On 30/3/2007 Nisaba Merrieweather wrote:
If I person with only the usual non-laboratory stuff available to them
wanted to build a Foucault's Pendulum, how would they do it? (no, I don't
want links, or even rechts).
Peter Macinnis replied:
The big problem is the suspension point. Anything ordinary has too much
friction, and the pendulum loses speed. Also, you need a LOT of mass,
and preferably a height of more than 60 metres, like the Panthéon in
Paris, which was bloody closed when I dropped in there several years
back. I have a photo of the sign saying it was opened, with closed and
locked doors behind it.
Harumph!
and:
small amplification:
I wrote:
The big problem is the suspension point. Anything ordinary has too much
friction, and the pendulum loses speed.
Well, in a sense, it loses speed, but what I really meant was range,
from side to side, amplitude. With a smaller amplitude, it moves less
rapidly through the central point where speed is greatest.
Alan Emmerson responded:
The reason for having a free suspension is to allow the plane of the
swing to remain stationary in inertial space. Anti friction bearings
top and bottom with centreing devices. The problem with any Foucalt
pendulum is making it swing in a plane rather than a cone. Unless it
swings in a plane, or very nearly so, the demonstration value is lost.
This is difficult when you have to impulse the pendulum to prevent it
from decaying. You need a very dense bob, a cable at least 14ft long, a
really rigid support, a method of releasing the bob without applying
out of plane force, and a means of impulsing the pendulum in plane-
usually electromagnetically as it passes through the vertical which
means some method of continually sensing the pendulum's position and
plane of swing and is further reason to ensure the swing is planar.
..( These days I think I might use Gorilla Braid. )
If you have to ask the question, you are not going to be able to make a good one without help.
Jim Smart answered:
Leon Foucault's original pendulum is now in Musee des Arts et Metiers in
Paris, suspended from the ceiling of the Chappelle of Saint Martin des
Champs.
His pendulum does have a lot of mass and is suspended from a great
height. It is difficult to see the suspension bearing which, of course,
is crucial to the success of the device.
Peter Macinnis replied:
Good, then I have seen it. As you say, it wasn't easy to see. I knew
it was no longer in the Panthéon -- it was briefly deconsecrated at just
the right time for Foucault, then Napoleon III emerged, and it became
Ste-Geneviève once again. Anyhow, I just wanted to go there.
Which raises an interesting question that I will pose separately so as
not to pollute this thread
Brian Lloyd commented:
I would use piano wire for the cable and attach it rigidly at the
top. Energy losses in the piano wire should be very minimal given the
high modulus of elasticity of steel. Steel will also let you carry
something like 100Kg of mass without any problem. I bet it would
swing for many hours, especially if the mass were formed into a disk
whose plane is normal to the suspension cable. The disk, if tapered
at the edges, would probably not have much air resistance (little
frontal area). You might be able to get away from needing something
to put back the energy.
Peter Schmedding commented:
I fully agree with the piano wire. After all, consider a 30 day
grandfather clock. Minimum loss of energy is the aim. The pendulum
works on a similar principle.
The sad fact is, for continuous operation, air resistance will stop
the pendulum sooner or later even if a large body of mass has been
employed. I had some thoughts building a smaller - e.g. room-size FP
one day. While the details have not been worked out, what I had in
mind is to use a directional light sensitive diode under the dead
centre of the stationary pendulum. As the pendulum swings a shadow
will send a signal to a monostable multivibrator, suitably timed to
switch on an electromagnet. That should be in the form of a coil
around dead centre. With appropriate choice of the R/C values in the
multivibrator it should be easy enough to time a small electric
current to create an omnidirectional magnetic field that starts
before the pendulum approaches the centre and stops at the moment of
passing over the light sensitive diode.
Also note: While the ON period can start any time once the pendulum
is on the return trip, keeping the multivibrater in synch by
triggering a new cycle (switching off the current exactly at dead
centre from either direction) is the task of the light sensitive diode.
In this way it should be possible to apply the small push that is
needed to keep the FP going and be independent from which direction
it approaches dead centre.
