Appendix 6 to ETSO-C117b - Wind Shear Simulation Model

• ED Decision 2020/011/R found in: CS-ETSO Amdt 17 - European Technical Standard Orders (Oct 2026)

###### Appendix 6 to ETSO-C117b – Wind Shear Simulation Model *ED Decision 2020/011/R* The following computer listing (written in QuickBasic) provides a simplified aircraft simulation model for evaluating the effectiveness of various guidance schemes. This simulation runs on a personal computer, and the results obtained using it have been found to be comparable to those obtained on a full six-degrees-of-freedom simulator. This model was developed by J. Rene Barrios of the Honeywell Company. The Wind Shear Simulation Model (WSSM) is a point mass three-degrees-of-freedom mathematical model which simulates the motion of an aeroplane in a vertical plane. The equations of motion, which are described in the wind axes, include the wind components of velocity and acceleration so that the aeroplane dynamics during a wind shear encounter are accurately modelled. This model has been used by several investigators to study the behaviour of an aeroplane during wind shear encounters. Note: The Wind Shear Simulation Model provided at the end of this Appendix is an example written in Microsoft QuickBasic. Other programming languages such as Microsoft FORTRAN, C, or assembly language are also acceptable. The Equations of Motion The motion of a constant mass point in the vertical plane may be described by four equations of state and a control variable. For an aeroplane, it is convenient to use an orthogonal reference frame which is attached to the frame of the aeroplane, and its x-direction points in the direction of motion. Such a reference frame is the relative wind reference frame. The following equations model the states of the aeroplane in the wind axes: Vdt = g[(T.csalf) − D)/W − sngam] − Wxdt.csgam − Wzdt.sngam (1) Gdt = {g[(T.snalf + L)/W − csgam] + Wxdt.sngam − Wzdt.csgam}/V (2) Hdt = V.sngam + Wz (3) Xdt = V.csgam + Wx (4) where: <table cellpadding="7" cellspacing="0"> <col/> <col/> <tr valign="top"> <td><p> Vdt</p> </td> <td><p> Rate of change of true airspeed in knots/second</p> </td> </tr> <tr valign="top"> <td><p> G</p> </td> <td><p> Gravitational constant in knots/second</p> </td> </tr> <tr valign="top"> <td><p> T</p> </td> <td><p> Total engine thrust in lb</p> </td> </tr> <tr valign="top"> <td><p> csalf</p> </td> <td><p> cos (alpha)</p> </td> </tr> <tr valign="top"> <td><p> alpha</p> </td> <td><p> Angle of attack in radians</p> </td> </tr> <tr valign="top"> <td><p> D</p> </td> <td><p> Total drag in lb.</p> </td> </tr> <tr valign="top"> <td><p> W</p> </td> <td><p> Gross weight in lb</p> </td> </tr> <tr valign="top"> <td><p> sngam</p> </td> <td><p> sin (gamma)</p> </td> </tr> <tr valign="top"> <td><p> gamma</p> </td> <td><p> Flight path angle in radians</p> </td> </tr> <tr valign="top"> <td><p> Wxdt</p> </td> <td><p> Inertial wind shear x-component in knots/second</p> </td> </tr> <tr valign="top"> <td><p> Gdt</p> </td> <td><p> Rate of change of gamma in rad/second</p> </td> </tr> <tr valign="top"> <td><p> snalf</p> </td> <td><p> sin (alpha)</p> </td> </tr> <tr valign="top"> <td><p> L</p> </td> <td><p> Total lift in lb</p> </td> </tr> <tr valign="top"> <td><p> V</p> </td> <td><p> True airspeed in knots</p> </td> </tr> <tr valign="top"> <td><p> Hdt</p> </td> <td><p> Altitude rate in knots</p> </td> </tr> <tr valign="top"> <td><p> Wz</p> </td> <td><p> Inertial wind z-component in knots</p> </td> </tr> <tr valign="top"> <td><p> Xdt</p> </td> <td><p> Ground speed in knots</p> </td> </tr> </table> In the above equations, the positive directions are upwards and forwards. This implies that tailwinds and updrafts are positive, while headwinds and downdrafts are negative. All the states can be determined from a given alpha; therefore, alpha is the control variable. Since the model is that of a point mass, it is necessary to introduce the concept of alpha\_command and actual alpha to account for the effect of the horizontal tail/elevator. This is done by introducing a lag between the alpha\_command and the actual alpha. Therefore, any command that is given to the elevator or stabiliser can be interpreted as an alpha\_command, which will cause a change in the angle of attack. From equations 1, 2, 3 and 4, it can be seen that any change in alpha will produce a change in the longitudinal and normal accelerations, which in turn will change the states of the aeroplane. The Path Control Function The different segments of the trajectory flown by the WSSM are described by a series of alpha\_commands, which are generated by the procedure explained below. 