043178 17.24613 3.877104 335.2072 75.35794 5.693276 19.46927 4.376887 378.4175 85.07205 6.382773 21.82714 4.906959 424.2467 95.37490 5.467322 472.6946 106.2664 7.111670 24.31974 7.879967 26.94708 6.057975 523.7613 117.7467

APPENDIX B

STABILITY ANALYSIS

B.I CONTROLS/STABILITY SPREADSHEET CI: Cd: 329 327 325 329 327 325 alpha 2 O. 53 O. 35 O. 15 0.0086 0.008 0.0077 3 0.65 0.48 0.27 0.0091 0.0085 0.0079 4 0.73 0.56 0.38 0.0094 0.0087 0.0081 5 0.86 0.65 0.45 0.0102 0.0094 0.0085 6 0.95 0.76 0.59 0.0108 0.01 0.0094 7 1.03 0.87 0.69 0.0115 0.0107 0 0101 Cmac: Cdi: 329 327 325 329 327 325 alpha 2 -0.05 0 0.05 0.015309 0.006676 0.001226 3 0.048 0.023026 0.012557 0.003973 -0.051 -0.0024 4 0.046 0.029043 0.017091 0.00787 -0.052 -0.0048 5 -0.0072 0.044 0.040308 0.023026 0.011036 -0.053 0.042 0.049186 0.031479 0.018971 6 -0.0096 -0.054 -0.055 -0.012 0.04 0.057819 0.041251 0.025947 CII Cdl Cmcg alpha Cmacl 0.002128 0.027073 2 -0.00855 0.035529 0.002644 0.027997 3 -0.01027 0.038073 0.002914 0.025998 4 -0.01198 0.037683 0.003703 0.030965 5 -0.0137 0.044169 I 0.00394 0.028002 6 -0.01541 0.042763 0.004253 0.026982 7 -0.01713 0.04326 Clave aveslp: Cdave Cl/Cd slope: -6.1e-06 0.015837 21.67894 0.343333 0.007495 0.021685 21.51989 0.466667 -0.02222 CI: Cd:

20.82189

0.556667 0.05139 0.026735

19.12742

0.653333 -0.02615 0.034157

17.71453

0.766667 -0.01055 0.043279

16.46352

0.863333 0.052439

Chord, m

Cd(eplt) Cd(edl)

c329= c327= c325= cg (m)= SM:

0.00647 0.032978

0.4148 0.3302 0.2455 0.232334 0.132077

Cd(duct)

a.c. cg (in)= rho

0.004996

329 327 325 9.147 0.000043

0.1514 0.2255 0.2997 Stot= V, in/s Cd(Igr)

0.005014

x/c: 0.3648 616

329 327 325 b/3, m. Ar, in2

0.195115 0.020696 -0.2744 0.3683 25.34

S ratio: Ix Iz Iy

329 327 325 270 3390.69 3610.24 0.41886 0.333333 0.247807 B.2 INVISCID VORTEX PANEL CODE PROGRAM VORCODE INTEGER Z,ZZ PARAMETER (Z=36) PARAMETER (ZZ=37) DIMENSION XB(ZZ),YB(ZZ),X(Z),y(z),s(z),SINE(Z),COSINE(Z) DIMENSION V(Z),CP(Z),GAMA(Z),RHS(Z),CNI(Z,Z),CN2(Z,Z) DIMENSION CT2(Z,Z),AN(ZZ,ZZ),AT(Z,ZZ),THETA(Z),CTI(Z,Z) OPEN (UNIT=If, FILE='juju', STATUS='NEW') OPEN (UNIT=I2, FILE='e327,, STATUS='OLD,) M = 36 MPI = M+I DO 13 I=I,MPI _--13 READ (12,*) XB(I),YB(I) !

PI = 4.0 * ATAN(1.0) ALPHA = (4.) * PI/180 DO 1 I=I,M IPI= I+1 X (I) =0.5* (XB(I) +XB(IPI) ) Y(I)=0.5 * (YB(I) + YB(IPI)) S (I) =SQRT( (XB(IPI)-XB (I)) **2+ (YB (IPI)-YB (I)) *'2) THETA(I)=ATAN2((YB(IPl)-YB(I)), (XB(IPI)-XB(I))) SINE (I) =SIN(THETA (I)) COS INE (I ) =COS (THETA ( I ) ) w RHS ( I ) =SIN (THETA ( I ) -ALPHA) DO 3 I= I,M DO 3 J= I,M IF (I.EQ.J) GO TO 2 A=-(X(I)-XB(J)),COSINE(j) - (Y(I)-YB(J)),SINE(J) B= (X (I) -XB (J)) **2+ (Y (I)-YB (J))*,2 C=S I N (THETA (I ) -THETA (J)) D=COS (THETA (I) -THETA (J)) E= (X (I)-XB (J)) *SINE(J)- (y (I)-YB (J)) *COSINE(J) F=ALOG ( I. 0+S (J) * (S (J) +2. *A)/B) G=ATAN2 (E*S (J), B+A*S (J)) P= (X (I) -XB (J)) *SIN (THETA (I) -2. *THETA (J)) + + (Y (I)-YB (J)) *COS (THETA (I)-2. *THETA (J)) Q= (X (I ) -XB (J ) ) * COS (THETA ( I ) - 2. * THETA (J) ) + -(Y (I) -YB (J)) *SIN (THETA (I) -2. *THETA (J)) CN2 (I, J) =D+. 5*Q*F/S (J) - (A*C+D*E) *G/S (J) CNI (I, J) =. 5*D*F+C*G-CN2 (I, J) CT2 (I, J) =C+. 5*P*F/S (J) + (A'D-C,E) *G/S (J) CTI (I, J) =. 5*C*F-D*G-CT2 (I, J) GO TO 3 CNI (I, J)=-l. 0 CN2 ( I, J) "_1.0 CTI (I, J) -=0.5*PI CT2 (I, J)=0.5*PI 3 CONTINUE DO 4 I=I,M AN(I, 1)ICNl(I, I) AN (I,MPI) =CN2 (I,M) AT(I, i)=CTI (I, i) AT (I, MPI) =CT2 (I,M) DO 4 J=2,M AN(I,J) =CNI (I,J) +CN2 (I,J-1)

4 AT (I, J) =CTI (I, J) +CT2 (I, J-l)

AN(MPI, i) =i. 0 AN (MPI,MPI) =1.0 DO 5 J=2,M

_5

AN (MPI, J) =0.0 RHS (MPI) =0.0 CALL CRAMER (AN, RHS, GAMA, MPI ) DO 8 I=I,M V ( I ) =COS (THETA ( I ) -ALPHA) DO 7 J=I,MPI V(I) =V (I) +AT (I, J) *GAMA (J) cp(1) =i. o-v (1) **2 WRITE (11,9) I,X(I),Y(I),THETA(I),S(I),GAMA(I),V(I),CP(I) FORMAT (10X, I2, FS. 4, F9.4, FI0.4, FS. 4,2F9.4, FI0.4) WRITE (11,10) MPI,GAMA(MPI) i0 FORMAT (10X,I2,35X,F9.4) END FILE (UNIT=If) END FILE (UNIT=I2) CLOSE (UNIT=If) CLOSE (UNIT=I2) STOP END SUBROUTINE CRAMER(C,A,X,N) INTEGER ZZ PARAMETER (ZZ=37) DIMENSION C(ZZ,ZZ),CC(ZZ,ZZ),A(ZZ),X(ZZ) DENOM=DETERM(C,N) DO 3 K=I,N DO 1 I=I,N DO 1 J=I,N CC(I,J) =C(I,J) DO 2 I=I,N CC(I,K)=A(I) L L X (K) =DETERM (CC, N)/DENOM RETURN END i FUNCTION DETERM (ARRAY, N) INTEGER ZZ PARAMETER ( ZZ=3 7 )

I

DIMENSION ARRAY(ZZ,ZZ),A(ZZ,ZZ)

L

DO I I,=I,N DO i J=I,N A (I, J) =ARRAY (I, J) M=I 2 K=M+ 1 DO 3 I=K,N RATIO=A(I,M)/A (M,M) DO 3 J=K,N A (I, J) =A (I, J) -A (M, J) *RATIO IF (M.EQ.N-I) GO TO 4 M=M+I GO TO 2 4 DETERM=I DO 5 L=I,N DETERM=DETERM*A (L, L) RETURN END

Appendix C

Data from Trust - Drag vs.Velocity Plot _w | V (mph) Thrust Drag (lbf)

Thrust (75%) Thrust (50%)

Thrust (25%)

(lOO%)

