Engines of Our Ingenuity


No. 1664:
NOMOGRAM

by John H. Lienhard

Click here for audio of Episode 1664.

Today, nomograms, analogs, and a forgotten world. The University of Houston's College of Engineering presents this series about the machines that make our civilization run, and the people whose ingenuity created them.

A digital computer works a lot like counting on our fingers. It adds up numbers, one by one. We can afford to do that when even our home PCs do a billion calculations per second. But the older analog computer had to go at calculation in subtler ways.

Just as an analog watch is analogous to the face of a sundial, an analog computer carried out some process that was analogous to a calculation. The process gave an approximate (but often quite accurate) output that looked like the result we wanted.

For example, some people created electrical circuits that obeyed the equation we needed to solve. The output voltage then behaved like the solution to our problem. The slide rule was a simpler and more familiar form of analog computer. Its scales were logarithmic. Since we can multiply by adding logarithms, adding distances on two slide rule scales was analogous to multiplying.

A variation on that idea was a graph called a nomogram. It was set up to solve just one equation that would've taken a lot of time on a slide rule, or required scales that no slide rule had.

Here's how a nomogram worked: we had a page with several lines on it. The lines could be stretched out in many ways. They might be straight, curved or tilted. We'd connect points on two lines with a straightedge. Where the straightedge intersected a third line, we read the answer. Sometimes we'd have more lines, and we'd have to get our answer in more than one step.

I have here an old book of nomograms, published in 1911. We can use them to adjust our pile-driver, design a masonry arch, size a water pipe, or calculate the water flow in a canal. Some of the diagrams get really ornate. To get the power output of a steam engine, we navigate a chart with eleven different lines on it.

Charts like these were once a staple of the engineering world. Sometimes called alignment charts or straight-line diagrams, engineering handbooks had long sections on how to construct them. As a young engineer, I collected nomograms made in the form of specialized cardboard slide rules. Advertisers handed them out like candy, and we used them to select springs, gears, or bearings.

Down through the 1950s I cooked up one analog trick after another for getting numbers. I plotted graphs and aligned scales. I read books about fancy new forms of analog computers that inventive people were dreaming up. But the digital computer, invented in 1939, was quietly catching up with all this cleverness.

Soon muscle replaced guile in our calculations. We began to speak of number crunching. But the pendulum swings. Today, we again look for ways to reclaim the intimacy-with-process we once had. We use neural networks and fuzzy logic. We develop analog interfaces -- joy sticks and touch screens. We again seek to make the computer more nearly analogous to the smooth flow of action in nature, as well as to the subtle movements of the human mind.

I'm John Lienhard, at the University of Houston, where we're interested in the way inventive minds work.

(Theme music)


Manifold and Poole, Straight Line Engineering Diagrams. San Francisco: Technical Publishing Co., 1911.


Nomogram for direct current wiring



The Engines of Our Ingenuity is Copyright © 1988-2001 by John H. Lienhard.