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The field discharge method works because of f(t). Here's a brief math lesson.
First, we'll define coulomb (unit of charge): One ampere for one second. It is a specific quantity of electrons (6.24 x 1018). Voltage is immaterial. It is not a factor in the coulomb. Whether this quantity of electrons is being pushed along by one volt or 1,000 volts, the number of electrons remains the same. The actual charge transferred by a lightning strike is described by scientists in coulombs.
Consider a 100W light bulb on a 100V supply. Because the current for this bulb would be 1A, in one second it uses 1 coulomb of charge to provide light. In each additional second, it transfers another coulomb of charge through the light bulb. Remember that the coulomb is not dependent on voltage. Lightning scientists say that a typical lightning strike transfers about 10 to 70 coulombs of charge in about 30 to 50 microseconds. Not a big charge, but it is compressed into a very short period of time (this translates into about 200,000 to 1,000,000 amperes). That's why a strike does so much damage. Yes, the voltage and current are both very high, but the fact that it occurs in such a short length of time is why it can be so damaging.
The importance of f(t)
Recall studying functions in high school math. We started with f(x), but here we use f(t) for time.
Compare MW hour, kW hour, watt hour, watt minute, watt second. Each is a function of time f(t). But if we cram 1kWH of energy into one minute in time, what is the equivalent energy rate?
How much power would this be in one minute? 60 x 1kW = 60,000 watt hours = 60kW rate
If we cram this energy into one second, what is it equivalent to in kW? 60 x 60,000 = 3,600kW rate
Into 0.1 second = 100,000 microseconds is equivalent to 10 x 3,600,000 = 36 MW rate
Into 0.01 second = 10,000 microseconds is equivalent to 10 x 36,000,000 = 360 MW rate
Into 0.001 second = 1,000 microseconds is equivalent to 10 x 360,000,000 = 3,600 MW rate
Into 0.0001 second = 100 microseconds is equivalent to 10 x 3,600,000,000 = 36,000 MW rate
Into 0.00005 second = 50 microseconds is equivalent to 10 x 36,000,000,000 = 72,000 MW rate
In other words, if a strike carrying charge of one coulomb every 50 microseconds continuously discharged for an hour, it would transfer 72,000 megawatt hours of energy to ground in that hour.
Clearly, a lightning strike is a function of time as well as voltage and current.
If we can discharge the same energy over just a few minutes, the current would be very small. Damage from lightning is the result of a huge amount of current for a very small period of time, not from a massive discharge of energy.
Nott is director of research and development for Nott Ltd.
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