Burning Desire For Efficiency
by Do The Math 
I kept the electronics in the garage (only the laser and sensor were outside), accompanied by a data acquisition unit and a computer to log the continuously sampled series (3 second samples were sufficient). Not the most elegant way to get the data, but I used stuff I had on hand. And it worked. And the plots are nice.
Here we see the hot water heater pilot light causing the sensing circuit to respond in a periodic fashion. Every time the needle crosses in front of the laser, the sensor voltage goes way up. The needle can be a little jerky, so it sticks and slips—causing some spikes to be stunted and steppy. In this plot, ten revolutions span 11.2 hours. At 510 Btu per revolution, this corresponds to 133 W of continuous power in the pilot.
Most of the time, the water heater pilot light creates our only gas demand. In the summertime, even our shower activity—albeit modest—is satisfied by the pilot. We can see in the plot above the periodic signature of the needle interrupting the laser, and also a sinusoidal behavior between needle crossings. Unintentionally, the sinusoid gives a useful cue as to exactly when a high-flow demand (stove, oven, heater) is initiated, so that one does not have to wait until the needle event for the first indication. The sinusoidal pattern is presumably from scattered light off of irregularities in the needle hub.
Even without the extra benefit from the hub, one can determine how much gas was used by noting how many cycles appear between the languid pilot spikes, compared to how many revolutions the pilot would have produced in the same period.
Each half-cubic-foot of gas is equivalent to 510 Btu, since 100 cubic feet delivers 1.02 Therms, and a Therm is 100,000 Btu. Therefore, each turn amounts to 538 kJ, or 0.149 kWh.
Stove-top Boil
Enough with the preliminaries. I lured you in with promises of efficiency measurements, and went off instead into some mad scientist tangent.
If I place 500 mℓ of water in a copper-bottomed 4-quart (approx. 4 ℓ) pot, and set this pot—without lid—on top of the largest burner and let-er rip, what efficiency do I get? The flames are mostly hitting the bottom of the pot, but maybe a smidgeon of curling around the sides. Any guesses?
Two languid pilot light needle sweeps frame this series. Shortly after the first pilot spike, the gas stove was turned on, producing two quick spikes and a sped-up periodic signature in the baseline. It is 65.3 minutes between pilot spikes, during which time the needle made three turns. Ordinarily, it would take 67 minutes between pilot spikes (one turn). We can therefore attribute 2.03 turns to the gas stove, amounting to 1033 Btu, or 1.09 MJ. The 1.95 minutes between stove spikes translates to a burn rate of 15,700 Btu/hr, about 460 of which are from the pilot light.
Starting from an ambient temperature of 18°C (water at equilibrium), and heating to a boil, the gas meter reveals 1.09 MJ of energy was used on top of the steady burn from the hot water heater pilot light, at a rate of 4500 W (about 15,000 Btu/hr). Meanwhile, it was supposed to take only 171.5 kJ of energy to boil this amount of water. So the efficiency was a mere 16%.
