Out of frustration in trying to quantify the tangent rule effect in the original clock I rigged up an hyper-simple magnetic escapement for my synchronome
It consists in a 200 turns coil (right in the picture) attracting the ferromagnetic bob for a brief period (20 ms) at the pendulum vertical.
There is no significant difference between impulsing the original gray cast iron bob and the new lead, steel encased, bob. other than reduced aerodynamic friction. They are both the same weight, 7.8 kg.
Impulse angle scans, the argument of the tangent in the tangent rule, are particularly easy to perform with this arrangement by varying the time delay between the pendulum position detector output and the power pulse timing.
The pulse timing is formed starting from the signal of the shown photo-interrupt which detects the bob transition from the vertical.
Typical impulsing parameters are:
one 22 ms long impulse, corresponding to 2 mm of bob shift, every 5 pendulum periods
the coil current is around 1 A for a pendulum half angle of around 2 deg.
I designed the magnetic impulsing device described with simplicity in mind above all. Both my two bobs, the original Synchronome one and the steel encased lead one (shown in the above image) can only be attracted by the coil current, hence only the left to right opto-interrupt signals need to be selected for triggering the coil current pulse.
The following circuit has been devised to perform the selection
After my best efforts to reduce the escapement error with the original gravity escapement the residual noise difference between the synchronome mechanical escapement and this magnetic impulsing scheme is quite dramatic, as shown in the following graph of the period (in μs from average, one dot per pendulum period )
At the low level of high frequency noise permitted by the magnetic impulsing scheme my clock shows a relatively strong sensitivity to the outdoor wind turbulence induced vibrations of its support which is tied as rigidly as possible to an internal, load bearing, wall of my ground level apartment. I live in Venice and, to a lesser extent, the water waves of a nearby canal ( 10 m between the clock and the canal bank) can also be detected by the clock (not shown).
An example of what just said, with a wind speed of roughly 20 km/h as measured by an outdoor anemometer, is represented by the red trace of the following picture where the same data of the previous picture , still in μs but on a different scale, are represented in blue.