/*
Automag.c version 1.0 08/17/94
This program calculates the behavior of an automag paintball gun using
a simple model of the gun. See file "automag.txt" for an explanation
of the program.
I have no proprietary feelings about this code. If you can improve it,
please feel free to do so, offer it to anyone you want, I don't need to
be notified or credited, or anything.
- Paul Reiser -
*/
#define VAX /* Compiler Specification */
#ifdef LSC /* For use with Lightspeed C compiler */
#include "math.h"
#include "unix.h"
#include "stdio.h"
#include "ctype.h"
#include "storage.h"
#define MAC
#endif
#ifdef THC /* For use with Think C compiler */
#include "math.h"
#include "unix.h"
#include "stdio.h"
#include "ctype.h"
#include "Memory.h"
#define MAC
#endif
#ifdef VAX /* For use with VAX C compiler */
#include <math.h>
#include <stdio.h>
#endif
/* General Globals and defines */
#define pi 3.1415926535
typedef struct /* Thermodynamic variables */
{ double Ps; /* Gas pressure of source (psi) */
double Pr; /* Gas pressure after reg. valve (psi) */
double Pa; /* Gas pressure in air chamber (psi) */
double Pb; /* Gas pressure in barrel (psi) */
double Px; /* Atmospheric pressure (psi) */
double Vr; /* regulator volume (in^2) */
double Va; /* air chamber volume (in^2) */
double T; /* Temperature (deg F) */
double m; /* Atomic weight of gas */
double GC; /* Gas consumption (oz) */
}VARpv;
typedef struct /* Regulator valve variables */
{ double S; /* Surface area of regulator piston (in^2) */
double x0; /* Nominal R-valve to top of R-seal (in) */
double Cl; /* Leakage flow conductance */
double Z; /* Flow conductance/length */
double T; /* Position of regulator nut (turns) */
double K; /* spring constant of the reg piston spring (lb/in) */
double H; /* Regulator nut turns per inch */
double x; /* Position of regulator valve (in) */
}VARr;
typedef struct /* on-off valve variables */
{ double C; /* Leakage conductance */
double Z; /* Flow conductance/Length */
double x; /* On-off pin position (in) */
}VARo;
typedef struct /* Power tube variables */
{ double M; /* Mass of bolt (oz) */
double S; /* Area of bolt (in^2) */
double xc; /* Position of bolt when it latches (in) */
double Cl; /* Leakage conductance */
double Z; /* flow conductance/length */
double K; /* Spring constant of power tube spring (lb/in) */
double R; /* Friction coefficient (lb-sec/in)*/
double x0; /* Relaxed length of power tube spring (in) */
double xi; /* Length of p.t. spring when bolt is latched (in) */
double xm; /* Maximum position of bolt (in) */
double x; /* Position of bolt (in) */
double v; /* Velocity of bolt (fps) */
}VARp;
typedef struct /* barrel & ball variables */
{ double M; /* Mass of ball */
double D; /* Diameter of barrel and ball */
double L; /* Length of barrel (in) */
double x; /* Position of ball (in) */
double v; /* Velocity of ball (fps) */
}VARb;
typedef struct /* trigger variables */
{ double B; /* Sear angle (deg) */
double Bo; /* Sear angle at which on-off valve turns on (deg) */
double Bb; /* Sear angle at which bolt is released (deg) */
double xs; /* Sear pivot to on-off pin distance (in) */
}VARt;
/* Functions */
/*int tstep();*/
double Qsr(); /* Rate gas enters the regulator (m/s) */
double Qra(); /* Rate gas enters the air chamber (m/s) */
double Qab(); /* Rate gas enters the barrel (m/s) */
