Range (drag)
—
Projectile Launcher with Drag
Compare no-drag vs drag trajectories using 4th-order Runge–Kutta integration.
Range (no drag)
—
Max height
—
Time of flight
—
Formula
Drag force: Fd = ½ · ρ · Cd · A · v²
Equations of motion (per component):
ax = −(Fd/m) · (vx/v)
ay = −g − (Fd/m) · (vy/v)
Equations of motion (per component):
ax = −(Fd/m) · (vx/v)
ay = −g − (Fd/m) · (vy/v)
Physics behind projectile drag
In reality every object moving through air experiences a drag force that opposes its velocity. At speeds above a few m/s this force goes as v² (quadratic regime). The effect is dramatic: a baseball hit at 45 m/s travels about half the no-drag range because drag saps kinetic energy throughout the flight and drops the optimum launch angle to around 35–40°. This simulator integrates the equations numerically because no closed-form solution exists.
Related tools
FAQs
What drag model does this use?
Quadratic drag F = ½·ρ·Cd·A·v².
Which numerical method?
4th-order Runge–Kutta.