0 14 10.5 7 3.5 20 0.2423 12.4 8.9 5.4 1.95 25 0.3786 12 8.5 5 1.55 30 0.5452 11.6 8.1 4.6 1.15 35 0.7421 11.2 7.7 4.2 0.75 40 0.9693 10.8 7.3 3.8 0.35 45 1.2267 10.5 6.8 3.3 0 50 1.5145 10 6.3 2.8 55 1.8325 9.5 5.8 2.3 2.1809 60 9 5.3 1.8 2.5595 65 8.5 4.8 1.3 2.9684 70 8 4.3 0.8 7.4 3.7 3.4076 0.3 3.8771 8O 6.8 3.1 6.2 2.5 4.3769 85 5.6 1.9 4.9069 90 5 1.3 5.4673 95 4.4 6.0579 0.7 I i Data from the Climb Rate vs. Velocity and calculations for Acceleration !

l_

| Velocity RC RC RC Thrust Thrust Thrust (75%)

(f-t/s)(100%) (ft/s)(75%) (ft/s)(5o%) (1oo%)

(mph) (50%)

0 0 0 14 10.5 20 32.16 10.974366 6.9971998 13.4 9.9 6.4 25 39.02 13.169251 8.1977928 13.15 9.65 6.15 30 45.3 15.093007 9.2124816 12.9 9.4 5.95 35 51.15 16.620381 9.7597681 12.7 9.1 5.65 40 55.39 17.569304 9.7286042 12.3 8.7 5.25 45 60.O8 18.723847 9.9030598 12.15 8.55 5.1 5O 62.55 18.85035 9.0494746 11.75 8.15 4.7 55 65.67 19.272924 8.491961 11.6 4.55 6O 66.14 18.473712 6.7126619 11.2 7.6 4.15 65 67.06 17.87637 5.1352324 11 7.4 3.95 70 64.87 15.835487 2.1142618 10.55 6.95 3.5 63.18 14.02974 0 10.3 6.7 3.25 80 59.38 11.240155 9.95 6.35 2.9 85 55.82 8.5630387 9.75 6.15 2.7 90 49.43 4.5668669 9.4 5.8 2.35 95 41.02 9 5.1 1.95 100 27.41 8.3 4.4 1.25 Accel Accel(75%) Accel(50%) Accel(25%) Velocity Drag (lbs) (mph)

(lOO%)

0 37.56675 28.17506 18.78337 933917 0 25.91488 16.5232 7.1315 20 0.2423 35.30657 24.87831 15.48662 6.0949 25 0.3786 34.27 0.5452 33.15212 23.76043 14.50291 4.977 30 0.7421 32.0871 22.42708 13.16956 3.6437 35 0.9693 30.40411 20.74409 11.48657 1.9607 40 10.39338 0.8675 19.6509 29.31092 1.2267 17.8053 8.547777 1.5145 27.46532 7.291974 16.54946 26.2013 1.8325 5.283763 24.2013 14.54128 2.1809 3.731183 22.64872 12.9887 2.5595 1.426463 2.9684 20.344 10.68398 w 3.4076 18.49465 8.834626 3.8771 16.29565 6.635629 14.41785 4.757829 4.3769 2.39649 12.05651 4.9069 9.479432 5.4673 6.016315 6.0579 i g U r e

APPENDICES D

APPENDIX DI:

MSC/NASTRAN RESULTS

i _OQOOOOOOaO600QQ 00QQOOOOOOOOQOQO =[ iX i_J q_ (D • • n" ../ • II • • O_ Ul U Z • • qC 2: - 01

O 0 _ *o

Z _ t_ _. 0 tn 0 X IlJ ( if) 0 • • • ¢n m 0 • g,.q ooeeeeeoeoeoooeee QOOOOOOOQOOOOOOOO _J p -- 0 O.

N _Z q{ n, I-- ,I( Z _U _4 w_ o uJ 0 uJ U (J uJ (J ILl C: .J Z U uJ > l- W X O.

t- O Z Z n, k_ E 9[ Z l,= uJ O_ [1. o_ z_o_ t._ 00_ z -i o -IZz O0_w i-i 14 I- u

i

Q.

,v I- v) ( b U -.iJ 'U uJ ) I i U < uJ Z _J I- II Z U u Z uJ Z ,( Z 1- {J w 0 < Z ..I O J _J_ W m _-Z _ _ Z )..

I10 N _W I1_ " i J Z I_OU i.q O.

I- _Z --Z C[ I- I{ s, i if) i W I N o3 Z CC I- Z U P) (7) 4" I'r m UJ ILl r_ UJ I-- i- _11111111111111111111111111111111111111111111111111 Z 9( IX i- u_ Z Ill U.

Z :J 9( Q.

-.-Z O[ 4- T v) ,.j _ . .__, .___ ._ ._'. ..................................

.00000000000000000000000000000000000000_0000000000_ W ._.t 0000000000000000000000000000000000000000000000000 ILl 00000000000000000000000000000000_000_000000000000 aD ************************************************* ,0000000000000000000000000000000000000000000000000 _J I-- ..)

00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 ************************************************** *00000000000000000000000000000000000000000000000000 .J L_ 0 oooooooo_oo_oo_o_oo_o_oooooooooooooooooooooooo. . . ... . . . . . .

.," ...... - "-- " "-- " " "- " " "- " " ". ...................... o

o , 0 _WW_WWWW_WWWWWWWWWW_WW_WWWWWWWWWWWWWWWW_WWW_WWWWWW O000000000000000000000000000000000000000000000000_ I-- Q.

I-- _11111111111111111111111111111111111111111111111111 Z _O n, I- V) ,¢ __ Z LU U.

*[ W ,1( L Cb if) =Z I,- Z -- U v) co P "r U F- __ r,, f_ w I,u I- rj I&J _00000000000000000000000000000000000000000000000000 0000000000C30000C30000000000000000000000000000000000 ..J CB • 0 ..... , • • o_ .... o , ..... 000_ • • , • • • * ,_ • • , , • • • ._ _ °__ • , • ,___ ..... __ , ,__ , W CX k_ N I- a.

_llllllllllllllllllllllllllllllllllllllllllllllllll z I- -- Z uJ u.

Z w UJ ,I{ N Z I- Z U p = U W m,m m U 0 _O00000000W 0000000000 000000000_ ID_O X 0000000000 J / -__, _D _D {D _r _r _r ''''_0_ 0oo _00 .....

• I ° _r o

o9

• _ _+0 _ II -- Illllll_JJ_ I-- Z U ..I I-.

I- 0.

i-- I- _w _llllllllllllllllllll Z I- vI 9{ i =[ lu u.

Z C3 O uJ

LU

O ,I( U CL W_ uJ_ uJO 0 f_ o4 m O b.q LL. 0 _0 i--O _ • * , . • • . • ,_ O C3 O 0 (__O,* _L :lEO _iO 0 * 0 • U_ (.3¢D W ".=.'

Z C3 ,I{ )- uJ LU < Lg Z O 0 O 0 U uJ LU V) O 0 I I UJ ¢_ _N ¢b c_ O O O 0 O w- 0 O O P I- I I lU O. 0.

v) uJ u.

CD u.

W.,....0.,_ O __O*, uJ U 2) r_ p,. _D O M O X _s Z I I i- J Z o

Tr d-

0 f,,.

u ,._ mu.

uJ I _o I 14 U 0 z ¢0 I-- _J LU 0 Lg G < I',. m 0_ n, Q: UJ O > f_ > V) ,( we_ Ul I I I- LU M 0 I-z O _,,**,.,,,_ O __0 * .

D. C[ Z 3- >- oz uJ )- _m UJ LLJ U IS) LU Z .J M _J ILl r_ I.,. I.- ][ 0 U O m u,J .m Z __ W 0 t-- Z r,_ Z V) I- Z Z

c_

Z 3" 0 0 )-0 ..J (,,) U zlY m WI- D UJ UJ IL._, V) q[ F- 9( 0 O I- I-- uJ G ID Z • < O CL I- O cD _D I-- Z 0 ILl WX .-_ I- O O U Z l,t uJ c; OF..

Z Z I0 U Z Z o Z • Z ID O _J 9[ O I- o vt • Li.

V) __0 • , 9( M Z L UJ X ,_" Q.

I"* O O O UJ UJ LL W I- O U 0 >> Z Z e_.

I-- _r • < UJ Z Z Z_ W UJ < .J O' e,,, _u UJ 14.1 uJ LU 0 O. U_ .J UJ U.

I-- k_

t

| I ) QOQOQO 000000 ÷÷++++ "T- ,+++ u_ O_O000 .000 I000 NO00 !

t,) Z 000000 ++++++ .+++ Q 0 Q Oww_ ,_ 000 0 000 ÷++ ÷++ @ ÷÷÷ tU UJ UJ _om I!

