Circular Error Correction
The completed clock movement with a temporary wood pendulum; running on a temporary stand. The escapement crutch is extended and a weight added to form the secondary pendulum which serves to counter circular error. The horizontal link connects it to the main pendulum. It is the intention is to make a grid iron pendulum, and mount the clock in a wall mounted clock case.
The photo above shows an experimental set-up with a prototype grasshopper movement. Circular error correction is achieved using the dual pendulum system described by Dallas Cain and Pierre Boucheron, published in the Horological Science Newsletter (HSN Issue 1993-1. 18 January 1993). The Microset timer with infra red sensor measures the clock rate and calculates the Instability and Average Error. It also records atmospheric data such as air temperature, barometric pressure and relative humidity. Both pendulums have ball-race suspensions.
Graph 1. Free seconds pendulum coast-down from 7.5 degree semi-arc, without circular error correction. Pale blue graph show decreasing amplitude over time, red graph shows corresponding increase in rate, (i.e. pendulum swings faster over smaller arcs).
Graph 2. Free seconds pendulum coast-down from 7.5 degrees semi-arc with secondary pendulum attached by horizontal link. Pale blue graph again shows decreasing amplitude over time, and blue graph shows an initial increase in rate, then levels off between a pendulum amplitude of 6 to 4 degrees semi-arc, and then declines in rate after 4 degrees, (i.e. the pendulum rate remains constant between 6 and 4 degrees even though the amplitude is decreasing). The level portion of the rate graph can be varied by changing the relative masses of the two bobs, their relative lengths, and the position of the link.
Graph 3. Part of a Microset timer reading for the prototype clock movement. The graph shows the characteristic saw-tooth profile with the spikes in the rate coinciding with rewinding of the remontoire every minute. This variation in rate can be further reduced by adding Harrison’s solution of remontoire cams to provide a constant force on rewind. The trial period was 7.4 days. The resolution on the vertical axis is 0.000049 seconds, the average error from target rate over that period was 3.4 seconds and the instability is 4 seconds per day. The clock itself was constructed from left over bits and pieces and scrap.
Will Matthysen
October 2010.
