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<html>
<head>
<title>Canvas tutorial</title>
<script type="text/javascript">
function draw(){
var canvas = document.getElementById('tutorial');
if(canvas.getContext){
var ctx = canvas.getContext('2d');
}
}
</script>
<style type="text/css">
canvas { border: 1px solid black; }
</style>
</head>
<body onload="draw();">
<canvas id="tutorial" width="2000" height="150"></canvas>
</body>
<script>
var canvas = document.getElementById("tutorial");
var ctx = canvas.getContext("2d");
////////////////////////////////////////////////////////////////////
//Funktion
elemmult = function(array1, array2)
{
var l = array1.length;
if(l>=1){
var res = [];
for(var i=0;i<=l-1;i++)
{
res[i] = array1[i]*array2[i];
}
}
else {
var res = array1*array2;
}
return res;
}
//läuft
sign = function(x)
{
if (x<0) { return -1}
else if (x==0) { return 0}
else { return 1}
}
//läuft
min = function(a,b)
{
if (a<=b){
return a;
}
else {
return b;
}
}
//läuft
max = function(a,b)
{
if (a>=b){
return a;
}
else {
return b;
}
}
zeros = function(i,j)
{
var zeros=[];
for(i;i<=j;i++)
{
zeros = [zeros,0];
}
return zeros;
}
//läuft
elemdiv = function(array1, array2)
{
var l = array1.length;
var res = [];
for(var i=0;i<=l-1;i++)
{
res[i] = array1[i]/array2[i];
}
return res;
}
//läuft
elemqu = function(array1)
{
var l = array1.length;
var res = [];
for(var i=0;i<=l-1;i++)
{
res[i] = array1[i]*array1[i];
}
return res;
}
//läuft
find = function(x,y) //nur fuer sortierte Vektoren
{
var n = x.length;
var ind = [];
for (var i = 0; x[i] <= y; i++)
{
ind[i] = i;
}
return ind;
}
//läuft
sort = function(x)
{
var n = x.length;
var k = [];
for (var l = 0; l < n; l++)
{
k[l]=l;
}
for (var i = n-1; i>=0; i--)
{
for(var j = 1; j<=i; j++)
{
if(x[j-1]>x[j])
{
var temp = x[j-1];
x[j-1] = x[j];
x[j] = temp;
var temp2 = j-1;
k[j-1] = j;
k[j] = temp2;
}
}
}
return x;
}
//läuft
interp1 = function(x,y,xi) //xi muss ein Skalar sein!!
{
x = sort(x); // sortiere x
var r1 = find(x,xi); // Vektor der die Indizes speichert, die kleinergleich xi sind
var n1 = r1.length; // Laenge des Indizevektors
var r = r1[n1-1]; // maximaler Eintrag des Indizevektors
var n = x.length; //
if (xi == x[n])
{
r = x.length-1;
}
/*if (isempty(r)) // Wenn r leer ist, gibt es ein Problem!
{
yi = NaN;
return
}*/
if ((r>0) && (r<x.length))
{
var u = (xi-x[r-1])/(x[r]-x[r-1]);
yi=y[r-1]+(y[r]-y[r-1])*u;
}
else
{
yi = NaN;
}
/* if ((min(size(yi))==1) & (prod(siz)>1)) // prod(siz) ist bei uns 1!! Sonst Fehler!!
{
yi = reshape(yi,siz);
}*/
return yi;
}
var Trimhist, x, u, V;
/*// Supporting Calculations for Geometric, Inertial, and Aerodynamic
// Properties of BizJet B
// June 12, 2015
// Copyright 2006-2015 by ROBERT F. STENGEL. All rights reserved.
clear
disp('==============================================')
disp('Geometric and Inertial Properties for BizJet B')
disp('==============================================')
Date = date
*/
// Comparable Bizjet Weight Distribution, lb, based on empty weight less engine weight.
