Pendulum clocks
by Chris Woodford. Last updated: March 2, 2023.
Tick tock, tick tock—that's the sound we think of when we think
of clocks, even though the vast majority of modern timekeepers make
hardly any sound at all. Not so long ago, virtually every clock and
watch made a tick-tock noise because it was completely mechanical
rather than electrical or
electronic. Instead of your clock being
powered by a battery, you wound it up with a key and there was a long
swinging rod inside, called a pendulum, that made sure the
whirring gears kept good time. So how did these old-fashioned
pendulum clocks actually work? Let's take a closer look!
Photo: A compact, wall-mounted pendulum clock. On clocks like this, the swinging pendulum is
very much a feature; in grandfather clocks, the pendulum is often discreetly hidden behind a door (see below).
What is a pendulum?
A pendulum is a rod hanging vertically from its top end (or a
weight called a bob hanging from a string) that swings from
side to side due to the force of gravity. As Italian scientist
Galileo Galilei (1564–1642) discovered, the clever thing about a
pendulum is that it always takes the same amount of time to make one
complete swing.
[1]
In theory, the only thing that affects how fast a
pendulum swings is its length and the strength of gravity.
For relatively small swings, the time (T) it takes to make one complete
swing (known as the period) is given by
this little equation:
Here, l is the length of the pendulum and g is a measure of gravity's strength (what we call the acceleration due to gravity). You can see from this equation
that you need to quadruple the length of a pendulum to double the time it takes to make a swing.
How does a pendulum work?
A pendulum works by converting energy back and forth, a bit like a
rollercoaster ride. When the bob is highest (furthest from the
ground), it has maximum stored energy (potential energy). As it accelerates
down toward its lowest point (its midpoint, nearest the ground), this
potential energy is converted into kinetic energy (energy of
movement) and then, as the bob climbs up again, back to potential
energy. So as the bob swings (oscillates) back and forth, it
repeatedly switches its energy back and forth between potential and
kinetic. Something that works this way is called a harmonic
oscillator and its movement is an example of simple
harmonic motion, though we won't go into those things here.
Artwork: A pendulum is constantly swapping potential energy and kinetic energy.
If there were no friction or drag (air resistance), a pendulum would
keep on moving forever. In reality, each swing sees friction and drag
steal a bit more energy from the pendulum and it gradually comes to a
halt. But even as it slows down, it keeps time. It doesn't climb as
far, but it covers the shorter distance more slowly—so it
actually takes exactly the same time to swing. This handy ability
(technically called isochronism,
which just means "equal amounts of time") is what makes a pendulum so useful
for timekeeping.
Galileo figured that out straight away
and though he never actually managed to build a complete pendulum clock.
he came quite close (here's a model of the
1642 pendulum clock he
was designing just before his death); it was left to
another brilliant scientist, Dutchman Christiaan Huygens (1629–1695),
to finish the job in the 1650s.
(Read more about Huygens and his clocks and see a photo of the first Huygens pendulum clock of 1656.)
“I do not make use of a weight hanging by a thread, but a heavy and solid pendulum, made for instance of brass or copper... and on this new principle, that the pendulum makes its great and small vibrations in the same time exactly, they will invent contrivances more subtle than any I can suggest...”
Galileo Galilei
[2]
How does a pendulum clock work?
Suppose you want to build a clock from scratch in the simplest way
possible with the fewest number of parts. You could start with a dial
and some hands and move them around the face with your finger,
counting seconds to yourself and moving the hands accordingly. You
move the second hand once a second, the minute hand once every 60
seconds, and the hour hand once every 60 minutes (3600 seconds).
Some clock! That's going to get tedious quite quickly, so what about automating
things? You could mount the hands on a little axle driven by what
we'll call "timekeeping gears," so that the second hand automatically
turns the minute hand at 1/60 of its speed, and the minute hand,
likewise, turns the hour hand at 1/60 of its speed. Then all you have
to do is count seconds, turn the second hand, and the rest of the job
is done for you.
But, hang on, that's still pretty tedious. What we really need is some way of
powering the hands automatically. You could wrap a piece of string
around the axle and attach a weight to it. As the weight falls, it
will pull the axle around, turn the second hand, and that will drive
the rest of the clock. The only trouble is, the weight is going to
fall really quickly and the second hand will whizz around too fast so
the clock won't keep time. Okay, let's introduce another set of
gears—we'll call them "power gears" (to avoid confusing them with the
timekeeping gears)—that will take power from the falling weight and
transform it so that, as the weight falls, the second hand advances
exactly one position on the dial in one second. But that still won't
work because the weight is going to accelerate as it goes down, like
any falling object. In other words, the clock is going to get faster
and faster until the weight hits the ground with a smack!
What we need to add is a mechanism that regulates how fast the weight can
fall, allowing the whole timekeeping mechanism to advance so the
second hand moves one second on the dial (and only one second) in a
time of one second. That's what the pendulum does. As it swings from side
to side, it rocks a lever called an escapement that locks and
then unlocks the part of the mechanism driven by the falling weight.
