The Sand Casting Gating Ratio & Choke Area Runner Sizer provides an interactive three-variable algebraic modeling tool for exploring foundry mold feeding geometry, sprue choke sizing, and runner flow proportions.

### Algebraic Ratio Formulation The component evaluates foundry mold inputs through three generalized algebraic relationships: - Primary Metric: $(val_1 \times val_2) / \max(0.01, val_3)$. In casting gating systems, this represents volumetric metal flow throughput relative to friction loss and runner resistance. - Geometric Mean (Secondary Index): $\sqrt{\max(0, val_1 \times val_2)}$, modeling transitional fluid velocity through gating orifices. - Efficiency Ratio (%): $\min(100, \max(0, (val_1 / (val_1 + val_2)) \times 100))$, modeling sprue-to-runner volume distribution efficiency.

### Note on Foundry Metallurgy & Fluid Mechanics This tool computes a generalized three-parameter algebraic proxy. In professional metal casting design, choke area determination requires Bernoulli fluid mechanics and Torricelli velocity equations ($A_c = \frac{W}{\rho \cdot t \cdot c \sqrt{2 g H}}$ where $W$ is pour mass, $\rho$ is liquid metal density, $t$ is pour time, $c$ is gating discharge coefficient, and $H$ is effective sprue height). Standard gating ratios ($A_{\text{sprue}} : A_{\text{runner}} : A_{\text{ingate}}$) must also account for pressurized versus unpressurized gating designs.

### Worked Numeric Example Using default component parameter values: - Primary Dimension / Load ($val_1$): 100 - Operating Coefficient ($val_2$): 20 - Safety Factor / Loss Ratio ($val_3$): 5 - Evaluated Outputs: - Primary Metric: $(100 \times 20) / 5 = 400.00$ - Geometric Mean: $\sqrt{100 \times 20} = \sqrt{2000} \approx 44.72$ - Efficiency Ratio: $(100 / (100 + 20)) \times 100 = 83.33\%$

### In-Browser Processing Note All foundry parameters and gating equations calculate locally inside your web browser with zero server data storage.