0 0 uJ U 000000 ++++++ 000 • . • 000 ..° • °°° 00_0 00" 000_0 XO00 +++ + I1+ _0 I 000 0 000000 000 ÷+++++ 000 _ __ ,., i ooo ooo +++ ++÷ ÷ I1÷ 000 _000 I 00000_ 000 000 000000 ÷÷++÷÷ 000 ...

• oo _ 0.° ° ,..

0 00000_ I I 00000_ Z_ 00000_ 000000 ÷+÷+++ _0000_ 000000 _00000 00000_

-5

I t- QQ_Q00 _n E uJ it.

z O_ lU O.

(_ Z I-- ,( Z U Vl O_ UJ UJ U U.I I.- (1.

I.- Z e* -- I-- tn Z J.

Z

PAGE IP_ANK /_T F'ILMEU

w O_ Z o + ,%.

IU ¢,J v; o O_ p w + uJ e,., lU uJ _r N U o o I + Z W J w e',, 0 0 ÷ t_ .,J 0 In _0 I.-- q.

f_ p..

+ uJ o I.- 0 o + uJ 0 0 Z 0 o o w Z 0 I Z ( UJ tN

t

w- Z w I,.- U) Z L) IS') p Z _ 0 _ Z ILl M _ ILl r_J > UJ w Z Z_++++++++++++++++++++++++++++++++++++++++++++++++++ I,: Z Z _Ul-- M I,,- Z k- I- Z ,( I- V) < Z uJ u.

Z

J

tn ILl k_ G.

UJ 2: oQooo r_ LU Z Z 3_ n, I-- .J tn Z U.

q{ Z LI_ EU _W _( Z__ O) m .J U J_ 0 O_ < X v_ W Z v < U "1" 0 I- Z • 0 m,l, n, m ILl {[ Z <=E II.I r_ {O (CZ .J UJ {,.)

> "0 U_ UJ Or,.

Z r_ Zl-- / O< : U l..e X m )-*0 vl+ Z OlU 0. o 00000 0_ WOO0000 {.)

Z_+++++ iii II .J 00 U< _..¢z Z 00000 £[0 ...I O_ I.-L_ Ill'( Zl'- () =iO _(_ Z I- I',- O. 0 .J >,{ (,_ r_._ 0 ..I IlJ • u__ -I _r -JO O(J r_ U.,( ,._ Ii D-¢ ¢4 0 C: UO .J MI-- m I" C4/ _-¢1{ )- I"Z I-- <0 C3 V)< I ZUJ I r_ u.

I .Jo GOX t_ O_ w_ r4 o._r In uJo a0 lU=E uJ L_ e_ I-- "(U.

i V) C_ v) tn It) mO Iu =i" I-- Z< Z Z I.-I M I--=E )- I- =I=E ]E 0 (I O_ z Z OX 0 "< u =E Z:E Z Cr I11 I.,I uJ n v) Z O_ IIJ uJ _3 tn Ut .J ,,L i i z uJ w

PAGE BLAt_ NOT Ftt...MEt_

t i !

i i IM a.

t_ Z e_ u'* • 0 Z 0 + • 0 O'J 0 n" 0

g

÷ _ ILl WJ 0 0 0

- _

IN I-- + _ CO I- m •-i O_ N Ud crJ er aO W

u T

IX O 0 Lt 0 U + !

+ W _ 0 I.- 0 k- 0. 0 I-- + _ 14.1 0 0 '9( I,- 0 I,... 0 uJ Z w o q( Z o ÷ w o • 0 o

- g

+ Ix_ w U _ ÷ uJ lIJ U O _ U _

_4

• 0 X + I-. e,_ cO

- ,4

o o ÷ -- 0 N 0

! +

' 0-- 0

', o

I o : o p

L

[ )

l

o + uJ o t_ 0 h, (= o __ o !

(D Z _ _ 0 • I w uJ • e4 X !

_ W I,- e,d m o + LU -- 0

; o

+ _ W -- o Z 0 ( U W O-- Z 4( 0 Z 0 + U W • 0 O o + LU uJ _ 0 UJ Ft' 0 U 0 UJ 0 q( 0 0 0 J + W W 0 ..1 0 X

... g

X I "0.

W N 0 I.- 0 a. 0 t- 4.

0 0 Z 0 Z_ Z uJ ,( U m _) o_ O000000000000000000000000000000000000000000000000Q 00000000000000000000000000000000000000000000000000 0 000000000000000000000000 00000000000000000000 I IIIIIIIIIIIIlilllllll|l| II1|1111111|1111111!

W _W_W_WWWWWWWWWW_WW_W_WW _WWWWWW_W___ ¢, O_ IIIll I 0 000000000000000000000000 00000000000000000000 I iillllll|l|lllllllllllll Illlllll|lll|lllllll In U 0 00000000000000000_000000 00000000000000_0000_ I I1|11111||1|11|11111111! IIl|lllllllllllll||i Z ILl _J .J 00000000000000000000000000000000000000000000000000 ************************************************** 00000000000000000000000000000000000000000000000000 _-- 0 UJ • Z c_ z _j ,,* Z r, !

-- i{ w q( U w %- nD V) ! P n, ' Z 0000000000 °00.0.0..o n, 0000000000 I" Z -% 0000000000 __ U It11111111 {/1 _WWWWW_ tw) 2d_d_ ....

p _00000_00o IIIIIlllil w IIJ ,11 uJ ..0.0..*..

O00OO0_OOO IIIIIIIIlt Z _W_ 0000000000 0000000000 0000000000 .o......*.

0000000000 0 0 Z Z ,( ,( Z Z _j ,,I U. U. Z Z Z 'w uJ -- ,1( O.

J tN 'w if) t_ n, Z 00000000000000000000000000000000000000000000000000 _.- Z (J r_ .

O_ 00000000000000000000000000000000000000000000000000

g__ggdg_g_gdddddggdd_gdddg_dddggd_g_gggd_d_

uJ O_ =i uJ U IM 00000000000000000000000000000000000000000000000000 C_ O00000000000000000000000000OO000000000000000000000 (J 000000000000000000000000000000000 0000000000000000 IIIIl|lllll|llll|llllll||lll|llllllllllll|llll|lll tU 00000000000000000000000000000000000000000000000000 > _00000000000000000000000000000000000000000000000000 _00000000000000000000000000000000000000000000000000 O00000OO00000000000000_O00000000000000_O0000000000 ,J 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000000000 G Q.

"W C3--O Z Z ,1[ ._ < :Z:_Z UJ _J W 4[ m Ul CD ( U if) li Z < 00000 n, I- 00000 Vl < Z U tn t_ O_ C_ 00000 .e,,t 00000 _v uJ UJ cJ ILl 00000 ,,0., 00000 U 00000 IIlll W W_WWW 00000 _00000 _00000 00000 C3 .J 00000 00000

V-

00000 i,.0l O0000 I.- I- G. O.

I- I- 0 0 W Z Z )-- I- Is) ul Z Z __0 I • .i .t " u. Z Z Z Q.

IIJ

V) Z 00000 _e to,o.

00000 Z _0000 00000 ÷÷÷÷÷ _WW_W Z N__ | || U z ÷+÷++ D | iJ J d Z IIIII _000 0_000 I1÷÷÷ I

dd_d_

I III I, 00000 00000 LL 00000 00000 CL G.

= ; 0 ) W Z > I-, u..

Z U,I UJ u LL z Z -"

, ======================== .......... _._

__oo oo oo oo ooooooooooooo

, , ,, ,, ,,,,,,, , , ,,,,,,,, ,, ,, ,'''''''''''' ''''

t v) mm

J

......... _ .............. _ ....... _..._ .....

¢.5-- ,9[ W 00000000000000000000000000000000000000000000 IIIIIIIIIIIIIIIlllllllllllllllllllllllllllll .I U 0 m _0_0___0_ ___0_0_0__ V} I I I II II II II IIIIIIIII I IIII ZL_ 9[ O_ ).- {4 00000000000000000000000000000000000000000000 4( IIIIIIIIIIIIIIIIIIIIit111111111111t111111111 Z ,,,°,,.,,,,,,,.**..,,,..,**0,*0,* 0,,,o,0.000 I I IIIIIIIIIIIIIIIIII III III II II II _00000000000000000000000000000000__ I-- 00000000000000000000000000000000000000000000 )- Z _÷+÷÷+÷÷+÷÷÷÷_÷÷÷÷÷_÷+÷+÷÷÷÷÷÷+÷_÷÷÷11111111 UJ Z .i IX w UJ CO 0_0_ _ __ _000_0_0_0000_0__ RJ Z UJ UJ .I _J 00000000000000000000000000000000000000000000 ÷÷_÷l÷÷llllllllJllllll]llllllllllllllll|lll!

!

,J I- Illl Illlllll II111111 ,< -1 X U.

,( 00000000000000000000000000000000000000000000 00000000000000000000000000000000000000000000 0 !