// (from Stanford AA241 Notes, Ilan Kroo)
var GEAR=0;
var SPOIL=0;
var WingSys = 1020;
var TailSys = 288;
var BodySys = 930;
var GearSys = 425;
var NacelleSys = 241;
var PropSys = 340;
var ControlSys = 196;
var InstrSys = 76;
var HydrPneuSys = 94;
var ElecSys = 361;
var AvionSys = 321;
var FurnEquipSys = 794;
var ACSys = 188;
var AntiIceSys = 101;
var LoadHandSys = 2;
var EmptyStruc = (WingSys+TailSys+BodySys+GearSys+PropSys+ControlSys+InstrSys+HydrPneuSys+ElecSys+AvionSys+FurnEquipSys+ACSys+AntiIceSys+LoadHandSys); // Less nacelles and engines
var EngWgt = 1002;
var EmptyWgt = (EmptyStruc+EngWgt); // Less nacelles
var EmptyStrucWgt = EmptyStruc/EmptyWgt;
var WingRatio = (WingSys+GearSys+HydrPneuSys+AntiIceSys)/EmptyStruc;
var HTRatio = 0.75*(TailSys)/EmptyStruc;
var VTRatio = 0.25*(TailSys)/EmptyStruc;
var FusRatio = (BodySys+PropSys+ControlSys+InstrSys+ElecSys+AvionSys+FurnEquipSys+ACSys+LoadHandSys)/EmptyStruc;
var Total = (WingRatio+HTRatio+VTRatio+FusRatio);
var NacelleRatio = (NacelleSys)/EngWgt; // Related to engine weight rather than empty structure
// BizJet B Geometric Properties
// x measurements from nose along centerline, negative aft
// y & z measurements from centerline, positive right and down
var S = 19.51 // Reference Area, m^2
var taperw = 0.5333 // Wing Taper Ratio
var cBar = 1.56 // Mean Aerodynamic Chord, m
var sweep = 11*0.01745329 // Wing L.E. sweep angle, rad
var xcp = -5.7473 // Wing center of pressure, m
var GamWing = 3*0.01745329 // Dihedral angle of the wing, rad
// BizJet B Mass and Inertial Properties
var m = 3000 // Total mass for simulation (USER-specified), kg
var mEmpty = 2522 // Gross empty mass, kg
var mEng = (1+NacelleRatio)*240 // Mass of engines + nacelles, kg
var mStruc = mEmpty - mEng // Empty structural mass (less engines + nacelles), kg
var mWing = WingRatio*mStruc // Wing mass, kg
var mHT = HTRatio*mStruc // Horizontal tail mass, kg
var mVT = VTRatio*mStruc // Vertical tail mass, kg
var mFus = FusRatio*mStruc // Empty fuselage mass, kg
var mPay = 0.5*(m - mEmpty) // Payload mass, kg
var mFuel = 0.5*(m - mEmpty) // Fuel mass, kg
var xcm = xcp - 0.45*cBar// Center of mass from nose (USER-specified), m
var lWing = xcm - xcp // Horizontal distance between c.m and wing c.p., m
var zWing = -0.557 // Vertical distance between c.m and wing c.p., m
var b = 13.16 // Wing Span, m
var lenFus = 10.72 // Fuselage length, m
var xcpFus = -0.25*lenFus // Linear-regime fuselage center of pressure, m
var xcpFusN = -0.5*lenFus // Newtonian-regime fuselage center of pressure, m
var lFus = xcm - xcpFus; // Linear fuselage lift cp offset,m
var lFusN = xcm - xcpFusN; // Newtonian fuselage lift cp offset, m
var dFus = 1.555 // Fuselage diameter, m
var Sfus = (Math.PI/4)*lenFus*dFus // Plan or side area of fuselage, m
var Sbase = (Math.PI/4)*Math.pow(dFus,2) // Fuselage cross-sectional area, m^2
var bHT = 5.3; // Horizontal tail span, m
var cHT = 1.1; // Mean horizontal tail chord, m
var swpHT = 38*0.0174533; // Horizontal tail sweep, rad
var SHT = bHT*cHT // Horizontal tail area, m^2
var xHT = -11.3426; // Linear xcp of horizontal tail
var lHT = xcm - xHT; // Horizontal tail length, m
var zHT = 1.5; // zcp of horizontal tail, m
var xVT = -10.044; // Linear xcp of vertical tail, m
var lVT = xcm - xVT; // Vertical tail length, m
var bVT = 2.409; // Vertical tail span, m
var cVT = 1.88; // Mean vertical tail chord, m
var swpVT = 50*0.0174533; // Vertical tail sweep, rad
var SVT = bVT*cVT; // Vertical tail area, m^2
var zVT = 1.5; // zcp of vertical tail, m
var xEng = -7.735; // xcm of engine, m
var lEng = xcm - xEng; // Engine length, m
var yEng = 1.1325; // ycm of engine, m
var zEng = 0.4038; // zcm of engine, m
var xNac = -7.7252; // xcp of engine, m
var lNac = xcm - xNac; // Nacelle length, m
var bNac = 2.5; // Nacelle span, m
var cNac = 1.82; // Nacellechord, m
var dNac = 0.73; // Nacelle diameter, m
var SbaseNac = 0.25*Math.PI*Math.pow(dNac,2); // Nacelle base area, m^2
var Snac = bNac*cNac; // Nacelle plan area, m^2
var xVent = -9.94; // xcp of ventral fin, m
var lVent = xcm - xVent; // Ventral fin length, m
var zVent = 0; // zcp of ventral fin, m
var bVent = 1; // Ventral fin span, m
var cVent = 0.85; // Ventral fin chord, m
var Svent = bVent*cVent; // Ventral fin area, m^2
var swpVent = 60*0.0174533; // Ventral sweep angle, rad
