Ballistic Range

Fire a projectile and compare trajectories with and without air resistance. Click the canvas to set launch angle, or use the sliders.

No drag (vacuum) With drag (air) 45° optimal (vacuum)

Parameters

Launch angle 45°

Speed (m/s) 50 m/s

Drag coeff (Cd) 0.30

Mass (kg) 1 kg

Gravity (m/s²) 10 m/s²

Vacuum range: —

Max height (vacuum): —

Time of flight: —

Drag range: —

Range reduction: —

Physics: Vacuum trajectory: x=v₀cosθ·t, y=v₀sinθ·t−½gt². Range R=v₀²sin(2θ)/g, maximum at θ=45°. With drag: F_drag=½ρCd·A·v², integrated numerically via RK4. Drag always reduces range and shifts the optimal angle below 45°.