Clocks - Basic Principles

In this page we cover the basic principles of timekeeping, underlying the operation of all practical clocks.

Summary

Horology, or the science and practice of clocks and clock making has seen many changes with evolving technology, from pre-history to the present day. This is a fascinating topic, and will give you an insight into what repairs might be possible.

For information on clock repair, see our Clocks page.

Safety

You may miss your bus if your clock is wrong. This could really spoil your day.

The consituents of a clock

All clocks can be considered to be composed of two parts:

• Some kind of time standard for measuring the passage of time, and
• Some kind of display for displaying the measured time.

In principle you can mix and match the two, so for the purposes of explaining basic principles it's worth considering them separately.

Time Standards

Historical

Astronomical phenomena such as the passage of the sun across the sky are the most ancient accurate means of telling the time. Sundials were used in ancient Babylon and Egypt, and remain a nice garden feature, but even the most ardent gardeners are likely to refer to a wristwatch rather than a sundial (even if the sun is out) in order to decide when to take their tea break.

Having discovered the moons of Jupiter, Galileo worked on a method of using a knowledge of their orbits to tell the time. Comparing the time so determined with the solar time at your current location offered an accurate means of determining longitude.

Water clocks have been used since antiquity. They depend on the steady flow of water through a small orifice to measure the passage of time. But the rate of flow is dependant on the viscosity of water, which varies with temperature. This limits their accuracy.

A Chinese incense clock, at the Museum of Timekeeping.

The hourglass or sand clock uses sand or some other granular substance instead of water. This is less dependant on temperature and hence more accurate. They are still in use as egg timers.

A constant rate of combustion has also been used historically to measure time. A candle clock has time divisions marked along the length of a candle. A particularly ingenious variant is the Chinese incense clock. This consists of a series of weights suspended above a metal tray, each held by a piece of string. The strings, equally spaced, are stretched across an incense stick. As the stick burns it burns through the strings one by one, giving an audible indication of the passage of time as the weights fall onto the tray. A fine example can be seen at the Museum of Timekeeping. As with the flow of water or sand, a rate of combustion depends on various environmental conditions, making it a poor timekeeper.

Mechanical

A verge and foliot mechanism in Salisbury Cathedral.

The first mechanical clocks date from the 13th Century and depended on a verge and foliot for timekeeping. This consisted of two weights on the ends of a horizontal bar (the foliot), attached at its centre to a vertical shaft. The shaft is driven by the verge escapement, comprising two small pallets along its length. These engage alternately with teeth in the top and the bottom of a toothed crown wheel, driving the foliot clockwise with one pallet and anticlockwise with the other.

Such clocks were poor timekeepers, typically gaining or loosing an hour or more a day, since the time for the foliot to rotate one way then the other was highly dependant on the driving force, friction and other factors. Consequently, if they were fitted with a clock face it would only have an hour hand, as the indication of a minute hand (if provided) would be fairly meaningless.

These and all previous clocks (excepting sundials) relied on the speed of a continuous process, whether combustion, the flow of water or sand, or the accelleration of a weight acted on by a force, all of these being highly dependant on environmental and other factors.

An undamped spring–mass system undergoes simple harmonic motion.

But in the late 1500's, Galileo noticed that the time a pendulum took to swing back and forth didn't depend on the angle of swing (for small angles) but only on its length, in other words it exhibited isochronicity. In fact, a pendulum is one of many systems in which a mass is subject to a restoring force proportional to its displacement from an equilibrium position. The result is that the mass will execute "Simple Harmonic Motion", characterised by an oscillation or vibration at a well defined frequency, independant of the amplitude of the motion. Hence a wind-up clock can be made which (ideally) doesn't run slower as it runs down, as a wind-up toy car or a spring-driven foliot clock would.

However, it was not until somewhat later that Dutch mathematician, physicist, engineer, astronomer, and inventor Christiaan Huygens realised the application to horology, inventing the first pendulum clock in 1657. The improvement was dramatic, suddenly enabling clocks to achieve accuracies measured in minutes per day. Within a fairly short period of time, nearly all existing clocks were retrofitted with a pendulum, though still driven by the verge escapement.

In watches and smaller clocks, a more compact balance wheel constrained by a spring may be used, typically rotating back and forth several times a second. Some mantlepiece clocks have a balance wheel consisting of several metal balls. With a much greater mass, these rotate much more slowly allowing some "anniversary clocks" to run for a year without winding. The rotating balls also serve as an aesthetic feature.

