Avian’s Blog

Proper use of units is another one of my pet peeves. I usually can't keep my mouth shut when I see someone throwing around numbers without clearly defining what unit of which quantity they represent.

A while ago I stumbled upon the Electronics Engineering videocast, and unfortunately the very first episode I watched left a very bad impression in this regard. While the show was informative, I just couldn't forgive the presenter the way he did his calculations live on a piece of paper.

It was a bit of a shock to see an engineer have amperes squared on one side of the equals sign and watts on the other, or the result presented in watts per second. Of course I sent a comment and the answer I got back was that we're not in school and this is how real-life engineering looks like.

It's engineering, Jim. But not as I know it.

I find that being strict with notation is most helpful especially in quick back-of-the-envelope calculations. When you're skipping two steps at a time in solving some equation it's easy to make a mistake. And if you're only working with dimensionless numbers, it's nearly impossible to spot the error. Well, if you're lucky and you've made a big one you have a chance that your gut feeling will tell you your result is off by a couple of orders of magnitude.

However, if you keep units attached to all the values you write down all the way through to the final solution, you have a number of ways to easily spot mishaps early on. A sum of values of a different quantity (e.g. you've come to a point where you would have to add 3 volts to 1 ampere) is a reliable indicator that you should recheck your calculation. At least in my experience when I'm expanding polynomials in my mind I often miss a factor somewhere and conflicting units in a sum make the error obvious.

Another useful rule is that the argument of exponent or trigonometric functions may only be a pure number. That's of great help when you can't exactly recall an equation, but know the general form.

Once you get the result you also have an additional means of boosting your confidence in it. If you want to calculate the amount of work required and you arrive at watts per second that should start ringing some pretty big bells.

I agree that there are situations where a system of measurement is agreed-upon and well defined and the field of electric engineering is full of them. Just think how many circuit diagrams say 10 k instead of 10 kΩ. But there such notation is unambiguous because it's accompanied with a symbol for a resistor and giving resistance in ohms is a de-facto standard.

On the other hand if you're writing such a document for long-term use, you're (hopefully) doing that with much more care than some napkin calculation at the last minute.

Anyway, being strict with your calculations is certainly most useful outside of the classroom. And in fact, my advice would be not to believe anyone that says that a particular skill is only useful in school.