Journal of Physics Special Topics
P6_5 Harnessing Lightning Energy
L. K. Wharton, S. J. Wharton, J. A Paice, A. Joshi and R. Sankdecha
Department of Physics and Astronomy, University of Leicester, Leicester, LE1 7RH.
November 10, 2015
Abstract
Harnessing energy from lightning strikes has been trialled many times since the early 20th century
[1]. We have proposed a circuit that has the potential to harness lightning energy. We found that
using a supercapacitor could reduce the energy lost while capturing the incoming lightning energy.
The efficiency of our proposed circuit is over 99%.
Introduction
Experiments have been performed using artificial lightning to determine the conducting properties of
certain materials and advance the techniques used to capture lightning energy. The energy stored
from lightning strikes has so far been very small. Due to the random nature of lightning strikes it is
difficult to determine when the strike will occur and also how much energy the strike will contain.
Theory
Tall structures with metal lightning conductors running from the tip to the ground are used to harness
the electrical energy. The resistance of this structure must be low so that the conductor on our circuit
is the favoured path for the electrons.
It has been found that the average energy of a lightning strike, 𝐸𝑠 is about 5 billion joules [2]. This is
an incredible amount. As lightning strikes only last for a period similar to a few milliseconds [2] so the
conducting material must be able to cope with an immense amount of power.
𝑄2
𝑄𝑞
(1)
∫0 𝑐 𝑑𝑞 = 2𝑐
The amount energy stored on the plates of a capacitor is given by Eq. (1) where 𝑄 is the maximum
amount of charge that can be stored on the capacitor, 𝑐 is the capacitance and 𝑞 is the charge. To
determine the minimum capacitance value required we can make the energy stored in the capacitor
equal to 𝐸𝑠 and rearrange.
𝑄2
2𝐸𝑠
=𝑐
(2)
20
The charge 𝑄 in the typical lightning strike is due to approximately 10 electrons [3]. We can find the
total charge by multiplying the number of electrons 𝑁 by the charge on a single electron e which is
1.6x10-19C.
𝑒 2𝑁2
2𝐸𝑠
=𝑐
(3)
After inserting the proposed values we find that 𝑐=25.6x10-9F. This is the minimum capacitance value
that is needed to contain all the energy from a lightning strike. For a parallel plate capacitor the
capacitance is given by certain properties of the material. The area of the plate 𝐴, the distance
between the plates 𝑑 and the relative permittivity 𝜀𝑟 of the material can change the capacitance value
while the permittivity of free space 𝜀0 is constant.
𝐴
𝑐 = 𝜀0 𝜀𝑟 𝑑
(4)
We thought that it would be sensible to use several identical capacitors that are all in parallel (figure
1). Designing the circuit this way reduces the chances of the circuit being destroyed by the immense
power of the lightning strike. If the strike contains more energy and hence more charge than
anticipated, the energy is then split between all the capacitors in this circuit. Hence the fractional
1
Harnessing Lightning Energy, November 10, 2015.
increase in charge on each capacitor is a fraction
of the total charge increase. The time taken for a
capacitor to completely charge up is dependent
on the resistance of the circuit and the
capacitance. The time constant is RC. The total
capacitance, 𝐶𝑇 of our circuit is given by Eq. (5).
𝐶𝑇 = 𝐶1 + 𝐶2 + 𝐶3 + ⋯ 𝐶𝑛
(5)
The charging time, t for the capacitor can be
found by Eq. (6). 𝑄0 is the total amount of charge
that the capacitor can store. The charging time of
the capacitor needs to be of the order of
milliseconds as this is the duration of a lightning
strike.
Figure 1: Capacitors in parallel
Figure 1: Capacitors in parallel
−𝑡
𝑄 = 𝑄0 [1 − 𝑒 𝑅𝐶 ]
(6)
After 5RC, the capacitor will be fully charged because of the exponential relationship. 5RC must be
equal to the duration of the strike, 𝑡𝑠 if the capacitors are to charge fully in this time. We will assume
𝑡𝑠 =0.005s [2]. Increasing the permittivity of the dielectric will increase capacitance so consequently
the resistance decreases. Calcium copper titanate has a relative permittivity of 12,000 at room
temperature [5] making it the best dielectric material that has been made. The capacitance using this
dielectric is found using Eq. (4). The area of the plate and the distance between the plates are the
standard values for supercapacitors using this dielectric material [4].
This gives us a capacitance of 1.06x10-6F which we can use to find the resistance of the circuit. Eq. (7)
gives us the resistance of the circuit assuming that the charging time is the time of the strike.
𝑡
𝑅 = 5𝐶𝑠 = 943Ω
(7)
This resistance value is relatively low therefore there will be less energy loss, 𝐸𝐿 via ohmic heating.
The energy loss is given using Eq. (8)
𝐸𝐿 =
𝑄2
𝑅
𝑡𝑠
= 48.3𝑥106 𝐽
(8)
Discussion
The energy that is lost is large and cannot be decreased unless there is a way to increase the amount
of time taken for the transfer of energy to pass through the circuit. However the amount of energy
lost is only 1/100th of the input energy so harnessing lightning energy is by this method is very efficient.
Conclusion
We have found that it is impossible to harness all the energy from a lightning strike because the energy
is supplied to the circuit so rapidly. However the efficiency is very high and it could be increased if
there was a way of using the thermal energy without shorting the circuit. We have also only calculated
a maximum energy loss assuming there is one capacitor. In our design we considered a set of parallel
capacitors so this would decrease the energy loss further. Future investigation of temperature
dependence of the dielectric would also be beneficial.
References
[1] http://www.mikebrownsolutions.com/tesla-lightning.htm accessed on 26/10/2015
[2] “Could you power a city with lightning?” Phyiscs.org, retrieved September 1, 2011
[3] www.hyperphysics.phy-astr.gsu.edu/hbase/electric/lightning2.html accessed on 16/10/2015
[4] “Dielectric properties of CaCu3Ti4O12 based multiphased ceramics” Science direct, retrieved
September 30, 2004
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