This page last updated on 04/17/2024.

Copyright © 2001-2022 by Russ Meyer

I've always loved weather...the worse it is, the better.  It just seems so entertaining to me.  I mean, it is only sunlight, air, and water vapor, but man, the amazing stuff it can do.  It gives rise to lightning, hail, tornados, rain, beautiful clouds, snow, roaring winds, hurricanes, etc.

It takes a lot of energy to drive all those weather processes.  Just consider a summer rain shower.  How many gallons of water are suspended in the air; just floating around as a cloud?  Then all those gallons of water condense to form rain.  These untold gallons fall thousands of feet to the Earth.  Man, that's gotta be millions of gallons of water, weighing tens of millions of pounds dropping thousands of feet.  That is a lot of energy.

Imagine all those gallons of water somehow held in an impossibly large bucket.  Attached to the bucket is a rope that goes up though a pulley in the sky then down to wrap around a drum on the ground.  The drum is connected to a generator so that as the rope is pulled out, the generator spins.  I wonder how much electrical power could be generated like that.  I've always suspected the answer was A LOT!

I've pondered this question since I was in 8^th grade.  Finally, after 25 years, I've decided to have a go at calculating the answer!  Brace yourself against something sturdy...here 't goes...

Framing the Question

First we need to clarify the problem we're trying to solve, so we have some specifics to work with.  What I'm trying to do is calculate the amount of energy released during a moderate summer cloudburst...whatever that is.  I've arbitrarily designated a summer cloudburst as the depositing of one inch of water over one square mile.  That seemed like a fair "cloudburst" model to me.  From these specifications, I will be able to calculate the number of pounds of water dropped from the cloud.  To compute the energy released, I have to estimate the altitude from which the water dropped.  This is kind of tricky because clouds can be pretty tall.  In fact, in my mind, a cloudburst is actually a small isolated shower emanating from a towering cumulus cloud.  These kinds of clouds can be anywhere from 10,000 to 60,000 feet tall.  Just so we don't get too carried away, let's just assume our cloud is on the smallish size at 15,000 feet tall.  We will further assume that the entire cloud is involved in generating raindrops, so that the average raindrop falls from 7,500 feet up inside the cloud.  (Some from the 0 foot level in the cloud and some from at the 15,000 foot level, so that it averages out at 7,500 feet...half-way up in the cloud.)  Now, normally, the cloud isn't sitting right on the ground, so let's just say the base of the cloud is at 2,500 feet above the ground with the top at 17,500 feet.  Therefore, on average, a raindrop falling from this cloud will drop 10,000 feet.  (That's an average 7,500 foot drop through the cloud + 2,500 foot drop through clear air to the ground.)  Here's a drawing illustrating the particulars:

• One square mile contains just a hair over 27,878,400 square feet.
• One gallon of water occupies 0.1337 cubic feet.
• One gallon of water weighs 8 pounds.

Now for the key-punching...

• The total volume of water in one square mile covered to a depth of 1 inch is 2,323,200 cubic feet.
  (1 mi² * 1 inch = 27,878,400 ft² * ¹/₁₂ foot = 2,323,200 ft³)
   
• That is equivalent to about 17,376,216 gallons of water.
  (2,323,200 ft³ / 0.1337 ft³ per gallon = 17,376,216 gallons)
   
• That much water weighs 139,009,724 pounds.
  (17,376,216 gallons * 8 pounds per gallon = 139,009,724 pounds)
   
• The total energy released is 1,390,097,241,713 foot-pounds!
  (139,009,724 pounds * 10,000 feet = 1,390,097,241,713 foot-pounds)

Wow, that is a heck of a lot of energy!  Just to put this in perspective, that is equivalent to:

• 1,786,368,592 BTUs
  (Your 50 gallon home water heater could heat 63,800 batches of water from 60º to 130º degrees.  That's a lot of hot showers.)
   