1. The aeroplane is trimmed for the initial conditions specified by the user. The initial conditions are usually specified as the altitude, gross weight, flaps, speed, flight path angle, and wind characteristics. The trimming operation consists in finding the angle of attack that satisfies the equations of state and will result in an unaccelerated motion. 2. After the initial trim, alpha\_command must be specified for each segment of the trajectory, which usually consists of a climb or descent segment at constant speed or constant path angle, and guidance through wind disturbances. The wind disturbance is provided by wind models that can be selected at initialisation time. 3. In order to specify an alpha\_command, the user must supply a subroutine where a quadratic function is defined in such a way that when minimised with respect to alpha, and constrained by the equations of state, the minimising alpha will produce the desired path in an optimal manner. For example, if we want to fly initially at a constant path angle, say 8 degrees, then the quadratic function may be defined by the expression: (5) where: <table cellpadding="7" cellspacing="0"> <col/> <col/> <tr valign="top"> <td><p> cst</p> </td> <td><p> Function to be minimised w.r.t alpha</p> </td> </tr> <tr valign="top"> <td><p> dt</p> <p> Gdt*dt</p> </td> <td><p> Time increment used in simulation in sec.</p> <p> A predictive term which anticipates the change in gamma</p> </td> </tr> </table> Other expressions follow: The minimisation of the function cst is performed by a subroutine at each time frame and is totally transparent to the user, who has to supply only the objective function cst. 4. Each expression defining a different value of the objective function cst is called a ‘LAW’. The user selects the guidance law to be used during the wind shear encounter at the time the menu is displayed. This method allows the user to compare different guidance laws under the exact same conditions. The Wind Models The WSSM has two types of wind models: the Dallas-Ft Worth accident wind field, simulated by a quad\_vortex model, and the constant shear model, which is user defined via the initial conditions menu. Plotting Capabilities The WSSM can plot up to 3 runs with 10 parameters per run. The length of each run should be kept under 60 seconds. This feature allows the user to compare different trajectories by overlaying the results. The Programme The WSSM is written in Microsoft QuickBasic, which is a highly structured language with a very friendly full-page editor. QuickBasic is very convenient for development, since it allows the user to stop execution, change the programme and continue executing. It also interfaces with Microsoft FORTRAN, C, or assembly language. The procedure suggested for this application is that the WSSM be compiled without subroutines DETECT and GUIDE. DETECT and GUIDE can be separately compiled and put in a library called WNDSHR.QLB. These external subroutines may be written in Microsoft FORTRAN, C, or assembly language. Listing of Programme '\*\*\*\*\*\*\*\*\*\*\*\* AIRCRAFT FLIGHT PROFILE SIMULATION \*\*\*\*\*\*\*\*\*\* DECLARE SUB PLOT ( ) DECLARE SUB TAKEOFF ( ) DECLARE SUB EULER ( ) DECLARE SUB MCRBRST ( ) DECLARE SUB WINDS ( ) DECLARE SUB OPT ( ) DECLARE SUB MIN (DM, M2, C1, C2, C3, M) DECLARE SUB BEGIN ( ) DECLARE SUB VSHAKER ( ) DECLARE SUB COST ( ) DECLARE SUB LIMIT ( ) DECLARE SUB RATES ( ) DECLARE SUB THRUST ( ) DECLARE SUB ATMOS ( ) DECLARE SUB PRINTS ( ) DECLARE SUB DRAGS ( ) COMMON SHARED FLPS%, GEAR%, GEAR$, CL, CD, LIFT, DRAG, ALPHA COMMON SHARED SEC, ALT, DST, HDOT, ALF, GAM, GAMREF, GREF, G COMMON SHARED WSALERT%, WXO, WL, WX, WXDT, WZ, WZDT, DFW COMMON SHARED WV, LC%, GM, GREFF, NOSAVE, GMO COMMON SHARED DELTA, ISA, T0, SPDSND, VT, VC, MACH, A0, TAT, TAMF COMMON SHARED THRST, EPR, TFCT, APPFLG% COMMON SHARED SNGM, CSGM, CSAL, SNAL, VDOT, WG, GDOT, XDOT COMMON SHARED AWX, AWZ, AU, AZ, VG, GRND, KF1, GMIN, KF2 COMMON SHARED ACMD, OLDALF, DT, HP, LP, ALFLIM COMMON SHARED LAW%, GMR, ASS, CST, VTO, GCMD COMMON SHARED OUTFILE$, DM, ALT1, PL$, TTT, WXDTO, TDX, TSH, WZO, TDZ, TSV