Today, we find some technologies that you don't see
when you first look. 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 laser or a VCR is an
invention that's right out in the open where we can
see it. We admire such devices, and we admire the
people who made them. But have you ever thought how
much ingenuity is hidden from view -- how much
ingenuity we don't even realize is there?
For example, were you aware that gear teeth are far
more than just wedges protruding from a wheel --
that their shapes have been mathematically
contrived so that smooth, almost-flat surfaces push
against one another without any sliding?
Furthermore, gears are designed so the back of each
tooth very nearly stays in contact with the mating
tooth. That way the gear can be reversed without
backlash. Some very complex human ingenuity has
been used to avoid the sharp edges, sliding motion,
and backlash that wear gears out.
Or consider the huge twelve-foot-long Swiss
alpenhorn. Not many people realize that it's
virtually the same instrument as the French horn in a modern orchestra
-- that some ingenious musician realized it was
possible to roll that great length of tubing into a
compact coil without losing tone.
It's unlikely that you know what a complex
mathematical shape an ordinary highway curve is if
you're not trained as a civil engineer. These
aren't simple arcs of a circle. They're made from
two pieces of Archimedean spirals that start out
straight, go to maximum curvature, and return to
straight again.That way, you don't have to turn
your steering wheel all at once. Furthermore, the
highway is banked from flat to a maximum angle and
back to flat again. The shape is very complex.
These examples go on. The sticky yellow paper squares you
use to put a temporary note on a piece of paper
came into being when an engineer at the 3M company
invented a glue that didn't quite work. It wouldn't
completely harden. Someone realized that those
remarkably useful stick-on notes to make use of a
glue that couldn't dry out.
An engineer doesn't have to build the Brooklyn
Bridge or invent the radio to change the world. We
encounter a thousand instances of dazzling
ingenuity every day as we manipulate the machines
around us. Creative expression is there among the
anonymous parts of our machines as well as in the
I'm John Lienhard, at the University of Houston,
where we'reinterested in the way inventive minds
For the matter of highway design, see, e.g., Davis,
R. E., and Foote, F. S., Surveying Theory and
Practice (third ed.). New York: McGraw-Hill Book
Co., 1940, Sections 526 through 528, Spiral Curves.
Gear design is treated in any mechanical
engineering design text. See, e.g.: Shigley, J. E.,
and Uicker, J. J., Theory of Machines and
Mechanisms. New York: McGraw-Hill Book Co.,
1980, Chapter 7, Spur Gears.
Nayak, P. R., and Ketteringham, J. M.,
Breakthroughs: How the Vision and Drive of
Innovators in Sixteen Companies Created Commercial
Breakthroughs that Swept the World. New York:
Rawson Associates, 1986, Chapter 3.
This episode has been rewritten as Episode 1293.
Drawing by John Lienhard
The Complex Shape of Modern Gear Teeth
The Engines of Our Ingenuity is
Copyright © 1988-2018 by John H.