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 Foucault precession.
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 almost completely.
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.
company 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.
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.
states 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
Witzel 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.
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.
states 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 suppressed completely.
The distance d depends only on the Length, the Amplitude and the
Q-factor of the pendulum.
My 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 called vertical 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 mechanism 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).