Interactive

Parameter explorer

The Master Formula is a product of five factors. Take the logarithm and the product becomes a sum:

\log_{10} P \;=\; \log_{10}\Phi + \log_{10}\sigma + \log_{10}\Delta p + \log_{10} v_{\text{ph}} + \log_{10}\eta_{\text{conv}}

That single fact is the key to reading the formula as an engineer. Each factor contributes independently to the exponent of the result, so the outcome is decided by which factors are large and which are vanishingly small. Move the sliders below — each runs over many orders of magnitude — and watch the running estimate and the contribution bars.

Presets:

Φ m⁻²s⁻¹sr⁻¹J⁻¹ 10^10

σ m² 10^-44

Δp kg·m/s 10^-21

v_ph m/s 10^4

η — 10^-2

Estimated integrand of P(t) —

Contribution to log₁₀ P (orders of magnitude)

Values are illustrative orders of magnitude in SI-like units — not a device rating. The explorer evaluates the integrand at one representative energy and direction; the real power integrates over the whole spectrum.

How to read it

The tiny coupling term $\sigma$ pulls the result down by dozens of orders of magnitude; the enormous flux $\Phi$ pushes it back up. This tension — a colossal supply against a minute interaction probability — is the entire engineering problem of continuous ambient conversion, and it is why the framework treats $\sigma$ and $\eta_{\text{conv}}$ as the design levers. For the physics behind each slider, read the variable definitions and the per-parameter chapters; for the exact bookkeeping, see the full derivation.