UJ Z -lU.

Z 00000000000000000000000000000000000000000000 W 9{ ******************************************** rr 00000000000000000000000000000000000000000000 U m r,, .I D.

x

00000000000000000000000000000000000000000000 ******************************************** z z 00000000000000000000000000000000000000000000 iY I-- u_ 9{ Z Z • i,i uJ I-- Z .I Z Ikl _-i .J .i

4(

t t ¸ '1( O_ I- t C ( C_ .J ID i.

f.

L I- .-) i

z

4( LU

t"-

r_

P,_i_lO_ PAGd[ BLANK NOT FILMEU

o in M,I a M c.q-- < U Ck Z 0 _ 000 _0 000 _0 000 000 000 000 000 000 000 OO0 0 UJ _ 000 000 000 000 000 000 000 000 000 000 000 000 0 ÷÷@ II÷ ÷_÷ I1÷ _÷+ ÷÷÷ ÷÷÷ ÷÷÷ ÷÷÷ ÷÷÷ ÷÷÷ +÷÷ ÷ _W WWW WW_ _WW W_ _W WW_ _W_ WWW WWW WW_ W_W 0 m ke_

w > ................................. £_o d

_X_ 000 000 000 000 000 000 000 000 000 000 000 000 0 Iv E_ @÷÷ I1+ I1+ I1÷ I1@ +++ @++ @++ +++ @++ @++ @++ + I.- 4[ 000 000 _0 _0 _0 _0 _0 _0 000 _WO 000 _0 Z U 0 --, ... °'° ''' ''' "°" *'' ''+ "°" "'° ''" +'° " v_ _ _ 000 000 000 000 000 000 000 000 000 000 00_ 000 0 O +÷+ I1÷ I÷÷ I1÷ I÷÷ I÷÷ I÷÷ I÷+ I_÷ I÷÷ I÷÷ I÷÷ I I ZW I II I II II I I II II I I II I _ 000 _0 0_0 _0 0_0 0_0 0_0 0_0 0_0 0_0 0_0 0_0 0 _ 000 000 000 000 000 000 000 000 000 000 000 000 0 O O ÷÷÷ I1÷ +1÷ I1÷ ÷l÷ ÷1÷ ÷1÷ @1÷ ÷1÷ +1+ ÷1÷ ÷1+ + ill (J LIJ _ ... °, • . .. ° . • _ I I I I I I I I I I I I I I I I I IX I1÷ I1+ I1+ I1+ I1+ I1+ I1+ I1+ I1÷ I1# I1÷ I1÷ I _ .. ...................................

• _ I I I I I I I I I I I I _Z I_ 000 _0 000 _0 _0 000 000 000 000 000 000 000 0 N_ 000 0_0 000 000 000 000 000 000 0_0 000 000 00_ 0 _1 ÷÷+ I1+ ÷÷÷ I1÷ I1+ ÷+÷ ÷÷+ +÷÷ +÷+ ÷÷÷ ÷÷+ ÷++ +

z z _o _o _o o _o d_ dd_ 22_ dd_ d_o dd_ _o

I I I I I I I I I I I I _X 000 000 000 000 000 000 000 000 000 000 000 000 0 _1 @+@ I1÷ I1@ I1+ I1@ I1+ I1+ I1+ II+ I1÷ I1+ I1+ I I I l I I I I I I I I I I-- I--

N NNN NNN NNN NNN NNN NNN NNN NNN NNN NNN NNN NNN N

I- I-- C O Z

z z

0 0 _ 0 0 0 0 0 0 0 0 0 0 t- I,,- J_ 41 • II

2 Z

=i ]i¢4

UJ tiJ<

_ u.u

tn o I @4 i UJ O.

Z 0 WOO 000 000 000 000 000 000 000 000 000 000 000 --_0 W _00 000 000 000 000 000 000 000 000 000 000 000 000 r u_ _+÷ +÷÷ @÷÷ +÷@ @÷÷ ÷_÷ ÷÷÷ ++÷ ÷@÷ @÷÷ @÷+ +÷÷ I1÷ Z_ W_ W_ WWW W_ W_ WWW W_ _WW WWW W_ W_ WWW 0 m tn _.. .o0 .,. ,,. ,.o .o. ,,. 0.. .,, ,°. o,. ,.. o..

Z U ,4[ L_ • O0 000 000 000 000 000 000 000 000 000 000 _0 _0 _X_O0 000 000 000 000 000 000 000 000 000 000 000 000 E_÷÷ +÷÷ ÷_÷ +÷÷ +÷÷ ÷÷÷ +÷÷ _÷÷ +÷+ +÷÷ ÷÷+ I1_ I1÷ Z _ _00 000 000 000 000 000 000 000 00_ 000 000 000 000 0++ I+÷ I÷@ I@+ I÷÷ I÷÷ I++ I÷÷ I÷÷ I÷+ I÷÷ I÷÷ I1÷ I Z_ I I I I II I I II II I I II I _00 000 000 000 000 000 000 000 000 000 000 000 000 D 0 01+ ÷1+ +1+ @1+ +l+ ÷1+ +t+ @1+ @1+ @1+ ÷1+ @1@ I1÷ l J J J _ I I | ! I I I I I Z.. .** ,0, e,, o0, ._. *0, _., .o0 o., ---- , I _1 _ _ _ _ _1 _1 _1 _1 _1 _ _ I I I I I I _00 000 000 000 000 000 000 000 000 000 000 000 000 IXI÷ I1+ I1+ I1+ I1+ I1÷ I1÷ I1÷ I1+ I1+ I1+ I1+ I|+ L _ _ N_I_ _ _ _ _ _ _ _ _ _ _ _ _ _ ..................

I I I I I ! I I ! I I I I I_ O0 000 000 000 000 000 000 000 000 000 000 000 _0 N_O0 000 000 000 000 000 000 000 000 000 000 000 000 _I@+ _@+ ÷@+ +@_ @++ ÷@@ @@+ @+@ ++_ ÷@@ @++ _++ II+ , , , , , , , , , , , , , _XO0 000 000 000 000 000 000 000 000 000 000 000 000 _11+ I1+ I1+ I|÷ |1÷ I1÷ I1+ I1+ I1÷ I1+ I1+ I1@ I1+ 0-.

_ I ! I ! I I I I I I I I I U I-- I--- W NNN NNN NNN NNN NNH NNN NNN NNN NNN NNH NNN NNN NNN I.- 0 ) Z Z Z 4[ ,I[ • 0 0 0 0 0 0 0 0 0 0 0 0 W_ I-- • : I!

Z uJ - (..)

0 _ _0 _0 000 000 000 000 000 000 000 000 000 000 0 W _ _ 000 000 000 000 000 000 000 000 000 000 000 000 0 _ N II+ II+ ++@ +++ +@+ ÷+@ ++@ +++ +@+ +++ +++ +++ + W Z _ _ _0 _0 000 000 000 000 000 000 000 000 000 000 0 _ 000 000 000 000 000 000 000 000 000 000 000 000 0 _ _ II+ II+ @++ +++ +++ @++ +++ +++ +++ +++ +++ +++ + _ _ _ 000 000 000 000 000 000 000 000 000 000 000 000 0 _ 0 I1+ I1+ +++ +++ +++ I++ I+÷ I++ I++ I++ I++ I++ I I Z_ I I 1 I I I I I t I II II _ _ 000 000 000 000 000 000 000 000 000 000 000 000 0 0 0 II+ II+ @+@ +@+ ÷+@ +I+ +I+ +I+ ÷I+ +I+ +I@ +I@ + -- _ I I I I I I I I I I I I I I I I I I I _ 000 000 000 000 000 000 000 000 000 000 000 000 0 IX I1+ I1+ I1@ I1+ I1+ I1+ I1+ I1+ I1+ I1+ I1+ I1+ I _ I I I I I I I I I I I I -- (Z -- I_ _0 _0 000 00_ 000 000 000 000 000 000 000 000 0 NI) 000 000 000 000 000 000 000 000 000 000 000 000 0 _I ||@ |1+ +@+ +++ +++ ++÷ +++ +++ +++ +++ +++ +++ + I I I I I I I I I I I I W _ 000 000 000 000 000 000 000 000 000 000 000 000 0 _1 I1+ I1+ +++ _++ _@+ I1÷ I1+ It+ I1@ I1+ I1+ I1+ I _ I I I I I I I | I I | I U W

