RocketWorkbench/libsimulation/modeles.cc

/* modeles.cc  -  Simulation of rocket flight                              */
/* Copyright (C) 2000                                                  */
/* Antoine Lefebvre <antoine.lefebvre@polymtl.ca>                      */

/* This program is free software; you can redistribute it and/or modify*/
/* it under the terms of the GNU General Public License as published by*/
/* the Free Software Foundation; either version 2 of the License, or   */
/* (at your option) any later version.                                 */

/* This program is distributed in the hope that it will be useful,     */
/* but WITHOUT ANY WARRANTY; without even the implied warranty of      */
/* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the       */ 
/* GNU General Public License for more details.                        */

/* You should have received a copy of the GNU General Public License   */
/* along with this program; if not, write to the Free Software         */
/* Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.           */

#include <cmath>
#include "simulation.h"

#include "c++rocket.h"

// modified arctan function
double Atan(double x, double y);
double coef(double v);
double T(double time);
double mass(double time);



int model_1(int neq, double time,
	    double *z, double *dy, int ierr);

int model_2(int neq, double time, 
	    double* z, double* dy, int ierr);


extern simulation *simptr;

/**********************************************************************
MODEL_1: This model takes care of the principal aerodynamic effects
         that takes place in a rocket flight. The mathematical relation
	 come from 'Mathematical theory of rocket flight' McGraw-Hill
	 Book company. Author are J. Barkley Rosser, Robert R. Newton,
	 George L. Gross.

COMMENTS: I will eventually explain the theory in some documentation

**********************************************************************/


int model_1(int neq, double time,
	    double *z, double *dy, int ierr)
{

//double s     = z[0];     not use
  double x     = z[1];     // position in the x coordinate
  double y     = z[2];     // position in the y coordinate
  double theta = z[3];     // angle about the horizontal
  double phi   = z[4];     // angle of the rocket axis about the horizontal
  double v     = z[5];     // speed
  double dphi  = z[6];     // first derivative of phi

  double h = sqrt(pow(x,2) + pow(y,2));
  double g = G*simptr->p_data[masse]/(pow(h,2));
  double delta = phi - theta;
  double rho = simptr->densiteatm(h - simptr->p_data[rayon]);
  double drag_correction = coef(v)/0.15;
  double Drag = -simptr->r_data[Kdrag]*(1+simptr->r_data[Kdd]*pow(delta,2))\
    *rho*pow(simptr->r_data[Diameter],2)*pow(v,2)*drag_correction;     
  double Lift = simptr->r_data[Klift]*rho*pow(simptr->r_data[Diameter],2) * pow(v,2)*sin(delta - simptr->r_data[dlift]);
  double Spin = simptr->r_data[Kspin]*rho*pow(simptr->r_data[Diameter],3)*v*dphi;
  double Moment = -simptr->r_data[Kmoment]*rho*pow(simptr->r_data[Diameter],3)*pow(v,2)*sin(delta-simptr->r_data[dmoment]);
  double Damping = -simptr->r_data[Kdamping]*rho*pow(simptr->r_data[Diameter],4)*v*dphi;
  

  double thrust = T(time); 
  double dmasse = 0;       // mass flow
  
  double angle = Atan(x, y);
  
  dy[0] = v;
  dy[1] = v*cos(theta);
  dy[2] = v*sin(theta);
  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
  dy[4] = dphi;
  dy[5] = (thrust*cos(delta-simptr->r_data[dt])-mass(time)*g*sin(theta+PI/2-angle) + Drag + Spin*sin(delta))/mass(time);
  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));
  
  return 0;
}




double Atan(double x, double y) 
{
  double angle;
  if ((x == 0)&&(y > 0))
    angle = PI/2;
  else if ((x == 0)&&(y < 0))
    angle = -PI/2;
  else if ((x > 0))
    angle = atan(y/x);
  else if ((x < 0))
    angle = PI + atan(y/x);
  return angle;
}


// table de variation des du coefficient de frottement en 
// fonction de la vitesse

// table of the drag coefficient variation with speed
// 
double coef(double v) 
{
  static const int V[] = {0, 50, 100, 150, 200, 250, 300, 350, 400, 450, 
			  500, 550, 600, 650, 700, 750, 800, 850, 900, 950, 
			  1000, 1050, 1100, 1150, 1200};

  static const double C[] = {0.15, 0.13, 0.125, 0.12, 0.135, 0.15, 0.2, 
			     0.3, 0.37, 0.39, 0.38, 0.37, 0.36, 0.35, 0.34, 
			     0.33, 0.32, 0.315, 0.31,0.305, 0.302, 0.3, 
			     0.299, 0.298, 0.297};
  
  if (v > 1200)
    return 0.295;
  else {
    int b = (int)floor(v/50)+1;
    return  ( (C[b+1]-C[b]) / (V[b+1]-V[b]) )*(v-V[b]) + C[b];
  }
}


double mass(double time) 
{  
  double trel = 0;
  double M = simptr->r_data[Mass];
  
  if (simptr->n_prop() == 0)
    return M;
   
  for (int i = 0; i < simptr->n_prop(); i++)
    M += simptr->prop[i].M(0);
  
  
  if (time < simptr->ta[0])
    return M;
  
  M -= simptr->prop[0].M(0);
  for (int i = 0; i < simptr->n_prop(); i++)
    if (time < (simptr->tl[i]+simptr->ta[i]+simptr->prop[i].burntime+trel) )
      return (M + simptr->prop[i].M(time - trel - simptr->ta[i]));
    else 
    {
      trel += simptr->ta[i] + simptr->tl[i] + simptr->prop[i].burntime;
      M -= simptr->prop[i].M(0);
    } 
    
  return simptr->r_data[Mass];
}


// give the thrust of the rocket in function of time, flight program and
// motor that are loaded

double T(double time) 
{
  double trel = 0;
  if (simptr->n_prop() == 0)
    return 0.0;
  if (time < simptr->ta[0])
    return 0.0;
  for (int i = 0; i < simptr->n_prop(); i++) {
    if (time < (simptr->tl[i]+simptr->ta[i]+simptr->prop[i].burntime+trel) )
      return simptr->prop[i].T(time - trel - simptr->ta[i]);
    else
      trel += simptr->ta[i] + simptr->tl[i] + simptr->prop[i].burntime;
  }	       
  return 0.0;
}



/**********************************************************************
MODEL_2: Simple model that do not take care of aerodynamic parameter

**********************************************************************/

int model_2(int neq, double time, 
	    double* z, double* dy, int ierr) 
{
//double s     = z[0];
  double x     = z[1];
  double y     = z[2];
  double theta = z[3];
  double v     = z[4];
  
  double h = sqrt(pow(x,2) + pow(y,2));
  double g = G*simptr->p_data[masse]/(pow(h,2));

  double rho = simptr->densiteatm(h - simptr->p_data[rayon]);
  double drag_correction = coef(v)/0.15;
  double Drag = -simptr->r_data[Kdrag]*rho*pow(simptr->r_data[Diameter],2)*pow(v,2)*drag_correction;     
  
 
  double thrust = T(time); 
  //double dmasse = 0;         //mass flow     
  double angle = Atan(x, y);
  
  dy[0] = v;
  dy[1] = v*cos(theta);
  dy[2] = v*sin(theta);
  dy[3] = (thrust - mass(time)*g*cos(theta+PI/2-angle) )/(mass(time)*v); //dtheta
  dy[4] = (thrust-mass(time)*g*sin(theta+PI/2-angle) + Drag )/mass(time);
  
  return 0;
}