double Qbx(); /* Rate gas leaves the barrel (m/s) */
int UpDate_r(); /* Update regulator valve */
int UpDate_o();
int UpDate_p();
int UpDate_b();
int UpDate_t();
/*----------------------------------------------------------------------*/
main()
{ int i;
VARr Zr;
VARo Zo;
VARp Zp;
VARb Zb;
VARt Zt;
VARpv PV;
double t; /* time (sec) */
double dt; /* time increment */
int n; /* number of iterations */
/* Thermodynamic variables */
PV.Px = 14.6959; /* atmospheric pressure (psi) */
PV.Ps = 1000.0; /* source pressure (psi) */
PV.Pr = 449.0; /* regulator pressure (psi) */
PV.Pa = 449.0; /* air chamber pressure (psi) */
PV.Pb = PV.Px; /* barrel pressure (psi) */
PV.Vr = 0.05; /* Volume of regulator chamber (in^3) */
PV.Va = 0.463; /* Volume of air chamber (in^3) */
PV.T = 70.0; /* Temperature (deg F) */
PV.m = 44.0; /* Atomic weight of gas */
PV.GC = 0.0; /* Gas consumption (oz) */
/* Regulator valve variables */
Zr.S = 0.19635; /* Surface area of regulator piston (in^2) */
Zr.x0 = 0.0625; /* Nominal R-valve to top of R-seal (in) */
Zr.Cl = 0.0; /* Leakage flow conductance */
Zr.Z = 200.0; /* Flow conductance/length */
Zr.T = 0.0; /* Position of regulator nut (turns) */
Zr.K = 1367.5; /* spring const. of reg piston spring (lb/in) */
Zr.H = 32.0; /* Regulator nut turns per inch */
Zr.x = Zr.x0; /* Position of regulator valve (in) */
/* on-off valve variables */
Zo.C = 0.0; /* Leakage conductance */
Zo.Z = 200.0; /* Flow conductance/Length */
Zo.x = 0.0; /* on-off pin position */
/* Power tube variables */
Zp.M = 1.848; /* Mass of bolt (oz) */
Zp.S = 0.181; /* Area of bolt (in^2) */
Zp.xc = -0.1; /* Position of bolt when it latches (in) */
Zp.Cl = 0.0; /* Leakage conductance */
Zp.Z = 360.0; /* flow conductance/length */
Zp.K = 11.3; /* Spring constant of power tube spring (lb/in) */
Zp.R = 1.0; /* Friction coefficient (lb-sec/in)*/
Zp.x0 = 1.89; /* Relaxed length of power tube spring (in) */
Zp.xi = 1.65; /* Length of pts. when bolt is latched (in) */
Zp.xm = 1.18; /* Maximum position of bolt (in) */
Zp.x = Zp.xc; /* Position of bolt (in) */
Zp.v = 0.0; /* Velocity of bolt (fps) */
/* barrel & ball variables */
Zb.M = 0.113; /* Mass of ball (oz) */
Zb.D = 0.68; /* Diameter of barrel and ball (in) */
Zb.L = 11.0; /* Length of barrel (in) */
Zb.x = 0.00; /* Position of ball (in) */
Zb.v = 0.00; /* Velocity of ball (fps) */
/* trigger variables */
Zt.B = 0.0; /* Sear angle (deg) */
Zt.Bo = 2.0; /* Sear angle at which on-off valve turns on (deg) */
Zt.Bb = 4.0; /* Sear angle at which bolt is released (deg) */
Zt.xs = 0.8; /* Sear pivot to on-off pin distance (in) */
t = 0.0; /* beginning time (sec) */
dt = 0.0002;/* time step (sec) */
n = 75; /* number of steps */
/* Step through time and print out some variables */
for(i=0;i<n;i++)
{
printf("\nt=%6.4lf Pr=%6.2lf Pa=%6.2lf ",t,PV.Pr,PV.Pa);
printf("GC=%e Zb.v=%6.4lf Zp.x=%6.4lf Zt.B=%3.1lf",PV.GC,Zb.v,Zp.x,Zt.B);
tstep(&t,&dt,&PV,&Zr,&Zo,&Zp,&Zb,&Zt);
}
printf("\n\nDONE");
}
/*----------------------------------------------------------------------*/
int tstep(pt,pdt,pPV,pZr,pZo,pZp,pZb,pZt)
#define t (*pt)
#define dt (*pdt)
#define PV (*pPV)
#define Zr (*pZr)
#define Zo (*pZo)
#define Zp (*pZp)
#define Zb (*pZb)
#define Zt (*pZt)
double t;
double dt;
VARpv PV;
VARr Zr;
VARo Zo;
VARp Zp;
VARb Zb;
VARt Zt;
/* step forward in time dt seconds */
{ int i;