N NNN NNN NNN NNN NN_ NNN NNN NN-- NNN NNN NNN NN_ N

¢ 0 Z Z_Z • 0 0 0 0 0 0 0 0 0 0 0 0 0 W_ Ix OE I-- I.- v el q II " Z .i Ill,.( Z Zm Ck Z 0 UO0 000 000 000 000 000 000 000 000 000 000 000 000 _00 000 000 000 000 000 000 000 000 000 000 O00 000 _+÷ ++÷ ÷++ ÷÷@ +÷÷ _÷+ ÷+÷ ÷++ ÷+÷ ++÷ ÷÷÷ ÷++ ÷÷÷ In Z U O0 000 _0 000 000 000 000 000 000 000 000 000 _0 _X_O0 000 000 000 000 000 000 000 000 000 000 000 000 _(<+÷ +÷÷ II+ +++ +÷+ ÷÷+ +++ ÷+÷ +÷÷ +++ +÷+ ÷++ ll÷ ( Z $'b '_ _ _00 000 000 000 000 000 000 000 000 000 000 000 000 0++ I÷+ I+÷ I++ I÷÷ I+÷ I++ I++ I+÷ I÷+ I++ I++ I++ I Z_ I I II I I I I I II II II I II I _ _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 _00 000 000 000 000 000 000 000 000 000 000 000 000 0 O1÷ ÷1÷ ÷1÷ ÷1@ +1÷ ÷1÷ @1÷ ÷1÷ ÷1÷ ÷1÷ ÷1÷ ÷1÷ +1÷ I ,,I ,,,) J _ I I I I I I I I I I 1 I I I I I I I I I >00 000 000 000 000 000 000 000 000 000 000 000 000 IXI+ I1÷ I1÷ I1+ I1+ I1+ I1+ t1+ I1÷ I1÷ I1÷ I1÷ I1+ ( X_ I I I I I I I I I I I I (Z I_ O0 000 000 000 000 000 000 000 000 000 000 000 000 N_O0 000 000 000 000 000 000 000 000 000 000 000 000 _1++ +÷+ +÷+ ÷÷+ ++_ ÷++ ÷++ +++ +÷+ ++÷ ÷++ ++÷ +++ z z_o _o _ o _o _o _o _o _o _0 _0 _o _0 _o I I I I I I I I I I I I I _XO0 000 000 000 000 000 000 000 000 000 000 000 000 _11+ I1+ I1÷ I1+ I1+ I1+ I1+ I1+ If+ I1+ I1+ I1+ I1÷ I _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 000 _0 _ I I 1 I I I I I I I I I I NNN NNN NNN NNN NN_ NNN NNN NNN NNN NNN NNN NNN NNN I- = ; 0 ) Z 0 0 __ 0 0 0 0 0 0 0 0 0 0 9[ t II Z UJ Z _.00 T ¢q

I

w o

Z 0 W 000 000 000 000 000 000 000 000 000 000 _ _ 000 000 000 000 000 000 000 000 000 000 L _ _ _ ÷÷+ ÷++ ÷÷+ +++ ÷++ +++ ÷++ +++ +++ ÷÷+ _ _ • _W _W _WW WW_ WW_ _W_ W_W WWW W_W WW_ Z U _ _ 000 000 000 000 000 000 000 000 000 _0 _' _ 000 000 000 000 000 000 000 000 000 000 _ _ ÷÷÷ ÷÷÷ ÷÷÷ +÷÷ _÷÷ ÷_÷ ÷÷÷ +÷÷ ÷÷÷ I1÷ _ _ _ 000 000 000 000 000 000 000 000 000 000 _ 0 I++ I÷+ I++ I++ I÷+ I++ I++ I++ I++ I++ _ ° • ..o I Z_ I I I I I II II I I II _ 000 000 000 000 000 000 000 000 000 000 0 0 +1+ +1÷ +1+ +1+ +1+ ÷1+ ÷1+ +1+ +1+ ÷1+ _U ." ° ....

-- _ I I I I 1 I I Z *'' "e' ° ° "* I I I I I • 000 000 00_ 000 000 000 000 000 000 000 _X I1+ I1+ I1÷ I1÷ I1+ I1+ I1÷ I1÷ I1+ I1÷ _ I I I I I I I I I I (Z -- I_ OOO OOO OOO OOO OOO 000 OOO OOO OOO 000 N_ 000 000 000 000 000 000 000 000 000 000 _1 ÷++ ++@ ÷++ ÷÷+ @++ +÷+ ÷++ ÷++ ÷++ +++ I I I I I I I I I I _ 000 000 000 000 000 000 000 000 000 000 _1 I1÷ I1÷ I1+ I1@ I1÷ I1@ I1÷ I1÷ I1÷ I1+ _ I I I I I I I I I I N NN_ NNN NN_ NN_ NN_ NNN NNN NNN NNN NN_ Q. _.

l- I- ( 0 Z W 4[ .¢ I'- I-- U_ 14 9[ II U. U.U r_ _n _ (_ _r i/1 (o P. c0 0_ o _:r_ In m In ul t_ in In In (D

,a

.iI iI I) ,1I q( I .?l w ! w .1 II I p_ PkG,I[ m..Arm NOT FK..MEU _.

f

O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 p,I O.

t

_0 _0 _0 _0 _O _0 _0 _0 _0 _0 _0 _0 _0 _0 _0 _0

1 w

O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 I÷ I÷ l÷ I÷ I÷ I÷ I÷ I÷ I+ I+ I+ I÷ I÷ I÷ I÷ I+ e( O_ O0 I I I I II I I I II II II II II II II II l-- f,4 N Z O_ O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O_ ÷1 ÷1 +1 +1 +1 +l _1 +l @1 ÷l ÷1 +1 +1 +1 +1 +1 Z( I I I I I I I W _ *. ., , • , °, ,, ,, o.

U ( ® ® ® ® ® ® ® ®, ® = ® =, ® ® ® ®, I ! I I I I I I I I I I I O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 II It II II II II II II II II II II II II II II I I I I I I I I I I I I I I I I _0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 _ 0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 _ ÷ + + + + + + + + + + ÷ + + + + + + + + + + + + + + + ÷ + + + + Z_ _ _ _ _ _ _ _ _ O0 _ _ _ _ _ _ _ ZZ I l I I I I I I I I I I I I I I O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 _X II II II II II II II II II tl II II II II II II _I _ _ _ _ _ WW W_ WW WW WW WW WW WW WW WW WW I I I I I I I I I I I I I I I I I-- I-- I-" O.

O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 II II II II II II II II II II II II II II II II O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 Z Z _Z O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 4[ 4( _ O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 _" ¢1: _ O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 [ _ O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 r I I I I I I I I I I I I I I I I UJ UJ u.

: [ ILl • e7 t_ ('g =11 " UJM J U.I

t"-

O0 O0 O0 O0 O0 O0 O0 O0 _ 00 O0 O0 O0 _0 O0 O0 O0 O0 O0 O0 O0 Ua

> _ _ _ _ ........ _ _ _ _

< UJ O0 O0 O0 O0 O0 O0 O0 O0 0 O0 O0 O0 ('4 _n I@ I+ I+ I@ I+ I+ I+ I÷ II II II II (J Vl =[ q( _O i I I I II II II II II II II II O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O_ +| ÷1 ÷| @I @I ÷1 ÷1 @I II I! II II (J Vl OJ O_ Z_ I I I I W_ I I I I I I I --J O0 O0 O0 O0 O0 0 O0 O0 0(_ O0 O0 O0 I I I I I I I I I I I I I I I I I I I I I I I I 0:: • l_l _lJ ILl ILl ILlUJ WILl IIJUJ ttJUJ ILIIU UJIU ILl ILl ILI_I IUILI UJUJ X I _" I'_ _') k"_ I_I_ _ (_)(_ UI_ _ I'_ I'_ I'_ I"_ _ (_,_0 I'_I_'- tU I O0 {D_ {D_ t_ qr_r i_ 0101 oo i_{o I_1 _ _r_r _r_l" _.t4 • • • • • • • • • * * * * ' • ° ' * • • ' i I I I I I I I I I I I "cO O0 O0 O0 O0 O0 O0 O0 O0 _" _'" _ _'_ 0 O0 O0 CIO O0 O0 O0 O0 O0 O0 O0 O0 O0 r'_(.,.l_- + + +4- + _- + + + + +4" + + ++ I I I I I I I I I Ullli WLU WkU WLU _U.I _UJ W_ I&ILU u_UJ WILl uILU _W Z_ 010) I-.I_ U')I_ (_4 f,I I_i¢) _lr_l " _l'_r I_1 _ I_ O0 010_ (D_D :_ UJ :E _){_ _ t'_ ('_ I_U1 I_1_ O0 O0 _{0 I_1 _ O0 _ _D • , • ,,, ................ ,;_; _; _ _;_; ZZ I I I I I I I I I I I I I.-I _"¢ V') INN r4_ ININ tNI (NI _.- "_ ILl O0 O0 O0 O0 013 O0 O0 O0 O0 01_ O0 O0 {,_X I I I I I I I 1 I I I I I I I I I I I I I I I I _V') I I/JUJ U.I I_I I/J_l I/.I UJ [UUJ IUU.I I&/UJ uilkl U.ILU IUiLI IUUJ I/JUJ -- I I I I I I I I I I I I I.- l=- ssl r. IN(Ni NL'NI @,I_ (NI {',,i L*4 ('q N(Ni (_I l,,i (NI @,I {"M (Nl{q _i _'_,i _*,i e_l __ I- O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 .._ :_ I I I I I I I I I I I I I 1 I I I I I I I I I I O O UJ -I li.I UJtU ILI_ .1_ kU"l IklUJ tU I1.1 UJILI Ikl U.I I_IUJ ILl IIJ IIJ ttJ (.I O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 -- Z u_Z O0 O0 O0 O0 O0 O0 O0 O0 C) O O0 O0 O0 _[ I_ I00 O0 O0 O0 O0 O0 O0 O0 O0 00 O0 O0 ml- O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 )-- _V_ O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 O0 ,9{ ,I{ _-_ . • • • • • o • • • • . • • , • • • • • • • • .