• 14,304 gallons of automotive gasoline
  (Enough to drive 429,120 miles @ 30 MPG; about 50 round trip journeys from New York to LA.)
   
• 450 tons of TNT
  (This is in the energy range of very small nuclear devices.  For example, the tiny W-54 Davy Crockett nuclear warhead developed by the US in 1958 had an adjustable yield from 10 to 1,000 tons of TNT.  Nuclear artillery shells based on the 1958 US W-48 design had 70-100 ton yields.)
   
• 523,533 kilowatt-hours of electricity
  (My 1,475 ft² house is all electric and I use about 20,000 kilowatt-hours per year.  I could power my house for over 25 years with the energy released in that single rainfall.)

So, where does all that energy go during the rain shower?  Most of the energy is transferred to the atmosphere in the form of heat through friction and turbulence as each rain drop passes through the air.  The net effect is to heat a large body of air just a fraction of a degree.  Ultimately, most of that heat is radiated back into space as infrared radiation.  A small amount of kinetic energy of is transferred to the soil when the rain drop impacts the ground.  This ultimately heats the soil just a shade, most of which, again, ends up being re-radiated into space as infrared radiation.

The Deeper Meaning

One thing I get from this analysis is a new appreciation for the amount of energy infused in the environment around us.  There is a lot of energy flowing through the natural environment every day...way more than than the amount coursing through man-made systems (like electrical lines).

Another thing underscored by this exercise is how diffusely concentrated energy is in most natural systems.  It is not concentrated in either space or time.  In the cloudburst example above, the storm releases the equivalent energy of 450 tons of TNT.  If you actually imagine 450 tons of TNT exploding, that is one heck of a spectacular event.  Why isn't the energy release of the cloudburst that spectacular?  Because the energy is released over the course of an hour and is spread out over one square mile.  The exploding TNT is spectacular because the energy is being released at a single point in space and time.  One big sudden blammo!  It is really valuable to appreciate the difference between these two energy release events, because it has significant public policy implications.

Consider the generation of electricity.  Why are burning fossil fuels such a popular way to generate kilowatt-hours?  Well, there are a lot of reasons, but it basically boils down to economics; it's cheap.  Why is that?  Two reasons; 1) there is an abundance of coal, oil, and gas, and most importantly, 2) those substances contain concentrated energy.  All you have to do is get some and burn it.  With very little effort and expense, you can access huge amounts of energy tied up in that fossil fuel.  That's what makes it so economical in the production of electricity.  The principle thing I'd like to point out is that fossil fuels represent concentrated energy.  You know the story...millions of years ago the sun was shining.  Plants grew.  Animals ate the plants and other animals.  The plants and animals died and were buried.  After millennia, these plants and animals were compressed and heated deep underground where a chemical transformation occurred.  They gradually transformed into coal, oil, and gas.  This natural process had the net effect of concentrating solar energy into a very dense chemical form.  That pound of coal releases many years of solar energy when it is burned.  Natural processes have, in effect, concentrated that ancient solar energy in time and space.

This is very different from alternative energy sources like sunlight, wind, tides, etc.  Sunlight and wind in the raw are not very concentrated forms of energy, and that makes harnessing it difficult.  Sure you can do it, but you have to have a lot of apparatus spread out over a large area (solar cell or wind turbine farms) to capture all that diffused energy.  There is a lot of energy to be had, but it is spread out all over the place in space and time...just like our little cloudburst.  The wind is free but putting in place and maintaining all that low-energy-yield apparatus is expensive and drives up the cost of generating a kilowatt-hour.  You're on the backside of a cost/benefit curve.  That is why you don't see a proliferation of wind and solar farms all over the world.  The method of choice in generating electrical power is fossil fuels.  Fundamental physical principles drive the economic issues that make it so.