double hQsr,hQra,hQab,hQbx;
double Vb;
double Vbo;
double TK;
TK = 273.16 + (PV.T-32.0)/1.8; /* Temperature in kelvin */
/* Update source pressure */
{ double c[4];
static int ok;
c[0] = -47.922400;
c[1] = 0.51399206;
c[2] = -1.67373965e-03;
c[3] = 1.89693767e-06;
PV.Ps = 0.0;
for(i=0;i<=3;i++)PV.Ps = PV.Ps + c[i]*pow(TK,i);
PV.Ps = exp(PV.Ps);
if(ok == 0)
{ printf("\nPV.Ps = %6.2lf",PV.Ps);
ok = 1;
}
}
/* Update moving parts */
UpDate_t(&Zt,&Zb,&Zp,&PV,t,dt);/* trigger variables */
UpDate_o(&PV,&Zo,&Zt,t,dt); /* on-off valve */
UpDate_p(&PV,&Zp,&Zt,t,dt); /* power tube */
UpDate_r(&PV,&Zr,t,dt); /* regulator valve and piston */
Vbo = 0.25*pi*Zb.D*Zb.D*(Zb.x+0.1); /* save old barrel volume */
UpDate_b(&PV,&Zb,&Zp,t,dt); /* ball & barrel */
/* Update Pressures */
hQsr = Qsr(PV.Ps,PV.Pr,&Zr);
hQra = Qra(PV.Pr,PV.Pa,&Zo,&Zt);
hQab = Qab(PV.Pa,PV.Pb,&Zp);
hQbx = Qbx(PV.Pb,PV.Px,&Zb);
PV.Pr = PV.Pr + (hQsr - hQra)*dt/PV.Vr;
PV.Pa = PV.Pa + (hQra - hQab)*dt/PV.Va;
if(Zb.x < Zb.L)
{ Vb = 0.25*pi*Zb.D*Zb.D*(Zb.x+0.1); /* Vb = new barrel volume */
PV.Pb = (PV.Pb*Vbo + (hQab - hQbx)*dt)/Vb;
}
else PV.Pb = PV.Px;
/* Update gas consumption */
PV.GC = PV.GC + 4.85e-4*hQsr*dt*PV.m/TK;
/* Update time */
t = t+dt;
return;
}
#undef t
#undef dt
#undef PV
#undef Zr
#undef Zo
#undef Zp
#undef Zb
#undef Zt
/*----------------------------------------------------------------------*/
double Qsr(Ps,Pr,pZr)
#define Zr (*pZr)
double Ps; /* source pressure (psi) */
double Pr; /* regulator pressure (psi) */
VARr Zr; /* regulator variables */
/* calculate the rate of flow from source to regulator */
/*
{ double S; / Surface area of regulator piston (in^2) /
double x0; / Nominal R-valve to top of R-seal (in) /
double Cl; / Leakage flow conductance /
double Z; / Flow conductance/length /
double T; / Position of regulator nut (turns) /
double K; / spring constant of the reg piston spring (lb/in) /
double H; / Regulator nut turns per inch /
double x; / Position of regulator valve (in) /
}VARr;
*/
{ double Q,L;
if(Zr.x < 0.0)L=0; else L=Zr.x;
Q = (Zr.Cl+Zr.Z*L)*(Ps-Pr);
return(Q);
}
#undef Zr
/*----------------------------------------------------------------------*/
double Qra(Pr,Pa,pZo,pZt)
#define Zo (*pZo)
#define Zt (*pZt)
double Pr; /* regulator pressure (psi) */
double Pa; /* air chamber pressure (psi) */
VARo Zo; /* on-off valve variables */
VARt Zt; /* trigger variables */
/* calculate the rate of flow from regulator to air chamber */
/*
{ double C; / Leakage conductance /
double Z; / Flow conductance/Length /
double x; / On-off pin position (in) /
}VARo;
{ double B; / Sear angle (deg) /
double Bo; / Sear angle at which on-off valve turns on (deg) /
double Bb; / Sear angle at which bolt is released (deg) /
double xs; / Sear pivot to on-off pin distance (in) /
}VARt;
*/
{ double Q,L;
if(Zo.x < 0.0)L=0.0; else L=Zo.x;
Q = (Zo.C + Zo.Z*L)*(Pr-Pa);
return(Q);
}
#undef Zo
#undef Zt
/*----------------------------------------------------------------------*/
double Qab(Pa,Pb,pZp)
#define Zp (*pZp)
double Pa; /* air chamber pressure (psi) */
double Pb; /* barrel pressure (psi) */
VARp Zp; /* power tube exit variables */
/* calculate the rate of flow from air chamber to barrel */
/*
{ double M; / Mass of bolt (oz) /
double S; / Area of bolt (in^2) /
double xc; / Position of bolt when it latches (in) /
double Cl; / Leakage conductance /