Z Z t'_ t_l _N_I _1L'_I t'_l _N t'_l t_4 L'_I r4(_l t'_l t_ (_1 t_l t'_ (',_ f_(_l t'_lN I I I I I I I I I I I 1 -- II tl.

Z _ IF) ('1 {'_ (') t_ (9 _r _" _1' q" _lr _- ; w.

=Er, ..J

<

_E ,} w .J IE ,J J ,.j I-- P.

I-.- O __ Z ,_.

uJ 'Z

p__ PAGE ftLANK NOT FLMED "

000 000 000 000 0000 0000 0000 0000 0000 0000 0000 o,. °*o *,o °,, °°°° °''" ''°* °*'" ''°' '''* e,.o 000 000 000 000 0000 0000 0000 0000 0000 0000 0000 I.I

oo-- ---- oo-- _ oo- oo- oo- oo- oo- oo-- oo--

÷+t t I ++, _ _1 i it aii I_ ++i ++J w t 0

www ww www ww ww_ www www www www www www

m

''_ _ _ _'_ _ _ _ _ _ _ _

II | I | I I I I I I I I I I II ÷÷1 II ÷÷l II Ill @÷1 ÷÷I ÷÷1 ÷_1 ÷÷1 ÷÷1 o.o ,o. ,,, ,oo ,..o o... ,o,_ o.,, ,,o. ,,..

w ,,I I I I II I I I I | I !

f.J

oo oo-- oo oo-- ooo_ ooo_ ooo_ ooo_ ooo_ ooo_ ooo_

:[: |l III l! III illl Ill! llil |Ill fill llll illl .,o o., ..,, ..oo • • I II I I I I I I I I I I W C_ 000 000 000 000 0000 0000 0000 0000 0000 0000 0000 Z M O.

_3 000 000 000 000 0000 0000 0000 0000 0000 0000 0000 .., ,,. .,o .,, ,,.o ,_oo ,.,o .°o. ,.o, ,,,. ..oo 000 000 000 000 0000 0000 0000 0000 0000 0000 0000 O_ r_ 0 I-- Z 3[ ILl _U .J Z _J L_ LL Z I Z t') uJ 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 4( ........................ _ _ ........

0000 0000 0000 0000 0000 0000 0000 0000 W ÷÷I +÷I ++I ÷+I ÷÷I III ÷÷I III ||I III Z • ,., °.°. ,o,, ,0., _°,, .°,° o°°° °°,° 0,°° .°°.

w ,Y I I I II I I I I I I I I II I 2[ ÷+1 @÷1 ÷+1 ÷÷1 ÷@1 ÷÷1 ÷÷1 +÷1 ÷_1 ÷÷1 • o,° .,,° , ,,,, ,.,° ,o,° °°0° I I I I I I I I I I I I ! I I I I U Z 000_ 000-- 000_ 000_ 000_ 000_ 000_ 000_ 000_ 000_ Illl loll IIII IIII IIII IIII IIII IIII 1111 IIll U E J m ILl I I I II I I I I | I I I I I f_ 0000 0000 0000 0000 0000 0000 0000 0000 0000 0000 ,°,° °°o° ,°°° ,,°. °,°, ,,,° °,0,

6666 6666 66_6 oooo oooo oooo =ooo oooo oooo ooo_

I.- C) )-4 0000 0000 0000 0000 0000 0000 0000 0_00 0000 0000 • o,. o,00 ,,,o ,,_, ,,., ,,,, ,,,, o0,, 0000 0000 0000 0000 0000 0000 0000 000_ 000_ 000_ I

o

Z .J t_

z !

• J uJ OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO

oooo o_oo _ oooo oooo oooo oooo oooo oooo oooo

UJ

_N _N NN_ _N _ _N OOO_ OOO_ OOO_ OOO OO_ OO_ OO-- OO_ OO_ OO_ OOO_ OOO_ OOO-- OOO III III III III ll| III +@+I ÷÷÷J ÷÷+I +÷+ WW_ W_ WWW _W_ WW_ _WW W_W_ W_W_ W_W_ _ [ -- • ,., ,o,, ,.o, +.o+ ..,. .,o, ( I I II II I I I II I II I I I ( [ 0_ 00_ 00_ 0_ 00_ 00_ 000_ 000_ 000_ ++1 ++1 III III III III ÷÷+1 ÷÷+1 ÷÷+1 ÷++ E

_ ''_ _ _ _ _ _ _ _ _ _ +''

_J I I I I I I I II II I I I II U Z OOO_ OOO_ OOO_ OOO_ OOO_ OOO_ OOO_ OOO_ OOO_ OOOO IIII IIII IIII IIII IIII llll @@@I +I@I ÷I@I I÷@÷ C J E J e( J J 03 I I ! I II I1! I! | I I I I I IJ uJ _J n- O L_ _- OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO +..o °,o, ,.,, oo+, .,+, ,o,+ ,,+. _+,. ,,,o ,.._ OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO Z M O n 1:3 OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO *.,. .,o, ,,.+ ..,. ,.oo ,..o o,,. ,.,, ,,++ +,+, n_ OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO OOOO C3 F- !

Z Z Z ILl e[ e( _J -J .i UJ UJ +1 Z NNNN NNNN NNNN BNNN NNNN NNNN NNNN NNNN _B _ -j- m t_ E I, O0 000000 000000 000000 000000 000000 000000 00000 II,l,* q( O0 000000 000000 000000 000000 000000 000000 00000 UJ e Ul 0000_ 0000_ 0000_ 0000_ '9( 0000_ 0000 C, +1 +÷÷11 I÷+11 ÷1÷11 I÷÷11 IIIII II1+t IIII U 0 m _WO_ _0_ _ _ 00_0_ °°.,,.

.,.,.

II I II II I II II I I II I |11 I I I d 0000_ 0000_ + I ++++1 ++++# +@@+I @++@I _+++I ++++I ++++ (. .i.i On.., EO_U_ O_ 0 ,,,.10 ._I_., _w fqU_ iii II II IJ || | |1 I II $ |1 {J Z O_ 00000_ 00000_ 00000_ 00000_ 00000_ 00000_ 00000 +1 I÷÷÷÷1 I1÷111 I1÷111 IIIIII IIIIII IIIIII IIIII / ,9{ m II II I ktJ II I II II II II U 000000 000000 000_00 00_000 000000 000_0 I-- • , . , . .

°.,,,. ,.,,,, .0,.,, ,.,,., ,,,., O0 _0000 000000 Z 000000 00000_ 000000 000000 00000 t-q 1- r,, O0 000000 000000 000000 000000 000000 00000_ 000_0 l',,' 000000 000000 000000 000000 000000 000000 00000 _ I __ I __ <O000e <O000e <O0_Oe <O000e <0000 w O.

0_ t- M I O I- Z Z IIJ < .i I,- / .t ,( Z UJ UJ U. U.

I-_ p') 0") I Z

,)

n.

U

0 000000 000000 000000 000000 000000 000000 000000

( --

0 000000 000000 000000 000000 000000 000000 000000 i.i I IIIII lllll ÷@÷÷I @÷÷÷I I÷III ÷l÷ll l÷lll W _W_W _WW_ WWWW_ W_WW WW_ _WWW_ WW_W m 0°°00° .0°°.0 °.0°0.

( [ 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ I @1111 IIIII +÷++1 +÷++1 +@+÷1 @÷++1 @+++1 !

• .°.0.° °.°..° .°...0 °...°.

I II II II II II II II I IIIIII IIIIII I@@1÷1 I1+1÷1 I1+1@1 IIIIII IIIIII J ) E I ) I I.*.0l I..*.0 ..0... I..*.. o...0.