COMMON SHARED GM1, VTP, THETA COMMON SHARED ALFRTE, PLMFLG% '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' MAIN PROGRAM \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* START: '< ----------------<< RE-RUNS START HERE CLOSE : CLEAR COLOR 15, 1: CLS : VIEW PRINT LOCATE 8, 23: PRINT "WINDSHEAR SIMULATION" LOCATE 10, 23: PRINT "FOR " LOCATE 12, 23: PRINT "BOEING 737/200 " LOCATE 23, 23: PRINT "TYPE " + CHR$(&H22) + "I" + CHR$(&H22) + " FOR INFORMATION" DO WHILE a$ = "" a$ = INKEY$ LOOP IF a$ = "I" OR a$ = "i" THEN a$ = "": CLS '---------------------- INFORMATION PAGE----------------------------------------- LOCATE 2, 2: PRINT "BOEING 737/200 INFORMATON" LOCATE 3, 2: PRINT "JT8D-17 ENGINES" LOCATE 5, 2: PRINT "-------------------------------------------------------------------------" LOCATE 7, 2: PRINT "ALLOWABLE WEIGHT RANGES..................: 75,000 TO 120,000 POUNDS" LOCATE 9, 2: PRINT "ALLOWABLE TAKEOFF FLAP SETTINGS.........: 1, 2, 5, 15, 20, 25 DEGREES" LOCATE 11, 2: PRINT "ALLOWABLE LANDING FLAP SETTINGS.........: 30, 40 DEGREES" LOCATE 13, 2: PRINT "TAKEOFF EPR AT SEA LEVEL, STD. DAY...: 2.1 " LOCATE 15, 2: PRINT "REFERENCE WING AREA.......................: 980 SQUARE FEET" LOCATE 17, 2: PRINT "REFERENCE TAKEOFF SPEED..................: V2 + 10" LOCATE 19, 2: PRINT "REFERENCE LANDING SPEED..................: 1.3 Vs" LOCATE 23, 2: PRINT "Press Any Key to Continue..." DO: LOOP WHILE INKEY$ = "" END IF ANS$ = "2" CLS WHILE (ANS$ = "2") LOCATE 10, 30: PRINT "Fly ..... 1" LOCATE 12, 30: PRINT "Plot ..... 2" LOCATE 14, 30: PRINT "Exit ..... 3" LOCATE 18, 30: INPUT "Selection ....."; ANS$ IF ANS$ = "2" THEN CALL PLOT COLOR 15, 1 CLS END IF WEND IF ANS$ = "3" THEN END CALL BEGIN 'GET DATA/INITIALIZE VARIABLES CALL THRUST 'INITALIZE THRUST CALL TAKEOFF 'INITALIZE TAKEOFF CALL COST 'SUBROUTINE COST CALL PRINTS 'SUBROUTINE PRINT FOR ICL% = 1 TO TTT ' TTT IS THE RUN TIME IN SECONDS CALL THRUST ' SUBROUTINE EPR/THRUST CALL WINDS ' SUBROUTINE WINDS ' CALL DETECT ' SUBROUTINE WINDSHEAR DETECTION ' SUPPLIED BY USER ' MUST RESIDE IN LIBRARY WNDSHR.QLB CALL OPT ' SUBROUTINE OPTIMIZE CALL LIMIT ' SUBROUTINE ALPHA RATE CALL EULER ' SUBROUTINE INTEGRATE CALL ATMOS ' SUBROUTINE ATMOSPHERE CALL PRINTS ' SUBROUTINE PRINT IF ALT < 0 THEN EXIT FOR NEXT ICL% PRINT "RUN IS COMPLETE" PRINT "TYPE " + CHR$(&H22) + "D" + CHR$(&H22) + " FOR RUN DATA" a$ = "" DO WHILE a$ = "" ' Wait for key to be pressed a$ = INKEY$ LOOP VIEW PRINT: COLOR 15, 4: CLS IF a$ = "D" OR a$ = "d" THEN a$ = "" LOCATE 2, 2: PRINT "DATA FROM CURRENT RUN" LOCATE 4, 2: PRINT "--------------------------------------------------------------" LOCATE 6, 2: PRINT "GROSS WEIGHT: "; WG; " POUNDS" LOCATE 7, 2: PRINT "ISA DEVIATION: "; ISA; " DEG C" LOCATE 8, 2: PRINT "FLAP POSITION: "; FLPS%; " DEGREES" LOCATE 9, 2: PRINT "GEAR POSITION: "; GEAR$ LOCATE 11, 2: PRINT "CONTROL LAW: "; LAW% LOCATE 12, 2: PRINT "GAMMA REFERENCE: "; GAMREF LOCATE 13, 2: PRINT "PITCH LIMITING: "; PL$ IF PL$ = "YES" THEN LOCATE 14, 2: PRINT "MAXIMUM PITCH: "; HP \* 57.3; " DEGREES" LOCATE 15, 2: PRINT "MINIMUM PITCH: "; LP \* 57.3; " DEGREES" END IF LOCATE 16, 2: PRINT "TIME OF RUN: "; TTT \* DT; " SECONDS" IF DFW = 1 THEN LOCATE 17, 2: PRINT "DALLAS/FW Wind Model" ELSE LOCATE 17, 2: PRINT "HORIZ. WIND MAGNITUDE "; WXO; " KNOTS" LOCATE 18, 2: PRINT "HORIZ. SHEAR MAGNITUDE: "; WXDTO; " KNOTS/SECOND" LOCATE 19, 2: PRINT "HORIZ. SHEAR DURATION: "; TDX; " SECONDS" LOCATE 20, 2: PRINT "VERT. WIND MAGNITUDE: "; WZO \* 1.689; " FT/SECOND" LOCATE 21, 2: PRINT "VERT. WIND DURATION: "; TDZ; " SECONDS" LOCATE 22, 2: PRINT "--------------------------------------------------------------" END IF IF LEN(OUTFILE$) = 0 THEN OUTFILE$ = "NONE" LOCATE 23, 2: PRINT "OUTPUT FILE: "; OUTFILE$ LOCATE 24, 2: PRINT "Press Any Key to Continue...." DO: LOOP WHILE INKEY$ = "" 'Wait for key to be pressed END IF GOTO START END SUB ATMOS STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE ATMOSPHERE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* STATIC THETA L% = ALT > 36089! FISA = 1.8 \* ISA IF ALT > 36089 THEN TMP = .7519 \* T0 DELTA = .2234 \* EXP((36089! - ALT) / 20806) ELSE TMP = T0 - .0035662 \* ALT DELTA = (TMP / T0) ^ 5.256 END IF TAMB = TMP + FISA 'TAMBient in deg. R TAMF = TAMB - 459.7 ' " " F THETA = TAMB / T0 SQRTH = SQR(THETA) SPDSND = A0 \* SQRTH IF VT > 0 THEN MACH = VT / SPDSND VC = A0 \* SQR(5 \* (((1 + MACH \* MACH / 5) ^ 3.5 - 1) \* DELTA + 1) ^ .28571 - 5) TAX = (TMP + FISA) \* (1 + .2 \* MACH \* MACH) 'Deg. R TAT = 5 \* (TAX - 459.7 - 32) / 9 'Deg. C IF INKEY$ < > "" THEN PRINT : INPUT "Press ENTER to continue...."; XXX END SUB SUB BEGIN STATIC CLS : VIEW PRINT '<--------------------------------- DATA\_INPUT ------------------------------> PRINT INPUT "OUTPUT FILE (DEFAULT IS NO FILE) "; OUTFILE$ IF OUTFILE$ = " " THEN NOSAVE = 1 ELSE NOSAVE = 0 END IF ' CONSTANTS USED IN CALCULATIONS: A0 = 661.478599# 'Speed of sound at sea level in knots G = 19.07583 'Gravitational constant in knots/sec T0 = 518.67 'Standard temperature at SL in deg Rankine DT = .25 'Simulation time step in seconds ' ---------------------------------- INITIALIZATION OF VARIABLES-------------------------- GMIN = 0 VDOT = 0 ALT1 = 0 INPUT "TAKEOFF OR APPROACH (T/A) (Default is T)....."; ANS$ IF ANS$ = "a" OR ANS$ = "A" THEN INPUT "ENTER ALTITUDE IN FEET (Default is 1000' . "; ALT1 IF ALT1 = 0 THEN ALT1 = 1000 APPFLG% = 1 TFCT = 1 END IF ALT = ALT1 ' ----------------------- CONFIGURTATION CONSTANTS------------------------------------------ ASS = 16.5 'Stick Shaker alpha in degrees ASS = ASS / 57.3 ' " " " "radians ' ------------------------------------------- GROSS WEIGHT ENTRY------------------------------------------ PRINT : INPUT "ENTER GROSS WEIGHT IN POUNDS (Default is 110000) "; WG IF WG = 0 THEN WG = 110000! ' DEFAULT SETTING FL% = 0 WHILE (NOT FL%) INPUT "ENTER FLAPS SETTING (Default is 0)............."; FLPS% SELECT CASE FLPS% CASE 0, 1, 2, 5, 15, 20, 25, 30, 40 FL% = -1 CASE ELSE FL% = 0 PRINT "Invalid flaps setting" PRINT "Only 0, 1, 2, 5, 15, 20, 25, 30, & 40 are supported" PRINT END SELECT WEND IF FLPS% < 15 THEN GEAR% = 1 IF FLPS% = 15 THEN INPUT "GEAR UP OR DOWN (1/0) (Default is Down)....."; GEAR% IF GEAR% = 1 THEN GEAR$ = " UP" ELSE GEAR$ = " DOWN" END IF INPUT "ENTER ISA DEV. IN DEGREES C (Default is 0)......"; ISA PRINT CALL VSHAKER ' COMPUTE V2+10 FOR FLAPS<33 OR 1.3Vs FOR FLAPS>32 PRINT " CONTROL LAW SELECTION:" PRINT PRINT " Speed = 1.1\* V\_stall = 1" PRINT " Alpha = Stick Shaker Alpha = 2" PRINT " Horizontal Acceleration = 0 = 3" PRINT " 15\_Degree Pitch = 4" PRINT " Theoretical HONEYWELL/SPERRY = 5" PRINT " User Defined = 6" PRINT INPUT " SELECT CONTROL LAW ....................... "; LAW% IF LAW% = 0 THEN LAW% = 5 PRINT : PRINT ' ----------------------------------- GAMMA REFERENCE INPUT--------------------------------- IF LAW% > 4 THEN INPUT "ENTER GAMMA REFERENCE IN DEGREES (Default is 0)........."; GMR PRINT GAMREF = GMR GMR = GMR / 57.3: GMIN = GMR END IF ' --------------------------------------- PITCH LIMITING SELECTION--------------------------------------------- INPUT "PITCH LIMITING DESIRED (y/n) (Default is NO)..............."; PL$ IF PL$ = "Y" OR PL$ = "y" THEN PL$ = "YES" INPUT " MAXIMUM PITCH ALLOWED IN DEGREES "; HP INPUT " MINIMUM PITCH ALLOWED IN DEGREES "; LP HP = HP / 57.3: LP = LP / 57.3: PL% = 1 ELSE HP = 100 LP = -100 PL% = 0 PL$ = "NO" END IF CLS ' ----------------------------------------------- TIME FOR RUN---------------------------------------------------------------- PRINT INPUT "ENTER TIME OF RUN IN SECONDS (Default is 45).............."; TTT TTT = TTT / DT IF TTT = 0 THEN TTT = 45 / DT ' DEFAULT SETTING ' ------------------------------------- WINDSHEAR SET UP---------------------------------------------------- INPUT "DALLAS/FW Wind Model (y/n)...(Default is constant Shear)....."; ANS$ IF ANS$ = "Y" OR ANS$ = "y" THEN DFW = 1 ELSE DFW = 0 PRINT INPUT "MAGNITUED OF HORZ. WIND IN KNOTS......(Head wind < 0)......"; WXO INPUT "MAGNITUED OF HORZ. SHEAR IN KT/SEC. (Dec. Perf. > 0)......"; WXDTO INPUT "DURATION OF HORZ. SHEAR IN SEC.............(Default is 0)......"; TDX INPUT "TIME FOR SHEAR TO START IN SEC..............(Default is 0)......"; TSH PRINT INPUT "MAGNITUED OF VERT. WIND IN FT/SEC. (Down Draft < 0)......"; WZO WZO = WZO / 1.689 'Convert to knots INPUT "DURATION OF VERT. WIND IN SEC...........(Default is 0)........"; TDZ INPUT "TIME FOR SHEAR TO START IN SEC...........