shithub: ballistics

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add air drag.

--- a/dat.h

+++ b/dat.h

@@ -1,4 +1,6 @@

-#define Eg	9.81

+#define Eg	9.81	/* earth's gravity (m·s⁻²) */

+#define Cd	0.45	/* drag coefficient for a sphere */

+#define ρ	1.293	/* air density (kg·m⁻³) */

 #define PIX2M	0.001

 #define M2PIX	(1.0/PIX2M)

@@ -6,6 +8,7 @@

 	Stheta = 0,

 	Spos,

 	Svel,

+	Sdrag,

 	Sdeltax,

 	Seta,

 	SLEN,

@@ -17,4 +20,5 @@

 {

 	Point2 p, v;

 	double mass;

+	double r;

 };

--- a/main.c

+++ b/main.c

@@ -15,6 +15,7 @@

 Projectile ball;

 double t0, Δt;

 double v0;

+double A;	/* area of the projectile that meets the air */

 Point2 target;

 char stats[SLEN][64];

@@ -47,11 +48,27 @@

 }

 void

+∫(double Δt)

+{

+	Point2 Fd;	/* drag force */

+

+	Fd = mulpt2(mulpt2(ball.v, -vec2len(ball.v)), 0.5 * Cd*ρ*A);	/* ½CdρAv² */

+	ball.v = addpt2(ball.v, mulpt2(addpt2(Vec2(0,-Eg), divpt2(Fd, ball.mass)), Δt));

+	ball.p = addpt2(ball.p, mulpt2(ball.v, Δt));

+	snprint(stats[Spos], sizeof(stats[Spos]), "p: %v", ball.p);

+	snprint(stats[Sdrag], sizeof(stats[Sdrag]), "Fd: %v", Fd);

+	if(ball.p.y <= (2+1)*M2PIX){

+		ball.p.y = (2+1)*M2PIX;

+		ball.v = Vec2(0,0);

+	}

+}

+

+void

 drawstats(void)

 {

 	int i;

-	snprint(stats[Svel], sizeof(stats[Svel]), "v: %gm/s", vec2len(ball.v));

+	snprint(stats[Svel], sizeof(stats[Svel]), "|v|: %gm/s", vec2len(ball.v));

 	snprint(stats[Sdeltax], sizeof(stats[Sdeltax]), "Δx: %gm", target.x-ball.p.x);

 	for(i = 0; i < nelem(stats); i++)

 		stringn(screen, addpt(screen->r.min, Pt(10, font->height*i+1)), statc, ZP, font, stats[i], sizeof(stats[i]));

@@ -86,7 +103,8 @@

 	switch(menuhit(2, mc, &menu, nil)){

 	case SETV0:

 		enter("v0(m/s):", buf, sizeof(buf), mc, kc, nil);

-		v0 = strtod(buf, 0);

+		if(buf[0] != 0)

+			v0 = strtod(buf, nil);

 		break;

 	}

 }

@@ -124,7 +142,7 @@

 	if(ball.p.y <= (2+1)*M2PIX){

 		p = subpt2(fromscreen(mc->xy), ball.p);

 		θ = atan2(p.y, p.x);

-		snprint(stats[Stheta], sizeof(stats[Stheta]), "θ: %g°", θ*180/PI);

+		snprint(stats[Stheta], sizeof(stats[Stheta]), "θ: %g°", θ/DEG);

 		dist = v0*v0*sin(2*θ)/Eg;

 		target = Pt2(ball.p.x+dist, 0, 1);

 		eta = 2*v0*sin(θ)/Eg;

@@ -204,6 +222,8 @@

 	ball.p = Pt2((2+1)*M2PIX,(2+1)*M2PIX,1);

 	ball.v = Vec2(0, 0);

 	ball.mass = 106000;

+	ball.r = 0.1;		/* 10cm */

+	A = 2*PI*ball.r*ball.r;	/* ½(4πr²) */

 	v0 = 1640; /* Paris Gun's specs */

 	scrsync = chancreate(1, 0);

@@ -227,14 +247,8 @@

 		case 2: key(r); break;

 		case 3: redraw(); break;

 		}

-		Δt = (nsec()-t0)/1e9;

-		ball.v = addpt2(ball.v, mulpt2(Vec2(0,-Eg), Δt));

-		ball.p = addpt2(ball.p, mulpt2(ball.v, Δt));

-		snprint(stats[Spos], sizeof(stats[Spos]), "p: %v", ball.p);

-		if(ball.p.y <= (2+1)*M2PIX){

-			ball.p.y = (2+1)*M2PIX;

-			ball.v = Vec2(0,0);

-		}

-		t0 += Δt*1e9;

+		Δt = (nsec()-t0);

+		∫(Δt/1e9);

+		t0 += Δt;

 	}

 }