PSN-L Email List Message

Subject: pendulum suspensions
From: holmstro@..........
Date: Sat, 10 Nov 2007 13:22:28 -0800 (PST)


This is my first post to the list. I am Bob Holmström, Editor of the
Horological Science Newsletter (NAWCC Chapter 161).  Pendulum suspensions
are of great interest to those interested in precision time keeping.
Perhaps there is some use discussing what clockmakers have learned even
though a clock pendulum needs to move constantly over a much larger angle
than the devices discussed here.

But first, since Dr. Peters suggestion to use a magnet suspended carbide
ball is what prompted my response, I want to discuss a prior experiment:

Marcel Bétrisey, a Swiss artist who has created many clocks and Foucault
pendulums from "found materials", has experimented with a Foucault
pendulum suspended from a ball attracted to a high strength magnet.  He
found that the motion was not "homogenious", in that the amplitude of the
motion and the rate of change of the direction of motion had significent
variations. Anyone who has attemped to build build an accurate Foucault
pendulum can attest to the fact that the suspension design is critical and
even then error correction devices such as Charon rings or Eddy current
damping are required to get anthing close to accurate motion.
Unfortunately the error correction devices add there own errors!
Kammerling Onnes (1890's) used a crossed knife edge suspension without
error correction for a Foucault pendulum and achieved some of the most
accurate results ever obtained.  Marcel's best results have been with
pendulums suspended from guitar wire located by a stack of close fitting
watch jewels in a collet.  Some of Marcel's work can be seen at and  For a real treat on the interaction
of art, science, and horology see his radiometric pendulums.

re clock pendulum suspensions:  Most pendulums hang from flexures,
including very precise clocks such as those constructed by Shortt and
Fedchenko.  The connections between the flexure and its support and
pendulum are very important - simple clamping can be problematic - Shortt
and Fedchenko used spring machined from blocks (i.e. thick ends) with
great success.  Modern edm techniques make this type of spring relatively
easy to construct.  Gravity wave detection pendulums use similiar
suspensions constructed from low loss materials such as indium.

True knife edge suspensions probably do not exist - contact forces and
irregular contact geometry produce something less than ideal.  Much better
results are obtained with edges shaped to a small radius that can be
obtained by lapping with an appropriate jig or by more modern edm methods.

One test of a pendulum suspension for a clock is to see if it shows true
"circular error" (a horological term probably best expressed as period
error due to the fact that a pendulum is not truely isochronus - i.e. the
period varies with amplitude).  It is very difficult to construct a
pendulum that agrees well with theoretical predictions. Plotting period
versus amplitude squared makes extrapolating the data to zero amplitude
much simpler than the traditional form of plot and it shows the errors
quite readily. The idea was suggested by Stroud and Matthews, "Period of a
rigid pendulum pivoting on flattened knife edges" Physics Education,
Volume 22 (1987) pages 170 - 173.

I intend to evaluate Chris Chapmen's crossed roller suspension and
Meredith Lamb's hard disc id suspension when I return home in a couple of

The best pendulum suspension results that I have obtained so far are with
an air bearing suspended pendulum.  The pendulum was suspended from both
ends of a rod passing through a porus graphite air bearing, first with
magnets controling side to side drift and then air bearings on the ends
also.  Some results and photos of the setup are at  Perhaps not the most practical - the air
bearings are not cheap and a continuly running air compressor is a bit

Note: John Harrison used a third method to control end to end drift and to
reduce friction in his H1 chronometer e.g. he used a small fiber from each
end of the rod to a fixed support - in addition the rod was supported on
"anti-friction" rollers (imagine segments of two large wheels with the
shaft resting at the intersection of their radii at each end of the

Bob Holmström


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