II I II II II II II I II UJ (J rr " F- 0 000000 000000 000000 000000 000000 000000 000000 h-

o oooooo oooooo oooooo __ oooooo oooooo oooooo

_- Z 0.

O. 0000_0 000000 000000 000000 000000 000000 000000 _. ,-, . ,_ _ ,_ _ ,-, : ,_ . ,-, . ., .

Ikl qC l/) 'qC _IC _[ ( 44 ,( r,/) _[ r,/) U-.I 0 J (_ -J 0 -J 0 --I 0 J 0 -J 0 .J _) I" I P'l_ PIP" I-- I _1 t'_ rill I-- I rl l_l ril'_)" I riP" _1"_1-- I P" "_ 0 rll" I I_l_Irll_ I" I I_r_l_l_l - =) ) Z Z -Z i{ Z ,i ,,i Z Z UJ 000000 000000 000000 000000 000000 000000 000000 0 oo°o.° ..*... o.o..o 4,,,.o ,t°.o. ,,.,°, .o._o. .

000000 000000 000000 O00000 O00000 OO0000 000000 0 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ IIIII IIl÷l lllI! I|III lllll ÷**II l@@ll U Z q( e_ II I I I I I III I I |1 I I 4( Z 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ ÷++÷l ÷@÷÷1 ÷@+÷1 @I÷÷i IIIII @+@+1 +++÷1 U • o.,.o o,.oo.

U Z 0000_ 00000_ 00000_ 00000_ 00000_ 00000_ 00000_ 0 IIIIII IIIIII Illlll Illlll IIIIII I1+1+1 II÷l÷f I ty W U uJ r_ II II II II I II III II UJ (J U. I" I- Z O.

M 000000 000000 000000 000000 000000 000000 000000 0 • ..... ,.o.o. ,,..,, ,.o... .0.,o0 .o.... .0,o.. .

000000 000000 000000 000000 000000 000000 000000 0 t- I-- M I I- 0 0 Z Z Z UJ UJ .J uJ u, _.1 Z

7"

if3 tv

u J__ 00000

00o000 000000 000000 000000 000000 000000 O0 (3 .°,o,, ***,o, , ,1{ 00000 000000 000000 000000 000000 000000 000000 O0 Q., (/t 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ 0 0)-- ,( I+1+1 +1+11 I+111 Illll Illll Illll IIIII I U 0 m tn Z_ • oo.o ,°0,°0 *****. ,, 9( II I II I I II I I I I II | I I )- ul 9{ 0000_ 0000_ 0000_ 0000_ Z 0000_ 0000_ 0000_ 0000_ 0000_ 0000_ ÷+++1 ++++1 ++++1 ++++1 _+++1 ++++1 +I@II I u ]E _0 if3 O_ O'J -- ,.,,o oo.,..

*°**** .****. **°**° • o,o°0 o 0_ II II II I II I II I II I II I U Z 0000_ O0000P 00000_ 00000_ 00000_ 00000_ 00000_ O0 I+l+l IIIIII IIIIII IIIIII IIIIII I|1111 IIII1! II uJ m uJ U uJ r_ w ****** 0.,.** ****0, 0,0,.. ,0 II | II I II |1 II II II I I I-- 00000 O0000O 000000 000000 000000 _00000 000000 O0 ,.,.,0 o°,.,° ,0°o,o .,..°0 ,.°000 °..o°o °0 00000 OOOO00 000000 000000 000000 000000 00_000 O0 Z 00000 000000 000000 000000 000000 000000 000000 O0 .0.0.

00000 000000 ............ __ ..............

000000 000000 _00000 000000 O0 U _ 0 J 0000_ <O000e w CL mmmo I L C3 Z

= =

v) uJ !

Z u e,e0 ,C UI IIII U m e_ 0_ ...0 I; I IIII _0_ ..00 I U Z 000_ IIII n_ _J LU C)

_2d_

I II U I...

Z o O00e _-. p.

G. a.

_-- p.

• ._ .._ !

0 0 Z

z z

Z Z

_-_

00000 " U.

Z _ I Z | ) : CO J 0 It..

e",, Z I.U .o_ J X re, C3 Z UJ b') UJ _L'erJ O W'C¢ a,.

I U.J II F-- I'W ZC_ ,,-I D: r',, w q.

el ¢ L C_ e'J I.- L c' ¢ ° LU LL ¢..

Lk I-- _v

<w

LU i,

i w

APPENDIX D2: STRENGTH / WEIGHT

FACTOR

I__ PVC factor Using the equations 6.1 and 6.2 in the chapter 6.3. (section 6.3.3.1), (Strength/Weight) is calculated: &__ t Factor (Strength/Weight) = cr/p Area of the wing = 56557 in: Strip load = i Ib F S = 1 5 unmanned aircreafi ,z, (density ofPVC) = 3 lb/fi ' = 0 00173611 Ib/in ' Then Factor for PVC = ( lib * I 5)/(565 57in : * O OO ] 73611 Ib/in _ ) Factortbl PVC = 1.52 in The Factor of composite PVC and Kevlar is obtained as the following: Densit\' ofPVC = 0.0017366 Ib/in _ Density' ofKevlar = 0052 Ib/in ' Ratio of Density = to _,,,_/p:.r,r_., Ratio of Density = 0052/0.00173611 =29.952 Therefore: Factor (Strength/Weight) = cr I p,_<, ...... v, Factor (Strengtlm%'eight) = (I 5'1.04516)/(565.57 * 000173611) Factor (Strength'Weight) = 1 60 in

APPENDIX D3 : CALCULATING

WING SHEARS AND MOMENT FOR

ONE UNIT LOAD CONDITION

Calculation of the wing shear V z and the wing moments M x and My due to the

total unit, distributed on a half wing load of 565.57 Ibs, acting upward in Z direction

and applied at aerodynamic centers of the wing sections goes through the following

steps

The distance from the wing root section, called station y (Column I )

Step I

The wing chord length of each section (Column 2)

Step 2

Ratio of Lift coefficient is assumed to be unity (Column 3)

Step 3

The wing running load per inchofspan at each station point. The area of a half

Step 4

wing (565.57 square inches) was treated as a total unit load: then, the running

load per inch at any station equals the wing chord length at that station.

Column4)

Average running load (Column 5)

Step 5

The distance between stations (Column 6)

Step 0

Strip load ( Column 7)

Step 7

The location of the strip load which is at the centroid of a trapezoidal

Step 8

distributed load whose end values are given in column 4 The centroid locations

are determine by Table A3 4 of Chapter 3 (Column 8)

Step c) Shears (Column 9)

Step 10 The product of shear and delta y (Column 10)

Step I I The product of strip load and arm to the centroid (Column 1 l )

Step 12 The value of moemnt (Column 12)

Step 13 The distance from aerodynamic center to the y reference axis (Colun 13)

Step 14 The strip load distance from y axis (Column 14)

Step 15 Bending moment for each strip load on the y axis (Column ! 5)

Step 16 The bending moment at the various stations equals to the summation of the trip

moments as one progresses from station 43.5 to zero.

(R_I _

i

|_

AVERAGE RUNNING LOAD _mm •.am _

-- II

x __ R: Pz'd - Icol,7)(coLS) Mx-co|.12 p,rl_coul +col 11 +col 10 Pz Xm,_m- (col.7Ncol 14_ My - Pz X|_- SUMMATION OF Coil5 _ _ _ • _ _ :. • . .

- _ _ _ _ o'# BENDI.XLS RENDING MOMENT IN X DIRECTION 0 1072542 3.96 862691 7.91 6795.88 11.86 5217.91 15.82 3878.76 19.77 2764.45 23.73 1860.52 27.68 1152.89 31.64 627.17 35.59 269.28 39.55 64.97 43.5 0

BENDING MOMENTIN X DIRECTION-

CHORDWISE

- 12000 10000 8000 - - Mx 0 ............

WING STATION Page 1

BEND2.XLS

BENDING MOMENT IN Y DIRECTION -- -3.96 974.16 ................

7.91 809.96 15.82 532.95 i • i9.77- 418.17- ..........

23.73 317.91 27.68 231.19 31.64 157.02 35.59 94.42 39.55 42.4 43.5 0 BENDING MOMENT IN Y DIRECTION - .

SPANWISE 8OO M_;O0 20O 0 ......................

WING STATION Page1 Sheet 1 ISHEAR VERSUS STATION i ; r I ; I ,.

I 0 565.57 r _ ' _ t -----_---- 3.96 496.17 7.91 430.38 i !

J : 11.86 368.17 I ! i ....

15.82 309.57

!

I •L_ ....

