## Sunday, September 29, 2013

### You Do The Math - Harnessing the Power of Lightning

Many people have seen lightning storms last a long time, and wondered how to capture all that energy and store it somehow.  It's worth a shot, right?  Parts of Florida receive 150 strikes per year per square mile, parts of Zambia and Congo get 300, and the Empire State Building gets 1000.  And Lake Maracibo near the Catatumbo River gets as much as 280 strikes per hour, 10 hours a night, for about 150 nights a year.  If the average is 140 strikes per hour, that's 210,000 strikes per year.

Many people suggest capturing lightning with electrical batteries or capacitors.  But, because one lightning strike is 100 million volts, you would need a million capacitors in series, if each capacitor could hold 100 volts.  But at 10,000 amps per strike, it has a trillion watts (100 million x 10,000 = 1 trillion).

Such a powerful strike lasting 1 second would have this many watt-hours of energy:

1,000,000,000,000 W / 3,600 seconds = 27,777,777 watt hours.

But most strikes are more like 10 or 20 milliseconds.  Let's use 10 milliseconds:

1,000,000,000,000 W / 3,600 seconds / 1000 milliseconds * 10 = 277,777 watt hours.

Since electricity goes for 11 to 50 cents per kilowatt hour across the US, let's use New York City's 2013 price of about 20 cents (http://www.bls.gov/ro2/avgengny.pdf):

277,777 watt hours / 1000 * 20 cents = \$555.55

New York State had the first hydro powered electrical utility at Niagara Falls, so let's put the first lightning power plant in the Empire State Building, which gets 1000 strikes per year.

\$555.55 x 1000 = \$555,555

Roughly half a million dollars worth.  Maybe enough for 277 suburban homes.  Lame.   But, it's worth the effort, right?  Of course, because it's so f'ing cool.

Let's not use capacitors.  That's too easy.  Let's make a huge solenoid a quarter mile tall.  The coil of steel will need to be coated in a thick insulator to keep the lighting going around and around, instead of leaping through the air between each coil.

The coil's magnetic field will act on a huge, iron weight, shooting it upwards violently with each strike.  The counter force on the coil from the weight will compress the coil like a spring, so the coil will need to be encased in a solid material to prevent this.  The weight is also insulated, to prevent the lightning from bypassing the coils and choosing a shorter path.  The weight will be suspended by a long cable, that is not a conductor.  This wraps around spring-loaded drums at the top of the building, so that as the weight rises, the drums take up the slack.

The weight will need a ratcheting system to keep it from falling back down.  After all, the cable will not rise very fast, and will be slack for some time until the drums can wind it up.  These drums are attached to AC generators using very "tall" gearing to increase the torque and decrease the speed, so that  the weight can be lowered at a slow rate between lightning strikes.

At 1000 strikes per year, that's about 3 strikes a day.  However, there are many days without storms.  If New York weather is anything like my midwest home, and it is, I would say it receives 10 or 20 big storms a year, so a maximum of 100 strikes in an afternoon and evening.  We should be able to store this much energy in a quarter-mile tall solenoid.

277,777 watt-hours per strike x 100 strikes x 3,600 seconds = 99,999,720,000 Joules

Since potential energy equals mass times height times the acceleration due to gravity (9.8 meters per second squared), let's see how big a weight we'll need for a quarter mile height.

99,999,720,000 = 0.25 x 1609 meters x 9.8 m/s^2 x Mass in kilograms

The mass equals 25,367,441 kilograms, times 2.2 is 55,808,370 pounds, or 27,904 tons.  Seeing as how the entire Sears Tower weighs about 220,000 tons, I'm thinking this weight wold bring the Empire State Building DOWN.  Whatever.

Iron is about 10 cents per pound at the recycler, so this weight would cost about \$5,580,837 in scrap metal.  Since there's \$555,555 worth of electricity a year striking the building, this weight would take 10 years to pay off in the very least.  But at the outrageous cost of union labor, special insulators, concrete, magnets, copper, etc, this project may take 100 years to pay off.

Let's move it to the Catatumbo River.  This place receives roughly 200 times more lightning.  So, the solenoid might actually pay for itself in a few years.  But, at 140 nights of storms a year, you would need to build 14 of these solenoids to make use of all that lightning.  Maybe a payoff of 28 to 42 years.  Buena suerte, mis amigos.