All practical clocks need an escapement both to give the pendulum or balance wheel the regular kicks it needs to keep it in motion indefinitely, and to count off the swings in order to drive the hands on a dial. The escapement can be powered by a spring, or in the case of larger clocks, by weights. Increasingly from the 19th Century it might be driven electrically.

A mainspring and fusee

Most spring-driven clocks will in fact run slightly slower as the spring unwinds and looses tension. The fusee mechanism, invented in the 15th Century uses a cone-shaped pulley to decrease the gearing applied to the spring as it winds down, so maintaning a constant torque applied to the escapement. The bulk, complication, expense and issues with reliability and maintenance caused it to fall out of favour as improved escapements made it less necessary.

These improvements focused particularly on arranging that the escapement use the lightest possible touch to maintain the oscillation of the pendulum or balance wheel, allowing it to closely follow its natural periodicity. The verge escapement was particularly poor in this respect as the pallets were driven continuously in one direction or the other.

The drive for accuracy was spurred in particular by the need for an accurate timepiece for navigation at sea for the estimation of longitude. This was famously achieved in the 18th Centurury by John Harrison.

Occasionally in clocks predating quartz movements, you might find an electrical or electronic mechanism. A fascinating very early example is the earth-driven clock, invented in 1911 by Percival Arthur Benson. Two different metal stakes driven into the ground served as a primitive battery, delivering just a volt or so. This fed an electromagnet which applied a tiny force to a permanent magnet attached to the pendulum. As the pendulum swung back and forth it operated a set of contacts which reversed the direction of the current, ensuring that the force applied by the electromagnet was always in the direction of the pendulam's swing.

A Shortt Synchronome clock, its master pendulum on the left and the secondary o the right.

The pinnacle of achievement in the development of accurate pendulum clocks is probably the Shortt Synchronome. This used a metre-long pendulum inside a copper cylinder, swinging in a partial vacuum to reduce air resistance. There was no escapement as such, as this would necessarily degrade, however slightly, the pendulum's isochronicity. Instead, its swings were detected electro-mechanically and used to synchronise a secondary pendulum, which, every 30 seconds, provided an impulse to the primary pendulum to maintain it in motion.

Such was its accuracy that it could detect variations in the time of rotation of the earth, and variations in gravity due to the Sun and Moon, and geographic location.

After transistors were invented these were sometimes used in electric clocks to amplify a voltage induced in a coil in proximity with a pendulum or balance wheel, and to feed this back to reinforce the motion.

Very rarely you might find a clock which uses a tuning fork kept vibrating electronically as the time standard instead of a pendulum or balance wheel.

Quartz crystals

A quatz crystal used as a time standard depends on a mechanical vibration essetialy no different from a pendulum or balance wheel, though sustained electronically and at a much higher frequency.

Quartz is an example of a piezoelectric material, that is, an electical charge appears on opposite faces if you stress it, and conversely, applying a voltage will cause it to deform slightly. Using this property, a piece of quartz is carefully cut and ground so as to "ring" at a specific resonant frequency, the vibration being sustained electronically.

Quartz crystals used in simple clocks and watches nearly always have a resonant frequency of 32,768Hz. This might seem an odd number until you realise that halving it 15 times successively gives a 1 second tick. This is easily done with simple electronic circuits. An advantage of such a high frequency is that you just have to count the oscillations in 1 second and check there are exactly 32,768 (not even just one more or one less) to assure the accuracy of your clock to a minute in 3 weeks! If a clock ticks just a few times a second, you would have to count the ticks for a much longer time or time them much more precisely to achieve the same accuracy. Fine adjustment is possible by connecting a variable capacitor in the circuit with the crystal.

Quartz crystals provide a more accurate and more stable time source than all but the best mechanical clocks but nevertheless they are somewhat temperature dependant. Additionally, quartz crystals are subject to ageing, causing a small additional drift over a number of years, and are also affected by the heat of the soldering process at the time of manufacture. Those used in cheap clocks and watches typically have an accuracy of a few seconds per day.

In a Temperature Compensated Crystal Oscillator (TCXO) the control IC contains a temperature sensor and is incorporated in the same package as the crystal. This allows the IC to compensate for temperature variations by adjusting the capacitance included in the crystal oscillator. By this means, an accuracy of 10 seconds per year is achievable.

MEMS Resonators

A resonator can also be constructed as a MEMS (MicroElectroMechanical System) device in which a microscopic mechanical resonator and the required control circuitry are all fabricated on a single silicon chip. This can give an accuracy similar to a TCXO, but it is inherently much less temperature dependant, less subject to ageing and the effects of soldering, and at the same time much more rugged.

