Question

It has been proposed that lightning be harvested for energy. Measurements of lightning strikes indicate that they have the following average properties (note, these are reasonable approximations):

• Potential difference between each end of 100 million V

• Current of 30000 A

• Time of 1.67E-4 seconds

• 20 strikes per square kilometer per year in lightning prone regions of the United States and 200 strikes per square kilometer per year in the most lightning prone regions in the world (Congo).

"Lightning collectors" are devices which have the following properties (I'm just making these up, though I think they are wildly optimistic):

• They can only collect lightning that would strike within a 100 m x 100 m area

• They each cost $10,000

• They last 40 years

• Maintenance costs and scrap value are negligible

The following economic data are also known (these are very rough estimations):

• Electrical energy is worth about $0.17 per kWh and is not expected to increase in value

• Investors in such projects expect to get back triple their initial investment in total after 40 years

As an independent energy consultant, it is your job to check if this project is a good investment in either the United States or Congo. Provide a report detailing your assertions and your reasoning. Assume that your audience is investors who have perhaps taken high school physics or college physics many years ago. You will be graded on both the correctness of your physics (and accounting) and your ability to explain the physics to such an audience.

Answer 1

Energy during one lighting strike is given by

Energy per year per square km=Energy per strike x No. of strikes per year per square km

Energy collected over 40 years per square km=Energy collected per year per square km x 40

Since a single device covers only 100m x 100m, it will collect only one hundredth of the power of the total lightning strike per square km.

Energy collected by a single device=(Energy per square km) / 100

Using the above mentioned concepts the energy per device over a period of 40 years is given as

This energy can be sold for $0.17 kWh. Thus, the money obtained per device is

Subtracting the const of the device(i.e. $10000)

The project will result in a loss in United States and a profit in Congo. In addition, the profit in Congo over 40 years is more than triple the value invested initially(3 x $10000=$30000).

Thus, the project is a good investment in Congo but not in United States.