Ellipse Latest change 2017-10-11
One of the
biggest problems with a Foucault pendulum is that it tends to follow an
elliptical path, even when it was launched in a perfect straight line
and there is a perfect rotational symmetry in the whole construction.
This ellipse has it's own precession which can easily overwhelm the
This problem is bigger for shorter pendulums. There are several methods
to suppress ellipse forming c.q. the precession of it.
Onnes describes in his thesis a.o. that the ellipse will
periodicaly change direction.
The so called Charron Ring is
a ring, placed somewhat below the top, which the cable of the pendulum
touches slightly with each swing. This limits the amplitude of the
swing, but also -and stronger- supresses ellipse forming, because at
the moment of touching the velocity of the unwanted ellipsoical
component is at its maximum and so is reduced the most by the friction.
The drawback of this method is that the ring sits in a very high
location, often difficult to access and it must be adjusted quite
precise to prevent a preference for the direction of the swinging
plane. A second drawback is that the mechanical contact introduces wear
on the cable with the risk of breaking.
For the pendulum in the UN-building in New York this principle is also
used, but with a totally different implementation which eleminates wear
I also heard about variants where the ring is covered with a rubber
like lining. That may damp the ellipse perhaps better and eliminates
wear, but these materials themselves may become brittle or pulverized.
Not a good idea if you cannot access it.
uses on the cable near the top a cylinder with 2 O-rings which,
according to the installation manual, must make a solid contact with a
fixed safety collar. O-rings probably have an acceptable long liftime.
Another effect of the Charron ring is that it reduces the average
period time of the long axis of the ellipse because during part of the
swing the effective cable length is reduced. By adjusting the amount of
energy delivered by the drive coil it might be possible to make the
long and short-axis swing times exactly equal, thus eliminating the
precession of the remaining ellipse.
and some others place a thick metal ring (preferably copper) such that
a small magnet in the bob flies over it at the maximum amplitude. The
eddy-currents in the ring will damp the movement somewhat, but again
the damping is stronger for the elliptical component.
that a repelling drive will lessen the ellipse and an attracting drive
will amplify it. He does not provide arguments for this except a
little drawing which t.m.h.o. shows the opposite. Several sources I
found have conflicting opinions on this.
puts a weakly attracting magnet below the center. For the
movement in the long axis this has no effect, the bob is accellerated a
bit when approaching and decellerated the same amount when leaving. But
for the short axis of the ellipse the force is always attracting,
unless the short axis becomes zero, and that's just what we want.
A variant could be to engage the drive coil in attracting sense,
symmetrically around the center.
also mentions a permanent magnet in the center, but this time
repelling. This would not suppress the ellipse but, when correctly
adjusted, the precession of the ellipse. Crane uses attracting and
repelling drive (switch over at center passage) which he hopes should
eliminate the effects of certain asymmetries in the
system, which he does not mention.
that repelling drive counteracts the precession of the ellipse (not the
ellipse itself) and he derives that activating the drive coil when the
bob is at a certain distance d from the center, the precession will be
The distance d depends only on the Length, the Amplitude and the
Q-factor of the pendulum.
experiments up to now tend to confirm this. In all pendulums I operated
up to now I've seen alternating ellipses, changing direction around E-W
and around N-S. When the impulse is
given to early the ellipse precession is overcompensated, that is,
during a CCW ellipse the precession goes CW and during a CW ellipse the
precession goes CCW. When the kick is given to late it is just the
Some sources, like Pippard, suggest that a parametric drive, also
or piston drive, would counteract ellipse forming. The trick is to lift
the cable's mounting point a bit when the bob passes the center
and let it go at maximal amplitude. Very much like driving a playgound
swing by lifting or lowering your body's center of gravity.
Another method, related to an invention of Huygens, could perhaps
also work. Here a small trumpet-shaped tube sits below the mounting
point of the cable. As the pendulum swings out of the center, the
effective length of the cable is gradually reduced an so the swing time
decreases. With the proper shape of the trumpet the swingtime could
perhaps become perfectly independent of the amplitude, and then the
which transfers energy from the long to the short axis of the ellipse
is eliminated and with that the precession of the ellipse. The art is
to find -and machine- the proper shape of that trumpet.
Look at some details of the pendulum in
the Thij College in Oldenzaal (NL).