Atomic clocks

These are the most accurate clocks available, the best typically gaining or losing no more than the equivalent of 1 second in 30 billion years, or half a second in the age of the universe. Unfortunately they are very expensive and usually very bulky. Chip-scale versions are now available but these are still by no means cheap.

Atomic clocks depend not on a mechanical vibration but on an atomic resonance, most usually in caesium or rubidium atoms. In fact the second is now officially defined as 9,192,631,770 oscillations in a caesioum-133 atom. National and international time standards are based on the averages of a number of atomic clocks, and it is on these that all the remaining time standards are based.

Rubidium frequency standards (not quite as accurate as caesium ones) are widely used in cell phone towers. In fact, if you wanted your very own atomic clock there are second hand ones from decommissioned cell towers going on eBay for only a few hundred pounds!

Atomic clocks operate at gigahertz frequencies, but even greater accuracy still can be achieved by using light, which is in the hundreds of terahertz range. The Nobel Prize for Physics in 2005 was awarded for work on applying optical frequency combs to lock an atomic clock to the frequency of the light from a laser.

Nuclear clocks

Atomic clocks depend on resonances amongst the electrons forming the outer shell of an atom, responsible for chemistry. Although atomic clocks are incredibly accurate, these electrons are nevertheless affected to some extent by stray electric and magnetic fields, which must be minimised in order to make the best atomic clocks.

The nucleus of an atom, on the other hand, is subject to similar resonances but governed by the very much more powerful strong nuclear force, exploited in the generation of nuclear power. These resonances are generally at much greater energies and hence correspondingly higher frequencies, but are barely affected, if at all, by stray fields. It has been known for many years that a nuclear clock could theoretically be much more accurate even than an atomic clock.

The difficulty is that for the most part we're talking about energies and frequencies well beyond what would currently be feasible to exploit. Fortunately there is one resonance at an energy just about within reach of current technology, in the nucleus of a rare isotope of thorium. A major advance was made in 2024 by researchers who finally managed to pin down the frequency of this resonance with unprecedented accuracy. Even so, much work remains to be done before a practical nuclear clock could be constructed. This will undoubtedly be achieved in the coming years, pushing the best timekeeping from one second in 30 billion, to 300 billion years!

You might well ask why anyone would want such a clock. For one thing, a thorium-based nuclear clock could potentially be made much more compact and robust than the best atomic clocks, portable, even. For another, such incredibly stable timekeeping could make it possible to study the nucleus in new ways, pushing back the frontiers of physics. There are suggestions, even, that it could reveal interactions with the mysterious dark matter, known by its gravity to pervade the universe, but which otherwise has totally defeated all attempts to date to identify it.

So if you want a Nobel Prize to proudly display on your mantelpiece, all you have to do is build the first nuclear clock! What are you waiting for?

Radio Time Signals

In the UK, the National Physical Laboratory's time standard is based on three atomic clocks, and is broadcast as the "MSF Signal". This can be received across much of northern and western Europe. Numerous other radio time signals are available in different parts of the world.

Domestic clocks which automatically synchronise with one of these radio broadcasts are widely available, sold as "radio controlled clocks", or even "atomic clocks" though they are actually using someone else's atomic clock!

GPS

Satellite navigation depends on a constellation of satellites each with its own on-board atomic clock and transmitting a signal containing encoded time information. Consequently not only can you get your geographical position by receiving these signals, but also an extremely accurate time.

Pulsars

Neutron stars are the incredibly dense remains of dead stars not quite massive enough to collapse into a black hole. A teaspoonful of their matter might weigh as much as a mountain. As they spin, their magnetic field may generate beams of radio waves or x-rays which sweep across space like the beams of a lighthouse. When these are detectable as a series of pulses by a radio or x-ray telescope, they are then known as pulsars. Being so massive, the pulses are extremely regular and could be used as the basis of a highly accurate clock. There are more convenient methods of telling the time here on earth, but if you're navigating across the solar system or beyond, comparing the times of arrival of the pulses from several different pulsars can make a very accurate and effective means of telling where you are.

AC Mains

The AC mains supply has a nominal frequency of 50Hz (or 60Hz in some regions). Although the frequency can vary slightly, the total number of cycles in a day is very carefully controlled. The reason for this is that if demand exceeds supply, all the generators naturally tend to slow down under the load, so reducing the frequency, or conversly, speed up in the case of over-supply. Hence the frequency is used as a vital tool in matching supply to demand in the National Grid.

