Interactive note. Edit the highlighted values; the trajectory redraws.
A shell is launched from a prescribed initial state. The dashed curve is the closed-form no-air result; the red curve integrates the drag model. The difference between the two curves is the useful part of the experiment.
In this run, the launch speed is m/s at degrees from height m. The shell mass is kg, diameter m, drag coefficient , wind m/s, and the RK4 step is s.
Ignoring air, horizontal motion is uniform and vertical motion is accelerated by gravity. This baseline makes the effect of drag visually measurable.
y(t) = y0 + v0 sin(theta)t - 12gt2
The simulated shell is treated as a circular projectile moving through still or moving air. Air resistance grows with the square of relative velocity, so wind changes the drag force even when launch conditions are unchanged.
Fd = 12rho Cd A|v-w|2, A = pi(d/2)2
The red trajectory is advanced with fourth-order Runge-Kutta. Smaller time steps cost more computation but reduce integration error.
The plot uses locked x/y scale, so equal distances have equal visual length.