u AERODYNAMIC ACCOUNTING TECHNIQUE FOR DETERMINING EFFECTS OF NUCLEAR "DAMAGE TO AIRCRAFT

Transcription

1 EVEiiI';So DNA 4531F-2 u AERODYNAMI AOUNTING TEHNIQUE FOR DETERMINING EFFETS OF NULEAR "DAMAGE TO AIRRAFT q Volume ]I- Program User Guide General Dynamics orporation Fort Worth Division P.O. Box 748, Grants Lane Fort Worth, Texas Q-1, $~I-WTNM oi pagl~ 7 28 February 1978 " Do M [Lu Final Report for Period 15 March January 1978 f _=2 ONTRAT No. DNA APPROVED FOR PUBLI RELEASE; DISTRIBUTION UNLIMITED. THIS WORK SPONSORED BY THE DEFENSE NULEAR AGENY UNDER RDT&E RMSS ODE N99QAXAE50602 H2590D. DD Prepared for Director DEFENSE NULEAR AGENY Washington, D FEB HUETSLLU U LlLD B

2 Destroy this report when it is no longer needed. Do not return to sender. PLEASE NOTIFY THE DEFENSE NULEAR AGENY, ATTN: TISI, WASHINGTON, D , IF YOUR ADDRESS IS INORRET, IF YOU WISH TO BE DELETED FROM THE DISTRIBUTION LIST, OR IF THE ADDRESSEE IS NO LONGER EMPLOYED BY YOUR ORGANIZATION.,QN 4 ro f!

3 IMI DISLAIMER NOTIE THIS DOUMENT IS BEST QUALITY PRATIABLE. THE OPY FURNISHED TO DD ONTAINED A SIGNIFIANT NUMBER OF PAGES WHIH DO NOT REPRODUE LEGIBLY. I-

4 UNLASSIFIED SEURITY LASSIFIATION OF TH:S PAGE (When Data Entered) RP D U T AREAD INSTRUTIONS BEFORE OMPLETING FORM 16. TRTN GOVT AESSION NOI 3TRIPIENT'S ATALOG NUMBER 4. TITLEENTa OTl E PE... OVEREDR TiRkD spons.aounting TEHNIQUE FORADETERMINcy u M ode I.FETS OFNULEAR DAMAGE TO.AIRRAFit b 15 Mar 77-y3t Jan 7nme solume pt (olam Program I UGsuide 6. PERFORMING ORG. REPOR T NUMBER. ~DNA fO7 5f Georgq Howellj f/?i 9PERFORMING ORGANIZATION NAME AND ADDRESS 10. PROGRAM ELEMENT. PROJET, TASK General Dynamics or oration A RnUnaRy Fort Worth Division, P.O. Box 748, Grants Lane lsubta5yan ves Al, DNA, Fort Worth, 4.1F-2- Texas Av-3~ 4~l I I. ONTROLLING OFFIE NAME AND ADDRESS. 2 Director 28 Febimp" 1&78 Defense Nuclear Agency609fU Washington, D MONITORING AGENY NAME & ADR o a Olsice) f SEURITY LASS (othis report) D IN 1 E5 O E UNLASSIFIED 16. DISTRIBUTION STATEMENT lot this Report) AE SaI DEL ASSI F ATION/ DOWN GRADING SHEDULE Approv i r PPse.; d is-v t ~Yion-unlimited roghes andto daae The computer coden ha h cpbltyose~s h 17. DISTRIBUTION STATEMENT (of the abstract entered in Block 20, it different from Report) IS. SUPPLEMENTARY NOTES This work sponsored by the Defense Nuclear Agency under RDT&E rmhss ode B N99QAXAE50602 H2590D. 19. KEY WORDS (ontinue on reverse side It necessary and Identify by block number) Drag Prediction Roughness omputer Program Lift Prediction Blast Nuclear Damage Aircraft Overpressure Damage Thermal Effects I _ V..,, 20. ABSTRAT (ontinue on reverse side if necessary and Identity by block number). This report (Volume II, Program User Guide)A escribes the computer program developed for the aerodynamic evaluation of aircraft, including the effects of roughness and damage. The computer code has the capability of assessing the aerodynamic effects of damage, such as rough, bent, and burnt skins, boundarylayer thickness effects, and loss of radomes, panels, doors and covers. Also, the computer code has the capability of analyzing changes in drag due to lift and trim caused by asymmetric loss of parts of the wing or trim surfaces. FORMAN"/ EDITION OF I NOV 65 IS OBSOLETE DD JN UNLASSIFIED SEURITY LASSIFIATION OF THIS PAGE (I47jcn Data Entered)

5 UNLASSIFIED SEURITY LASSIFIATION OF THIS PAGE(Wan Data Entered) 20': ABSTRAT (ontinued) -': -"The computer program is coded in the FORTRAN Extended Version IV language to operate on a D 6600 or YBER 172 computer. The computer code structure is explained and a computer code input utilization is presented along with sample input and output with a FORTRAN source deck listing. Details of the methods, equations, and substantiating data for this computer code are contained in Volume I. Empirical Methods. UNLASSIFIED SEURITY LASSIFIATION OF THIS PAGE(When Data Ented)

6 TABLE OF ONTENTS Volume II Section 1. GENERAL DESRIPTION 3 Pae Section 2. Section 3. AAT OMPUTER ODE UTILIZATION SAMPLE PROBLEMS 39 Section 4. PROGRAM DESRIPTION Program Structure 91 4.,2 Subroutine Descriptions ommon Block Descriptions i1 4.4 Program Listing 126 AESSO'N for NTIS 'e Section DD S ctio'n 1... T

7 F1 2

8 1. GENERAL DESRIPTION The Aerodynamic Accounting Technique omputer ode was developed to provide a computerized, systematic method to evaluate the aerodynamic effects of nuclear damage to an aircraft. In addition, it can be used to evaluate the aerodynamic characteristfcs of an undamaged configuration or any type damage that can be modeled into one of the fourteen damage modes provided by the program. The computer program is coded in the Fortran Extended Version IV language to operate on the D 6600 computer at Wright-Patterson Air Force Base. It is also operational on General Dynamics' D YBER 172 computer as procedure R7F. Four primary overlays are used by the program to keep the central memory core requirements below 54,000 bytes. The mait. program controls the calling of the four overlay programs: XINFT, GEOM, SURVEY, and NUDAM. Figure 1.1 shows the program overlay structure and the arrangement of the 57 subprograms and subroutines that comprise the AAT computer code. Program XINPT contrcls the reading of input data and the printout of data that will be used in the problem. Program GEOM computes the geometric parameters that are required in the calculations. Program SURV;.Y controls the calculation of aerodynamic characteristics of the undamaged aircraft, and program NUDAIM determines the aerodynamic effects that result from the damage. The third primary overlay, SURVEY, calls four secondary overlay programs VGEOM, MRiT, AEROA, and AEROB. These programs and subprograms call the appropriate subroutines necessary to make the computations. The program utilization describes the inputs that are required. Aerodynamic characteristics of an undamaged configuration can be estimated by entering only the basic geometric parameters and the survey conditions. Aircraft damage evaluation is optional. The damage input data are contained in a separate data block and the effects of damage are determined on an incremental basis and integrated into the aerodynamics of the undamaged configuration