(Think of it this way: the mechanism is locked and the escapement
releases it so it can move—in other words, lets it escape—once per second.)
It's this repeated locking and unlocking that makes the tick-tock
sound you can hear. Since (in theory, at least) a pendulum of a certain length always takes
the same amount of time to swing back and forth, the pendulum is what
keeps the clock to time. The escapement mechanism that the pendulum regulates
also (cleverly) keeps it moving back and forth by repeatedly giving
it a slight nudge—an extra injection of energy to counteract
friction and drag.
That's not exactly how pendulum clocks work; it's a very simplified approximation of what's
going on that's reasonably easy to follow.
Photo: The escapement is a rocking lever that allows
the gears in a clock to advance only at a certain rate, determined by the swings
of the pendulum. Photo by Anders Sandberg published on Flickr in 2009 under a Creative Commons Licence.
Animation: How the escapement works: 1) The falling weight powers the clock.
2) As it drops, the weight pulls the gears around. Left to its own devices, the weight would accelerate,
falling faster and faster. 3) The rocking escapement engages and disengages the gears, so they
turn at a constant rate, and the clock tells accurate time.
4) The swinging pendulum rocks the escapement and sets the rate at which it moves.
The escapement sits between the pendulum and the gears that turn the hands round the clockface.
You can see it in more context in this diagram by Christiaan Huygens, which dates from 1673.
I've flipped it left-to-right so the logical sequence of what's happening "reads," as we look at it,
from left to right. On the left, shown in red, we have the swinging pendulum. This trips the escapement (blue), which powers the gears (orange), and the clockface hands (yellow).
Artwork: How an escapement (blue) regulates a pendulum clock.
Artwork from Horologium Oscillatorium by Christiaan Huygens. Paris, Apud F. Muguet, 1673,
courtesy of US Library of Congress.
A summary of how clocks work
In summary, then, the key parts of a pendulum clock are:
- A dial and hands that indicate the time.
- A weight that stores (potential) energy and releases
it to the clock mechanism as it falls, very gradually, over the
course of a day (or several days, if you're lucky). Winding the clock raises the weight back
up, storing more potential energy to power the mechanism.
- A set of power gears that take energy from the falling weight and use it to drive the clock mechanism at the correct speed. If we use a really heavy weight and the right power gears, the weight will store enough
energy to drive the clock for days without us having to wind it up.
(Remember the law of conservation of energy here:
the longer the clock runs, the more energy it uses; a clock with a heavier weight
can store more potential energy so, generally speaking, it's going to run for longer without winding
than one with a lighter weight.)
- A set of timekeeping gears that drive the different
hands around the clockface at different speeds. These are usually finer and more precisely made than the power gears.
- A pendulum and escapement that regulate the
speed of the clock and keep it (more or less) constant.
In practice, clocks have lots of other bits, pieces, parts, and
features that horologists (master clockmakers) like to refer to—with splendid honesty—as "complications."
Photo: 1) When most people think of a pendulum clock, this is what they picture in their mind: a grandfather clock
(also called a longcase clock). 2) Clocks like this have a long pendulum that makes only a relatively narrow sweep back
and forth. 3) Grandfather clocks often have very ornate and beautifully painted dials.
Some drawbacks of pendulum clocks
Photo: One of the most accurate pendulum clocks ever made
before better technologies made them obsolete. This was the official US timekeeping standard from 1904 until 1929.
It was made by Clemens Riefler in Germany.
Photo by courtesy of National Institute of Standards and Technology, Gaithersburg, MD 20899.
Can you see any problems with pendulum clocks? Me too! A pendulum of a
certain length takes the same amount of time to move back and forth
if the strength of gravity stays the same. But what if the length of
the pendulum changes? That could certainly happen if it's a metal
pendulum and the room temperature goes up or down (say, between
winter and summer), because metals expand in the heat and contract in
the cold.
Now what about gravity? We treat it as though it were a
constant, but the strength with which Earth's gravitational force
pulls on objects varies across the surface of our planet: it's
greatest the closer you are to the center of Earth, so it gets slightly less as you climb
mountains and slightly more as you get closer to sea level. That means the same pendulum
clock will keep different times in New York City and Colorado, for
example! And talking of sea, imagine taking a pendulum clock on a
ship. What's all the pitching and rolling of the waves going to do to
the neat back and forth movements of your pendulum? Not going to work
very well, is it?
The first of these problems—the slightly changing length of the
pendulum—is relatively easy to fix. We simply use compensating pendulums
that automatically adjust ("compensate") as the temperature changes.
Two early kinds were mercury pendulums
(incorporating glass tubes full of liquid mercury) and
gridiron pendulums
(made by using two different metals, such as steel and
copper,
zinc and steel,
or steel and brass, that cancel out one another's expansions and
contractions). At the start of the 20th century, people started
making pendulums from a new material called invar (an alloy
of nickel and steel), which expanded very little with temperature
changes and virtually solved the problem.
There's not much you can do about gravity, though, and as for
taking pendulum clocks on ships, better forms of timekeeping were
gradually developed that made them unnecessary. But that's another
story! (You can follow it up in the "Find out more" section below.)