var Splan = S + Sfus + Snac + SHT + Svent // Plan area of airplane
var Swet = 2*(Splan + Sfus + SVT) // Wetted area of airplane
var ARwing = (b*b) / S // Wing aspect ratio
var ARHT = (bHT*bHT) / SHT // Horizontal tail aspect ratio
var ARnac = (bNac*bNac) / Snac // Engine nacelle aspect ratio
var ARvent = (bVent*bVent)/ Svent // Ventral fin aspect ratio
var ARVT = (bVT*bVT) / SVT // Vertical tail aspect ratio
// Moments and Product of Inertia
var Ixx = (1/12)*((mWing+mFuel)*b*b + mHT*Math.pow(bHT,2) + mVT*Math.pow(bVT,2)) + (0.25*(mFus+mPay)*Math.pow(dFus,2) + mEng*Math.pow(yEng,2) + mVT*Math.pow(zVT,2));
var Iyy = (1/12)*((mFus+mPay)*Math.pow(lenFus,2) + (mWing+mFuel)*Math.pow(cBar,2) + mVT*Math.pow(cHT,2)) + (mEng*Math.pow(lEng,2) + mHT*Math.pow(lHT,2) + mVT*Math.pow(lHT,2));
var Izz = (1/12)*((mFus+mPay)*Math.pow(lenFus,2) + (mWing+mFuel)*Math.pow(b,2) + mHT*Math.pow(bHT,2)) + (mEng*Math.pow(lEng,2) + mHT*Math.pow(lHT,2) + mVT*Math.pow(lVT,2));
var Ixz = mHT*lHT*zHT + mVT*lVT*zVT + mEng*lEng*zEng
var dEmax = 20 * 0.01745329 // Maximum Elevator Deflection is ±20 deg
var dAmax = 35 * 0.01745329 // Maximum Aileron Deflection is ±35 deg
var dRmax = 35 * 0.01745329 // Maximum Rudder Deflection is ±35 deg
// BizJet B Aero Properties
var AlphaTable = [-10, -8, -6, -4, -2, 0, 2, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90];
var Points = AlphaTable.length;
var AlphaRad = 0.0174533*AlphaTable;
var SinAlpha = Math.sin(AlphaRad);
var CosAlpha = Math.cos(AlphaRad);
// Newtonian Coefficients
var CN = 2*(Splan/S)*SinAlpha*SinAlpha;
CN = elemmult(CN,sign(AlphaRad));
var CDNewt = 2*(Splan/S)*Math.abs(elemmult(SinAlpha*SinAlpha,SinAlpha));
var CLNewt = elemmult(CN,CosAlpha);
var cpNewt = (S*lWing + Sfus*lFusN + SHT*lHT + Svent*lVent + Snac*lNac)/ (S + Sfus + SHT + Svent + Snac);
// Longitudinal Aerodynamics
// =========================
// Lift
var CLaWing = Math.PI*ARwing / (1 + Math.sqrt(1 + Math.pow((0.5*ARwing/Math.cos(sweep)),2)));
var deda = 0; // T-tail
var CLaHT = (1 - deda)*(Math.PI*ARHT / (1 + Math.sqrt(1 + Math.pow((0.5*ARHT/Math.cos(swpHT)),2))))*SHT / S;
var CLaFus = 2*Sbase / S;
var CLaNac = 2*SbaseNac / S;
var CLaVent = (Math.PI*ARvent / (1 + Math.sqrt(1 + Math.pow((0.5*ARvent/Math.cos(swpVent)),2))))*Svent / S;
var CLaTot = CLaWing + CLaHT + CLaFus + CLaNac + CLaVent;
// Assume CL is linear to Alpha = 10 deg = 0.1745 rad
var CL10 = CLaTot*0.174533;
// Assume CL is symmetrically quadratic about CLmax
var CLmax = 1.35;
var delAlph = 4*0.0174533; // Stall occurs at 14 deg
var CLstatic = zeros(0,39);
for (var i = 1; i <= 11; i++)
{
CLstatic[i] = CLaTot*AlphaRad[i];
}
var kStall = (CLmax - CL10)/Math.pow(delAlph,2);
for (var i = 12; i <= 21; i++)
{
CLstatic[i] = CLmax - kStall*elemmult((AlphaRad[15] - AlphaRad[i]),(AlphaRad[15] - AlphaRad[i]));
}
CLstatic[22] = 0.73;
CLstatic[23] = 0.73;
CLstatic[24] = 0.74;
CLstatic[25] = 0.76;
CLstatic[26] = 0.78;
for (var i = 27; i <= 39; i++)
{
CLstatic[i] = CN[i]*CosAlpha[i];
}
var CLTable = CLstatic;
// Drag
var Re = 1.225*100*lenFus / 1.725e-5; // Reynolds number at 100 m/s
var Cf = 0.46*Math.pow((Math.log10(Re)),-2.58); // Flat plate friction coefficient
var CDf = Cf*Swet / S;
var CDbase = 0.12*Sbase / S; // Base pressure drag
var CDo = CDf + CDbase;
var OEF = 1.78*(1 - 0.045*Math.pow(ARwing,0.68)) - 0.64; // Oswald Efficiency factor, Raymer (straight wing)
var CDstatic = zeros(0,39);
for (var i = 1; i <= 10; i++)
{
CDstatic[i] = CDo + elemmult(CLstatic[i],CLstatic[i]) / (OEF*Math.PI*ARwing);
}
CDstatic[11] = CDstatic[10]*1.15;
CDstatic[12] = CDstatic[11]*1.15;
CDstatic[13] = CDstatic[12]*1.15;
CDstatic[14] = CDstatic[13]*1.15;
CDstatic[15] = CDstatic[14]*1.1;
CDstatic[16] = CDstatic[15]*1.1;
CDstatic[17] = CDstatic[16]*1.1;
CDstatic[18] = CDstatic[17]*1.1;
CDstatic[19] = CDstatic[18]*1.1;
CDstatic[20] = CDstatic[19]*1.1;
CDstatic[21] = CDstatic[20]*1.1;
CDstatic[22] = CDstatic[21]*1.1;
CDstatic[23] = CDstatic[22]*1.1;
CDstatic[24] = CDstatic[23]*1.1;
CDstatic[25] = CDstatic[24]*1.1;
CDstatic[26] = CDstatic[25]*1.1;
for (var i = 26; i <= 39; i++)
{
CDstatic[i] = 2*(Splan/S)*Math.abs(SinAlpha[i]*SinAlpha[i]*SinAlpha[i]);
}
var CDNewt = 2*(Splan/S)*Math.abs(elemmult(elemmult(SinAlpha,SinAlpha),SinAlpha));
var CDTable = CDstatic;
// Pitching Moment (c.m. @ wing c.p.)