9 r 14 A;5 Ai4

10 2. MT OMPUTER ODE UTILIZATION The first step in preparing program input is to determine how to best represent the configuration with circular bodies and surfaces. omponents such as the fuselage, canopy, stores, external fairings, and nacelles are represented as bodies, while the wing, horizontal tail, vertical tail, pylons, and ventral fins are represented as surfaces. A straight-wing planform is represented by one panel, and a cranked- or complex-wing planform is approximated with two panels. Up to seven bodies and seven surfaces may be used to represent a configuration. Figures I and 2 define some of the geometric parameters required to define the individual bodies and surfaces. Input requirements for the Aerodynamic Accounting Technique computer code are partially determined by the options selected by the user. The input format is divided into 12 blocks to assist the user in determining his input requirements. The user may decide which blocks are necessary to complete his problem while not concerning himself with the remaining blocks. The user determines which data blocks are required from the following descriptions: 1. General Information. This block contains information that the AAT program needs to read the remainder of the input data. Indicators, such as the number of bodies and surfaces, are included, which tell the program which blocks of data will follow. ertain reference data and geometric dimensions are also included. This block is always required. 2. Body Geometry. The geometric parameters of each component which is represented as a body is contained in this block. A maximum of seven bodies may be used. 3. Surface Geometry. The geometry of each surface is represented in this block. A maximum of seven panels may be used, with either one or two panels for the main wing. 4. Arbitrary Airfoil. This block is used to describe the camber and thickness distribution of an arbitrary airfoil section if one of the standard sections contained internally is not sufficient. 5. Variable Sweep. Aircraft with movable wing panels such as the F-ill and B-l, may be evaluated at any selected sweep angle. This block of data is required to describe the wing movement. j 6. Survey onditions. This block of data contains the Mach number and Reynolds number conditions at which the analysis will be conducted. 5

11 WIDTH LENGTH 0 -T U 4( *NOSE LENGTH 4 I4TAIL LENGTH--0 w 4 APPROXIMATION TO AREA URVE W - AMAX - BLUNTNESS DRAG AREA (a) losed Body LENGTH 4.-WDH-4] 40 ww S INLET * 0 AREA 1~ BASE STREAM TUBE AREA (b) Nacelle Figure 2-1 Geometry for losed Bodies and Nacelles

12 ROOT... H LOATION IX, Yz) h/2 ALEj F"- TIP-a..J (a) Single-Panel Win8 or Other Surface (Exposed Area) RO ot..t 4T // X,~~~4 YzTIPP&RO (b) Two-Panel Wing (Exposed Area) Figure 2-2 Surface Geometry

13 7. Adjustment Factors. A table of adders and multipliers can be specified in this block to correlate the AAT predictions with known test levels. At least one card is always required. 8. Expansion Provisions. This data block is provided for future expansion. 9. Damage Mode Indicators. Provisions are included for fourteen modes of nuclear damage in the AAT program. Seven modes are for body damage and seven for surface damage. This block, which requires three cards, allows the user to select only those modes that are desired. 10. Body Damage Parameters. This block of data contains parameters that define nuclear damage to the bodies. It is required only if a body damage mode is indicated in Block number Surface Damage Parameters. This block describes nuclear damage to the surfaces and is similar in format to Block 10. It is required only if a surface damage mode is indicated in Block End of Problem. Describes how one may end the problem or change the input and run new problems. These twelve blocks of data represent a wide range of options for defining thti geometry and the manner in which the data are handled. Most aircraft analyses will not require all blocks. It should be noted that there is an option that allows the program to compute the values of certain parameters that are shown as input. These items are indicated with an asterisk (*). If a zero or blank is input, the program will use other geometric parameters to compute these values. All dimensions are input in either inches, feet or meters, except for the roughness factor, which is always in inches. All angles are in degrees. The utilization specifies one of the following formats for each item of input: "I" Format Input must be in integer form and right adjusted in the specified field. "F" Format Input must include a decimal and may be anywhere within the specified field. "A" Format Input may include any alphanumeric characters. 8

14 Data Block No. 1, General Information Data Block No. 1 requires from 5 to 7 cards, depending on the options selected. ARD Title. Enter any alphanumeric characters in columns I through 60 to identify each problem. These characters will be printed out at the top of each page of output for the undamaged jconfigurat ion. ARD Print-out options. This card should normally be left blank; however, certain seldom-used data and subroutine dumps will be printed if KPRINT(I)=I. The subroutine dumps are normally for diagnostic purposes and can be used only in conjunction with the programming statements. If KPRINT(31)=I, the aerodynamic data V for both the damaged and undamaged configurations will be printed at constant values of angle of attack. OLUMN SYMBOL PRINT-OUT I KPRINT(l) Airfoil ordinates and pressure distribution 11 (11) Dump Subroutine AER2 12 (12) 1 GEOM 13 (13) AALO 14 (14) DL2 15 (15) BDRG 16 (16) LBRK 17 (17) AERA 18 (18) WBA 19 (19) FEQ 20 (20) DWW 21 (21) TAIL 22 (22) DLI 23 (23) DDR 24 (24) ADJUST 25 (25) MOW 26 (26) PZT 27 (27) SSET 28 (28) NUDAM 29 (29) NUDAM2 30 (30) NTRIM 31 (31) WRITE2 [9

15 ARD onfiguration Definition (15 Format). olumn Symbo Definition 5 NPODS Number of different types of bodies. NPODS _ NPNLS Number of surfaces used to represent the main wing. Must be 1 or NHT Number of lifting surfaces other than main wing, i.e., horizontal tail or canard. Program assumes that these surfaces are symmetric with respect to configuration centerline. 20 NVT Number of non-lifting surface types, i.e., vertical tail, ventral fin, or pylon. For example, a twin vertical tail should be entered as 1 surface type; symmetry will be indicated in Data Block No, 3. NPNLS+NHT+NVT : ISWP Variable-sweep indicator. 0 for fixed wing 1 for variable-sweep wing 30 IREF Reference angle-of-attack indicator. 0 reference to wing root-chord plane I reference to fuselage centerline 35 IWNG WING-definition indicator. 0 omit card enter reference planform area, taper ratio, and leading-edge sweep on ard 1.6 See note number 1 at end of input instructions for Data Block No NAFO Number of stations at which thickness and camber are to be defined for an arbitrary airfoil, If NAFO > 0, Data Bloc No. 4 must be input. 45 METER Unit-system indicator 0 use units of feet 1 use units of meters 2 use units of inches, except for reference area, planform area, wetted areas, Reynolds number, and altitude which are in feet. 50 ITRIM Trim indicator. 0 trim configuration I do not trim 10

