Worthington Water Splash

High-speed fluid drop impact mechanics capturing the elevated crenellated Worthington splash crown, Rayleigh-Plateau capillary central jet, and pinch-off droplet ballistics.

Playground

60 FPS • Canvas 2D

Click + Drag to interact with field

Live Parameters

Impact Cycle Speed 1.1

Water impact repetition frequency

Splash Amplitude 1.2

Crown height & jet ejection reach

Mathematical Formulation

91 chars high

Analytical Equation

r(\theta) = R_{\text{rim}} [1 + A_c \sin(n \theta)], \quad y_{\text{drop}}(t) = y_0 + v_{y0} t - \frac{1}{2} g t^2, \quad \lambda_{\text{opt}} \approx 4.51 d_{\text{jet}}

Compact Formula

crown_h = sin(age * π) * 110, jet_h = sin(jetAge * π) * 160, drop_y += vy*dt + 0.5*g*dt^2

Renderer Logic

const cuspHeight = crownH * (1 + 0.35 * Math.sin(phi * 8));
const jetH = Math.sin(jetAge * Math.PI) * (160 * splashHeight);
const topDropY = waterLineY - jetH - 18 * Math.sin(jetAge * Math.PI * 1.5);

Open in Playground Zero Dependencies • Standalone

Mathematical Tags

#splash #water #worthington #fluid #droplets #hydrodynamics #capillary

Author: Math Art Core Target: 60 FPS

Worthington Water Splash

Live Parameters

Mathematical Formulation

Mathematical Tags

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