Independent educational model of a fictional headland light (Gullrock Head). Not affiliated with Trinity House or any lighthouse authority; not for navigation. Values marked (model) are illustrative; (typical) are textbook figures to spot-check.
1. The lens floats on mercury
A lens and frame of M = 2500 kg (model) displace V = M/ρHg = 0.185 m³ of mercury (ρ = 13 534 kg/m³, typical), a draught of h = V/(πR²) = 0.163 m on a 0.60 m float; the buoyant force ρgV = Mg = 24.5 kN carries the lens. Mercury is a thin liquid (η = 1.5 mPa s), so the Couette drag τ = 2πηωR³L/hg is only about 0.016 N m, about 0.5 % of the total resistance: the point of the bath is a nearly frictionless bearing. Mercury is toxic. This page shows the historical arrangement only; modern lights use ball bearings and sealed drives. Never handle it.
2. A falling weight is a motor
The weight drops Δh = κΔθ as the lens turns, with κ = 16.7 mm/rad (model: it folds in the drum radius, the gear train and the efficiency). Torque at the lens is τd = m g κ = 9.83 N m for 60 kg. Re-wind interval tw = H T /(2πκ): with H = 8 m (model) and T = 40 s it is 3 050 s = 50.8 min; at T = 10 s only 12.7 min. Energy stored mgH = 4.7 kJ; the lens only receives τω = 1.5 W while the rest is burned off in the governor.
3. The governor is a feedback controller
Resistance is τr = τbearings + τHg + τwind (3.30 N m constant bearings, model; wind 0 to 8 N m, model, torque proportional to dynamic pressure). The governor brakes in proportion to the excess speed, τg = Kg max(0, ω − ωe) with Kg = 400 N m s/rad (model), so I dω/dt = τd − τr − τg with I = ½MR² = 450 kg m² and settles to ω = ωe + (τd − τr)/Kg in about I/Kg = 1.1 s. This is a proportional controller with droop: a storm that adds 4 N m of wind leaves less torque for the governor to absorb: the speed falls by 0.010 rad/s and the period of a 40 s light grows by 6.8 % (42.7 s), which is why the keeper trims the spring. If the wind exceeds the drive, τd < τr and the lens stops (the minimum weight for a 4 N m wind is 44.6 kg). The drawn flyballs use the conical pendulum law cosα = g/(Ω²L) with a model gear ratio of 47; the gear train between drum and governor is illustrative.
4. Flash, period and character
A lens turning at ω = 360°/Trot sweeps a beam of width θb = 3° (model) past the ship, so one flash lasts tf = θb/ω: 0.33 s at 40 s, 0.083 s at 10 s. With n evenly spaced panels the pattern repeats every Trot/n; grouping panels in pairs or triples gives Fl(2), Fl(3). Wider panels make long flashes (LFl, at least 2 s), isophase (equal light and dark) and occulting (light longer than dark). The code is derived from the exact on/off intervals, not read from a table. A character is only useful if the neighbouring lights differ: the builder lists how confusable your pattern is with each light on the fictional coast.
5. Why the tower stands
A tapered masonry shell (H = 26 m, D = 7.0 to 4.2 m, wall 1.0 to 0.5 m, ρ = 2 400 kg/m³ typical) weighs W = ρgV = 7.18 MN. Wind gives q = ½ρav², F = q Cd Dmean H, M = FH/2 (Cd = 0.7, model). The resultant sits e = M/W from the axis; the section stays in compression while e is inside the core radius (D/8)(1 + (d/D)²) = 1.32 m. At 40 m/s: F = 99.9 kN, M = 1.30 MN m, e = 0.18 m, a factor of safety against overturning of 19. The tiered integral that uses the real taper gives a smaller moment; both are shown. Spray (model: 0.2 % water by mass in the lowest 8 m) adds a few percent. The vulnerable parts are the lantern panes: suction p = q Cp with Cp = −1.5 (model).
Simplified
The lens is a rigid disc, gear and bearing friction is constant, the governor is linear, no backlash, torsion or tooth-meshing ripple, no turbulence in the mercury, constant air density, no gusts. The weight is wound at a game-compressed 2 m/s. The ocean and sky are scenery.