A useful consequence is that the mains supply can be used as a time standard with guaranteed long term accuracy, though like several others, it's in reality a 2nd hand atomic clock.

Internet Time Sources

Your computer, smartphone or tablet contains a quartz crystal from which it determines the time on a continuous basis, but this is regularly synchronised with time sources available on the Internet. NTP (Network Time Protocol) is the means by which any computer on the Internet can request the time from a chosen time server and estimate the adjustment required to account for the transmission delay. The necessary correction to the system clock is then made gradually so as to avoid a sudden jump in the time, especially a jump backwards which might be very confusing to some applications.

NTP time sources are each given a "Stratum" classification. A Stratum 0 reference is an actual atomic clock or equally authoritative time source. A Stratum 1 device periodically synchronises against a Stratum 0 reference. This might be a rubidium clock or a server accessble on the Internet. An organisation might have its own Stratum 2 server which periodically queries a Stratum 1 server, and in turn is used as a reference by Stratum 3 devices, which might be employees' PCs.

Time Displays

Not all clocks have a display. If you picked up a rubidium atomic clock from a decommissioned cell tower, all it would give you would be an extremely precise 10MHz output. If you wanted a display you'd have to add your own.

Analogue Displays

Historical clocks were all analogue, whether displaying the time as a shadow on a sundial or markings on a candle or water container.

For centuries, an analogue clock face with a minute and an hour hand has been the standard method of displaying the time, which we all learned to read from an early age. Imaginative novelty variations on the idea are sometimes seen.

In fact, early mechanical clocks only had an hour hand as they were terrible timekeepers, perhaps loosing as much as 45 minutes a day. Furthermore, domestic clocks would be set daily from the church clock, which in turn would be set from the church sundial, or perhaps on a cloudy day from the movement of the verger's bowels. Hence, a minute hand would be pretty meaningless for telling the time of day. The widespread introduction of the pendulam by clock makers in the 17th Century suddenly made possible domestic clocks with a timekeeping accuracy of a few seconds a week!

A display doesn't have to be visual. The speaking clock (dial 123 in the UK) uses a recorded voice to give you the time. Speaking clocks and wrist watches and watches with a tactile display are available for the blind.

Digital Displays

Arguably, the most primitive form of digital display is the egg timer. It doesn't tell you the time, but simply displays one bit of information: is my boiled egg ready yet?

Electromechanical digital displays have been around for many years, an early form being the flip-down display. A series of cards flip down one after another, each card containing the top half of a digit on one side and the bottom half of the next digit on the reverse. These clocks are now often collector's items or cherished heirlooms. They are described in their own page: How flip clocks work.

Nixie tubes were used as an early form of digital display. A Nixie tube consists of a glass envelope containing neon gas and 10 digits, each formed out of wire. Any one of these can be illuminated by applying a voltage to it, causing it to light up with the characteristic orange neon glow. Special driver circuits are required as Nixie tubes need around 150V to work. Nowadays these clocks are purely a novelty item, popular amongst the maker community.

Vacuum flourescent displays (VFDs) are most often seen on older devices such as video recorders. Flourescent segments making up the display are housed in an evacuated glass envelope. Streams of electrons cause activated segments to glow, often with a blueish green colour. These displays tend to use higher voltages than most logic circuits but not as high as Nixie tubes.

Modern digital clocks generally use a familiar 7-segment display. The entire display may be formed as an LCD panel, often including additional symbols for AM/PM or an alarm indication. Alternatively, each segment may be lit by an LED, eliminating the need for a back light for it to be seen in the dark. LCDs and LEDs have the advantage of working on similar low voltages to the logic circuits driving them.

Other novelty forms of digital display are sometimes seen, for example, a row of LEDs on a blade of a fan or on a radius of a spinning disk can be made to flash in such a way as to trace out the time. Persistence of vision causes it to appear as a dot matrix display hanging in the air. A geeky alternative is a binary-coded decimal display in which the tens and units of the hours and minutes are displayed by 4 sets of 4 LEDs.

External links

• Watch and Clock Movements at Electropedia gives easily understood explanations of everything from pendulum clocks to atomic clocks.
• Hands of Time by master watchmaker Rebecca Struthers is a fascinating history of timekeeping from the earliest times, including personal stories of the key figures who advanced the science and art of horology.
• The Museum of Timekeeping (near Nottingham) is well worth a visit. Several of the clocks mentioned in this page can be seen there, along with many others.