Food for thought? I hope so.
Alan Emmerson added:
Once more into the mystery of the pendulum.
Remember that the important things
about the Foucalt pendulum require that it should swing at nearly
constant amplitude, in a single plane, for about 12 hours. That's about
22,000 swings for a 14ft pendulum.
Piano wire is not necessarily such
a good idea for the "string" in pendulums. Despite what one might
initially think, bending steel even within its elastic range does
consume energy. The energy used in bending a spring-steel suspension
spring only 0.003 inches thick is significant in precision pendulums.
Next, unless the design is clever, there is a real likelihood of a
fatigue failure of the wire. That is what happened to Foucalt himself -
60 ft of piano wire writhing on the floor.One research report I have
read said that the out of roundness of commercially piano wire is
enough to induce asymmetric bending leading to a favoured plane of
swing. That said, piano wire is in fact used in Foucalt pendulums. For
a small pendulum you could consider banjo strings. I would use
multistrand steel cable or one of the modern braided fishing lines eg
Gorilla Braid. The terminations of the string must be designed really
carefully.
The performance parameter usually
used for pendulums is "Q", although there are folks, including me, who
question whether Q is altogether satisfactory for the purpose. Q is 2pi
times the total energy of the pendulum divided by the energy lost per
cycle .At atmospheric pressure, values between 3000 and 15000 are
achieved. The Qmax bob shape for a clock has drawn a lot of attention
over two hundred years. The answer for a clock seems to be a paraboloid
of revolution or "parabolic spindle". The sharp edged disc or
lenticular form is not as good as the sphere especially in free air.
There are energy losses other than aerodynamic. . They include a
component from the displacement of the point of attachment to the Earth
This increases as the mass of the pendulum increases (and as the cube
of the pendulum's frequency) So making the bob very heavy is not always
a solution..
The optimum bob shape for the
Foucalt is a sphere but for a different reason. The pendulum bob in the
Foucalt must be axi symmetric about the wire. The lenticular bob, for
example, if aligned out of the plane of swing, will generate out of
plane forces leading to a conical swing and a rotation of the plane of
swing. (Actually the plane of orientation of the bob would be
dynamically unstable.)
Alan
(sometime horologist)
Brian Lloyd wrote:
I would use piano wire for the cable and attach it rigidly at the
top. Energy losses in the piano wire should be very minimal given
the high modulus of elasticity of steel. Steel will also let you
carry something like 100Kg of mass without any problem. I bet it
would swing for many hours, especially if the mass were formed
into a disk whose plane is normal to the suspension cable. The
disk, if tapered at the edges, would probably not have much air
resistance (little frontal area). You might be able to get away
from needing something to put back the energy.
I fully agree with the piano wire. After all, consider a 30 day
grandfather clock. Minimum loss of energy is the aim. The pendulum
works on a similar principle.
The sad fact is, for continuous operation, air resistance will stop
the pendulum sooner or later even if a large body of mass has been
employed.
True, but if you could start it and have it run on stored energy for
12 hours, it would be sufficient for a good demonstration.
I had some thoughts building a smaller - e.g. room-size FP one day.
While the details have not been worked out, what I had in mind is
to use a directional light sensitive diode under the dead centre of
the stationary pendulum. As the pendulum swings a shadow will send
a signal to a monostable multivibrator, suitably timed to switch on
an electromagnet. That should be in the form of a coil around dead
centre. With appropriate choice of the R/C values in the
multivibrator it should be easy enough to time a small electric
current to create an omnidirectional magnetic field that starts
before the pendulum approaches the centre and stops at the moment
of passing over the light sensitive diode.
Rather than a multivibrator I would use a PIC and a little bit of code.
Hmm, as the mass approaches bottom dead center the capacitance
between mass and floor would reach a maximum. That could easily be
used to detect bottom dead center. Use the capacitance of the mass to
control the frequency of an oscillator. Use frequency to voltage
conversion and differentiate. You will get a zero-crossing at BDC.
Use that to turn off your electromagnet until the next cycle.