(Default is 0)......"; TSV PRINT END IF ' -------------------- OTHER SET UPS---------------------------------------------------- VT = VTO WX = WXO CALL ATMOS ' SUBROUTINE ATMOSPHERE ' ---------------------------------- HEADERS FOR SCREEN DISPLAY---------------------------------------------------- CLS : PRINT PRINT "TIME ALT HDOT VT ALPHA GAMMA PITCH GREF WXDT WZ VDOT ALRT" PRINT "(SEC) (FT) (FPM) (KTS) (DEG) (DEG) (DEG) (DEG) (KT/S) (FPS) (KT/S)" PRINT STRING$(75, "-"): VIEW PRINT 5 TO 25 '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE INIT\_OUTPUT FILE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* IF NOSAVE THEN ' CREATE OUTPUT FILE ELSE OPEN "O", 2, OUTFILE$ FMT$ = " ###.## ##### ##### #### #### ## ###.## ###.## ###.##" FMT$ = FMT$ + " ###.## ###.# ###.# ##.## " END IF END SUB SUB COST STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE COST \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* CALL DRAGS ' SUBROUTINE DRAG & LIFT CALL RATES ' SUBROUTINE RATES IF LC% = 0 THEN 'Constant gamma segment FCT = (GM + GDOT \* DT - GMO) ^ 2 GREFF = 57.3 \* GMO ELSE 'All guidance laws SELECT CASE LAW% CASE 1 ' ---------------------------- 1.1\*Vstall----------------------------------- CST = (VT + VDOT \* DT - 1.1 \* 135) ^ 2 CASE 2 ' ---------------------------- Alpha = Ass----------------------------------- CST = (ALPHA - ASS) ^ 2 CASE 3 ' ---------------------------- Ax = 0----------------------------------- CST = (VDOT - VT \* GDOT \* GM + WXDT) ^ 2 CASE 4 ' ---------------------------- 15 Degrees----------------------------------- CST = (GM + 3 \* GDOT \* DT + ALPHA - 15 / 57.3) ^ 2 CASE 5 ' ---------------------------- User Defined----------------------------------- PRINT "Not defined" STOP CASE 6 ' ---------------------------- User Supplied----------------------------------- 'User must supply a subroutine called GUIDE 'which must reside in the WNDSHR.QLB Library 'GUIDE can have a list of arguments 'As an example 'ALF = 57.3\*ALPHA 'PTH = 57.3 \* (ALPHA + GM) ' units : ft fpm kt deg g's \* 'CALL GUIDE(ALT, HDOT, VC, ALF, PTH, AU, AZ, CST) END SELECT END IF ' CST is the Cost Function to be minimized END SUB SUB DRAGS STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE DRAG FOR B737/200 \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* X = 57.3 \* ALPHA + 1 CF5 = 0: CF4 = 0: CF3 = 0: CF2 = 0 SELECT CASE FLPS% CASE 0 CF1 = .091 CF0 = .0156 CASE 1 CF3 = -1.164058E-04 CF2 = 2.48561E-03 CF1 = .0905781 CF0 = .062114 CASE 2 CF0 = .101198 CF1 = .110993 CF2 = -.0015162 CF3 = 1.8931E-04 CF4 = -7.1427E-06 CF5 = -4.2776E-09 CASE 5 CF0 = .192638 CF1 = .123509 CF2 = -.0051477 CF3 = 6.4968E-04 CF4 = -3.0891E-05 CF5 = 4.1291E-07 CASE 10 CF0 = .249855 CF1 = .114005 CF2 = 7.1207E-04 CF3 = -9.9541E-05 CF4 = 7.0431E-06 CF5 = -2.3773E-07 CASE 15 CF0 = .40149 CF1 = .118723 CF2 = -6.4877E-04 CF3 = 6.6281E-05 CF4 = -1.6113E-07 CF5 = -1.4278E-07 CASE 25 CF0 = .592655 CF1 = .122433 CF2 = -.0026365 CF3 = 3.5963E-04 CF4 = -1.5579E-05 CF5 = 1.0894E-07 CASE 30 IF X < 4 THEN CF1 = .12 CF0 = .72 ELSE CF3 = -1.651192E-04 CF2 = 4.16461E-03 CF1 = 8.337061E-02 CF0 = .8350316 END IF CASE 40 IF X < 4 THEN CF1 = .12 CF0 = 1.08 ELSE CF3 = -1.689903E-04 CF2 = 3.733285E-03 CF1 = 8.483822E-02 CF0 = 1.201596 END IF CASE ELSE PRINT "Flaps "; FLPS%; " not available....." END END SELECT 'For CL computation CL = ((((CF5 \* X + CF4) \* X + CF3) \* X + CF2) \* X + CF1) \* X + CF0 SELECT CASE FLPS% 'Low Speed Drag Polars CASE 0 D0 = .013285: D1 = .052868: D2 = -.07182: D3 = .071561 CASE 1 D0 = .026143: D1 = .022358: D2 = -.00083: D3 = .016338 CASE 2 D0 = .070346: D1 = -.0852: D2 =.097453: D3 = -.01207 CASE 5 D0 = .045214: D1 = -.0178: D2 =.04373: D3 = .002101 CASE 10 D0 = -.04266: D1 = .19643: D2 = -.1152: D3 = .03966 CASE 15 IF GEAR% = 0 THEN D0 = .034954: D1 = .098892: D2 = -.04187: D3 = .020496 ELSE D0 = -.02822: D1 = .174631: D2 = -.0874: D3 = .029566 END IF CASE 25 D0 = -.10416: D1 = .327506: D2 = -.17059: D3 = .043313 CASE 30 D0 = .124697: D1 = -.03348: D2 =.055295: D3 = -.00311 CASE 40 D0 = .124925: D1 = .052537: D2 =.006912: D3 = .0058 CASE ELSE PRINT "Flaps "; FLPS% " not available...." END END SELECT CD = ((D3 \* CL + D2) \* CL + D1) \* CL + D0 Q = 1451770 \* MACH \* MACH \* DELTA 'B737/200 LIFT = Q \* CL DRAG = Q \* CD END SUB SUB EULER STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE EULER'S PREDICTOR/CORRECTOR \* ' (INTEGRATION SUBROUTINE) \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* DTH = DT / 3600: DTM = DT / 60: SEC = SEC + DT: VTP = VT CALL RATES ' SUBROUTINE RATES <<PREDICTOR>> ALT1 = ALT: HDOT1 = HDOT: ALT = ALT + HDOT \* DTM GM1 = GM: GDOT1 = GDOT: GM = GM + GDOT \* DT DST1 = DST: XDOT1 = XDOT: DST = DST + XDOT \* DTH VT1 = VT: