Frisbee Trajectory for KRAI

frisbee_trajectory.c

#include <stdio.h>
#include <math.h>

int main(){
    double x;
    //The x position of the frisbee.
    double y;
    //The y position of the frisbee.
    double vx;
    //The x velocity of the frisbee.
    double vy;
    //The y velocity of the frisbee.
    double g = -9.81;
    //The acceleration of gravity (m/s^2).
    double m = 0.175;
    //The mass of a standard frisbee in kilograms.
    double RHO = 1.23;
    //The density of air in kg/m^3.
    double AREA = 0.0568;
    //The area of a standard frisbee.
    double CL0 = 0.1;
    //The lift coefficient at alpha = 0.
    double CLA = 1.4;
    //The lift coefficient dependent on alpha.
    double CD0 = 0.08;
    //The drag coefficent at alpha = 0.
    double CDA = 2.72;
    //The drag coefficient dependent on alpha.
    double ALPHA0 = -4;

    //Calculation of the lift coefficient using the relationship given
    //by S. A. Hummel.
    double cl = CL0 + CLA * alpha * PI/180;
    //Calculation of the drag coefficient (for Prantl’s relationship)
    //using the relationship given by S. A. Hummel.
    double cd = CD0 + CDA * pow((alpha-ALPHA0) * PI / 180 , 2);
    //Initial position x = 0.
    x = 0;
    //Initial position y = y0.
    y = y0;
    //Initial x velocity vx = vx0.
    vx = vx0;
    //Initial y velocity vy = vy0.
    vy = vy0;

    

    double simulate(double y0, double vx0, double vy0, double alpha, double delta_t){
        printf("Veamus KRAI TRUI 2017.");
        printf("Frisbee Trajectory Simulation \n w/ initialized data.");
        printf("y0: %d", y0);
        printf("Vx0: %d", vx0);
        printf("Vy0: %d", vy0);
        printf("alpha: %d", alpha);
        printf("delta_t: %d", delta_t);
        printf("Running simulation ...");

        bool simulation_flag = true;
        i = 0;
        
        while (simulation_flag){
            // toggle flag if the iteration not the first and y is still real.
            if (i != 0 && y <= 0){
                simulation_flag = false;
            }

            //The change in velocity in the y direction obtained setting the
            //net force equal to the sum of the gravitational force and the
            //lift force and solving for delta v.
            let deltavy = (RHO * pow(vx, 2) * AREA * cl / 2 / m + g) * delta_t;

            //The change in velocity in the x direction, obtained by
            //solving the force equation for delta v. (The only force
            //present is the drag force).
            let delta_vx = -RHO * pow(vx, 2) * AREA * cd * delta_t;

            //The new positions and velocities are calculated using
            //simple introductory mechanics.
            vx = vx + delta_vx;
            vy = vy + deltavy;
            x = x + vx * delta_t;
            y = y + vy * delta_t;

            i++;
            printf("x: %d \t y: %d \t %d iteration", x, y, i)
        }
    }

    //initialize data at 0.
    double y0 = 10.0; 
    double vx0 = 5.0;
    double vy0 = 5.0; 
    double alpha = 30.0; 
    double delta_t = 0.001;

    // run simulation.
    simulate(y0, vx0, vy0, alpha, delta_t);
}