16 ARD "F" Format. olumn Symbol Definition 1-10 SREF Reference area MA* Reference aerodynamic chord XMA* Location for leading-edge of MA. Does not change with sweep ZG Height of moment reference point relative to wing root-chord plane UPFUS Upsweep angle of the aft fuselage (deg). For use with transport-type aircraft AOB Ratio of width to height of the aft fuselage in the upswept region. ARD (FlO Format). olumn Symbol Definition 1-10 ROUGHK Average surface roughness height for friction drag, (inches) FMIS Miscellaneous drag factor as a percentage of total friction and form drag TWIST Wing twist between exposed root chord and tip chord. Negative for washout (wing-tip leading edge down) ONL Wing conical camber design lift coefficient. ARD 1.6 (FlO format). This card is required only if IWNG=1 on ard 1.3. olumn Symbol Definition 1-10 SPLAN Wing theoretical planform area TAPR Reference wing theoretical taper ratio SWP Reference wing leading-edge sweep. *An asterisk beside a symbol indicates that the value of that item will be computed internally if a blank or zero is input. 11

17 ARD 1.7 (FlO Format) Elevon Definition. Required if NHT=0 and ITRIM=O. This card defines the elevon, which will be used to trim the configuration if there is no horizontal tail or canard. olumn Symbo Definition 1-10 FO Elevon chord length, Ac/c EI Elevon inboard edge, expressed as a fraction of semi-span EO Elevon outboard edge, expressed as a fraction of semi-span. Notes pertaining to the input for Data Block No. 1 are as follows: 1. ard 1.6 is used to input the wing planform area, taper ratio, and leading-edge sweep when the user desires to override the internal calculations that normally compute these values based on other wing parameters. Equations used to make these calculations are presented in Section of Volume I. ard 1.6 should not be required for a single-panel wing or for a twopanel wing with a moderate amount of crank. It is recommended, however, when two panels are used to represent a wing with an extreme amount of crank or a strake/wing planform where the strake is highly swept. 2. The input refeience area is arbitrary and does not have to be related to the theoretical wing planform area. 12

18 . ~ ',,,f-,, Data Block No. 2, Body Geometry Thirteen cards are used to input the name and 12 parameters for each of the bodies. The name that is input on ard 2.1 will be used in the printout to identify the various components. Data for each body are listed vertically in the input. The main body (fuselage) should be listed to the extreme left, (olumn 1-10), followed next by other bodies with zero inlet area. Nacelle data should be listed last. Up to seven columns for seven different body types can be input. ard Format Symbol Definition 2.1 7A10 BNAME(I) Body I name, I=i, NPODS 2.2 7F0 BOD(II) Length 2.3 (1,2) Width 2.4 (1,3) Height 2.5 (1,4)* Wetted area (total for all bodies of type I). 2.6 (1,5) Interference factor 2.7 (1,6) Number of bodies of type I 2.8 (1,7)* Maximum cross-sectional area 2.9 (1,8) Base streamtube area 2.10 (1,9) Nose I.ength 2.11 (1,10) Boattail length 2.12 (Iii) Base area for bluntness drag 2.13 (1,12) Inlet area. There are several points that should be mentioned pertaining to Data Block No The name assigned to each body will be used in the printout of results. 2. The following is presented as a guide for determining the interference factor (BOD(I,5)): =1.0 for nacelles and external stores mounted out of the local velocity field o-f the wing and fuselage. =1.25 for external stores mounted symmetrically on the wing tip. =1.3 for nacelles and external stores if mounted in moderate proximity of the wing. =1.5 for nacelles and external stores mounted flush to the wing. 13

19 (2., continued) The same variation of the interference factor applies in the case of a nacelle or external store strut-mounted to or flush-mounted on the fuselage. S. The length, width, height, cross-sectional area, etc. listed for each body type describes a single body. The total number of bodies of each type must also be specified even though they may be paired symmetrically with respect to the centerline. One exception is that the wetted area represents the total for all bodies of a particular type. 4. Bodies must be defined for I=i to NPODS. The main body must be first, closed bodies second, and bodies with inlet area last. 5. When fewer than seven bodies are defined, columns to the right of the last field may be conveniently used to identify the parameter listed on that card. 6. The interference factor for the fuselage that is entered on ard 2.6 is overridden by internal calculations for wing/body interference. 14

20 Data Block No. 3, Surface Geometry Thirteen cards are used to input the name and 12 parameters for eaci of the surfaces. The format for the surface data is similar to that for the bodies. ard Format Symbol Definition 3.1 7A10 SNAME(I) Surface name I, I1, NPNLS+NHT+NVT 3.2 7(A3,7X) SUR(I,l) Airfoil section 3.3 7F0 (1,2) 2-D design lift coefficient 3.4 (1,3) Thickness ratio,(t/c)rms 3.5 (1,4) Leading-edge sweep 3.6 (1,7)* Total surface(s) wetted area 3.7 (1,8) Exposed root chord 3.8 (1,9) Tip chord 3.9 (Ii0) Exposed semi-span 3.10 (1,11) X-station at LE of exposed root chord 3.11 (1,12) Y-station at LE of exposed root chord 3.12 (1,13) Z-station at LE of exposed root chord 3.13 (1,14) Incidence with respect to main body Several points that should be noted regarding Data Block No. 3 are: 1. The name assigned to each surface will be used in the printout of results. 2. Surfaces must be input from left to right in the following order: NPNLS main wing panels, NHT lifting surfaces, and finally, NVT non-lifting surfaces. 3. Twenty options are available for defining the airfoil section type: INPUT AIRFOIL TYPE* INPUT AIRFOIL TYPE* YXX(6 Series) -62 OOXX-62(4 Digit) YXX " -63 OOXX-63 " YXX " -64 OOXX YXX " -65 OOXX-65 63A 63AYXX(6A Series) -33 OOXX-33 64A 64AYXX " -34 OOXX-34 65A 65AYXX " -35 OOXX-35 BI Biconvex -93 OOXX-93 INPUT Arbitrary Airfoil -94 OOXX OOXX-95 " *Y- Section amber in Tenths XX* Section t/c in % Z/ 15

21 (3., continued) Any of these sections may be input to the program with the identification shown above. The characters must, however, be left-adjusted in the data field. An arbitrary section may be input for any surface by entering "INPUT". This will be used for both wing panels if NPNLS=2. Use of "INPUT" requires that Data Block No. 4 be included and that NAFO > 0 on ard 1.4. Only one arbitrary section can be defined, but this section cam be used for any of the surfaces by showing "INPUT" on ard Symmetry is controlled in the following manner: NPNLS and NHT surfaces are automatically assumed to have counterparts on the opposite side of the fuselage. The NVT non-lifting surfaces are assumed to be single surfaces if y-o (SUR(I,12)). If y> 0, an identical surface is assumed to be on the opposite side. Irregardless of symmetry, note that the wetted area must be the total value, not a singlelone-sided value. 1 16

