Based on the original Rocket Workbench on SourceForge in CVS at:
https://sourceforge.net/projects/rocketworkbench
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234 lines
6.9 KiB
234 lines
6.9 KiB
/* modeles.cc - Simulation of rocket flight */
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/* Copyright (C) 2000 */
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/* Antoine Lefebvre <antoine.lefebvre@polymtl.ca> */
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/* This program is free software; you can redistribute it and/or modify*/
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/* it under the terms of the GNU General Public License as published by*/
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/* the Free Software Foundation; either version 2 of the License, or */
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/* (at your option) any later version. */
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/* This program is distributed in the hope that it will be useful, */
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/* but WITHOUT ANY WARRANTY; without even the implied warranty of */
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/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the */
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/* GNU General Public License for more details. */
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/* You should have received a copy of the GNU General Public License */
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/* along with this program; if not, write to the Free Software */
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/* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA. */
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#include <cmath>
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#include "simulation.h"
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#include "c++rocket.h"
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// modified arctan function
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double Atan(double x, double y);
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double coef(double v);
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double T(double time);
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double mass(double time);
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int model_1(int neq, double time,
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double *z, double *dy, int ierr);
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int model_2(int neq, double time,
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double* z, double* dy, int ierr);
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extern simulation *simptr;
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/**********************************************************************
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MODEL_1: This model takes care of the principal aerodynamic effects
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that takes place in a rocket flight. The mathematical relation
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come from 'Mathematical theory of rocket flight' McGraw-Hill
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Book company. Author are J. Barkley Rosser, Robert R. Newton,
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George L. Gross.
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COMMENTS: I will eventually explain the theory in some documentation
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**********************************************************************/
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int model_1(int neq, double time,
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double *z, double *dy, int ierr)
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{
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//double s = z[0]; not use
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double x = z[1]; // position in the x coordinate
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double y = z[2]; // position in the y coordinate
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double theta = z[3]; // angle about the horizontal
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double phi = z[4]; // angle of the rocket axis about the horizontal
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double v = z[5]; // speed
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double dphi = z[6]; // first derivative of phi
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double h = sqrt(pow(x,2) + pow(y,2));
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double g = G*simptr->p_data[masse]/(pow(h,2));
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double delta = phi - theta;
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double rho = simptr->densiteatm(h - simptr->p_data[rayon]);
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double drag_correction = coef(v)/0.15;
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double Drag = -simptr->r_data[Kdrag]*(1+simptr->r_data[Kdd]*pow(delta,2))\
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*rho*pow(simptr->r_data[Diameter],2)*pow(v,2)*drag_correction;
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double Lift = simptr->r_data[Klift]*rho*pow(simptr->r_data[Diameter],2) * pow(v,2)*sin(delta - simptr->r_data[dlift]);
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double Spin = simptr->r_data[Kspin]*rho*pow(simptr->r_data[Diameter],3)*v*dphi;
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double Moment = -simptr->r_data[Kmoment]*rho*pow(simptr->r_data[Diameter],3)*pow(v,2)*sin(delta-simptr->r_data[dmoment]);
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double Damping = -simptr->r_data[Kdamping]*rho*pow(simptr->r_data[Diameter],4)*v*dphi;
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double thrust = T(time);
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double dmasse = 0; // mass flow
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double angle = Atan(x, y);
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dy[0] = v;
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dy[1] = v*cos(theta);
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dy[2] = v*sin(theta);
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dy[3] = (thrust* sin( delta - simptr->r_data[dt] ) - mass(time)*g*cos(theta + PI/2 - angle) + Lift + Spin*cos(delta))/(mass(time)*v); //dtheta
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dy[4] = dphi;
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dy[5] = (thrust*cos(delta-simptr->r_data[dt])-mass(time)*g*sin(theta+PI/2-angle) + Drag + Spin*sin(delta))/mass(time);
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dy[6] = (thrust*simptr->r_data[rcm_throat]*sin(simptr->r_data[dt]) + Moment + Damping - dmasse*dphi*(simptr->r_data[rcm_throat]*simptr->r_data[rcm_exit]-pow(simptr->r_data[k],2)))/(mass(time)*pow(simptr->r_data[k],2));
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return 0;
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}
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double Atan(double x, double y)
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{
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double angle;
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if ((x == 0)&&(y > 0))
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angle = PI/2;
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else if ((x == 0)&&(y < 0))
