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An automatic gas-lighting system associated with Gustaf Dalén. The sun valve decides whether daylight permits the main supply; a separate flashing mechanism determines the repeated light pattern. Keeping those functions distinct is useful when identifying what an apparatus actually controls.

Take a stipulated pair of effective rods with common length $L$, linear thermal expansion coefficient ${\alpha }_L$, heat capacity $C$, projected illuminated area $A$, and thermal conductance $G$ to an environment at constant temperature $T_a$. One reference represents the symmetric polished-rod assembly. Write ${\theta }_b=T_b-T_a$ and ${\theta }_r=T_r-T_a$. Let their effective radiometric absorptances be $a_b>a_r$ for a fixed incident optical spectrum, and let $E(t)$ be the common irradiance. A spatially uniform, linear heat-balance model givesHere $G$ includes a linear approximation to the relevant losses; changing the surface treatment can also change those losses in a real device. We stipulate equal $C$ and $G$ to isolate the response to absorbed illumination, with thermal coupling from the burner neglected. Small, mechanically unconstrained extensions then give a differential displacementThe time constant $\tau$ describes thermal memory. A common imposed temperature shift cancels from the extension difference under the matched-coefficient assumptions; mismatched materials, geometry or thermal coupling can spoil that cancellation.

For a step from darkness to constant irradiance $E_0$, with initially equal rod temperatures, the first-order linear differential equation givesChoose $L=0.20\mathrm{m}$, ${\alpha }_L=20\times 10^{-6}{\mathrm{K}}^{-1}$, $A=0.0020{\mathrm{m}}^2$, $a_b=0.9$, $a_r=0.1$, $C=5.0\mathrm{J}{\mathrm{K}}^{-1}$, $G=0.20\mathrm{W}{\mathrm{K}}^{-1}$ and $E_0=600\mathrm{W}{\mathrm{m}}^{-2}$. The calculated difference of absorbed powers is $0.96\mathrm{W}$, givingFor an illustrative ideal valve that closes at $\delta =g=10\mu \mathrm{m}$, the closing time isThis threshold is crossed only when $0<g<{\delta }_{\infty }$. These are chosen model parameters, not a fit to a historical valve.

After illumination stops at $t=t_1$, the displacement decays as $\delta (t)=\delta (t_1)e^{-(t-t_1)/\tau }$. With $t_1=180\mathrm{s}$, the model reopens about $16.3\mathrm{s}$ later. Thus a sun valve responds to the thermal history of illumination; it does not read a clock or directly measure the beacon's brightness.

Dalén's 1910 patent describes gas entering a diaphragm chamber. When its pressure overcomes a spring and magnetic restraint, a valve opens and the pilot ignites the burner. Escape of gas lowers the pressure, letting the valve close. A ratchet and cam alter an additional feed to create groups of flashes. This specification describes a pressure-driven flashing mechanism, rather than the sun valve's daylight sensor.^[ref]

The patent is evidence of the proposed mechanism, not an independent endurance or fuel-consumption test. For a simple original budget, suppose the pilot consumes gas at a steady rate $q_p$, the main burner consumes $q_m$ while lit, daylight shutoff permits operation for fraction $f$ of the day, and flashes occupy fraction $d$ of that permitted time. Then the daily mean consumption isFor stipulated $f=1/2$, $d=0.10$ and $q_p=0.02q_m$, this is $0.07q_m$, compared with $1.02q_m$ for a continuously lit main burner with the same pilot. The calculated saving is about $93.1\%$. The arithmetic explains the two independent opportunities for saving fuel; it does not establish those fractions or that performance for an actual lighthouse.

A mechanical engineer whose work connected gas lighting to automatic operation. Chalmers records his mechanical-engineering qualification in 1896.^[ref] After an accident left him blind in 1912, he returned to AGA in 1913 and continued leading the company.^[ref]

The sun valve links radiometric absorptance, thermal expansion and mechanical motion to a useful decision: whether a beacon should receive its main gas supply. The Dalén light combines this daylight response with repeated flashes. The Nobel Prize in Physics in 1912 recognized his automatic regulators for lighthouse and buoy lighting.

Awarded to Gustaf Dalén for automatic regulators used with gas accumulators for lighthouse and buoy lighting. The sun valve and Dalén light connect the award to mechanical engineering.^[ref]

A sun valve automatically restricts a gas light's supply in daylight and allows it again as illumination falls. In Gustaf Dalén's design, a blackened rod and three polished rods respond differently to sunlight. Their relative thermal expansion operates the gas valve through a membrane; a pilot flame permits relighting. The museum dates this design to 1907.^[ref]

The useful comparison is between two thermal responses. Both kinds of rod expand when warmed; a dark surface can absorb more incident radiant power, so its temperature rises more. Comparing their extensions can reject a common ambient-temperature change while responding to illumination. The mechanism converts light into heat, heat into a difference of length, and that difference into a change of gas flow. Differential thermal model of a sun valve makes those assumptions quantitative.