Lighthouse Beam Simulator (2D)

Rotation

Rotation speed 6.0 rpm

Lamp & Lens

Lamp intensity 1200 cd

Fresnel focusing (lens order) ×180

Atmosphere

Transmissivity 0.90 / km

Beam sweeping — watch for a ship to enter the lit arc.

Live Readout (Allard's Law)

Effective intensity

—

Nominal range

—

Rotation period

—

Ships lit / seen

0 / 0

How it works

A lighthouse lamp on its own radiates in almost every direction, so most of its light is wasted. A Fresnel lens — a ring of stepped prism segments instead of one thick piece of glass — bends that scattered light into a single narrow horizontal beam. The result is expressed as an effective intensity: I_eff = I_lamp × (lens order), because concentrating the same total light into a narrower beam raises its candela even though total power hasn't changed. A rotating lens assembly sweeps that beam past any given bearing once per revolution — this simulator turns the whole assembly, exactly like the drum lenses used at sea.

How far a ship can actually see that beam is governed by Allard's Law, the formula the Admiralty List of Lights uses for a "nominal range": E = I_eff × T^d / d², where E is the smallest illuminance the human eye can detect against the night sky (taken here as 2×10⁻⁷ lux), T is the atmosphere's transmissivity per kilometre (1.0 = perfectly clear, lower = haze or fog absorbing light), and d is distance. Because T is raised to the power of d, range collapses quickly once haze sets in — a small drop in transmissivity costs far more range than the same drop in lamp intensity.

This simulator solves that equation for d every frame (bisection search, since d appears both inside and outside the exponent) as you adjust lamp intensity, lens order and atmospheric clarity, then draws a ring at that radius: any ship inside the ring, when the beam sweeps across its bearing, is marked as "sighted".

Beacon beam sweep Nominal range ring Ship (lit when sighted)