Also note: While the ON period can start any time once the pendulum
is on the return trip, keeping the multivibrater in synch by
triggering a new cycle (switching off the current exactly at dead
centre from either direction) is the task of the light sensitive
diode.
In this way it should be possible to apply the small push that is
needed to keep the FP going and be independent from which direction
it approaches dead centre.
Food for thought? I hope so.
Sounds like a fun project.
Alan Emmerson responded:
This type of thing has been done
many times before. The problem with the particular method Peter
suggests is sensing the position of the bob. You need a ring shaped
sensor. Optical switching is fairly common in clocks built by
enthusiasts, but a sensing coil coaxial with the drive coil is more
often used and would be more appropriate for a Foucault pendulum.
Once you have decided to impulse
the pendulum, minimum loss of energy is not the aim. The key to good
performance is constant synchronisation and strength of the impulse.
Prima facie the drive should be applied close to and uniformly on both
sides of the equilibrium position.
Those with an interest in clock science may care to look at
http://www.hsn161.com/hsnauthorindex.php
and
http://www.precisionclocks.com/
David added:
At school we have a Foucaults Pendulum with a length of about 13 metres. We
originally tried piano wire but as Alan said it eventually fatigued. We have
tried woven steel wire but the "twist" in the cable imparts a "twist"in the
swing after a while. We eventually strung it up with kevlar fishing line
(Which I suppose is the Gorilla braid). If you set it in motion carefully it
swings quite well, But after a while the line stretches and the bob is on
the ground. Between uses, we rest the bob on a box to prevent this
happening. For teaching purposes, we set it in motion in the morning and the
students can take measurements over the course of the school day as desired.
The pendulum came about because when we were building our new Science block
we thought it would be fun to have one and the architects designed it into
the building. It is basically a tube between the various levels, with the
suspension point on the lower surface of the roof and the bob 4 levels below
in the bottom level.
Brian Lloyd answered:
Use the capacitive sensor to find BDC of the swing. Phase-lock to the
pendulum using a DPLL. You can apply the impulse as a function of
time since last BDC.
The goal is to keep a Foucault pendulum running rather than a super-
accurate time reference. That is probably a simpler problem.
Those with an interest in clock science may care to look at
http://www.hsn161.com/hsnauthorindex.php
and
http://www.precisionclocks.com/
Cool stuff. I love mechanical solutions to things. It never ceases to
amaze me what people were able to accomplish before we had digital
electronics.
OTOH, I would probably go for an atomic clock and discipline it for
long-term stability using GPS.
Alan Emmerson responded:
> Use the capacitive sensor to find BDC of the swing. Phase-lock to the
> pendulum using a DPLL. You can apply the impulse as a function of
> time since last BDC.
You are relying then on accurately knowing the period of the pendulum.
That is not easy, the period changes as the amplitude decays. The usual
technique is to use a ring conductor around the wire near the top as a
switch
>
> Cool stuff. I love mechanical solutions to things. It never ceases to
> amaze me what people were able to accomplish before we had digital
> electronics.
>
> OTOH, I would probably go for an atomic clock and discipline it for
> long-term stability using GPS.
For goodness sake why? They are ugly. .Any way , you already have
almost the same precision in your colour TV set . 1652Hz set by a
rubidium clock Throw an inductive loop around it and with a little help
it will drive a dial .
Fedchenko managed 1 part in 10
8 with a
pendulum and one transistor. More recently Professor Ted Hall at
Littlemore had a pendulum clock set up that was sensitive to the
position of heavy items in the clock room - he cheated a bit though by
having a sideways look at the GPS.. Incidentally, listers might like to
ponder over how you "set the time" accurately on such a precise clock
and:
I'll have to think about that a bit more. I would have thought there was no nett twist in a wire rope.
There are various sorts of modern fishing line It's interesting to hear that some of them stretch progressively..
Where abouts is your school David?
Brian Lloyd replied:
If I measure the zero crossing every time I can discipline my timing
clock to track the pendulum's period. I can know when the pendulum
will be on its downswing and initiate the drive pulse at the
appropriate time.
