// incline3.c // incline for logarithmic altitude launch loop track // with ramp and new track // also reverse track #define CL 80000.0 // cable material support length #define C0 20000.0 // z0 for cable #define CS 0.7 // Sideways fraction for cable #define OX -156323.926 // x data offset in meters #define X0 -20000.0 // Before ramps #define X1 200000.0 // End of track #define WZ 50550.0 // West station east altitude #define WA 5.48 // West station angle degrees #define WR 14000.0 // West station curvature radius #define TC 3.2E-7 // track curvature at west station #define VR 14000.0 // rotor speed at top of loop #define RE 6378000.0 // Earth Radius #define AG 9.81 // ag0 #define A0 20.0 // incline start angle degrees #define MF 3.000 // ms/mr #define MR 3.000 // rotor mass per meter #define DX 1 // computation delta x in meters #define NP 1000 // number of computation points per print #define HT 80000.0 // top of loop, meters #define LL 2000000.0 // launch loop length #define K 1000.0 // kilo #define EPS 1E-4 // comparison error #include #include int p ; // print counter double ra ; // degrees to radians double x ; // horizontal distance in meters double z ; // height in meters double zp ; // slope double zpp ; // curvature in inverse meters double vr ; // rotor speed double vr2 ; // rotor speed squared double vr0 ; // surface rotor speed double l ; // length of incline double dl2 ; // delta length squared double g ; // cable angle ratio double wz ; // west station magnet radius center z double wx ; // west station magnet radius center x double ag ; // gravity at altitude double zw ; // west station west end altitude double dx ; // increment for drawing west station double xw ; // west station x length double rx ; // ramp center horizontal double rz ; // ramp center vertical double a0 ; // ramp angle in radians double a1 ; // ramp feed part angle in radians double an ; // ramp angle loop index double da ; // ramp angle loop increment double z1 ; // height of reverse track double zp1 ; // slope of reverse track // ----------------------------------------- int prxz() { double sprt = MR * ((vr*vr*(zpp+1.0/RE)/ag) - 1.0 ) ; double xo = x + OX ; printf( "%11.6f%11.6f%12.6f%10.6f%10.3f%11.3f%9.5f%11.6f\n", xo/K, z/K, l/K, zp, sprt, vr, ag, z1/K ); return 0 ; } // ----------------------------------------- int main() { // initialization ------------------------------------------------------- ra = atan(1.0)/45.0 ; // degrees to radians conversion constant vr0 = sqrt( VR*VR+2.0*AG*HT/( 1.0 + HT/RE ) ) ; // rotor ground speed ag = AG ; // gravity at ground // ----------------------------------------------------------------------- // ramp dx = 0.2*rx ; a0 = ra*A0 ; // radians, second upturn and start of ramp a1 = acos(0.5*(1.0+cos(a0))) ; // radians, downturn and first upturn x = X0 ; z = 0.0 ; l = x - WR * ( (a0-sin(a0)) + 2.0*(a1-sin(a1)) ) ; zp = 0.0 ; zpp = 1.0/RE ; vr = vr0 ; z1 = z ; prxz(); // ramp downturn rx = -WR*(sin(a0)+2*sin(a1)); rz = -WR ; da = 0.2*a1 ; for( an=0.0 ; an < a1-EPS ; an += da ) { x = rx+WR*sin(an); z = rz+WR*cos(an); l = WR*(a0+2.0*a1-an); zp = -tan( an ); zpp = 1.0/(WR*cos(an)*cos(an)) ; vr2 = vr0*vr0-2.0*AG*z/(1.0 + z/RE ) ; vr = sqrt( vr2 ); ag = 1.0/(1.0+(z/RE)) ; ag *= AG*ag ; z1 = z ; prxz(); } // ramp upturn rx = -WR*sin(a0) ; rz = WR*cos(a0) ; da = 0.1*(a0+a1) ; for( an= -a1 ; an < a0-EPS ; an += da ) { x = rx+WR*sin(an); z = rz-WR*cos(an); l = WR*(a0-an); zp = tan( an ); zpp = -1.0/(WR*cos(an)*cos(an)) ; vr2 = vr0*vr0-2.0*AG*z/(1.0 + z/RE ) ; vr = sqrt( vr2 ); ag = 1.0/(1.0+(z/RE)) ; ag *= AG*ag ; z1 = z ; prxz(); } // ----------------------------------------------------------------------- // incline // initialize x = 0.0 ; p = NP ; z = 0.0 ; // zp = tan( a0 ) ; // first spatial derivative l = 0.0 ; wz = WZ - WR * cos( ra*WA ) ; // main loop while( p >= 0 ) { ag = 1.0/(1.0+(z/RE)) ; ag *= AG*ag ; vr2 = vr0*vr0-2.0*AG*z/(1.0 + z/RE ) ; vr = sqrt( vr2 ); g = sqrt( exp( 2.0*( z+C0 ) / CL ) - 1.0 ) ; dl2 = 1.0+zp*zp ; zpp = dl2 * ( (1.0/(RE+z)) + dl2*ag*MF/(vr2*(1.0-g*zp )) ) ; if( p++ >= NP ) { z1 = z ; prxz() ; // print every 1000 meters p = 1 ; } // increment values x += DX ; zp -= zpp * DX ; z += zp * DX ; l += DX*sqrt(dl2); // compute west station west end height WZ zw = wz + WR / sqrt( 1.0 + zp*zp ) ; // test for completion if ( z > zw ) { p = -NP ; } } z1 = z ; prxz(); // -------------------------------------------------------------------- // now, compute points for west station wx = x + WR*zp/sqrt( 1.0+zp*zp) ; // west station radius x center xw = wx - WR*sin( ra * WA ) ; // west station east end x location // find angles a0 = -acos( ( z-wz)/WR ) ; a1 = -acos( (WZ-wz)/WR ) ; da = 0.2*(a1-a0) ; for( an = a0+da ; an < a1+EPS ; an += da ) { x = wx + WR*sin( an ); z = wz + WR*cos( an ); zp = -tan( an ); zpp = 1.0/(WR*cos(a0)*cos(a0)) ; ag = 1.0/(1.0+(z/RE)) ; ag *= AG*ag ; vr2 = vr0*vr0-2.0*AG*z/(1.0 + z/RE ) ; vr = sqrt( vr2 ); l += da*WR ; // reverse track z1 = z ; prxz(); } // -------------------------------------------------------------------- // compute points for first part of track, constant curvature // also reverse track p = 1 ; zpp = TC ; zp = tan( ra * WA ); zp1 = (HT-WZ)/LL ; while ( x <= X1 ) { x += DX ; z += zp*DX ; zp -= zpp*DX ; l += DX*sqrt(1.0+zp*zp); ag = 1.0/(1.0+(z/RE)) ; ag *= AG*ag ; vr2 = vr0*vr0-2.0*AG*z/(1.0 + z/RE ) ; vr = sqrt( vr2 ); if( p++ >= NP ) { // reverse track, more station then flat dx = x - wx ; if( dx < 0 ) { z1 = wz + sqrt( WR*WR-dx*dx ); } else { z1 = dx*zp1+wz+WR ; } prxz() ; // print every 1000 meters p = 1 ; } } // -------------------------------------------------------------------- return 0 ; }