Magic math

John Gyorki
April 01st, 2007.

About 90% of the press releases and many of the articles I read are written by authors who do not know how to express quantities in percentages. I know of two cases in engineering where percentage is a valid unit for measuring quality or quantity: efficiency and duty cycle. Both parameters range from 0 to 100%. You just can’t get more than 100% efficiency or 100% duty cycle; 100% is the whole enchilada. At least when I was in grade school, I was taught that when I had an apple pie, cut it in half, and gave one half to my friend, I ended up with 50% of the pie. If I cut that in half, and gave away one piece, I ended up with 25% of the pie. I cannot recall when I ever had 110% or 2000% of the pie, no matter what! This brings to mind a recent product announcement that states their new product has a 2000% performance improvement over their older product. That’s it. First, what is the unit of measure for performance so I can attempt the calculation? Too bad, it has none. If I assume it produces 2000% more horsepower, what was the horsepower before the improvement? Again, unknown. Say it was originally 100 hp. Then do I multiply 2000 times 100 and get 200,000 hp, or do I multiply 20 times 100 and get 2000 hp or maybe 2100 hp – or something else? Probably the latter. I would prefer to express such gains as twice or 20 times the original hp, or whatever the multiplier is so I know the quantity I should end up with. A multiplier is a real number. What’s wrong with saying that? Now let’s look at multipliers. I’ve read ads that state the size of a motor is 4 times smaller than its predecessor. Two problems: First, is it shorter or lighter, have a smaller diameter, output less torque, run on lower voltage, or draw less current? We don’t know. Second, stating something is 4 times longer makes sense, but saying it is 4 times shorter makes no sense whatsoever. For instance, if I have a pencil that is 8-in. long, and yours is 4 times smaller, is yours 2 in. long? What you are really trying to say is that my pencil is 4 times longer than yours, or your pencil is 1⁄4 (times) the length of mine. Percentages are also widely used incorrectly for multipliers. For example, a new product is stated as 50% shorter or 200% shorter (or 200% longer) than the older one. Again, what does all that mean? We are engineers, and we should use the language of engineering correctly. It is up to all us to challenge ourselves to provide accurate technical data that allow us to correctly specify components. Let’s all take responsibility for improving the accuracy of available data. If we do, I will feel 100% better.

jgyorki@designworldonline.com