var CmStatic = zeros(0,39);
var SM = (CLaWing*lWing + CLaFus*lFus + CLaHT*lHT + CLaNac*lNac + CLaVent*lVent) /(cBar*(CLaWing + CLaFus + CLaHT + CLaNac + CLaVent)); // Static Margin at Alpha = 0 deg
for (var i = 1; i <= 21; i++)
{
CmStatic[i] = -(elemmult(CLstatic[i],Math.cos(AlphaRad[i])) + elemmult(CDstatic[i],Math.sin(AlphaRad[i])))*SM;
}
CmStatic[22] = CmStatic[21]*0.9;
CmStatic[23] = CmStatic[22]*0.9;
CmStatic[24] = CmStatic[23]*0.9;
CmStatic[25] = CmStatic[24]*0.9;
CmStatic[26] = 0.9*CmStatic[25] - 0.1*CN[26]*Math.sign(AlphaRad[26])*cpNewt/cBar;
CmStatic[27] = 0.4*CmStatic[26] - 0.6*CN[27]*Math.sign(AlphaRad[27])*cpNewt/cBar;
CmStatic[28] = 0.1*CmStatic[27] - 0.9*CN[28]*Math.sign(AlphaRad[28])*cpNewt/cBar;
var CN = 2*(Splan/S)*elemmult(SinAlpha,SinAlpha);
for (var i = 29; i <= 39; i++)
{
CmStatic[i] = -CN[i]*cpNewt/cBar;
}
var CmTable = CmStatic;
// CmdETable & CLdEo, Elevator Effect
var tauDE = 0.32; // Geometric elevator chord/horizontal tail chord
var tauCO = 0.68; // Elevator Carryover effect
var Sigmoid = [];
for (var i = 0; i <= 4; i++)
{
Sigmoid[i] = tauCO;
}
for (var i = 5; i <= 38; i++)
{
Sigmoid[i] = tauDE + elemdiv((tauCO - tauDE), (1 + Math.exp(-15.*(AlphaRad[26] - AlphaRad[i]))));
}
var CmdETable = zeros(0,38);
var CLdETable = zeros(0,38);
var CLdEo = tauCO*CLaHT; // CLdE at Alpha = 0
var CmdEo = -tauCO*(lHT/cBar)*CLaHT; // CmdE at Alpha = 0
for (var i = 0; i <= 38; i++)
{
CmdETable[i] = elemmult((CmdEo*Sigmoid),Math.cos(AlphaRad[i])); // Elevator effect on moment, per rad
}
for (var i = 0; i <= 38; i++)
{
CLdETable[i] = elemmult((CLdEo*Sigmoid),Math.cos(AlphaRad[i])); // Elevator effect on lift, per rad
}
// Longitudinal Rotary & Unsteady Derivatives
var CLqHat = 2*CLaHT*lHT/cBar;
var CmqHat = -CLqHat*lHT/cBar;
// Lateral-Directional Aerodynamics
// ================================
// CYBetaTable, Side Force Sensitivity to Sideslip Angle
var EndPlate = 1.1; // End-plate effect of T-tail
var CYBetaVT = -EndPlate*(Math.PI*ARVT / (1 + Math.sqrt(1 + Math.pow((0.5*ARVT/Math.cos(swpVT)),2))))*SVT / S;
var CYBetaFus = -2*Sbase / S;
var CDoWing = 0.005;
var CYBetaWing = -CDoWing - (Math.pow(GamWing,2))*Math.PI*ARwing / (1 + Math.sqrt(1 + Math.pow(ARwing,2)));
var CYBetaVent = -0.4*CLaVent;
var CYBetao = CYBetaVT + CYBetaFus + CYBetaWing + CYBetaVent;
var CYBetaTable = CYBetao*Math.cos(AlphaRad);
// ClBetaTable, Roll Moment Sensitivity to Sideslip Angle
var ClBetaWing = -((1 + 2*taperw)/(6*(1 + taperw)))*(GamWing*CLaWing + (elemmult(CLTable,Math.tan(sweep))));
var ClBetaWF = 1.2*Math.sqrt(ARwing)*(2*zWing*dFus/Math.pow(b,2));
var ClBetaVT = -zVT*CYBetaVT/b;
var ClBetao = (ClBetaWing + ClBetaWF + ClBetaVT);
var ClBetaTable = elemmult(ClBetao,Math.cos(AlphaRad));
// CnBetaTable, Yaw Moment Sensitivity to Sideslip Angle
var CnBetaWing = 0.075*CLTable*GamWing;
var CnBetaFus = CLaFus*lFusN / b;
var CnBetaVT = -CYBetaVT*lVT / b;
var CnBetaVent = -CYBetaVent*lVent / b;
var CnBetaTable = elemmult((CnBetaWing + CnBetaFus + CnBetaVT),Math.cos(AlphaRad));
// CldATable, Roll Moment Sensitivity to Aileron Deflection
var tauDA = 0.25;
var kDA = 0.38;
var CldAo = tauDA*(CLaWing/(1 + taperw))*((1 - Math.pow(kDA,2))/3 - (1 - Math.pow(kDA,3))*(1 - taperw)/3);
var CldATable = CldAo*Math.cos(AlphaRad);
var CYdAo = 0; // Side force due to aileron, rad
// CndATable, Yaw Moment Sensitivity to Aileron Deflection; Cessna 510 has an Aileron-Rudder Interconnect; assume CndA = 0
