The Ergosphere
Tuesday, December 19, 2006

Why unit analysis matters

"The two most common things in the universe are hydrogen and stupidity."  Every time I start to forget this, something comes along to remind me.  Sometimes forcefully.
I forget what prompted me to write Unit Analysis.  This time, it was a clown who can neither calculate the area of Earth's disc without getting off by a factor of a million (you'd think the ridiculous number would tip him off), nor can he grasp the meaning of "kilowatt-hour".  Indeed, he insists that "kilowatts per month" is what people pay for on their electric bill.  After receiving a free physics tutorial including definitions of basic units, he topped this off with an insult: "... it would seem you would have problems reading your own electricity meter."
Innumeracy is probably a guarantee of incompetence in basic science, but it takes a special combination of arrogance and ignorance to say "It was written for people to understand how many watts are required in unit time to power things in terms which they understand."
He's too wrapped up in himself to realize that the public doesn't understand these things any better than he does, and one of the biggest reasons they don't is that they don't speak the language.  They could learn it by osmosis, except for one thing:  all the clowns out there mangling the language of physics, producing such a cacophony that the voices of knowledge cannot be distinguished.  In short, Mr. Clown is part of the problem.
Well, why does it matter?
It matters because John Q. Public needs to know that a space heater which consumes 1.2 kilowatts is not going to cost 15 cents a month to run because the electric rate is "12.5 cents per kilowatt".  Anyone who does not understand the way time figures into the calculation — and why the electric bill speaks of kilowatt-hours — is almost certain to get it wrong.  The buyer who estimates the usage time as 6 hours per day, then multiplies 180 hours per month times 1.2 kW to get 216 kWh and calculates $27, will get it right.
To get it right, all you need is to know that a kilowatt-hour is a kilowatt times an hour.  If you keep calling it "kilowatts per hour", you're never going to understand that.
Scientists and engineers use precise language and correct units because that's the only way to get the RIGHT answer.  People who use WRONG language or WRONG units can do things like getting an electric bill of fifty dollars when they thought it was going to be fifty cents.
This is not a matter of opinion; there are a few ways of accurately describing how the world works, and innumerable ways of getting it wrong.  You can use English or MKS or CGS units, but any correct calculation is going to come up with the same answer after conversions.
This is one place where what you don't know really can hurt you.
Unit analysis matters.  Treat it that way.

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I am in favor of sticking with SI (MKS) units.

It would greatly advance our ability to understand alternatives if we used SI and got rid of customary and commercial units.

Example -- the BTU. Read this page:
British thermal unit.

There are 8 definitions of the BTU, ranging between 1054.35J and 1059.67J. This is because the BTU is based on the Calorie, and there 8 definitions of the Calorie.

Substitute the KiloJoule for the BTU. The units are close in size but the KJ is unambiguously defined.

The KiloWatt is SI, but the KiloWatt Hour is not. A KW Second is one KiloJoule. Using the KJ instead of the KW*H removes the confusion of the use of the word per which may contextually mean multiplied by or divided by.

1 KW*H = 3.6 MJ (MegaJoules).
I fear that converting a hundred million electric meters from kWh to kJ (or MJ, which is more suitable), plus the overhead involved in re-writing regulatory documents, would cost enough to put the kibosh on the whole thing.

Not that this matters.  Do the calculation correctly, and it doesn't matter if you use kWh or inch-pounds.  The problem is that too many people can't do that calculation, and have been so confused by the bull hockey of some self-appointed experts that they'd have to unlearn a great deal before they could begin.
I'm continually amazed by the mess of confused units in virtually *any* writing about electricity supply not written by engineers, for engineers, in an engineering journal or the like. People can sometimes get barrels of oil per year right, but kW, kW-hr, MW, GW, and so on get so garbled that while sometimes you can guess from the size of the number what they meant, much of the time there is no hope, and it's clear the author had no idea and was just scribbling down numbers randomly. It doesn't inspire much confidence in the rest of the book if author, editor, and everyone else involved had no idea, none at all, what the difference between rate and total amount is. Do they not understand the difference between speed, gas milage, and acceleration when they drive, and think the signs an the roadside are in MPG? Do they express their 0-60 time in miles per hour?
Good rant.

One of my engineering mentors had the habit of referring to the "English" system of units as the American Provincial System, which seems only a fair acknowledgement of the current world situation.

Of course, the other common name for that system is the Imperial system, which seems to be more and more appropriate as time goes on.
Add to that mistakes that are not even dimensionally consistent, never mind consistent in the units. Dimensional analysis can often clarify a problem by reducing the apparent number of parameters. If you can get your problem down to dimensionless parameters then you are, IMHO, a lot closer to understanding a problem.
Google Calculator does units.

You can calculate the speed of light in furlongs per fortnight or convert british pounds per BTU to dollars per kWh.
So they really don't have an excuse!  I'll have to direct the clueless to that henceforth.
Found this conversion calculator that I use.
For my level of accuracy it is fine. curious on how good it is?
It's Windows-only, so I'll never know.
I saw this today:

The Frink Programming Language

It tracks units in the calculation and enforces unit correctness. I've often wanted something like this built into my favourite programming language, Python.
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