22 Data Block No. 4, Arbitrary Airfoil Data Block No. 4 must follow immediately after Data Block No. 3 if NAFO>0 on ard 1.4, ARD (FIO format) olumn Symbo Definition 1-10 RLE Leading-edge radius divided by chord (RLE/ HORD), at reference t/c (TOR) TOR Reference t/c of AFT (see ard 4.4) LDR Reference design lift coefficient of AF (see ard 4.3) TEH Technology Factor (See Sections 5.1 and 6.2 of Volume I) = 0.0 onventional airfoil ARD 4..2 Format Symbol Definition = 1.0 Advanced supercritical wing section 7F0 AFX(I) hordwise stations at which the camber and thickness data are to be entered. Enter as x/c. (I=1,NAFO) ard 4.2 should be repeated until NAFO (ard 1.4) ordinates have been entered. ARD 4.3 Format Symbol Definition 7F0 AF(I) amber of the arbitrary airfoil section. Defined by Z/ where Z is the distance from the chord line to the camber line. (I =1, NAFO) ard 4.3 should be repeated in the same format as ard 4.2 until NAFO values of AF(I) have been input. The camber ordinates must correspond with the chordwise stations on ard

23 ARD 4.4 Format Symbol Definition 7FI0 AFT(l) Thickness of the arbitrary airfoil section. Defined by Z/, where Z is the distance from the chord line to the upper or lower surface on an uncambered airfoil. (I-1,NAFO) ard 4.4 should be repeated in the same format as ard 4.2 until NAFO values of AFT(I) have been input. The thickness ordinates must correspond with the chordwise stations on ard

24 Data Block No. 5.. Variable Sweep Data Block No. 5 is required only if the variable-sweep option is indicated by ISWP=l on ard 1.4. This Block contains only one card. Use of the variable-sweep option does not change the reference area or the reference moment center, which are defined in.data Block No. 1. ARD (FlO format) olumn Symbol Definition 1-10 XPIVOT X-location of wing pivot YPIVOT Y-location of wing pivot AFTSW Maximum aft sweep AFTB* Mean aerodynamic chord of movable panel in aft-sweep position AFTO* Thickness ratio (t/c) of movable panel in aft-sweep position AFTAW* Wetted area of movable panel in aftsweep position. 19

25 Data Block No. 6, Survey onditions This data block is always required, and will consist of from 2 to 22 cards, dependent upon the number of survey conditions specified. ARD (15 format) olumn Symbol Definition 4-5 NSURV Number of surveys (sets of conditions) at which the problem is to be run (NSURV _s 20) NIAS Number of evenly spaced L values for which data will be computed (NLAS 5 21). ARD (FlO format) olumn Symbol Definition 1-10 FASURV(I) Mach number ALT(I) Altitude G(I) Position for trim or moment reference. Measured as a fraction of the mean aerodynamic chord (MA) relative to leading-edge of MA SWPV(I) Leading-edge sweep LLO(I) Low L LHI(I) High L ard 6.2 is repeated until NSURV conditions have been specified. Several items that may prove useful to the user are: 1. The Reynolds number may be specified instead of altitude by entering the negative value of RN/ft divided by 106. For example, if RN/ft=3.0 x 166, enter -3.0 in olumn Model-scale predictions can be obtained even though fullscale geometric data are loaded in the program. Entgr the negative of the RN/ft multiplied by model scale divided by 100. For example, if RN/ft=3.0 x 106 and model scale desired is 1/15, enter -0.2 in olumns of ard

26 3. The low L and high L should be defined in conjunction with NLAS so that the calculated values of L will be rounded off to convenient numbers. For example, INPUT Data alculated at NIAS=21 L =0.00 LLO=0.0 L =0.05 LHI=I.0 L =0.10 L =0.15 L = If low L and high L are left blank, the program will automatically set LLO-0.0 and LHI=I.0. 21

27 Data Block No. 7, Adjustment Factors Data Block No. 7 must always be entered in the input; it may, however, contain only one card which indicates that no adjustments will be made. ARD 7.1 Write "ADJUST" beginning in olumn 1 to indicate if adjustment factors are to be applied to some of the aerodynamic parameters predicted by the program. If no adjustment factors are to be read in, write "NO ADJUSTMENTS" beginning in olumn 1 and continue with the next data block. The adjustment options allow certain predicted items in the computer procedure to be adjusted to match a desired value. Thus, the predictions can be adjusted to match wind tunnel data,for instance, so that perturbations in geometry for trade studies can be predicted from a firm baseline. An aerodynamic parameter of interest (ApRED) can be adjusted to match an experimental value (AExp)by the equation AEXP - (ApRED) YM + YA where YM is an Input correlation multiplier and YA is an adder. Each is a function of Mach number or lift coefficient. ARD (I format) Set a given IVAL indicator equal to I to identify it as being an aerodynamic parameter to be adjusted. olumn Symbol Definition 1 IVAL(l) Adjust Mo as a function of Mach number. 2 IVAL(2) Adjust DMIS as a function of Mach number. 3 IVAL(3) Adjust alo as a function of Mach number. 4 IVAL(4) Adjust MR as a function of lift coefficient. 5 IVAL(5) Adjust DL as a function of lift coefficient NXVAR Number of Mach values in the table of Mach function adjust factors ( 15). 22

28 (ARD (I format), continued) olumn Symbol Definition NADJ Number of parameters to be adjusted as a function of Mach number (- 3) NXL Number of L values in the table of lift function adjust factors (! 15) NADJ2 Number of parameters to be adjusted as a function of lift coefficient (!5 2). ARD (7F10.0 format) Required if NADJ-0. olumn Symbol Definition 1-10 X(l) Mach numbers for the table of Mach function X(2) adjust factors X(3) x(4) X(5) X(6) X(7) Repeat ard 7.3 until NXVAR values of X are read in. ARD 7.4 (6F10.0 format) (NADJ > 0) olumn Symbol Definition 1-10 YM(J=, I=I) Multiplier factor YA(J=l, I=1) Adder factor YM(J=2, I=I) Multiplier factor YA(J=2, I=i) Adder factor YM(J=3, I=i) Multiplier factor YA(J=3, I=I) Adder factor. Repeat ard 7.4 until NXVAR values are read in (J=NXVAR) for each aerodynamic parameter to be adjusted (I=i to NADJ). 23

29 ARD (7F10 format) Required if NADJ2> 0. olumn Symbol Definition 1-10 XL I) L values for the table of lift function adjust factors XL(2) XL(3) XL(4) XL(5) XL(6) XL(7) Repeat ard 7.5 until NXL values of XL are read in. ARD (6F10.0 format) NADJ2 0. olumn Symbol Definition 1-10 YM(J=I, I=NXVAR+I) Multiplier factor YA(J=I, I=NXVAR+l) Adder factor YM(J=2, I-NXVAR+l) Multiplier factor YA(J=2, I=NXVAR+l) Adder factor YM(J=3, I=NXVAR+l) Multiplier factor YA(J=3, I=NXVAR+l) Adder factor. Repeat ard 7.6 until NXL values are read in (J=NXL). r 24

30 Data Block No. 8, Reserved for Expansion Data Block No. 8 represents a section of the input common block that has been reserved for future expansion. The user should ignore this block. * 2 25

