Beat number (clock)

The number of beats ( n * ) is the number of audible drive pulses ( beats ) of a two-armed armature of a mechanical watch that it emits in one hour .

history

The stroke number is a historical value that is still used by watchmakers today in relation to two-arm lever escapements . In almost all other technical areas, the physical quantity frequency has established itself .

Beat number and frequency

A process that always recurs in the same way in a regular rhythm is called periodic. The time that elapses between two identical positions in a previous sequence and its repetition is called the period or oscillation period (symbol T ).

Frequency (symbol f ) denotes the number of identical events within a certain time interval . The frequency is the reciprocal of the period. Its dimension is 1 / time. The unit of frequency, the hertz , or 'Hz' for short, is derived from the SI base unit second

${\displaystyle 1\,\mathrm {Hz} ={\frac {1}{\mathrm {s} }}}$

Most mechanical clocks are built with two-armed anchors and therefore emit the familiar “tick-to-tack” noises. Both the “tick” and the “tack” are called “hit”. The number of audible beats and thus the number of vibrations per hour is the number of beats.

The relationship between beat number n * and frequency f is:

${\displaystyle {n^{*}}=2{f}\cdot 3600}$

${\displaystyle {f}={\frac {n^{*}}{\mathrm {7200} }}}$

Example: wristwatches

Beat number, period and frequency of the balance wheel of automatic wristwatches

Beat rate [1 / h]	Impact duration [s]	Vibration rate [1 / h]	Period duration [s]	Frequency [Hz]
0018,000	00000.200	00009,000	00000.400	002.50
0019,800	00000.182	00009,900	00000.364	002.75
0021,600	00000.171	00010,800	00000.333	003.00
0028,800	00000.125	00014,400	00000.250	004.00
0036,000	00000.100	00018,000	00000.200	005.00

Example: seconds pendulum

Beat number, period and frequency for a second pendulum

Beat rate [1 / h]	Impact duration [s]	Vibration rate [1 / h]	Period duration [s]	Frequency [Hz]
003,600	00001,000	00001,800	00002,000	000.50

A so-called second pendulum has a period of 2 seconds and oscillates at a frequency of 0.5 Hertz.

Measurement method

The audible drive impulses (beats) of a mechanical clock are monitored and processed with the help of a timing machine . Strictly speaking, the number of beats is measured, converted to the frequency and compared with a time standard . With this measuring method, any deviation in the accuracy of a mechanical watch can be quickly determined.

With some mechanical watches that do not have a two-armed armature, there is only a single audible drive pulse per oscillation, for example with the chronometer escapement. In this case, the measured number of beats has to be doubled in order to calculate the frequency from the "beat number".

Individual evidence

1. ^ Günter Krug: Mechanical clocks ; VEB Verlag Technology; Berlin 1987; ISBN 3-341-00356-8 ; P. 182f
2. ^ Friedrich Assmus: Technical drives including clocks ; Springer-Verlag Berlin, Göttingen, Heidelberg 1958; P. 213
3. ^ Hans Kocher: Automatic clocks ; Verlag der Neue Uhrmacher-Zeitung, Ulm 1969; P. 68