var CndATable = zeros(0,39);
// CldRTable, Roll Moment Sensitivity to Rudder Deflection
var tauDR = 0.5; // Geometric Rudder chord/horizontal tail chord
var tauCOR = 0.8; // Rudder Carryover effect
var CldRo = tauCOR*zVT*CYBetaVT / b;
var CldRTable = CldRo*Math.cos(AlphaRad);
// CndRTable, Yaw Moment Sensitivity to Rudder Deflection
var CndRo = -tauCOR*CnBetaVT;
var CndRTable = CndRo*Math.cos(AlphaRad);
// Lateral-Directional Rotary & Unsteady Derivatives
var CYrHat = -2*CYBetaVT*lVT/b;
var ClpHato = -(CLaWing + CLaHT*(SHT/S) - CYBetaVT*(SVT/S))*((1 + 3*taperw)/(1 + taperw))/12;
var ClpHatTable = ClpHato*Math.cos(AlphaRad);
var ClrHato = -(CLaWing + CLaHT*(SHT/S) - CYBetaVT*(SVT/S))*(1 + 3 * taperw)/(12 * (1 + taperw));
var ClrHatTable = ClrHato*Math.cos(AlphaRad);
var CnpHatTable = elemmult((- CLTable*((1 + 3*taperw)/(1 + taperw))/12), Math.cos(AlphaRad));
var CnrHatVT = -2*CnBetaVT*(lVT/b);
var CnrHatWing = -0.103*elemmult(CLTable,CLTable) - 0.4*CDoWing; // (from Seckel)
var CnrHato = CnrHatVT + CnrHatWing;
var CnrHatTable = elemmult(CnrHato, Math.cos(AlphaRad));
//läuft
Atmos = function(geomAlt)
{
/* 1976 U.S. Standard Atmosphere Interpolation for FLIGHT
// June 12, 2015
// ===============================================================
// Copyright 2006-15 by ROBERT F. STENGEL. All rights reserved.
// Note: Function does not extrapolate outside altitude range
// Input: Geometric Altitude, m (positive up)
// Output: Air Density, kg/m^3
// Air Pressure, N/m^2
// Air Temperature, K
// Speed of Sound, m/s
//Values Tabulated by Geometric Altitude*/
var Z = [-1000,0,2500,5000,10000,11100,15000,20000,47400,51000];
var H = [-1000,0,2499,4996,9984,11081,14965,19937,47049,50594];
var ppo = [1,1,0.737,0.533,0.262,0.221,0.12,0.055,0.0011,0.0007];
var rro = [1,1,0.781,0.601,0.338,0.293,0.159,0.073,0.0011,0.0007];
var T = [288.15,288.15,271.906,255.676,223.252,216.65,216.65,216.65,270.65,270.65];
var a = [340.294,340.294,330.563,320.545,299.532,295.069,295.069,295.069,329.799,329.799];
var R = 6367435; // Mean radius of the earth, m
var Dens = 1.225; // Air density at sea level, Kg/m^3
var Pres = 101300; // Air pressure at sea level, N/m^2
// Geopotential Altitude, m
var geopAlt = R * geomAlt / (R + geomAlt);
// Linear Interpolation in Geopotential Altitude for Temperature and Speed of Sound
var temp = interp1(Z,T,geopAlt);
var soundSpeed = interp1(Z,a,geopAlt);
// Exponential Interpolation in Geometric Altitude for Air Density and Pressure
var betap, betar, airDens, airPres;
for(k=1;k<=9;k++)
{
if (geomAlt <= Z[k])
{
betap = Math.log(ppo[k] / ppo[k-1]) / (Z[k] - Z[k-1]);
betar = Math.log(rro[k] / rro[k-1]) / (Z[k] - Z[k-1]);
airPres = Pres * ppo[k-1] * Math.exp(betap * (geomAlt - Z[k-1]));
airDens = Dens * rro[k-1] * Math.exp(betar * (geomAlt - Z[k-1]));
break;
}
}
var atmos = [airDens,airPres,temp,soundSpeed];
return atmos;
}
//läuft aber Werte noch überprüfen
AeroModelMach = function(x,u,Mach,alphar,betar,V)
{
//Typical Mass and Inertial Properties
var m = 4536; // Mass, kg
var Ixx = 35926.5; // Roll Moment of Inertia, kg-m^2
var Iyy = 33940.7; // Pitch Moment of Inertia, kg-m^2
var Izz = 67085.5; // Yaw Moment of Inertia, kg-m^2
var Ixz = 3418.17; // Nose-high(low) Product of Inertia, kg-m^2
//Geometric Properties
var cBar=2.14; // Mean Aerodynamic Chord, m
var b=10.4; // Wing Span, m
var S=21.5; // Reference Area, m^2
var ARw=5.02; // Wing Aspect Ratio
