Escapement - Accuracy

Accuracy

The accuracy of a mechanical clock is dependent on the accuracy of the timing device. If this is a pendulum, then the period of swing of the pendulum determines the accuracy. If the pendulum rod is made of metal it will expand and contract with heat, shortening or lengthening the pendulum; this changes the time taken for a swing. Special alloys are used in expensive pendulum-based clocks to minimize this distortion. The degrees of arc which a pendulum may swing varies; highly-accurate pendulum-based clocks have very small arcs in order to minimize the circular error.

Pendulum-based clocks can achieve outstanding accuracy. Even into the 20th century, pendulum-based clocks were reference time pieces in laboratories, although at sea the natural motion of the vessel severely impairs the accuracy of a pendulum.

Escapements play a big part in accuracy as well. The precise point in the pendulum's travel at which impulse is supplied will determine how closely to time the pendulum will swing. Ideally, the impulse should be evenly distributed on either side of the lowest point of the pendulum's swing. This is because pushing a pendulum when it's moving towards mid-swing makes it gain, whereas pushing it while it's moving away from mid-swing makes it lose. If the impulse is evenly distributed then it gives energy to the pendulum without changing the time of its swing.

Contrary to popular opinion, the time taken for a pendulum swing is not constant regardless of the size of the swing; the swing time changes with the size of the swing, see Pendulum. If the amplitude changes from 4° to 3°, the period of the pendulum will decrease by about 0.013 percent, which translates into a gain of about 12 seconds per day. This is caused by the restoring force on the pendulum being circular not linear; thus, the period of the pendulum is only approximately linear in the regime of the small angle approximation. To be time independent, the path must be cycloidal. To minimize the effect with amplitude, pendulum swings are kept as small as possible.

It is important to note that as a rule, whatever the method of impulse the action of the escapement should have the smallest effect on the oscillator which can be achieved, whether a pendulum or the balance in a watch. This effect, which all escapements have to a larger or smaller degree is known as the escapement error.

The only escapement which contradict this rule and is not detached at any time from the oscillator is Harrison's pivoted pallet grasshopper in pendulum clocks. This is a special case because Harrison was using the escapement characteristics to affect the pendulum. This was first noted by Henry Sully and set down in a Memoire around 1720. This is the first recognition that the pendulum's period may depend on a force applied during impulse at any particular degree of swing.

Any escapement with sliding friction will need lubrication, but as this deteriorates the friction will increase, and less power will be transferred to the timing device (for example, the pendulum). If the timing device is a pendulum, this means the pendulum will swing a shorter and shorter arc. Therefore, a dirty escapement will cause inaccuracy because the arc of the pendulum swing becomes shorter (the clock will speed up). For spring driven clocks, the force applied by the spring changes as the spring is unwound following Hooke's law. For gravity driven clocks this force also changes as the driving weight falls and more and more chain is suspended between the weight and the gear train, in practise however this effect is only seen in large public clocks.

Wristwatches, and smaller clocks, do not use pendulums as the timing device. Instead, they use a balance spring; a fine springs connected to the metal balance (imagine a bicycle wheel without the tire). The balance wheel rotates back and forth; a good Swiss watch has a frequency of 4 Hz (4 cycles, or 8 beats, per second). Faster speeds are used in some watches. The balance spring must also be temperature neutral. Very sophisticated alloys are used; in this area, watchmaking is still advancing. As with the pendulum, the escapement must provide a small kick each cycle to keep the balance wheel oscillating. Also, the same lubrication problem occurs over time; the watch will lose accuracy (typically it will speed up) when the escapement lubrication starts failing.

Pocket watches were the predecessor of modern wristwatches. Pocket watches, being in the pocket, were usually in a vertical orientation. Gravity causes some loss of accuracy as it magnifies over time any lack of symmetry in the weight of the balance . The tourbillon was invented to minimize this: the balance and spring is put in a cage which rotates (typically but not necessarily, once a minute), smoothing gravitational distortions. This very clever and sophisticated clock-work is a prized complication in watches, even though the natural movement of the wearer tends to smooth gravitational influences much more than for a pocket watch.

The most accurate commercially produced mechanical clock was the Shortt-Synchronome free pendulum clock invented by W. H. Shortt in 1921, which had an error rate of about 1 second per year. The most accurate mechanical clock to date is probably the Littlemore Clock, built by noted archaeologist E. T. Hall in the 1990s. In Hall's paper, he reports an error of 3 parts in 109 measured over 100 days (an error of about 0.02 seconds over that period). Both of these clocks are electromechanical clocks: they use a pendulum as the timekeeping element, but electrical power rather than a mechanical gear train to supply energy to the pendulum.