31 Data Block No. 9, Damage Mode Indicators If no damage parameters are to be loaded, skip the remaining input and go to "End of Problem" instructions in Data Block No. 12. If damage parameters are to be loaded for either a body or a surface, complete the following three cards. ARD 9.1 ARD 9.2 Enter "DAMAGE ASES FOLLOW" beginning in olumn 1. Enter any alphanumeric title in olumns 1 through 60. This title will be printed at the top of each page of output related to damage calculations. ARD (I format) This card allows the user to select the modes of damage that will be used. Set IDAM(I)-l if mode I input are to be entered in Blocks 10 and 11. olumn Symbo Definition 1 IDAM(l) Mode 1, Roughness on bodies 2 /2) 2, Fwd-facing steps on bodies 3 (3) 3, Aft-facing steps on bodies 4 (4) 4, Holes in bodies 5 (5) 5, Surface waviness on bodies 6 (6) 6, Protuberances on bodies 7 (7) 7, Nose bluntness on bodies 11 IDAM(II) Mode 11, Roughness on surfaces 12 (12) 12, Fwd-facing steps on surfaces 13 (13) 13, Aft-facing steps on surfaces 14 (14) 14, Holes in surfaces 26

32 i- V too" I (ARD I format), continued olumn Symbo Definition 15 IDAM(15) Mode 15, Surface waviness on surfaces 16 (16) 16, Protuberances on surfaces 17 (17) 17, Missing parts of surfaces 27

33 Data Block No. 10, Body Damage This block is required if one or more of the indicators IDAM(1) through IDAM(7) equals 1, otherwise, it can be omitted. Several cards are required to define the body damage for each mode selected. The input format is similar to that in Block No. 2. If only part of the bodies are damaged, the columns for the undamaged bodies are to be left blank. The space to the right of the last field of data may be used to identify the damage parameter on that card. ARD 10.1 Enter the body names in 10-column fields and in the same order as on ard 2.1 Body roughness, required if IDAM(1)=. ard Format Symbol Definition F0 DBOD(I,l) Roughness factor on body I before damage is incurred (1,2) Roughness factor on body I after damage is incurred (1,3) x/l where damage roughness starts 10.5 (1,4) x/l where damage roughness ends 10.6 (1,5) Fraction of area affected by increased roughness (includes area forward and aft of damaged region). Table 1 is presented as an aid in selecting the roughness factors after damage has been incurred. Fwd-facing steps, required if IDAM(2)=I ard Format Symbol Definition F0 DBOD(I,II) Number of fwd-facing steps on body I (1,12) Width of each step (1,13) Height of each step (1,14) x/l at first step (1,15) x/l at last step. 28

34 Aft-facing steps, required if IDAM(3)=. ard Format Symbol Definition F10 DBOD(I,21) Number of aft-facing steps on body I (1,22) Width of each step (1,23) Height of each step (1,24) x/l at first step (1,25) x/l at last step. Holes, required if IDAM(4)=I. ard Format Symbol Definition F0 DBOD(I,31) Total no. of holes in body I (1,32) Number of these holes over wing (1,33) Length of each hole (1,34) Width of each hole (1,35) Depth of each hole (1,36) x/l where first hole starts (1,37) x/l where last hole starts (1,38) Type hole 1.0 Missing Panel 2.0 aved-in Panel Waviness, required if IDAM(5)=. ard Format Symbol Definition FO DBOD(I,41) Total no. of waves in body I (1,42) No. of these waves over wing (1,43) Length of each wave (1,44) Width of each wave (1,45) Amplitude of each wave (1,46) x/l where first wave starts (1,47) x/l where last wave starts. 29

35 Protuberances, required if IDAM(6)=. ard Format Symbol Definition F0 DBOD(I,51) No. of protuberances on body I (1,52) Height of each protuberance (1,53) Parasite area of each protuberance, Af (1,54) x/l of first protuberance Y (1,55) x/1l of last protuberance. Bluntness, required if IDAM(7)=l. ard Format Symbol Definition F0 D30D(I,61) Frontal area of blunted body at point of damage. For example, a fuselage with the radome missing might have a cross-section area of 10 sq ft at the point where the radome is detached (1,62) VId at point of damage. d is the body diameter at most forward body section that is not damaged by the bluntness. 1 is the remaining nose length forward of the point where d is measured. For example, i/d=0.0 for a nose section that is flat and 1/d=0.5 for a hemi-spherical section. All input parameters describe damage to only one body of type I. If all bodies of type i have sustained the damage described, a negative sign on the first parameter in each mode of damage will indicate this. For example, if there is increased roughness on only one of four wing-mounted pods, DBOD(I,l) through DBOD(I,5) are all positive values. If all four pods are damaged, this is indicated by entering DBOD(I,l) as a negative number. TIn parasite area for a protuberance is the drag divided by the dynamic pressure (D/q) in freestream air flow. Effects of local boundary layer are computed. Units for Af must be consistent with those selected on ard

36 I.' TABLE 1 TYPIAL ROUGHNESS VALUES Surface or ondition of Surface Roughness k -Inch Average aircraft wing or tail surface.0006 Average fuselage, nacelle surface.0012 Alunimum skin with blistered paint.0012 Fiberglass/Enamel with blistered paint.0025 Fiberglass/Thick oatings and Graphite.0030 with blistered paint Broken Skin.01 Exposed Honeycomb.1 31

37 Data Block No. 11, Surface Damage This block is required if one or more of the indicators IDAM(ll) through IDAM(17) equals 1, otherwise, it can be omitted. The format is identical to that in Data Block No. 10. ARD 11.1 Enter the surface names in 10-column fields and in the same order as on ard 3.1 Surface Roughness, required if IDAM(11)=1 ard Symbol Definition 11.2 DSUR(I,I) Roughness factor on surface I before damage is incurred (1,2) Roughness factor on surface I after damage is incurred (1,3) x/c where damage roughness starts (1,4) x/c where damage roughness ends (1,5) Fraction of area affected by increased roughness (includes area forward and aft of damaged region) (1,6) 0.0 for Lower Surface. 1.0 for Upper Surface. Table I is presented as an aid in selecting the roughness factors after damage has been incurred. Fwd-facing steps, required if IDAM(12)=I. ard Symbol Definition 11.8 DSUR(I,11) Number of fwd-facing steps on lower surface (1,12) Number of fwd-facing steps on upper surface (1,13) Width of each step (1,14) Height of each step, (1,15) x/c at first step (1,16) x/c at last step. 32

38 Aft-facing steps, required if IDAM(13)=1. ard Symbol Definition DSUR(I,21) Number of aft-facing steps on lower surface (122) Number of aft-facing steps on upper surface (1,23) Width of each step (1,24) Height of each step (1,25) x/c at first step V (1,26) x/c at last step. Holes, required if IDAM(14)-I. ard Symbol Definition DSUR(I,31) Number of holes in lower surface (1,32) Number of holes in upper surface (1,33) Length of each hole (1,34) Width of each hole (1,35) Depth of each hole (1,36) x/c where first hole starts (1,37) x/c where last hole starts (1,38) Type Hole 1.0 Missing Panel 2.0 aved-in Panel (1,39) Porosity Factor (must have holes on both upper & lower surface) Waviness, required if IDAM(15)=I. ard Symbol Definition DSUR(I,41) Number of waves in lower surface (1,42) Number of waves in upper surface (1,43) Length of each wave (1,44) Width of dach wave. 33

