Directional Yagi-Uda beam antennas use precise physical spacing between active driven elements, passive reflectors, and forward directors to shape electromagnetic beam radiation patterns. In this calculation utility, three dimensional variables model element proportions: an active element dimension ($v_1$), an operating boom coefficient ($v_2$), and a secondary element spacing rate ($v_3$).

The utility evaluates the primary boom ratio metric ($[v_1 imes v_2] / max(0.01, v_3)$), the root beam factor ($sqrt{max(0, v_1 imes v_2)}$), and the relative element distribution percentage ($[v_1 / (v_1 + v_2)] imes 100$).

### Worked Numeric Example Consider an experimental VHF boom spacing calculation with custom inputs: - Primary Dimension / Load: 140 - Operating Coefficient: 28 - Secondary Factor / Rate: 7

Step-by-step results: - Primary Metric: $(140 imes 28) / 7 = 3920 / 7 = 560.00$ - Operating Metric: $sqrt{140 imes 28} = sqrt{3920} approx 62.61$ - Ratio Efficiency: $[140 / (140 + 28)] imes 100 = (140 / 168) imes 100 approx 83.33%$

### Client-Side Processing Note All mathematical logic runs 100% locally in your web browser via client-side JavaScript. Antenna dimensions and frequency inputs remain on your personal computer and are never logged or transmitted over the network.