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angle = -PI/2;
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else if ((x > 0))
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angle = atan(y/x);
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else if ((x < 0))
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angle = PI + atan(y/x);
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return angle;
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}
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// table de variation des du coefficient de frottement en
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// fonction de la vitesse
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// table of the drag coefficient variation with speed
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//
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double coef(double v)
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{
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static const int V[] = {0, 50, 100, 150, 200, 250, 300, 350, 400, 450,
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500, 550, 600, 650, 700, 750, 800, 850, 900, 950,
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1000, 1050, 1100, 1150, 1200};
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static const double C[] = {0.15, 0.13, 0.125, 0.12, 0.135, 0.15, 0.2,
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0.3, 0.37, 0.39, 0.38, 0.37, 0.36, 0.35, 0.34,
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0.33, 0.32, 0.315, 0.31,0.305, 0.302, 0.3,
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0.299, 0.298, 0.297};
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if (v > 1200)
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return 0.295;
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else {
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int b = (int)floor(v/50)+1;
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return ( (C[b+1]-C[b]) / (V[b+1]-V[b]) )*(v-V[b]) + C[b];
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}
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}
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double mass(double time)
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{
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double trel = 0;
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double M = simptr->r_data[Mass];
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if (simptr->n_prop() == 0)
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return M;
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for (int i = 0; i < simptr->n_prop(); i++)
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M += simptr->prop[i].M(0);
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if (time < simptr->ta[0])
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return M;
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M -= simptr->prop[0].M(0);
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for (int i = 0; i < simptr->n_prop(); i++)
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if (time < (simptr->tl[i]+simptr->ta[i]+simptr->prop[i].burntime+trel) )
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return (M + simptr->prop[i].M(time - trel - simptr->ta[i]));
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else
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{
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trel += simptr->ta[i] + simptr->tl[i] + simptr->prop[i].burntime;
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M -= simptr->prop[i].M(0);
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}
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return simptr->r_data[Mass];
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}
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// give the thrust of the rocket in function of time, flight program and
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// motor that are loaded
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double T(double time)
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{
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double trel = 0;
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if (simptr->n_prop() == 0)
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return 0.0;
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if (time < simptr->ta[0])
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return 0.0;
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for (int i = 0; i < simptr->n_prop(); i++) {
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if (time < (simptr->tl[i]+simptr->ta[i]+simptr->prop[i].burntime+trel) )
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return simptr->prop[i].T(time - trel - simptr->ta[i]);
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else
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trel += simptr->ta[i] + simptr->tl[i] + simptr->prop[i].burntime;
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}
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return 0.0;
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}
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/**********************************************************************
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MODEL_2: Simple model that do not take care of aerodynamic parameter
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**********************************************************************/
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int model_2(int neq, double time,
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double* z, double* dy, int ierr)
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{
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//double s = z[0];
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double x = z[1];
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double y = z[2];
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double theta = z[3];
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double v = z[4];
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double h = sqrt(pow(x,2) + pow(y,2));
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double g = G*simptr->p_data[masse]/(pow(h,2));
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double rho = simptr->densiteatm(h - simptr->p_data[rayon]);
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double drag_correction = coef(v)/0.15;
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double Drag = -simptr->r_data[Kdrag]*rho*pow(simptr->r_data[Diameter],2)*pow(v,2)*drag_correction;
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double thrust = T(time);
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//double dmasse = 0; //mass flow
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double angle = Atan(x, y);
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dy[0] = v;
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dy[1] = v*cos(theta);
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dy[2] = v*sin(theta);
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dy[3] = (thrust - mass(time)*g*cos(theta+PI/2-angle) )/(mass(time)*v); //dtheta
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dy[4] = (thrust-mass(time)*g*sin(theta+PI/2-angle) + Drag )/mass(time);
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return 0;
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}
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