## Monday, April 14, 2014

### The Langley, A Useful But Forgotten Unit

I like to collect units (like the Sverdrup), and came across an interesting one today -- the langley (ly), which is a unit of energy per unit area. Climate scientists back in the '60s used to use it for solar irradiance, and here's why -- it makes it easy to express the solar energy incident on the Earth.

The langley's definition is

1 ly = 1 calorie/cm2
where, as usual

1 calorie (cal) = the amount of heat required to raise one gram of water by 1 degree Celsius.

If you convert this to SI units, you get
1 ly = 41,840 Joule/m2
so
1 langley per minute = 1 ly/min = 697.3 Watts/m2

so the Earth's solar constant is
S = 1365 W/m2 = 1.96 ly/min ≈ 2 ly/min

which is a nice small, round number.

Going further, the "dietary calorie" -- how we measure the energy content of food -- is the Calorie (= 1000 cal). So

≈ 20 Cal/min per square meter Now, 20 Cal is the energy content of a lime (or 5 spears of asparagus, or 3/4ths of a cup of green beans, or 1/2 of a medium summer squash), so

≈ 1 lime per minute per square meter

which is an interesting way to think about the solar constant (which isn't really a constant, but the name sticks.) If the average person eats 2,000 Calories per day (call it one "eat"), then, if I did the conversions right

S ≈ 10,000 eats/min per square kilometer

But the average person lives about 20,000 days (hence the Moody Blues song), so the amount of food they will eat in one "lifetime" is about 20,000 eats. So

S ≈ 0.5 lifetimes/min per square kilometer

So a couple eating about average, and living about the average number of years, will together eat about as much food as the energy the sun delivers to a square kilometer in one minute.

At the top of the atmosphere, of course. The amount at the surface will depend on their culinary albedo.