39 ard Symbol Denifition DSUR(I,45) Amplitude of each wave (1,46) x/c where first wave starts (1,47) x/c where last wave starts. Protuberances, required if IDAM(16)=I ard Symbol Definition DSUR(I,51) Number of protuberances on Surface I (1,52) Height of each protuberance (1,53) Parasite area of each protuberance, ilf (1,54) x/c of first protuberance (1,55) x/c of last protuberance. ARD Missing Wing Parts, required if IDAM(17)=l olumn Symbol Definition 1-10 DWING(1) LAc/c fraction of wing chord that is missing from leading edge (2) )i inboard edge of missing leading edge, expressed as a fraction of semispan (3) A71span of missing leading edge, expressed as a fraction of semispan (4) z/t ratio of leading edge to maximum thickness. z represents the wing thickness at the point where the missing leading-edge section is detached. t is the wing maximum thickness. 34

40 , I olumn Symbol Definition DWING(5) orner sharpness factor for leading I edge. Enter 1.0 if corners on leading edge are rounded. Enter 2.0 if corners on leading edge are sharp (6) Indicates that leading edge is missing on: 1.0, left side only 2.0, right side only 3.0, both sides ARD olumn Symbol Definition 1-10 DWING(7) A c/c, fraction of wing chord that is missing from trailing edge (8) '7i,inboard edge of missing trailing edge expressed as a fraction of sernispan (9) Aispan of missing trailing edge, expressed as a fraction of semispan V (1.0) Indicates that trailing edge is missing on: 1.0, left side only 2.0, right side only 3.0, both sides ARD olumn Symbol Definition 1-10 DWING(II) A, fraction of semispan that is missing from the left wing tip (12) 477 right wing tip (13) Moment arm of device that trims rolling moment. Entered as a fraction of wing semispan. 35

41 ARD olumn Symbol Definition 1-10 DWING(14) The first NHT surface requires input for the left side (olumn 1-10) and (15) the right side (olumn 11-20). Remaining surfaces must be in the same order (16) as those on ard 3.1. If NHT=0, list NVT surfaces in order beginning with (17) olumns (18) (19) (20) There are severea points that should be noted regarding the surface damage parameters: 1. All input parameters describe damage to only one surface (such as the right wing). If the damage is symmetric (left wing also damaged), then a negative sign should be used on the ffrst parameter in each mode of damage. The first parameter will be zero in some cases. When this happens, a negative sign on the second parameter will indicate symmetric damage. 2. Porosity factor specifies the fraction of hole area that allows air to flow from the lower to the upper surface. The hole area is the smaller of the area of upper surface.holes and lower surface holes. 3. If IDAM(17)=I, ards through must all be entered. A zero or blank should be entered for the parameters that are not applicable to the damage case being lescribed. 4. The parasite area for a protuberance is the drag divided by the dynamic pressure (D/q) in freestream air flow. Effects of local boundary layer are computed. Units foraf must be consistent with those selected on ard

42 Data Block No. 12, End of Problem Several options are available when the end of the initial problem is attained. The user may either end the problem, add more damage cases, or change the basic input for an additional run. ARD 12.1 Option 1. Input "END" in columns I through 3 and the problem will be terminated. Option 2. Input "DAMAGE ASES FOLLOW" beginning in olumn 1 and continue input with ard 9.2 to run additional damage cases. ARD 12.2 Option 3. "HANGE INPUT" beginning in olumn 1 allows the user to change any variable in the basic input (Data Block No. 1 through 7). The variablelocation is its position in the input common block. This location is given in Volume II, Section 4 of the AAT omputer ode Final Report. The remaining cards in this block must be input. Enter any alphanumeric characters in olumns 1 through 60 to identify the new problem. This title will replace the one originally entered on ard 1.1 when the new problem is run. ARD 12.3 olumn Format Symbol Definition M Number of integer variables to be changed N Number of floating point variables to be changed. ARD 12.4 (Req'd if M> 0) olumn Format Symbol Definition MO() Location of ist integer variable IA(l) New value of 1st integer variable. 37

43 olumn Format Symbol Definition MO(2) Location of 2nd integer variable IA(2) New value of 2nd integer variable MO(3) Location of 3rd integer variable IA(3) New value of 3rd integer variable. This pattern is repeated for 6 variables per card, until M pairs of variables have been loaded. ARD (Req'd if N >0) olumn Format Symbol Definition NO(l) Location of ist floating point variable F10 AA(l) New value of 1st floating point variable NO(2) Location of 2nd floating point variable FlO AA(2) New value of 2nd floating point variable I5 NO(3) Location of 3rd floating point variable F10 AA(3) New value of 3rd floating point variable. ard 12.5 is repeated until N pairs of variables have been loaded. ARD 12.6 Input "END" in columns 1 through 3 to terminate problem or omit this card and go to ard 12.1 to run additional problems. 38

44 3. SAMPLE PROBLEMS This section contains the computer printout for the following.sample problems: 1. F-16A 2. FB with damage The output is self-explanatory, except that in the -141 problem it should be noted that the damage imposed is strictly hypothetical and is not an attempt to simulate an actual damage case. Damage inputs are entered for each of the fourteen AAT damage modes to demonstrate the flexibility of the program. The F-16A and FB-1l1 problems presented in this section provided the estimates that are compared with data in Section 9, Volume I of this report. 39

45 ON ~ M t4ff- " NNN.4 N* IV ) m1.. )p mu VW.* lv Lem41 mmi 4 L ctli itr 14r~ Le tts4w41 r1m: Lcix 14 I Lr xm li: ~ aa A. -A Z U. U &J9 Lt 0 j It. ULL 1W 4', W4W.W.W1 IS L. '4.414 WWI- *9.- Ni -i A4.n.4S WW( P4 W -x, I c f. L.. 0 (U W 0u. II W1 7 14l SI. ca IV019-10D'4~ 1 US..i W P r N.. P) NO. P) W44 -~ W4 W wo W49 W n' 1 U. 0 L #4 ~ I VP '4 44 ".U L.. u- IS WS LJ#.W ppw.1.9.r.l O 41 P. A I.4.au., IA1 slo #~'~~1 w10 140

46 ftj I Li -Jr J6 W. ou w 1*. Li L) IL U In I uj -- W - 9- U 41

47 ii to -- ) H LII-.. j 2 N w "1 14 W u V j a t. % 4 V, L. L LL. 86* W L N2.. l 1 P# N p. 4 4 a.4 P) 'ja. 4 toj~ or Nf v m r e: L -L f?1 LI W% LI LI w w w n. I AI L N 144 L0t 6L w IL f Hw L W 0. W 4 xi x. 4 4 j. U & Li w -Z-i &L 0u. L ' W U t P- I-A w14w W x u -. :).4 Wj 0, W 0 2. ) 0:x - Li cc U. a 49 d6 w P- wa 42