var taperw=0.507; // Wing Taper Ratio
var sweepw=13 * 0.01745329; // Wing 1/4-chord sweep angle, rad
var ARh=4; // Horizontal Tail Aspect Ratio
var sweeph=25 * 0.01745329; // Horiz Tail 1/4-chord sweep angle, rad
var ARv=0.64; // Vertical Tail Aspect Ratio
var sweepv=40 * 0.01745329; // Vert Tail 1/4-chord sweep angle, rad
var lvt=4.72; // Vert Tail Length, m
//Thrust Properties
var StaticThrust = 26243.2; // Static Thrust @ Sea Level, N
//Current Thrust
var atmos = [];
atmos=Atmos(-x[5]);
var airDens = atmos[0];
var airPres = atmos[1];
var temp = atmos[2];
var soundSpeed = atmos[3];
var Thrust=u[3] * StaticThrust * Math.pow((airDens / 1.225),0.7)* (1 - Math.exp((-x[5] - 17000) / 2000)); // Thrust at Altitude, N
//Current Mach Effects, normalized to Test Condition B (Mach = 0.1734)
var PrFac=1 / (Math.sqrt(1 - Math.pow(Mach,2) * 1.015)); // Prandtl Factor
var WingMach=1 / ((1 + Math.sqrt(1 + (Math.pow((ARw/(2 * Math.cos(sweepw))),2))* (1 - Math.pow(Mach,2) * Math.cos(sweepw)))) * 0.268249); // Modified Helmbold equation
var HorizTailMach=1 / ((1 + Math.sqrt(1 + (Math.pow((ARh/(2 * Math.cos(sweeph))),2))* (1 - Math.pow(Mach,2) * Math.cos(sweeph)))) * 0.294539); // Modified Helmbold equation
var VertTailMach=1 / ((1 + Math.sqrt(1 + (Math.pow((ARv/(2 * Math.cos(sweepv))),2))* (1 - Math.pow(Mach,2) * Math.cos(sweepv)))) * 0.480338); // Modified Helmbold equation
//Current Longitudinal Characteristics
//====================================
//Lift Coefficient
var CLo=0.1095; // Zero-AoA Lift Coefficient (B)
if (GEAR >= 1)
{
CLo=CLo - 0.0192; // Gear-down correction
}
if (u[5] >= 0.65)
{
CLo=CLo + 0.5182; // 38 deg-flap correction
}
if (SPOIL >= 1)
{
CLo=CLo - 0.1897; // 42 deg-Symmetric Spoiler correction
}
var CLar=5.6575; // Lift Slope (B), per rad
if (u[5] >= 0.65)
{
CLar=CLar - 0.0947;
}
var CLqr=4.231 * cBar / (2 * V); // Pitch-Rate Effect, per rad/s
var CLdSr=1.08; // Stabilator Effect, per rad
if (u[5] >= 0.65)
{
CLdSr=CLdSr - 0.4802; // 38 deg-flap correction
}
var CLdEr=0.5774; // Elevator Effect, per rad
if ( u[5] >= 0.65)
{
CLdEr=CLdEr - 0.2665; // 38 deg-flap correction
}
var CL=CLo + (CLar*alphar + CLqr*x[7] + CLdSr*u[6] + CLdEr*u[0])* WingMach; // Total Lift Coefficient, w/Mach Correction
//Drag Coefficient
var CDo=0.0255; // Parasite Drag Coefficient (B)
if ( GEAR >= 1)
{
CDo=CDo + 0.0191; // Gear-down correction
}
if ( u[5] >= 0.65)
{
CDo=CDo + 0.0836; // 38 deg-flap correction
}
if ( SPOIL >= 1)
{
CDo=CDo + 0.0258; // 42 deg-Symmetric Spoiler correction
}
var epsilon=0.0718; // Induced Drag Factor
if ( u[5] >= 0.65)
{
epsilon=0.079; // 38 deg-flap correction
}
var CD=CDo * PrFac + epsilon * Math.pow(CL,2); // Total Drag Coefficient, w/Mach Correction
//Pitching Moment Coefficient
var Cmo=0; // Zero-AoA Moment Coefficient (B)
if ( GEAR >= 1)
{
Cmo=Cmo + 0.0255; // Gear-down correction
}
if ( u[5] >= 0.65)
{
Cmo=Cmo - 0.058; // 38 deg-flap correction
}
if ( SPOIL >= 1)
{
Cmo=Cmo - 0.0154; // 42 deg-Symmetric Spoiler correction
}
var Cmar=-1.231; // Static Stability (B), per rad
if ( u[5] >= 0.65)
{
Cmar=Cmar + 0.0138;
}
var Cmqr = -18.8 * cBar / (2 * V); // Pitch-Rate + Alpha-Rate Effect, per rad/s
var CmdSr=-2.291; // Stabilator Effect, per rad
if ( u[5] >= 0.65)
{
CmdSr=CmdSr + 0.121; // 38 deg-flap correction
}
var CmdEr=-1.398; // Elevator Effect, per rad
if ( u[5] >= 0.65)
{
CmdEr=CmdEr + 0.149; // 38 deg-flap correction
}
