# Energy in a lightning strike

Summertime in Bulgaria is often befallen by thunderstorms involving a large number of lightning strike hits towards the ground, causing damages every year . This made me think about the energy stored in an average lightning bolt. What if we can capture and store it using a “lightning bolt farm”? Would it solve the world’s energy problems? Even Doc Brown used lightning bolts to power the De Lorian so that Marty can get back to 1985. Sounds as a promising energy source, but is it? Here are some of my very primitive thoughts:

According to some online sources an average lightning strike has an energy of 0.5 to 5 Giga Joules [1]. This energy of course, is released for time in the order of microseconds and capturing it is difficult and not the scope of this post. Let’s say that we can capture and store a 2.5 GJ lightning bolt. How much is this and would it be enough? According to Wikipedia the average energy density of coal is roughly 24 Mega Joules per kilogram. This yields roughly 100 kg of coal per lightning bolt. A few dozens of lightning bolts per storm brings us about 1 Ton of coal, not bad…

Assuming a 100 % capture efficiency ten lightning bolts can potentially bring us:

$E_{kWh} = \frac{2.5 GJ}{3600000} = 694 kW/h$

Comparing it to Bulgaria’s one and only nuclear power plant the ten lightning bolts’ energy forms about 0.03 % of its total power capacity as of today. Pretty low, hmm, so we need to capture more of them, just about 30 000 lightning strikes to achieve the same energy capacity… every hour! And this is to cover only one nuclear power plant, which is by far not enough even only for Bulgaria’s needs.

How much crude oil barrels are there in a lightning bolt?

One barrel of crude oil has an equivalent energy of 6 GJ/barrel. So, 1/2 barrel/lightning. The daily petrol consumption in the United States according to their U.S. Energy Information Administration for 2014 is 20 Million barrels per day. Thus, we need about 40 Million lightning strikes per day to satisfy America’s petrol needs. I wonder if EIA’s information can be trustworthy, but 40 M lightning strikes have an equivalent of about 1000 Bulgarian nuclear power plants used at full capacity for one hour every day in the US? On the other hand, it might not be that surprising. America has a population of about 300 million, even if half of its residents drive their cars about 50 miles every day, this is some 750 Million miles/day or in human units 1207 Million km/day. An average car burns 6l/100km and from there we get the number of 2 Million litres of, say gasoline. Assuming that with cracking processes [5] we can distil 20% gasoline out of a unit crude oil, we roughly reach the reported number of 20 Million barrels/day.

With the last fact it becomes apparent that humanity is not going to be powered by lightnings, at least not in the near future, however there is some ongoing research on the topic [2],[3],[4].

Last, a fun assumption. How many electrons are there in an average lightning strike?

2.5 Giga Joules converted to electron volts is:

$\frac{2,5 GJ}{q} = \frac{2,5 GJ}{1,602.10^{-19}} = 1,56.10^{28} eV$

If we assume that the 2.5 GJ work needs to move the electrons on a 1 Mega Volt potential (between the cloud and the ground), this yields:

$\frac{1,56.10^{28} eV}{1 MV} = 1,56.10^{22} \text{ electrons}$

Not a very meaningful comparison, but the average full-well capacity of a pixel in a standard CMOS image sensor is 20 000 electrons. 🙂

References:

[1] Yasuhiro Shiraishi; Takahiro Otsuka (September 18, 2006). “Direct measurement of lightning current through a wind turbine generator structure”. Electrical Engineering in Japan 157: 42. doi:10.1002/eej.20250. Retrieved 24 July 2014.

[2] Bhattacharjee, Pijush Kanti (2010). “Solar-Rains-Wind-Lightning Energy Source Power Generation System” (PDF). International Journal of Computer and Electrical Engineering 2: 353–356. doi:10.7763/ijcee.2010.v2.160. Retrieved March 20, 2014.

[3] Knowledge, Dr. (October 29, 2007). “Why can’t we capture lightning and convert it into usable electricity?”. The Boston Globe. Retrieved August 29, 2009.

[4] Helman, D.S. (2011). “Catching lightning for alternative energy”. Renewable Energy 36: 1311–1314. doi:10.1016/j.renene.2010.10.027. Retrieved March 5, 2013.

[5] James. G. Speight (2006). The Chemistry and Technology of Petroleum (4th ed.). CRC Press. ISBN 0-8493-9067-2.