VDOT1 = VDOT: VT = VT + VDOT \* DT CALL RATES ' SUBROUTINE RATES <<CORRECTOR>> ALT = ALT1 + (HDOT1 + HDOT) \* DTM / 2 GM = GM1 + (GDOT1 + GDOT) \* DT / 2 DST = DST1 + (XDOT1 + XDOT) \* DTH /2 VT = VT1 + (VDOT1 + VDOT) \* DT / 2 END SUB SUB LIMIT STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE ALPHA DOT AND PITCH LIMIT \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ALPHA = OLDALF + .25 \* (ACMD - OLDALF) 'Pitch dynamics CALL DRAGS ' SUBROUTINE DRAG (REQ'D FOR RATE SUB CALL) IF PLMFLG% = 0 THEN EXIT SUB OLDGM = GM PLIM% = 0 DO WHILE (PLIM% = 0) CALL RATES ' SUBROUTINE RATES X = ALPHA + OLGM + GDOT \* DT IF X > HP THEN ALPHA = .9 \* ALPHA IF X < LP THEN ALPHA = 1.1 \* ALPHA IF ALPHA > ALFLIM THEN ALPHA = ALFLIM PLIM% = 1 END IF LOOP END SUB SUB MCRBRST STATIC IF MU1 = 0 THEN MU1 = -37141! AV = 5500: H1 = 2500: G3 = 3: J1 = -700: J2 = 800: J3 = 6.5 MU2 = -20000 BV = 12000: H2 = 2000: N1 = 200: N2 = 2500: N3 = 4 WX = 5 IF ALT > 1000 THEN PRINT PRINT " DFW data not available above 1000'" PRINT " Please start at or below 1000'" END END IF END IF X = 6078 \* DST: Y = ALT: A1 = AV: A2 = BV NX1 = Y - H1: DENX1 = (Y - H1) ^ 2 + (X - A1) ^ 2 NY1 = X + J2 - A1: DENY1 = (Y + J1 - H1) ^ 2 + (X + J2 - A1) ^ 2 NX2 = Y - H2: DENX2 = (Y - H2) ^ 2 + (X - A2) ^ 2 NY2 = X + N2 - A2: DENY2 = (Y + N1 - H2) ^ 2 + (X + N2 - A2) ^ 2 NX3 = Y + H1: DENX3 = (Y + H1) ^ 2 + (X - A1) ^ 2 NY3 = X + J2 - A1: DENY3 = (Y + J1 + H1) ^ 2 + (X + J2 - A1) ^ 2 NX4 = Y + H2: DENX4 = (Y + H2) ^ 2 + (X - A2) ^ 2 NY4 = X + N2 - A2: DENY4 = (Y + N1 + H2) ^ 2 + (X + N2 - A2) ^ 2 XX = MU1 \* (-NX1 / DENX1 + NX3 / DENX3) + MU2 \* (NX2 / DENX2 - NX4 / DENX4) WX = WX + .65 \* (XX - WX) + 2 \* G3 IF DST = 0 THEN WXP = WX ZZ = MU1 \* (NY1 / DENY1 - NY3 / DENY3) \* J3 + MU2 \* (-NY2 / DENY2 + NY4 / DENY4) \* N3 WZ = WZ + .65 \* (ZZ - WZ) IF DST = 0 THEN WZP = WZ WX5 = WX4: WX4 = WX3: WX3 = WX2: WX2 = WX1: WX1 = WX WZ5 = WZ4: WZ4 = WZ3: WZ3 = WZ2: WZ2 = WZ1: WZ1 = WZ IF WCNT% < 4 THEN WXDT = (WX - WXP) / DT: WXP = WX IF WCNT% < 4 THEN WZDT = (WZ - WZP) / DT: WZP = WZ IF WCNT% > 3 THEN WXDT = (26 \* WX5 - 27 \* WX4 - 40 \* WX3 - 13 \* WX2 + 54 \* WX1) / (70 \* DT) IF WCNT% > 3 THEN WZDT = (26 \* WZ5 - 27 \* WZ4 - 40 \* WZ3 - 13 \* WZ2 + 54 \* WZ1) / (70 \* DT) IF ABS(WXDT) > 15 THEN WXDT = 15 \* SGN(WXDT) IF ABS(WZDT) > 15 THEN WZDT = 15 \* SGN(WZDT) WCNT% = WCNT% + 1 END SUB SUB MIN (DM, M2, C1, C2, C3, M) STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 'SUBROUTINE MIN\_CST BY LEAST SQUARES PARABOLA \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ALPHA = M2 + DM 'INCREMENT ALPHA CALL COST 'SUBROUTINE COST IF DM < 0 THEN C4 = CST ELSE SWAP C1, C3 C5 = CST END IF ALPHA = M2 - DM 'DECREMENT ALPHA CALL COST 'SUBROUTINE COST IF DM < 0 THEN C5 = CST ELSE C4 = CST END IF M = ABS(DM) \* (14 \* C1 + 7 \* C4 - 7 \* C5 - 14 \* C3) / (20 \* C1 - 10 \* C4 - 20 \* C2 - 10 \* C5 + 20 \* C3) END SUB SUB OPT STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 'SUBROUTINE OPTALF - DETERMINES THE ALPHA REQD FOR CMD GAMMA \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* OLDALF = ALPHA: GM1 = GM CALL ATMOS ' SUBROUTINE ATMOSPHERE CALL RATES ' SUBROUTINE RATES DM = 1 / 57.3 ' SET ALPHA INCREMENT TO 1 DEGREE C1 = 1E+20 C2 = 1E+20 C3 = 1E+20 OPTFLG% = 0 WHILE (OPTFLG% = 0) CALL COST ' SUBROUTINE COST C3 = C2: C2 = C1: C1 = CST M3 = M2: M2 = M1: M1 = ALPHA LGC% = C1 > C2 AND C3 = 1E+20 IF LGC% THEN DM = -DM ' Reverse search direction C1 = C2: C2 = CST: M1 = M2: M2 = ALPHA ALPHA =ALPHA + 2 \* DM ELSE IF C1 < C2 THEN L% = ABS(OLDALF - ALPHA) / DT > ALFRTE OR ALPHA > ALFLIM OR ALPHA < -.08 IF L% THEN OPTFLG% = 1 ALPHA = ALPHA + DM ELSE DM = DM / 2 CALL MIN(DM, M2, C1, C2, C3, M)'Fit parabola & find minimum ALPHA = M2 + M 'This is the optimum alpha OPTFLG% = 1 'Set flag to terminate END IF END IF WEND ALFLIM = ASS 'SET ALPHA LIMIT TO ALPHA STICK SHAKER SELECT CASE LAW% CASE 4 ALFLIM = ASS - .035 'LIMIT TO SS MINUS 2 DEG CASE 5, 6 ALFLIM = ASS - KF2 CASE ELSE END SELECT IF ALPHA < -.08 THEN ALPHA = -.08 IF ALPHA > ALFLIM THEN ALPHA = ALFLIM ACMD = ALPHA 'SET ALPHA COMMAND TO COMPUTED ALPHA END SUB SUB PLOT '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* '\* PLOT ROUTINE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* REM $DYNAMIC ' TWO DIMENSIONAL PLOTTER DEFINT I-L, N DIM F$(3) ' file name array DIM DTA(3, 250, 15) ' data array DIM TY$(14) ' title array (dependant variable) TITLE$ = "HONEYWELL WINDSHEAR SIMULATION" ' main title TX$ = "Time (s)" ' X title TY$(1) = "Altitude ft " TY$(2) = "Alt Rate fpm " TY$(3) = "T A S kts " TY$(4) = "Alpha deg " TY$(5) = "Gamma deg " TY$(6) = "Pitch deg " TY$(7) = "G\_ref deg " TY$(8) = "Hz Shear kps " TY$(9) = "Vt Wind fps " TY$(10) = "Vt rate kps " TY$(11) = "W/S Flag " NV = 12 CLS LOCATE 3, 15: PRINT "Enter the names of the data files you wish to plot." FOR NC = 1 TO 3 LOCATE 6 + 2 \* NC, 25 ' input PRINT "FILENAME "; NC; " "; ' filenames INPUT ; F$(NC) ' containing IF F$(NC) = " " THEN EXIT FOR ' data NEXT NC NC = NC - 1 ' number of curves to plot LOCATE 20, 15: PRINT "Reading from disk........." FOR I = 1 TO NC CLOSE OPEN "I", #1, F$(I) ' open file for input NP = 0 DO NP = NP + 1 ' number of points FOR J = 1 TO NV INPUT #1, DTA(I, NP, J) ' read data NEXT J LOOP UNTIL EOF(1) CLOSE NEXT I DO ' display all selected parameters DO ' prompt user until a valid parameter is selected 100 CLS LOCATE 3, 20: PRINT "Select the parameter you wish to plot." FOR I = 1 TO NV - 1 LOCATE 4 + I, 30: PRINT TY$(I); " = "; I NEXT I LOCATE 21, 30: INPUT "parameter number (0 to exit)"; PARAM% IF PARAM% = 0 THEN CLS EXIT SUB ' return to calling program END IF LOOP UNTIL 1 <= PARAM% AND PARAM% <= 14 'end of select loop PARAM% = PARAM% + 1 DX = 5 ' x axis grid increment GOSUB 400 ' find maximum x and y values IF PLTFLG% = 1 THEN PRINT "No information to plot...." PRINT "Press any key to continue..." DO: LOOP WHILE INKEY$ = "" GOTO 100 END IF GOSUB 600 ' grid and titles FOR I = 1 TO NC GOSUB 1110 ' plot graph NEXT I DO LOOP WHILE INKEY$ = "" CLS : SCREEN 0 LOOP '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* 400 '\* MAX SUBROUTINE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' MAXX = DTA(1, 1, 1) MAXY = DTA(1, 1, PARAM%) MINY = DTA(1, 1, PARAM%) FOR I = 1 TO NC FOR J = 1 TO NP IF DTA(I, J, 1) > MAXX THEN MAXX = DTA(I, J, 1) IF DTA(I, J, PARAM%) > MAXY THEN MAXY = DTA(I, J, PARAM%) IF DTA(I, J, PARAM%) < MINY THEN MINY = DTA(I, J, PARAM%) NEXT J NEXT I PLTFLG% = 0 DY = (MAXY - MINY) / 15 IF DY = 0 THEN PLTFLG% = 1 DY = 5 END IF MAG = 10 ^ (INT(LOG(DY) / LOG(10))): DY = DY / MAG IF DY <= 5 THEN DY = 5 ELSE DY = 10 END IF DY = DY \* MAG IF INT(MAXX / DX) < > MAXX / DX THEN MAXX = INT(MAXX / DX + 1) \* DX IF INT(MAXY / DY) < > MAXY / DY THEN MAXY = INT(MAXY / DY + 1) \* DY IF INT(MINY / DY) < > MINY / DY THEN MINY = INT(MINY / DY) \* DY NUMX = MAXX / DX NUMY = (MAXY - MINY) / DY RETURN 600 '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* '\* GRID AND TITLES \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' CLS SCREEN 2 ' 640\*200 monochrome graphics KEY OFF ' FOR J = 0 TO NUMX Z = J \* 580 / NUMX + 59 LINE (Z, 10) - (Z, 170) ' vertical grid line Z = J \* 71 / NUMX + 7 a = DX \* J IF a < > 0 THEN ' adjustment for D = INT(LOG(a) / LOG(10)) + 1 ' large numbers IF D > 1 THEN Z = Z - D + 1 END IF LOCATE 23, Z PRINT a; NEXT J FOR J = 0 TO NUMY Z = J \* 160 / NUMY + 10 LINE (60, Z) - (640, Z) ' horizontal grid line Z = 22 - J \* 20 / NUMY LOCATE Z, 2 Z = DY \* J + MINY AZ = ABS(Z) IF INT(Z) = Z THEN G$ = "######" ELSEIF AZ < .1 THEN G$ = "#.####" ELSEIF AZ >= .1 AND AZ < 1 THEN G$ = "##.###" ELSEIF AZ >= 1 AND AZ < 10 THEN G$ = "###.##" ELSEIF AZ >= 10 AND AZ < 100 THEN G$ = "####.#" ELSE G$ = "######" END IF PRINT USING G$; Z; NEXT J Z = (80 - LEN(TITLE$)) / 2 + 2 LOCATE 1, Z: PRINT TITLE$ ' print main title LOCATE 24, 36: PRINT TX$; ' X axis title LOCATE 8, 1 ' Y FOR J = 1 TO LEN(TY$(PARAM% - 1)) ' axis PRINT MID$(TY$(PARAM% - 1), J, 1) ' title NEXT J LOCATE 25, 10: PRINT "1"; ' curve LINE (90, 195) - (130, 195) LOCATE 25, 20: PRINT "2"; ' labels FOR J = 0 TO 40 STEP 8 XX = 170 + J PSET (XX, 195) CIRCLE (XX + 80, 195) , 2 NEXT J LOCATE 25, 30: PRINT "3"; RETURN '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* '\* PLOTTING ROUTINE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' 1110 FOR J = 1 TO NP XX = 580 \* DTA(I, J, 1) / MAXX + 60' calculate pixel X position YY = 170 - 160 \* (DTA(I, J, PARAM%) - MINY) / (MAXY - MINY) IF J = 1 THEN GOTO 1170 IF I = 1 THEN LINE (XXOLD, YYOLD) - (XX, YY) ' line 1170 1170 XXOLD = XX: YYOLD = YY IF I = 2 THEN PSET (XX, YY) ' point IF I = 3 THEN CIRCLE (XX, YY), 2 ' circle NEXT J RETURN END SUB REM $STATIC DEFSNG I-L, N SUB PRINTS '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE PRINT TO SCREEN AND FILE \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ACMDG = 57.3 \* ACMD ALF = 57.3 \* ALPHA GAM = 57.3 \* GM PITCH = ALF + GAM WZX = 1.689 \* WZ IF NOSAVE = 0 THEN PRINT #2, SEC, ALT, HDOT, VT, ALF, GAM, PITCH, GREFF, WXDT, WZX, VDOT, WSALERT% FMT1$ = "###.