var Cm=Cmo + (Cmar*alphar + Cmqr*x[7] + CmdSr*u[6] + CmdEr*u[0])* HorizTailMach; // Total Pitching Moment Coefficient, w/Mach Correction
//Current Lateral-Directional Characteristics
//===========================================
//Side-Force Coefficient
var CYBr=-0.7162; // Side-Force Slope (B), per rad
if ( u[5] >= 0.65)
{
CYBr=CYBr + 0.0826;
}
var CYdAr=-0.00699; // Aileron Effect, per rad
var CYdRr=0.1574; // Rudder Effect, per rad
if ( u[5] >= 0.65)
{
CYdRr=CYdRr - 0.0093; // 38 deg-flap correction
}
var CYdASr=0.0264; // Asymmetric Spoiler Effect, per rad
if ( u[5] >= 0.65)
{
CYdASr=CYdASr + 0.0766; // 38 deg-flap correction
}
var CY=(CYBr*betar + CYdRr*u[2]) * VertTailMach+ (CYdAr*u[1] + CYdASr*u[4]) * WingMach; // Total Side-Force Coefficient, w/Mach Correction
//Yawing Moment Coefficient
var CnBr=0.1194; // Directional Stability (B), per rad
if ( u[5] >= 0.65)
{
CnBr=CnBr - 0.0092;
}
var Cnpr=CL * (1 + 3 * taperw)/(12 * (1 + taperw)) * (b / (2 * V)); // Roll-Rate Effect, per rad/s
var Cnrr=(-2 * (lvt / b) * CnBr * VertTailMach - 0.1 * Math.pow(CL,2))* (b / (2 * V)); // Yaw-Rate Effect, per rad/s
var CndAr=0; // Aileron Effect, per rad
if ( u[5] >= 0.65)
{
CndAr=CndAr + 0.0028;
}
var CndRr=-0.0713; // Rudder Effect, per rad
if ( u[5] >= 0.65)
{
CndRr=CndRr - 0.0185; // 38 deg-flap correction
}
var CndASr=-0.0088; // Asymmetric Spoiler Effect, per rad
if ( u[5] >= 0.65)
{
CndASr=CndASr - 0.0106; // 38 deg-flap correction
}
var Cn=(CnBr*betar + CndRr*u[2]) * VertTailMach+ Cnrr * x[8] + Cnpr * x[6]+ (CndAr*u[1] + CndASr*u[4]) * WingMach; // Total Yawing-Moment Coefficient, w/Mach Correction
//Rolling Moment Coefficient
var ClBr=-0.0918; // Dihedral Effect (B), per rad
if ( u[5] >= 0.65)
{
ClBr=ClBr - 0.0092;
}
var Clpr=-CLar * (1 + 3 * taperw)/(12 * (1 + taperw))* (b / (2 * V)); // Roll-Rate Effect, per rad/s
var Clrr=(CL * (1 + 3 * taperw)/(12 * (1 + taperw))* (Math.pow(Mach * Math.cos(sweepw),2) - 2) / (Math.pow(Mach * Math.cos(sweepw),2) - 1))* (b / (2 * V)); // Yaw-Rate Effect, per rad/s
var CldAr=0.1537; // Aileron Effect, per rad
if ( u[5] >= 0.65)
{
CldAr=CldAr + 0.01178;
}
var CldRr=0.01208; // Rudder Effect, per rad
if ( u[5] >= 0.65)
{
CldRr=CldRr + 0.01115; // 38 deg-flap correction
}
var CldASr=-0.01496; // Asymmetric Spoiler Effect, per rad
if ( u[5] >= 0.65)
{
CldASr=CldASr - 0.02376; // 38 deg-flap correction
}
var Cl=(ClBr*betar + CldRr*u[2]) * VertTailMach+ Clrr * x[8] + Clpr * x[6]+ (CldAr*u[1] + CldASr*u[4]) * WingMach; // Total Rolling-Moment Coefficient, w/Mach Correction
var ret = [];
ret = [CD,CL,CY,Cl,Cm,Cn,Thrust];
return ret;
}
DCM = function(Phi,Theta,Psi)
{
var sinR = Math.sin(Phi);
var cosR = Math.cos(Phi);
var sinP = Math.sin(Theta);
var cosP = Math.cos(Theta);
var sinY = Math.sin(Psi);
var cosY = Math.cos(Psi);
var H = new Array(3);
for (var i=0;i<H.length;i++){
H[i] = new Array (3);
}
H[0][0] = cosP * cosY;
H[0][1] = cosP * sinY;
H[0][2] = -sinP;
H[1][0] = sinR * sinP * cosY - cosR * sinY;
H[1][1] = sinR * sinP * sinY + cosR * cosY;
H[1][2] = sinR * cosP;
H[2][0] = cosR * sinP * cosY + sinR * sinY;
H[2][1] = cosR * sinP * sinY - sinR * cosY;
H[2][2] = cosR * cosP;
return H;
}
WindField=function(height,phir,thetar,psir)
{
/*// FLIGHT Wind Field Interpolation for 3-D wind as a Function of Altitude
// June 12, 2015
// ===============================================================
// Copyright 2006-2015 by ROBERT F. STENGEL. All rights reserved.
