An inquisitive reader recently asked a curious question on Facebook: Does a bolt of lightning provide enough energy to power a town? I don’t know, but there is a way to get a fair estimate. Let’s find out how many volts are in a lightning strike:
From articles in Windpower Engineering & Development, we learn that lightning bolts carry from 5 kA to 200 kA and voltages vary from 40 kV to 120 kV. So if we take some averages, say, 100 kA and 100 kV, this bolt would carry this much power, P:
P = 100×103 A x 100 x 103 V
= 10,000 x 106 VA or Watts
= 1 x 1010 Watts
Recall that 1010 Watts is 10,000,000,000 or 10 billion Watts.
Now assume this energy is released in 1 sec. So the power is:
1010 W-sec. On your electric bill, you’ll see you pay for Watt-hours or Wh. So let’s convert W-sec to Wh:
Pl = 1010 Ws x 1 hr/3600 s
Pl = 1/36 x 108 Wh
= 0.0277 x 108
= 2.7 x 106 Wh or Watt-hour per our average lightning bolt.
But can that power a town? And if so, for how long?
How much power does a single house consume? Again we have to play with averages. So let’s assume one house needs 2,000 Watts/hour to keep the frig, furnace, computer, and all things plugged in going. In one day, 24 hours, the house consumes
Ph = 2,000 Watts x 24 hr.
= 48,000 Wh
So if we divide the power draw for the house into the power of a lightning bolt, we’ll have the number of houses that bolt can power:
N = 2.7 x 106 Wh per bolt / 4.8 x 104 Wh/house
= 0.5625 x 102
= 56 houses/bolt of lightning for one day. So the answer to the original question is that a big bolt could power a small, 56-house town for a day.
That assumes we can catch all of that average bolt of lightning in a large capacitor. If you assume a capture efficiency, that would add a few more calculations. Still, the original question is intriguing.
If you wish to take this math experiment a step further, consider how often the U.S. is struck with lightning each day. NOAA online says 22 million cloud-to-ground strikes per year.
If any of you EEs would like to comment or correct my assumptions or math, I welcome you to do so.