How Long Does a Fall Take? Compare Two Objects — Interactive

How Long Does a Fall Take?
Compare Two Objects — Interactive

Test the mass‑independence claim in vacuum vs real air. Choose two objects, set an environment and wind, then compare their descent. Quadratic drag + buoyancy with a robust RK4 integrator.

Setup & Theming

Preset object A

Environment A

Preset object B (for comparison)

Environment B

Height h (m)

Horizontal wind Ux (m/s) (+ right)

Vertical wind Uz (m/s) (+ up = headwind)

Mass A (kg)

Area A (m²)

C_d A

ρ_obj A (kg/m³)

Mass B (kg)

Area B (m²)

C_d B

ρ_obj B (kg/m³)

Air density ρ A (kg/m³)

Gravity g A (m/s²)

Air density ρ B (kg/m³)

Gravity g B (m/s²)

Time step Δt (s)

Theme (match your site)

Use presets to auto-fill, then tweak anything. Height and winds apply to both A & B. Theme pickers instantly recolor the widget to match your site.

Results

Vacuum time t₀ (A)

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Air/wind time (A)

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Impact speed (A)

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Vacuum time t₀ (B)

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Air/wind time (B)

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Impact speed (B)

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Object A: |v_y| vs time. Dashed line = terminal speed in still air.

Object B: |v_y| vs time.

Object	Env	h (m)	U_x (m/s)	U_z (m/s)	t (s)	t₀ (s)	v_t still‑air (m/s)	h* = v_t²/g (m)	Impact (m/s)	Drift x (m)

Charts show separate speed–time curves for A and B for fast visual comparison.

Physics notes

Vacuum law. No air, uniform g ⇒ t = √(2h/g) (mass‑independent).

Drag & buoyancy. m a = (m − ρV) g − ½ ρ C_d A ‖v − U‖ (v − U). If you enter ρ_obj, V = m/ρ_obj is used for buoyancy; else buoyancy is ignored.

Terminal speed (still air). v_t = √[ 2 (mg − ρ g V) / (ρ C_d A) ], giving a height scale h* = v_t²/g.

Integrator. Stable RK4. Stops when vertical displacement equals h. Winds: Ux (crosswind), Uz (vertical head/tail wind).

Self‑tests

Running…

How Long Does a Fall Take?