*/
var windh = [-10, 0, 100, 200, 500, 1000, 2000, 4000, 8000, 16000]; // Height, m
var windx = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; // Northerly wind, m/s
var windy = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; // Easterly wind, m/s
var windz = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]; // Vertical wind. m/s
var winde = [interp1(windh,windx,height),interp1(windh,windy,height),interp1(windh,windz,height)]; // Earth-relative frame
var HEB = DCM(phir,thetar,psir);
//var windb = HEB * winde; // Body-axis frame
var windb=[];
windb[0]=HEB[0][0]*winde[0]+HEB[0][1]*winde[1]+HEB[0][2]*winde[2];
windb[1]=HEB[1][0]*winde[0]+HEB[1][1]*winde[1]+HEB[1][2]*winde[2];
windb[2]=HEB[2][0]*winde[0]+HEB[2][1]*winde[1]+HEB[2][2]*winde[2];
return windb;
}
EoM = function(t,x)
{
var MODEL = 1; // Aerodynamic model selection: 0: Incompressible flow, high angle of attack; 1: Compressible flow, low angle of attack
var QUAT = 1; // 0: Rotation Matrix (DCM) from Euler Angles; 1: Rotation Matrix (DCM) from Quaternion
var TRIM = 1; // Trim flag (= 1 to calculate trim @ I.C.)
var LINEAR = 0; // Linear model flag (= 1 to calculate and store F and G)
var SIMUL = 1; // Flight path flag (= 1 for nonlinear simulation)
var GEAR = 0; // Landing gear DOWN (= 1) or UP (= 0)
var SPOIL = 0; // Symmetric Spoiler DEPLOYED (= 1) or CLOSED (= 0)
var CONHIS = 1; // Control history ON (= 1) or OFF (= 0)
var dF = 0; // // Flap setting, deg
var RUNNING = 0; // internal flag, -
// Initial Altitude (ft), Indicated Airspeed (kt)
var hft = 10000; // Altitude above Sea Level, ft
var VKIAS = 150; // Indicated Airspeed, kt
var hm = hft * 0.3048; // Altitude above Sea Level, m
var VmsIAS = VKIAS * 0.5154;// Indicated Airspeed, m/s
// US Standard Atmosphere, 1976, Table Lookup for I.C.
[airDens,airPres,temp,soundSpeed] = Atmos(hm);
// Dynamic Pressure (N/m^2), and True Airspeed (m/s)
var qBarSL = 0.5*1.225*Math.pow(VmsIAS,2); // Dynamic Pressure at sea level, N/m^2
var V = Math.sqrt(2*qBarSL/airDens); // True Airspeed, TAS, m/s
var TASms = V;
// Alphabetical List of Initial Conditions
var alpha = 0; // Angle of attack, deg (relative to air mass)
var beta = 0; // Sideslip angle, deg (relative to air mass)
var dA = 0; // Aileron angle, deg
var dAS = 0; // Asymmetric spoiler angle, deg
var dE = 0; // Elevator angle, deg
var dR = 0; // Rudder angle, deg
var dS = 0; // Stabilator setting, deg
var dT = 0; // Throttle setting, // / 100
var hdot = 0; // Altitude rate, m/s
var p = 0; // Body-axis roll rate, deg/s
var phi = 0; // Body roll angle wrt earth, deg
var psi = 0; // Body yaw angle wrt earth, deg
var q = 0; // Body-axis pitch rate, deg/sec
var r = 0; // Body-axis yaw rate, deg/s
var SMI = 0; // Static margin increment due to center-of-mass variation from reference, ///100
var tf = 100; // Final time for simulation, sec
var ti = 0; // Initial time for simulation, sec
var theta = alpha; // Body pitch angle wrt earth, deg [theta = alpha if hdot = 0]
var xe = 0; // Initial longitudinal position, m
var ye = 0; // Initial lateral position, m
var ze = -hm; // Initial vertical position, m [h: + up, z: + down]
// Initial Conditions Depending on Prior Initial Conditions
var gamma = 57.2957795 * Math.atan(hdot / Math.sqrt(Math.pow(V,2) - Math.pow(hdot,2))); // Inertial Vertical Flight Path Angle, deg
var qbar = 0.5 * airDens * Math.pow(V,2); // Dynamic Pressure, N/m^2
var IAS = Math.sqrt(2 * qbar / 1.225); // Indicated Air Speed, m/s
var Mach = V / soundSpeed; // Mach Number
var uInc = [];
// Initial Control Perturbation (Test Inputs: rad or 100//)
var delu = [0,0,0,0,0,0,0];
// Initial State Perturbation (Test Inputs: m, m/s, rad, or rad/s)
var delx = [0,0,0,0,0,0,0,0,0,0,0,0];
// Control Perturbation History (Test Inputs: rad or 100//)
// =======================================================
// Each control effector represented by a column
// Each row contains control increment delta-u(t) at time t:
var tuHis = [0, 33, 67, 100];
var deluHis = [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0];
// State Vector and Control Initialization, rad
var phir = phi * 0.01745329;
var thetar = theta * 0.01745329;
var psir = psi * 0.01745329;
var windb = WindField(-ze,phir,thetar,psir);
var alphar = alpha * 0.01745329;
var betar = beta * 0.01745329;
var u = [dE * 0.01745329,dA * 0.01745329,dR * 0.01745329,dT,dAS * 0.01745329,dF * 0.01745329,dS * 0.01745329];