Rainstorm Precipitation

Meteorological atmospheric downpour integrating aerodynamic terminal velocity fall rates, aerodynamic wind shear slant, and damped Bessel ground collision ripples.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Rainfall Intensity 450

Active precipitation streak count

Wind Shear Slant 0.15

Horizontal gale deflection angle

Mathematical Formulation

91 chars medium

Analytical Equation

v_{\text{term}} = \sqrt{\frac{2 m g}{\rho A C_d}}, \quad \mathbf{v} = v_{\text{term}} \begin{bmatrix} \sin\theta_{\text{wind}} \\ \cos\theta_{\text{wind}} \end{bmatrix}, \quad r_{\text{ripple}}(t) = v_{\text{wave}} (t - t_{\text{impact}})

Compact Formula

y += speed * dt, x += speed * sin(wind) * dt, ripple = ellipse(x, y, r, 0.35r) * exp(-γt)

Renderer Logic

dropY[i] += dropSpeed[i] * dt;
dropX[i] += dropSpeed[i] * windDx * dt;
ctx.ellipse(ripX[r], ripY[r], ripRadius[r], ripRadius[r] * 0.35, 0, 0, Math.PI * 2);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#rain #precipitation #weather #fluid #ripples #atmosphere #water

Author: Math Art Core Target: 60 FPS

Rainstorm Precipitation

Live Parameters

Mathematical Formulation

Mathematical Tags

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