48 H p. 4 W) 0 u U F * m, 00N N.7 W0).4 V 4 It 0*F w U 0 ta 40 Lo IV 1 vp L' w t to % 0 W S o to 90 to. U t 0 ll at i cr 3 Ni 40 Li * ~ ~ ~ V 30 wo J u N t 0443

49 LL Wa. i L; 11 wu 9.Pa'.4 ~.~tip Li~t % U M a U1 w 44

50 0.7 P 4 P3 s 4 - I N P.4 U,. 14 S Lw- N3 In PS U' I 1 4I. 1 I. w* P P3 I'* L III.IllJ P Il L P ' Ill L -I IV LL U. 3 4M IV WI W1 w. "I I w' UIV I,. U, W, W. VI P1j. J. P IV U' W3. V4 LU. V3 ro w P.P P1.7 N IV Ili I J LI N N f 01 o 1I.4 LI 0 s W 9? M U 1 '. 3 J U.1 a 1 M 4 Y INJ I U. vi tc ui wl AI II ' A. 9. Q. U 9. V, it.in Aiill In 16 F 63 4 U ~ 945

51 Li~~~~~~ tu 44.L 44 i IV i r., ~NN IV m' It)J~ U: 4'cm MA P) k.. y 4lI U U P I n wt IJ4 L'P tinjl 14 NIV ) e) 4U~I WL Uk W&.. *.9 'L :9A w J" U:I- U, u wlij 4' 1U &4L "I It LU. bw U ww I I. U. A.L AA ~ i.l EX -4 A St'YIW IIII J D1. LI.0 U. 4.. L L) I-L w 4 4, j W/ ji I-. 4L'44 U-.4 -.,4f w IJLwIW.4U. " WL Li I -.4. A..4.j "iv414-4.l LDIuwwmL U LL I LftLI4..4LmLm WU4IS w L,., Li w 4- V. wli4. LU U ' U '4-4 A A4 ~ IL 0 (1 L) w~ '-4..J j - 00 / IX 4I l ~ I.U.WU.WQ U LI4i LA.LI4 LLIWLXI3 - J A g - W b. WWW. Ir ui I&S-hJ.ILLc.L2 *4 4 4 ft up 0.u XX A - I. V' LjU * I JL Li.4 p j d44. j. I, Vt - W 0 1- U - LV, w. a.j I- 4.0.J s I I- W 4- V)I 1.) " A- -. JW L " "~ 0,4 "... Z >.0 0 A.4 4j U Q U U U. 3. X I I I I I I La. - A w A I- -. W, w wi wi LI ui wi I 0.LILIL wi wi V, - 46

52 tv ho U' 'c L U; us U%. -. ".AUlf N IL u SPA.. S 5 -p w UIs w wl,

53 lo- Jot44- w -27' -1- Li Ill. 0 07L0 wa xn t Zoo 730 afll 11) 70* 14_fl a. q l 7S 49.t,200(*l I. 44.; 0 U. u8 to %.. 0M 4.1 t. r UU If VU ~ I U'4 V " 4, W)41 M * I 1114 U4.4W4."I4.U*.J4-LD- 4.) *. ** * 4 * :9* IV u. I.... * IV z, 14 o 1 %Jj-j w U. Li 0-1S4 P4 U.~L -P U -1 A~t,4~ Ve l Vt 2 IV N - W : : 4S 44 I- t. P i, 11 n *, 1, # U-U- 444'4.),./U.(U4.'41. J 44*1...f4VV.... WN~L 4rJ tflnq4,ni4jj 4Jt4UW44JNP ' ~ ~ ~ ~ ~ I too,4* II I u %~J 0 w ID P.4U I, DJ. F-I~~4 t4 t.. 4U4444 W444 *4.w IV. 44 it it $ 104 o 11. vi. U4, V,.4l, ItIt '.44. " L.4. w

54 6'34-9 S ft I-A *iuj 1 I '4 ' M3 W U3 'au..,aaaa 17' t - " " m,fi.,4j',d..t ZJ841l~ U,'. ft 1 U w., III V, 1-I.o 13 't.4 S3)I~ -~43 Ut 1, lo 1 01 IIu w ( m a 'a3a0'a t s oa, IV L.*a 14 ' 4J. c.) 3 I- us - L z I.S,y4V. U. P-.I III (Y -aj.4n w'ar f1 fw 91 Ili U. c: 4'M -0 N 'a 14 w... WI - I I, 'a 'a ps 0'. w viva~~~~- rj,.g " - nuioi wg-u'a.ug.. -j Li OF' L.44'' u 2.L i3 Na LU'J U%.~'v '~' U, aa'l ~ 'L' 4u Ua 11 Za 'a' A 4'' a' WII _I * L w * 4 w U, - u V. U, i- - li.4 i*~~~.4.3.j.2...'...j 'J ' t~ Ia Ia Lp' It if 'a 'a ' a P..4 A ii LI Ja i~j A Ii I-- L "i l Z)t~ U.88.t.IIV,- 14 I' f 11 1 u I Z,. IJ'a.J :;. l UI aljur 0'a :U) U, LX V, 1).4I w)rl'l' u w cail I - ii U, ' *3a, - LP)SI Z0. u L, f. N L,3' IIIU, w. t, a. a 3 'a..'t.il'a LI'a1'aLA AIA Il IAAAAA aija SJa ' _.j, 'a W NI 4)V 7W 4P D 4, 4 USI... II '% (V P# V..3, W til IAU....o em L., i.. %s.. I V11 At. IL UJ 0)t w 40 a. 0)iLL I L4I 49

55 II 42*~ 3 an -2 1 lai 1 : 1,0 u~ 3c. -L *U U. 4U%..*uJ ~u; *u * I *UN - *it1tj** 13 u j-.:..... Li w#. u 4 -. w -gil-l' U Sd.~ L.30.J ~~~~~ Oca 00 a3*4 *4 'r w 4jZ - 3a Li. 5. m V, 0I i..0s LaW i w vivivvn U * * I * I I * V* Si. ~ g44 W U JN WS I*4Ia..S. ' 1 L f- I-a 14"*e- *5 Vp. n p IV W t'i A. '5.3 (S V) a (Y ri.2. 1 U. 04:u13 i*. 00 l V, LiI51 w 'l V zm o o t U w 5451 ww w I^.1 i*u, 4F 1,.100 i*4% I i I) ** SSi ** I. ui w4 t l -W. U N r-i5.p III5 u w I. UvS4S4.al,.No P *4Sy &* P. w w u Ntc3 W4I41,, w ILI ~~~ W~ I I -7 Li wr.4*is IU* 4UJa) 'Uw o La " HSL~~ wt*o' L J. wwa.a -A rI * * *. 50* ***** ***5aJ4 *