## #### ##### ### ###.# ###.# ###.# ##.# ###.# ###.# ###.# #" PRINT USING FMT1$; SEC, ALT, HDOT, VT, ALF, GAM, PITCH, GREFF, WXDT, WZX, VDOT, WSALERT% END SUB SUB RATES STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE RATES \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* SNGM = SIN(GM): CSGM = COS(GM): SNAL = SIN(ALPHA): CSAL = COS(ALPHA) VDOT = G \* ((THRST \* CSAL - DRAG) / WG - SNGM) - WXDT \* CSGM - WZDT \* SNGM GDOT = G \* ((LIFT + THRST \* SNAL) / WG - CSGM) + WXDT \* SNGM - WZDT \* CSGM GDOT = GDOT / VT HDOT = 101.28 \* (VT \* SNGM + WZ) XDOT = VT \* CSGM + WX AWX = VDOT + WXDT \* CSGM + WZDT \* SNGM 'Inertial Acc. along Wind\_x axis AWZ = VT \* GDOT - WXDT \* SNGM + WZDT \* CSGN 'Inertial Acc. along Wind\_z axis AU = (AWX \* CSAL + AWZ \* SNAL) / G 'LONG. ACCEL. ->=? AZ = (AWX \* SNGM + AWZ \* CSGM) / G 'VERT. ACCEL. UP=? VG = XDOT GRND = (VT \* GM + WZ) / (VT + WX) 'Gamma w/r ground KF1 = 1 GHAT = GMIN \* (1 + WX / VT) IF WZ > -30 AND WZ < -20 THEN KF1 = 1 + .025 \* (WZ + 20) IF WZ <= -30 THEN KF1 = .75 DGAM = 57.3 \* (20 \* GDOT - (GHAT - GRND + (1 - KF1) \* WZ / 152 + 20 \* GDOT)) IF DGAM < 0 THEN KF2 = (2 + .4 \* DGAM) ELSE KF2 = 2 END IF IF KF2 < 0 THEN KF2 = 0 KF2 = KF2 / 57.3 END SUB SUB TAKEOFF STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE INTIALIZE TAKEOFF \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* IF APPFLG% = 0 THEN ALPHA = .12 WHILE (LIFT <= WG) CALL DRAGS ALPHA = ALPHA + .01 WEND GM = (THRST - DRAG) / WG 'COMPUTE POTENTIAL GAMMA ELSE GM = -3 / 57.3 ALPHA = 2 / 57.3 CALL DRAGS TFCT = 1 CALL THRUST T = DRAG - .052 \* WG IF T < 0 THEN T = .2 \* THRST TFCT = T / THRST THRST = T END IF GMO = GM CALL RATES END SUB SUB THRUST STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE EPR/THRUST \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' TAKE-OFF THRUST FOR JT8D-17 ENGINES VE = 1.668 \* VT R00 = 14688.74: R01 = -.65187546#: R02 = 6.7371E-05 R10 = -13.9295: R11 = .000751143#: R12 = -1.5405E-07 R20 = .014643: R21 = 5.3444E-07: R22 = -4.8907E-10 AA0 = (R02 \* ALT + R01) \* ALT + R00 AA1 = (R12 \* ALT + R11) \* ALT + R10 AA2 = (R22 \* ALT + R21) \* ALT + R20 THRST = 2 \* ((AA2 \* VT + AA1) \* VT + AA0) 'Temp. = 100 F IF APPFLG% = 1 THEN IF LC% = 1 AND TFCT < 1 THEN GMO = .136 TSPL = 5.5 'Engine Spool Up Time TFCT = TFCT + DT / TSPL END IF IF TFCT > 1 THEN TFCT = 1 ELSE TFCT = 1 END IF THRST = TFCT \* THRST '' THRST = 2 \* (((2.64159E-05 \* VT + 5.110896E-03) \* VT - 12.56476) \* VT + 15550) END SUB SUB VSHAKER STATIC '------------------------------------ COMPUTATION OF Vss AND V2------------------------- V2 = 145 VTO = V2 + 10' SETS INITAL SPEED EQUAL TO V2 + 10 SELECT CASE FLPS% CASE 10 IF VTO < 150 THEN VTO = 150 ' TAKEOFF CASE 18 IF VTO < 148 THEN VTO = 148 ' FLAP CASE 22 IF VTO < 147 THEN VTO = 147 ' SETTINGS CASE 33 VTO = 63.11225 + .222468 \* WG / 1000 ' APPROACH CASE 42 ' FLAP VTO = 62.67386 + .21744 \* WG / 1000 ' SETTINGS CASE ELSE END SELECT END SUB SUB WINDS STATIC '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' SUBROUTINE WINDS \* '\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\*\* ' IF TDX > 0 THEN T1 = 4 T2 = TSH T3 = T1 + T2 T4 = -4 T5 = T3 + TDX T6 = T5 - T4 B1 = 3 \* WXDTO / T1 ^ 2 A1 = -2 \* B1 / (3 \* T1) B2 = 3 \* WXDTO / T4 ^ 2 A2 = -2 \* B2 / (3 \* T4) IF SEC > T2 AND SEC < = T3 THEN X = SEC - T2 WXDT = (A1 \* X + B1) \* X \* X END IF IF SEC > T5 AND SEC < = T6 THEN X = SEC - T6 WXDT = (A2 \* X + B2) \* X \* X END IF IF SEC > T6 THEN WXDT = 0 WX = WX + WXDT \* DT END IF IF TDZ > 0 THEN T1 = 4 T2 = TSV T3 = T1 + T2 T4 = - 4 T5 = T3 + TDZ T6 = T5 - T4 B1 = 3 \* WZO / T1 ^ 2 A1 = -2 \* B1 / (3 \* T1) B2 = 3 \* WZO / T4 ^ 2 A2 = -2 \* B2 / (3 \* T4) IF SEC > T2 AND SEC <= T3 THEN X = SEC - T2 WZ = (A1 \* X + B1) \* X \* X WZC = WZ END IF IF SEC > T5 AND SEC <= T6 THEN X = SEC - T6 WZ = (A2 \* X + B2) \* X \* X WZC = WZ END IF KALT = (-.0000011 \* ALT + .00212) \* ALT - .0251 IF KALT < 0 OR ALT <= 0 THEN KALT = 0 KALT = 1 WZ = KALT \* WZC IF SEC > T6 THEN WZ = 0 WZDT = (WZ - WZ1) / DT WZ1 = WZ END IF IF DFW = 1 THEN CALL MCRBRST 'DALLAS Model END SUB [Amdt ETSO/16]