t 0.00 sx 0.0 mheight 0.0 mspeed 0.0 m/sFPS 0

Drag to orbit, wheel / pinch to zoom. Green = velocity, amber = horizontal part v_x, blue = vertical part v_y. Ghost orbs are a strobe photo: equal time steps. 1 grid cell = 1 m of flight (the whole scene is a scale model).

Classroom Orb Launcher: Strobe Photo, Vectors and Drag

Aim a glowing orb across a lab bench and see why a path is a parabola: constant horizontal speed, steady vertical change, and what air does to both.

Scenarios

Launch

World

Place (sets gravity and air density)

Orb

Show

Live readouts

Path: height against distance

Velocity parts over time

Energy over time

Experiment: which angle goes farthest?

Same speed and same launch point, only the direction changes. The measured best angle (numerical flights) is compared with the exact vacuum answer.

Independent numerical checks

Controls

Fire: Space. Reset: R. Orbit: drag or one finger; zoom: wheel or pinch. Camera buttons: Lab view frames the whole flight; Side view looks along the flight plane, Top view down onto the bench, Follow tracks the orb.
Slow-motion slider slows the clock so you can read the numbers. The strobe interval sets the time between ghost orbs.
Presets change several sliders at once; every slider can be changed afterwards.

The science

Without air. Gravity acts only downward, so x = x₀ + v₀cosθ·t and y = y₀ + v₀sinθ·t − ½gt². The horizontal velocity never changes; the vertical velocity changes by exactly g every second. That is why the strobe ghosts are evenly spaced sideways while the vertical gaps grow and shrink. Time of flight from height y₀: T = (v₀sinθ + √((v₀sinθ)² + 2gy₀))/g, range R = v₀cosθ·T, top of the path H = y₀ + (v₀sinθ)²/2g. From table level the range is R = v₀² sin2θ / g, so θ and 90° − θ give the same range, and 45° is best. Launching from a height y₀ above the landing level makes the best angle smaller: tanθ* = v₀/√(v₀² + 2gy₀).

With air. Quadratic drag on a sphere: F = ½ ρ C_d A |v_rel| v_rel, with A = πd²/4, C_d = 0.47 held constant (a smooth-sphere value; a real C_d changes with the Reynolds number), and v_rel = v − wind (wind is horizontal, uniform). Equations of motion dv/dt = −g ŷ − k|v_rel|v_rel with k = ρC_dA/2m, integrated with fixed-step RK4 (Δt = 1/240 s); landing and the apex are found with a fractional final step. Drag lowers the range, makes the descent steeper than the climb, and pulls the best angle below 45°. A falling orb tends to the terminal speed v_t = √(2mg/ρC_dA), which is one of the checks.

What is simplified. Point mass (no spin, no Magnus force, no lift), constant air density and gravity (no height dependence), C_d constant, flat table with the landing at height 0 and no bounce. The orb is drawn larger than its physical diameter so you can see it; the diameter slider only changes the drag. The scene is a 1:10 scale model: 1 m of flight is 0.1 world units, so the launcher looks tiny next to a 25 m flight. The tube is a 2 m guide: the flight starts at its muzzle. Air density and gravity presets are typical round values (Earth sea-level air 1.225 kg/m³, Moon 1.62 m/s², Mars 3.71 m/s² and about 0.02 kg/m³, Titan 1.35 m/s² and about 5.4 kg/m³).

Safety and tone. A classroom physics model with an inanimate glowing orb. Not a design tool for real launchers. Models built with Blender, scene by Three.js.