double Z; / flow conductance/length /
double K; / Spring constant of power tube spring (lb/in) /
double R; / Friction coefficient (lb-sec/in)/
double x0; / Relaxed length of power tube spring (in) /
double xi; / Length of p.t. spring when bolt is latched (in) /
double xm / Maximum position of bolt (in) /
double x; / Position of bolt (in) /
double v; / Velocity of bolt (fps) /
}VARp;
*/
{ double Q,L;
if(Zp.x < 0.0)L=0; else L=Zp.x;
Q = (Zp.Cl+Zp.Z*L)*(Pa-Pb);
return(Q);
}
#undef Zp
/*----------------------------------------------------------------------*/
double Qbx(Pb,Px,pZb)
#define Zb (*pZb)
double Pb; /* barrel pressure (psi) */
double Px; /* Atmospheric pressure (psi) */
VARb Zb; /* barrel vent variables */
/* calculate the rate of flow from barrel to atmosphere */
/*
{ double M; / Mass of ball /
double D; / Diameter of barrel and ball /
double L; / Length of barrel (in) /
double x; / Position of ball (in) /
double v; / Velocity of ball (fps) /
}VARb;
*/
{ double Q;
Q = 0.0;
return(Q);
}
#undef Zb
/*----------------------------------------------------------------------*/
UpDate_r(pPV,pZr,t,dt)
#define PV (*pPV)
#define Zr (*pZr)
VARpv PV; /* Pressures and Volumes */
VARr Zr; /* regulator valve variables */
double t;
double dt;
/*
Update the position of the regulator valve. Its assumed
that the top of the valve is attached to the regulator piston.
*/
/*
{ double S; / Surface area of regulator piston (in^2) /
double x0; / Nominal R-valve to top of R-seal (in) /
double Cl; / Leakage flow conductance /
double Z; / Flow conductance/length /
double T; / Position of regulator nut (turns) /
double K; / spring constant of the reg piston spring (lb/in) /
double H; / Regulator nut turns per inch /
double x; / Position of regulator valve (in) /
}VARr;
*/
{ Zr.x = Zr.x0 + Zr.T/Zr.H - (PV.Pr-PV.Px)*Zr.S/Zr.K;
if(Zr.x > Zr.x0) Zr.x = Zr.x0;
if(Zr.x < 0.0) Zr.x = 0.0;
return(0);
}
#undef Zr
#undef PV
/*----------------------------------------------------------------------*/
int UpDate_o(pPV,pZo,pZt,t,dt)
#define PV (*pPV)
#define Zo (*pZo)
#define Zt (*pZt)
VARpv PV; /* Pressures and Volumes */
VARo Zo; /* on-off valve variables */
VARt Zt; /* trigger variables */
double t;
double dt;
/* Update the on-off valve */
/*
{ double C; / Leakage conductance /
double Z; / Flow conductance/Length /
double x; / On-off pin position (in) /
}VARo;
{ double B; / Sear angle (deg) /
double Bo; / Sear angle at which on-off valve turns on (deg) /
double Bb; / Sear angle at which bolt is released (deg) /
double xs; / Sear pivot to on-off pin distance (in) /
}VARt;
*/
{ Zo.x = -Zt.xs*(Zt.B-Zt.Bo)*pi/180.; /* position of on-off pin */
return(0);
}
#undef Zo
#undef Zt
#undef PV
/*----------------------------------------------------------------------*/
int UpDate_p(pPV,pZp,pZt,t,dt)
#define PV (*pPV)
#define Zp (*pZp)
#define Zt (*pZt)
VARpv PV; /* Pressures and Volumes */
VARp Zp; /* power tube variables */
VARt Zt; /* trigger variables */
double t;
double dt;
/*
Update the position and velocity of the bolt. If the bolt is inside
the air chamber, both the air chamber pressure and the power tube spring
exert a force on the bolt. When its outside the air chamber, only the
spring exerts a force. If the bolt position ever gets below Zp.xbl and the
sear angle is smaller than Zp.Bb, the bolt is stopped.