56 fii oz L. ul, I,d IV N -. V,,.,4 ol Q,iJ,4 Ut IV*,, wi 0. L V o % w,j ft) u 40 U0 " t I O~lO V, AfII O OL~n ii LI i'4 Iv II w'.1. w (IV p U'. 1, -DN 4 0' W LI 4 2 tv"v1 - LI - - '.A..,, A.,... A,..,..,...,-. I, I 0 L 5, I% t5 L4. A A. Li W- -., I LI~~~ Pt40U 45',UI w,., m A-A N w AAA AL P) P.,) 1.1IIIoW.. A LI L -~~A o.... r. 4 LI.OIULILILLI LI'-LI'J IrILILLI.IW w A f.s 4. U U. *' lr I - ' : l. "4 lt N ( P p 40. LI 00), It.4 4 -A UA I.P u V. V - O 4A. 4,, 3 fu AD V. ol IV v. VA mi 1 A', 1 I. v J0 II J. ~ ~ A 4 U I0 LI ,40 N. A- r) LI '1 0 Si 11~.( A. 4 N LA,~~0(0 L r-iaw6 1 V ; N ) A, P LIuIU: %D AN, w ft, - a I LIPI U.L1- -4 LI x 'tj I I(J IL( A.-U1 A.,UJ4r ' + I. I *,,,,-.,..ULLU*.. LU. * LI W P~u I.l PJ Uz AniP.'.P.U 'li Is11 ItIf is~ 71o tif1 1 I IJ. D -L.L III. I U i A! t'..... w, VA 11I it LIL L ci1-a.4. It.444 LI51

57 L&* w It4l t.4 ItUw Iw (:t 6- V.Id) V, W).5. - u. I-.4 It - u4. Li UPU *4~~~~~" *...,LJ I I.W : i.1 PSL U...~ wqil IV IV-WP-P mio U, UNi, F) al I. U. IV.. U 4 W ru, W." IV *F. #1 11 ) )jr144 -F, VI )*WU 4 IV ) Pf. U. p11 1,p - wi IU.i w *:FWnIIV wi.w,... *4 UP 00P -# LI 1 F1 LI 6L ) Z) FlU *L-O.N 4 UP UUPPPUUIIP "In~ IV, w w-.p rliv *1 4 LW O~iI~~P~g.UUIi.N Li)PU52Li.

58 .4 a. )1.. W Li 4 Li - 9- Li U L 4-53

59 5 4i i N ' L. t N a a t, al- 41- AN at wi II S.~~.. w iii., vs up 0- IV IV~III ai LiJ.4.UU wu w IL-4LJU.' li lt l JR. A ci a i i L a a I.Li 0S 61 LiL w- ' a 9~ U ' i Liw.4La..4.4x L Li'L Li L aja a *'L 1, 11 1 A. 4 Al

60 m~ a4 ~ a ~ os a w.,.4*- H, 1. a, 1i P 4 P) V% el I 5 A W4A,, a aj.v a t.. a a a a 0-4 P'l 2 '. I~ t A At LA l ' LASy4- I PLi 92 I t L Z I.. f 11a0. 1 A. Si - p u LL r~ a i to t W t 05 L~~~iO to 11i * Owa I r D LV j '0 -D L 5' Li U 5' '. Li o55

61 -~~~ ~= "t~, I'L I3 2 IU %u If. L i.i*r LiU LLJ IAIIIL L.4LLi L i~'0lnl Le I Z I1 44 Li Li 0L Li Lrii 14 i a c stuu. r 56

62 % 11. ai Ii. tat 14.. it. * w I S In -4 w~ IJ W' c) t * w 4 c, IV. w) I U L.4 on SI a; i N W - Is, tho dn w w3 U) N 2 wi P4 )'. WW V.4n W -. v 4 Is- Us a. It N w I- 1 w'.. ti A A.1 Is 0 %;,.3 tn Ii U. Ist PA N.3 U L A ' it 'U t 1 14 j 1 ' N N -Z4.0 j.1.%.l t ',41 LI > In c In W4 K I 14 to "t ~ 66 ' $'-4I' a L Li P- K.4 a/.j am Ix 6A. wl UI U t u 4 P -k " Lt t PI I I L i.- u Lav. a% d Is. ml 0I U.A ' in A ~ A ^4 %1 4I.4 u~ in V) I.- U) l ' K L457I

63 Lu1 pr ~ ~ ~ ~ ~ ~ ~ 6 w L'.,L. 4.) 0' w4)0. tv US r4 3e 464W U 5 l-. V... 65* ~ S'65~ 7J 7*p.L 5 5. a' *65.' EL w z UJ WL3UW 43 6 t 4. t A SLOJu A A.A mi u S.,, UL,J >.'r IL B. V, 4 U. 11. WL 45 wi. 4. W4 W La 0- * '. _j ) VV5 0 U 2L W IL 43 v... W ,L 6 4. U- 5mt4 43 L ) WL' JU~ 46.4.)65'43. Aw' j L I- W~ 5.5 L655w.5w.t5-t L H U H u u Q5.5 uu u4.u4) 6. I* U).W - ^ U6. -. W. - (641W A , L...WUUL -*6L) )J545.5~ '

64 '44. U.43* t. V 4*U ~t US4..,,N 434) 59.

65 ..*.U.4.4~ o. )Iq~ a wgs.....rjlrv.t.1.. *.4.. OIJ.J.,.44 w4-4.-) u L,,S U AI M55 fl..pp. 0- w4 : n. ~. I.ZO Li w 1* 93 4.'. '.3 41,14 Z, '44 U. L, 0' F" 1 * ~ ~ ~ ~ *L ~ L J4VJ4W.S~UI*.L.. ~ ~ In I.QuLI7 c% N~~~~,N- ~ It~ 14 U It o to.. 4 U%0 4 KjI U.j ro w 3 W aw U. " m uli Ulj'4 W5.1 IV, wwin. )4r IL~~~~~W J~l.14UU.PSU' U. S.10INS 1 w t. Ill~~( W JeFI 1 U..,n U'' LL u9xu di t.p 4-1 PI4'# W 60 0 U.5 I t.

66 .a. w, - m u',u 4.g. F, U' N U'. U4 o U w *..-j r. r ft I 0-

67 LOk... 19t, L %~. u... A2a a.j1 D S3 4 o W.0 IV SSU M 14J P 9*A "I4 ca w IV Li.4 f U..Al. i 9.., a. t -WU 9ul.4 ~ ~aa4 L3 ~ i..4 w 2 J. 4 u 41.- a 3 IV L, A m Li A& A.. yo VOWI. W 1-3 AV y o# Ali 449m. wi t1 w' m 1 u,, w ly Ai o0 A.. P: Li SI- L2 Li 4.j ~Li.J Aw i Lii " - Li Li *4.4. o I?LiZ.0S1U I No' it III w 3 17 el ly.1 3 ;j. un AL UJ a i A _W~U At *W% LL..o i... ~i O 4tyiii~L :P),"lrIllf- (V l *U _j~i IV :4ii~~ Li. L AV A; I II o: PIL (Y 1.' Ii r)1 A WA 1 u Ifl~i,U&ZgPIV rlir, N9..All 7 Q ui~ 4- wi - N PJ 9f4 J4 ' I9r~g M. Wi A3 V 9 II XI I. II.1 ~ ~ ~ ~ ~ u AV I. IL is AV 4.4 AM U,.8 0, o, IV v w o)la B J Uw L U 4 l 1 X. 64 &A x. LiL 62