Air Bearing Clock

Amplitude Measurements

Amplitude measurements were made using a MicroSet timer and the "Smith Method" as the pendulum "ran down" from an initial amplitude of approximately 5.5 degrees. The Smith Method is described starting on page 24 of the 1997-5 issue of the Horological Science Newsletter. The method uses Bryan Mumford's MicroSet timer with an offset sensor to measure the time taken by a portion of the pendulum swing. The method gives more accurate results if the sensor is located near the extreme of the pendulum swing. The method assumes that the pendulum behavior is sinusoidal and calculates the Amplitude by the following formula:

Amplitude = C / cos (p M/2T) [in the same units as used for C]

Where:

C = Horizontal displacement of the sensor from the center

M = MicroSet timer reading in seconds per beat

T = Beat time (i.e. time for one half-swing in seconds)

The amplitude in angle format is calculated by using the vertical position of the sensor

For these measurements the following values were used: C = 0.5 inches, T = 1.000 seconds, and vertical offset of sensor = 44.5 inches. The flag (interrupting the timer sensor) on the pendulum was 0.028" wide and the temperature was 13.5 degrees centigrade.

The Smith Method (as used here) is an approximation. Results may be improved by allowing for non-sinusoidal motion, width of the sensor flag, MicroSet errors, etc.

 

 Raw time data from MicroSet file.

 Calculated amplitude in degrees

 Damping Coefficient

Pierre Boucheron has made the point that it is necessary to calculate the damping coefficient in order to evaluate the run down performance of a pendulum. ["Sources of Pendulum Losses" in the Horological Journal (date?)] The damping coefficient is calculated by the formula at the top of the graph below which comes from the 3rd edition of Rawlings "The Science of Clocks and Watches" on page 377. The results of this calculation are shown below. The "noise" in the results could be caused by several sources. The large peaks may be due to my air compressor cycling on and off (it is located about 10 feet from the clock). The smaller variations may be due to the errors introduced by timing in the MicroSet timer. They may also be due to other sources such as the motion of the pendulum in an imperfect media (the air disturbed by previous passes of the pendulum)

 

 Q may also be calculated from the damping coefficent:

 Damping Coefficient after 10 point boxcar smooth. By "boxcar" - I mean a moving 10 point average .

 Rundown "Q" after 10 point boxcar smooth