{ double M; / Mass of bolt (oz) /
double S; / Area of bolt (in^2) /
double xc; / Position of bolt when it latches (in) /
double Cl; / Leakage conductance /
double Z; / flow conductance/length /
double K; / Spring constant of power tube spring (lb/in) /
double R; / Friction coefficient (lb-sec/in)/
double x0; / Relaxed length of power tube spring (in) /
double xi; / Length of p.t. spring when bolt is latched (in) /
double xm / Maximum position of bolt (in) /
double x; / Position of bolt (in) /
double v; / Velocity of bolt (fps) /
}VARp;
{ double B; / Sear angle (deg) /
double Bo; / Sear angle at which on-off valve turns on (deg) /
double Bb; / Sear angle at which bolt is released (deg) /
double xs; / Sear pivot to on-off pin distance (in) /
}VARt;
*/
{ if((Zp.x <= Zp.xc) && (Zt.B < Zt.Bb)) /* if Bolt is latched, stop it */
{
Zp.x = Zp.xc;
Zp.v = 0.0;
}
else
{ double vv,F,A;
/* Velocity (in/sec) */
vv = Zp.v*12.0;
/* Force (lb) */
F = -Zp.K*(Zp.x+Zp.x0-Zp.xi-Zp.xc) + (PV.Pa-PV.Pb)*Zp.S;
if(Zp.x <= 0.0)F = F - Zp.R*Zp.v;
/* Acceleration (in/sec^2) */
A = 514.784*F/Zp.M;
Zp.x = Zp.x + (vv + 0.5*A*dt)*dt;
Zp.v = (vv + A*dt)/12.0;
}
/* if bolt is at maximum position, stop it */
if(Zp.x > Zp.xm)
{ Zp.x = Zp.xm;
Zp.v = 0.0;
}
/* if bolt is at minimum position, stop it */
if(Zp.x < Zp.xc)
{ Zp.x = Zp.xc;
Zp.v = 0.0;
}
return;
}
#undef Zp
#undef Zt
#undef PV
/*----------------------------------------------------------------------*/
int UpDate_b(pPV,pZb,pZp,t,dt)
#define PV (*pPV)
#define Zb (*pZb)
#define Zp (*pZp)
VARpv PV; /* Pressures and Volumes */
VARb Zb; /* barrel & ball variables */
VARp Zp; /* power tube variables */
double t;
float dt;
/* Update the position and velocity of the ball */
/*
{ double M; / Mass of ball /
double D; / Diameter of barrel and ball /
double L; / Length of barrel (in) /
double x; / Position of ball (in) /
double v; / Velocity of ball (fps) /
}VARb;
{ double M; / Mass of bolt (oz) /
double S; / Area of bolt (in^2) /
double xc; / Position of bolt when it latches (in) /
double Cl; / Leakage conductance /
double Z; / flow conductance/length /
double K; / Spring constant of power tube spring (lb/in) /
double R; / Friction coefficient (lb-sec/in)/
double x0; / Relaxed length of power tube spring (in) /
double xi; / Length of p.t. spring when bolt is latched (in) /
double xm / Maximum position of bolt (in) /
double x; / Position of bolt (in) /
double v; / Velocity of bolt (fps) /
}VARp;
*/
{ if(Zb.x < Zb.L)
{ double A,vv;
/* Velocity (in/sec) */
vv = Zb.v*12.0;
/* Acceleration (in/sec^2) */
A = 6177.4*(PV.Pb-PV.Px)*0.25*pi*Zb.D*Zb.D/Zb.M;
Zb.x = Zb.x + (vv + 0.5*A*dt)*dt;
Zb.v = (vv + A*dt)/12.0;
}
if(Zb.x < 0.0)
{ Zb.x = 0.0;
Zb.v = 0.0;
}
return(0);
}
#undef Zb
#undef Zp
#undef PV
/*-----------------------------------------------------------------------*/
int UpDate_t(pZt,pZb,pZp,pPV,t,dt)
#define Zt (*pZt)
#define Zb (*pZb)
#define Zp (*pZp)
#define PV (*pPV)
VARt Zt; /* Trigger variables */
VARb Zb; /* ball and barrel variables */
VARp Zp; /* power tube variables */
VARpv PV; /* Pressures and volumes */
double t;
float dt;
/* Update the position of the trigger */
/* put a ball in the chamber if so desired */
/*
{ double B; / Sear angle (deg) /
double Bo; / Sear angle at which on-off valve turns on (deg) /
double Bb; / Sear angle at which bolt is released (deg) /
double xs; / Sear pivot to on-off pin distance (in) /
}VARt;
{ double M; / Mass of ball /
double D; / Diameter of barrel and ball /
double L; / Length of barrel (in) /
double x; / Position of ball (in) /
double v; / Velocity of ball (fps) /
}VARb;
*/
{
if(t >= 0.005)Zt.B=Zt.Bb; else Zt.B=0.0; /* pull trigger at t=0.005 sec*/
return(0);
}
#undef Zt
#undef Zb
#undef Zp
#undef PV
/*-----------------------------------------------------------------------*/
int Err0r(n)
int (n);
{
printf("\nError %d",n);
exit();
return(0);
}