Wind and solar power can be made to work and may even be economically competitive someday, but the cost of fossil fuels would have to be much higher for that to happen.  (Coal fired plants can now generate electricity at 2.5¢ per kwh.)  Wind power is gradually gaining ground in various places around the world, but almost exclusively because of state mandated renewable energy programs.  Some US states have required that 3 to 8% of all their electricity come from renewable sources (Pennsylvania, New Jersey, Wisconsin, Arizona, Texas, Washington, Oregon, etc.).  Many utilities have turned to wind power to satisfy this requirement.  For example, the State Line Wind Farm has been constructed on the Oregon/Washington border.  In 2015, they charged the consumer 5¢ per kilowatt-hour.  That sounds competitive with fossil fuels, but what is not mentioned is the 2.1¢ federal subsidy for every kilowatt-hour produced.  In addition, there are state construction subsidies, tax breaks, and tax write-offs that, in effect, typically contribute at least another 3.2¢ per kilowatt-hour.  The actual cost of generating a kilowatt-hour on the wind farm runs about 10¢ to 15¢, which is not a competitive price.  There is no way wind power will become a major contributor until the real cost per kilowatt-hour comes down into the range of nuclear or fossil fuels.  Economic reality just will not bear it.  If it were not for government mandates and subsidies, you would likely not see these wind farms being built.

On the surface, it seems that with just a little refinement in wind turbine technology, wind power would become competitive and sweep the world.  The science speaks otherwise.  The energy available in wind is just not concentrated enough.  Sure, there's a lot of energy available in a mass of moving air, but it is spread out all over hill and dale, hither and yon.  To tap into a significant amount of that energy, you have to have wind turbines everywhere...everywhere!  No amount of tweaking blade airfoils or tuning gear ratios is going to change that.  You are going to need raw square footage of turbine blades.  The challenge is to deploy that much blade area economically.  You have to be able to build large numbers of huge wind turbines, get them installed, operate them and do all that really, really cheaply.  There is a subtle common denominator in all those requirements, and that denominator is a material science breakthrough...light, strong, durable, cheap, easy to work materials enabling big wind turbines to be economically placed all over tarnation!  That's the only way, and technology is currently not up to the task.  By the way, only a certain percentage of the US land area is well suited for wind turbines.  Take a look at this map of Wind Power Potential produced by National Renewable Energy Laboratory.

In all this you're bucking a fundamental problem...the energy content is too diffuse!  Think of the old sailing ships...they had huge sails to catch a little of that wind energy.  Even then, they were typically only able to average maybe 7 knots.  The energy available from the wind is very diffused and they needed a lot of apparatus (sails, masts, booms, ropes) just to catch a little bit of it.  (Not to mention a big, expensive crew to operate and maintain all that apparatus.)  As soon as technology got to the point where we could dump sails, we did.  Guess what replaced them...coal powered steam ships.  Why is that?  It was the concentrated energy of coal.  More energy became available so ships could travel faster...remember the Titanic...it was chugging along at 22 knots when it hit the iceberg.  This difficultly of energy concentration applies in different ways to solar power, tidal power, etc.  They all share a similar problem.

Hydroelectric power is an interesting case.  Here you are harnessing the energy available in a mass of moving water and converting it to electric power.  Hydroelectric holds its own against fossil fuels and nuclear, and seems like a good analogy to wind and solar proposals.  But think about it.  Where did that river come from?  It is rain that fell over a large area and was concentrated by the topology of the land into a narrow river.  To harness that energy, all we had to do was build one dam across the river.  The diffused energy released by the rainfall over a large land area and over long periods of time is naturally concentrated by the lay of the land.  It becomes concentrated in time and space and that concentration is what makes it easy to harvest.  We put one big apparatus in the way (the dam) and we can recover a decent fraction.  That's what makes hydroelectric power competitive.  I just don't see a similar factor at work with solar or wind.

This little Storm Cipher exercise helps me understand the natural world better.  With that understanding comes a clearer, better view of issues which ultimately relate to public policies.  It helps me contribute to the forming of those policies in a rational way.