Tangent rule and synchronome


Nothing more fun than year end holidays to thinker with presents, this year is clocks. And I am out of the closet now, I completely electrified my synchronome. Out of frustration in trying to quantify the tangent rule effect in the original clock I rigged up an hyper-simple magnetic escapement.

Now parameter scans are particularly easy to perform, all by programming the control processor.

The subject today is the check of the relationship between the timing of the impulse and the period duration, Airy's tangent rule.


At this youtube video you can follow the development of the actual raw data of a power pulse delay scan, in the following graph the summary:

The parameters of this experimental run are:

one impulse very 5 periods, the 70 ms impulse occurs at 10 set delays from 100 ms (7 mm at bob's level) before to 100 ms after the pendulum crossing of the vertical, the coil current is around 300 A turn.

In agreement with Airy's tangent rule, see for ex. P.Woodward, My own right time, pag.69, the period at impulse lengthens for delayed impulses and shortens for the early ones, the period variations disappear in the noise when the impulse is centered within a few mm.


The amplitude of the period variations is in surprisingly good agreement with Woodward's theoretical expression:

The free pendulum Q, measured in the same run, is around 5500 at 1.8 to 2.2 deg of amplitude, the relevant amplitude for this experiment.

Interesting in itself the apparent relationship between period fluctuations and amplitude in the free pendulum data shown above.

Back to ΔP/P vs λ, the reported agreement with theory for small λ suggests that previously measured period shifts at impulse in the mechanical clock of 1 ms, ΔP/P~.5*10-3, imply an impulse/losses asymmetry 

λ = ATAN (2Q*ΔP/P) = 70 deg, a shift from vertical of almost half swing, it seems to me too large to be true. Nonlinearities at work or just a mistake somewhere? There are differences between the two cases, the mechanical impulse energy is substantially larger than the magnetic one since the magnetic cycle is 5 periods instead of 15 for the original escapement, the pulse lasts a lot longer than the 70 ms of the magnetic and the mechanical Q is around half of the one of the magnetic/free pendulum.

To summarize the results of these observations are fun but probably marginally relevant for accuracy, in my case the standard deviation of the mechanical impulse period is surprisingly similar to the one of any other period in the impulsing cycle, suggesting that it doesn't spoil significantly the overall time accuracy of the mechanical clock. A closer look at the spectrum is needed though to reach a definitive conclusion.

I will try again to center the mechanical impulse, at first with the added flexibility of the solenoid trigger described in a previous post and then with the original escapement trigger wheel.

I am working on the pretty poor aerodynamic performance of the synchronome bob, a friend is shaping for me a just as heavy but smaller lead bob with better aerodynamics.

I'll also pay some extra effort to keep the bob as far away from the walls as possible and position it symmetrically.



PS I designed the magnetic impulsing device above all with simplicity in mind, as you have probably guessed already from the picture. The design has the advantage of being roughly centered with the pendulum center of gravity, I wonder if this is the reason for the disappearance of the spurious period oscillations which normally follow the mechanical impulse.


John Haine

That's very nice Bepi!  A good way to magnetically impulse the bob, essentially like a single big Helmholtz coil.  I've been put off EM impulsing because of what I think is the difficulty of making sure the impulse is only in the direction you want, but this seems a more controllable way to do it.  How big is your current pulse, and do you make any attempt to shape it?


Yes, a whole Helmoltz coil couldn't work with the synchronome bob but would be a good choice for a magnetized one. The current depends on the pulse length, the number of impulses in a cycle and the pendulum swing, in the above case, one impulse every five periods, 50 ms pulse and 2.5 deg I believe it was 300 A-turn, I think I wrote more about it on youtube. As far as impulsing in line with the center of gravity anything is better than the synchronome and it shows, with magnetic impulsing the noise is a lot reduced .