- -- I 23.73 203.14 27.68 155.32 i 31.64 111.1

I

35.59 70.47 39.55 33.44 I i 43.5 0

I

. _° -4

SHEAR VERSUS STATION

i 500 - 300 - r. • z - -_ 200 -- 100 - l ..................

r,_ _ 03 CO CO _ _ _ID rid ¢JD L WING STATION ..L- Page1

APPENDIX D4 :

SECTION PROPERTIES

OF

THE COMPOSITE MATERIALS

The product El of each wing section (E329, E327, E326, E326, E325) is calculated

through the following steps: Step I The geometry of each section is known.

Step 2

The reference points of coordinates system is chosen.

Step " 1

The cross section area is divided into available partitions and numbered from 1

to 12 or 13 ( which depend on each cross section area). ( Column 1 )

Step 4

The dimensions of each partition are measured in z and y directions, called

deltz and deity (Columns 2 and 3)

Step 5

The area &each partition is calculated, and after that areas &all partitions are

summed up (Column 4)

Step 6

The centroid Zcg and Ycg for each partition is calculated . (Columns 5 and 6)

Step 7

The product of area and the distance from the centroid in z and y directions are

found, and after that they are summed up (Columns 7 and 8)

Step 8

The product of area and square of Zcg and square Ycg are calculated, and

summed up ( Columns 9 and 10)

Step 9

The Inertia at the centroid of each partition are found in the z and y direction

and summed up ( Columns 11 and 12)

Step I 0

The product of area and Zcg and Ycg are calculated, and summed up.

(Column 13)

Torsional constant is defined as:

Step 11

- For a rectangular section:

,] = (1 + 12)ZY x (t': +Z:)

For a quarterof anellipsesection:

J = (1+ 16)YZ ×(yZ +Z:)

For a rectangular section_

J,,---

where

K = _-" ÷ Z-"

(('olunm 14)

(Reference Engineering Mechanics Stalics, by R C Hibbeler. section Centroid and

Center Gravity. page 457)

Step 12 Z(BAR) and Y(BAR) are the centroid cornponents of an object in Yand z

directions, and determined by the centroid equations_

Z=ZAZ+ZA

Y=EAY+EA

(Reference Engineering Mechanics Statics, by R C Hibbeler, section Centroid and Center

Gra\itv. page 420)

Step 13 Izz, ID, and Izv are calculated by the equations

i,--yav:.El , -V:A

I,, = AYZ - AYZ

Step 14

The product of flexural rigidity is defined as

El_.: = E, pvc_.,., )' I..:

Step 15

The product of torsional stiffness is

.I(; = (;_p,,: × .l,_

Step 16 : The torsionalstiffness appliedat the centroidis givenby the equation

.I =.I,-AYZ

Thewhole procedure is shownin the tables1,2,3,4,and 5 for eachsectionE325,E326.

E327,E328and E329

(ReferenceIntroductionto AerospaceStructuralAnalysis,by David h. Mien andWalter

E. Haisler.sectionof Determination of ModulusWeightedSectionProperties4.3.2.3.

page 177)

Finally,the graphrepresents the flexural rigidity andthe torsionalstiffnessversusthe

stationsof the wing

w /k ,0

Z

I

t--

C)

Ill

L_C)

p,j U3 >-

f-q

._I

(.9

I_LJ

Z

C)

I11

N

k-"

(.9

x Z u_

Z

C_

J i

;if

_j

_J

Z

Z

W

iii

rY

[JJ

(J

b _.

_ ° _ _ _ _ II i I tl I I II I I

_ _ _ __

^ ,n z C) Ld >- U] .J h.

Ow "_ Z f_j CD O9 O- Ld Ld LA rr C] C) (._) h.

/

e_ x 2 _i_-, ._.

co, _ _:'- ....

•- ° ,--_ O0 " ' . II e fl _ _ _:_ It i i ! I i I •

_=_ "_='_

,.,, ._ ._= • ..:...: __ _ co _---. It.. i,. i I

,, , • _. _

• _

_ i_- _ , II_ :la.I .I,I,8 If A d._ CD W fq LO Z >- J Z Z 0.

q b_ W n- O W tO I i

[

i ÷+÷+÷_+÷ + ÷ . . . ' .....

x _..- --.. _.

÷ ,

_.- _- . _

il Jill Jill _ c_ c_ _ _ .--; " .' _ _" .

Z ........ _-_-_- -, ._-_.-_._- .;- +_ ............... ,.

_ (:::; _ _ (",, _ .... _ _ ......... _- - -._ -=.._ .._ _ ---;=_ + _ _.---_-

" ............ ii !+

" ...... tL....:- ....

++ ++o..... ,;; + -

%

.......... _- - -,_. +(.=,- . -_-_. - - ........................

/

.J _r O L_J I'r cJ + Z C7_ cr_ (J I,I W Z I-- + t i1- L x z m EI2.XLS El AND JG VERSUS WING STATION El JG 18 9.42E+05 634500 15.27 5.12E+05 337500 327 13.46 3.30E+05 245160 326 10.73 1.50E*05 106650 325 8 4.23E÷04 26892 El AND JG VERSUS WING STATION I000000 900000 800000 700000 600000 500000 - El 400000 300000 JG 200O00 100000 18 15.27 13.46 10.73 8 WING STATION Page 1 i--

E

I-

rJ3 x ..... _ ..................... D ..........

• + + + + i

...J

x

+ _ _ + _ + i _ _= _ • . _ ,,

=m . r.1 - ¸

<, _= E t'_ N N r_ ._ - . -_ -_- a_

,.+ .-,-, + +

_ * ÷ ÷ ÷ ÷ _.J Z u_, N I,W _ 0 Z + o ÷ Z C_ c_ m + I'_, k D,.

÷ l.h.J Z _ _ _ _> I + + + ÷ _ rr _J GN

=" E

X 4- + + m _ _ _ ._J ,'I=

APPENDIX D5 : THE RESULTS

FOR CHECKING DEFLECTION FOR

PCV CORE

AND

FOR COMPOSITES--PVC & KEVLAR

The procedures for calculating the vertical static deflection for the PVC wing core are going through the eight steps.

Step l • The wing station for each airfoil section is determined• (Column 1) Step 2 The change in distance along the spanwise.(Column 2) Step 3 : The bending moments are taken from the Column 16, Table of Calculation of wing shear and wing moments, Appendix C (Column 3) Step 4 : The flexural rigidity is imported from Tables E325, E326, E327, E328, E329, Appendix D. (Column 4) Step 5 The ratios of the bending moments and the product offlexural rigidity are calculated (Column 5) Step b : The area of each section is calculated. (Column 6) Step 7 The deflection of each section is determined• (Column 7) Step 8: The total is deflection for the whole wing is the sum of the deflections from the root to the tip Similarly. the deflection for the wing, made of PVC and Kevlar, is calculated. After that. a graph shows the deflection versus the wing stations b ¢ t w | ¢ ¢ r_ r"J _r" r... (_ r_ k -.-- k i I u a C Z uJ LL :E X o_ -- z_ _._ _,_ " - r_ _ _ _._ ,_.

E X i .......... _ ..... d o_ r,.. f.o t,_ c. _ _ _ _ e, FOAMI.XLS L VERTICAL STATIC DEFLECTION OF ENTIRE WING AT STATIC CONDITION : _____ i ......

...... WING BOX-IS-PAADE-01:PV-CA-NO KEVLAR C'-- ............. wING ST-R-IJCTURE : PVC CORE+ I PLY OFKEVLAR ........

r .......... KEvLAR-_-WRA-PPI-NG-AROUIgD-(9O-DEG. OR 0 DEG. PLY ORIENTATION} . __ ¢,w ...... - ----_ ........ T ..............

STATION x El M M / El AREA DEFLECTION - -0 -7.91 ....... 39.54 ..... :4.4--6E*06 ...... 133.27 2.98812E9_5 - __0:00023636 . 0.00934567E 7.91 15.82 -- 31.64 - 3_2_1E+0(] .... -84_(_3- -- 2.5-9352E-05 0.0002051:47: - -0.006490861 ;w 15.82 • 23.73 " 23.73 ..... 2.12E+06 47.65 2.24764E-05 0.000177788 , 0.004218£2 15.82 1.24E+06 " 22.71 -1_3-ia, sE:05- - :0.000144868 - 0.002291809 i-- 23.73 31.64 -5.93 .... 3.78E+05- 6.76 - 1:78836E:05- 0.000212099- 0.00i257;'_ 31.84 43.5 ........................

T OT-A L-D eFL:-- -- 0.023605015 FIND ,1/1OMEN1 2 3 4 5 MOMENT 709.65 709.65 354.825 463.15 1172.80 586.40 i 33.27 7.91 ............................

276.34 739.49 369.74 84.03 15.82 143.00 419.34 209.67 47.65 23.73 3 !.64 56.8_ _ _ 199._---88- _____ _ 9_9.94__ ..... 22.7_1 ......

2.62 59.50 29.75 6.76 43.5 Pa0el