Tuesday, 13 February, 2001

Debunking Conspiracy Theories

Conspiracy theorists are an odd breed.  Seemingly intelligent people will believe some of the most outlandish things, and will refuse to examine the "evidence" critically or even apply simple mathematics to verify claims.  A case in point:  weather modification conspiracy theorists are up in arms about the Navy's HAARP project, a study of the ionosphere with particular emphasis on using it to enhance communications and surveillance systems.  The system uses a phased array transmitter with 3600 KW (3.6 megawatts) available for transmission. It's powered by six 2500 KW generators, each powered by a 3600 hp diesel engine.

Enter the conspiracy theorists.  This 1998 article in Criminal Politics magazine claims that the system is "...capable of transmitting 500 million watts of radio frequencies into the ionosphere.  Their electricity is generated by six 3600 HP diesel driven generators using 95 tons of fuel from the ARCO North Slope oil fields."

Somebody hasn't done his math.  One horsepower is about 745 watts, so six 3600 hp diesel engines would provide (at most, assuming 100% efficiency), 16.1 megawatts.  That's a far cry from 500 megawatts.  But I'll give the author the benefit of the doubt and assume 500 MW.  The article goes on to say:  "The average kitchen microwave of 500 to 1000 watts will boil a cup of water in less than a minute. What do you think 500 million, 1.7 billion, 10 billion or 100 billion watts will do to a body of water or the ionosphere the size of the state of Alaska, or for that matter, the size of the United States?"

Well let's just figure that one out using the Baltic Sea (the smallest of the Seas) for an example.  Assuming you could actually focus 500 MW on the Baltic Sea for the purposes of heating it, just how long would it take?

The Baltic Sea has a surface area of 422,200 square kilometers (about the same size as California), and an average depth of 55 meters.  That works out to 23,221,000,000,000 cubic meters (about 6,130,344,000,000,000 gallons of water; the difference between the Baltic Sea and a cup of water is a heck of a lot bigger than the difference between 1000 watts and 500 million watts).  We'll be kind and say that the average temperature of the water in the Baltic is 10 degrees Celsius (50 degrees Fahrenheit).  It's probably closer to 2 degrees C (35 F), but the difference won't really matter that much for this demonstration.  Standard physical equations tell us that it takes one calorie of energy to heat one cubic centimeter of water one degree Celsius.  We need to heat the water by 90 degrees Celsius.  A cubic meter is 1,000,000 cubic centimeters, so it takes

1,000,000 cm^3 * 1 cal/deg/cm^3 * 90 deg = 90,000,000 calories

or 90,000 kilocalories to heat each cubic meter to boiling.  That works out to 2.1e+18 kilocalories to heat all of the water in the Baltic Sea to boiling.  Referring to standard physical equations again, we see that one kilocalorie is 1.16 watt hours (Wh), resulting in.

2.1e+18 kilocalories * 1.16 Wh/Kcal = 2.4e+18 Wh

So if we applied 500,000,000 watts continuously, it would take:

2.4e+18 Wh/500,000,000 W = 4,848,544,800 hours

or 553,486 years.  That's one degree every 6,150 years.  Stepping the power up to 100 billion watts will do the job in 27,674 years, or one degree every 107 years.  That's assuming that there are no cooling effects on the water, and that all of the power produced is actually used to heat the water.  I don't think I'll lose any sleep over this one.

What amazes me is that engineers—people who understand and live by these physical equations—believe this craziness.  What a wacky world.