Cool stuff. I love mechanical solutions to things. It never ceases to
amaze me what people were able to accomplish before we had digital
electronics.
OTOH, I would probably go for an atomic clock and discipline it for
long-term stability using GPS.
For goodness sake why? They are ugly.
I guess beauty is in the eye of the beholder. Every method has its
own beauty. There is a simple elegance to an atomic clock. There is
beauty in the mechanism of a mechanical clock. I like them both.
.Any way , you already have almost the same
precision in your colour TV set . 1652Hz set by a rubidium clock
Throw an inductive
loop around it and with a little help it will drive a dial .
The master oscillator for the TV network is probably disciplined from
GPS these days. (When I worked at PBS they had two clocks and dragged
one over to the NBS for synchronization.)
The TV as a clock source has some problems. First we have to transmit
the signal to the TV and we don't know the distance and the exact
time of flight. And while it gives me a frequency reference (albeit
with some phase noise) it does not give me an absolute time value.
The 1pps from a GPS receiver is pretty easy to come by these days and
it has the extra feature that it gives me the time too. It is also
considered to be a stratum-0 source.
I recently saw a good article about how to build a GPS-disciplined
TCXO master oscillator. Let me see if I can find it ... ah, here it
is, in the July 1998 issue of QST: "A GPS-Based Frequency Standard,"
by Brooks Shera. From the article:
"Figure 6 shows the DAC output voltage
during normal operation of the controller.
The data were accumulated over a period of
several days by recording the output from
the ASCII port. Several interesting things
can be observed. There is a slow decrease
in voltage, which corrects the long-term
aging of the VCXO crystal. Converting the
VCXO input voltage to relative frequency
indicates that the aging process is about 7 ×
10–12 per day; which is typical of a good
quality VCXO that was manufactured a few
years ago and has had a while to stabilize.
Superimposed on the slow decrease is a
nearly sinusoidal 24-hour variation caused
by a day-night temperature shift of about
4°C in my workshop. The data indicate a
temperature coefficient of about 4 × 10–12
per oC, a respectable value for an ovenized
crystal. The GPS phase lock has prevented
these normal aging and temperature effects
from significantly affecting the VCXO frequency. GPS jitter is also quite evident as
noise on the plot. The RMS jitter amplitude
has been reduced from about 35 ns at the
filter input to about 0.5 ns equivalent at the
output. Still, the noise dominates the plot
and suggests that an even-longer time constant could be used with this VCXO to further improve the short-term stability of the
output frequency."
Not bad for a home-built reference oscillator.
Fedchenko managed 1 part in 108 with a pendulum and one
transistor. More recently
Professor Ted Hall at Littlemore had a pendulum clock set up that
was sensitive to the
position of heavy items in the clock room - he cheated a bit
though by having a
sideways look at the GPS.. Incidentally, listers might like to
ponder over how you
"set the time" accurately on such a precise clock
Well, I imagine one could lead or lag the drive pulse. One could
insert or delete an extra pulse-per-second pulse in order to make
gross motion of a second.
Of course I am imagining that one is not extracting the zero
crossings of the pendulum mechanically but rather electronically and
then using that pulse to drive the clockwork.
Kevin Phyland commented:
If memory serves, the Earth Sciences building at Melbourne Uni had a
Foucault pendulum in the stairwell setup. It's thirty years since I was
there but it looked like it had some sort of magnetic impulse thingy
ringing it...
Alan Emmerson added:
There a couple of seemingly paradoxical situations with clocks.
The first is that the very best
pendulum controlled clock with a rate stable to one part in 100million
can not tell you the time to better than +1,-0 sec.
For the second, suppose you have
built and rated a clock that is better than any previous clock. How do
you set it to show the correct time to the limit of its precision. The
best record of the time of day is the previous clock which has
presumably been kept in step with the Earth's rotation but only to the
limit of its precision.(as amplified perhaps by using a chronograph).
So the setting of the new clock can be no better than the old clock and
this has been going on back into history each time we built a better
clock.
Brian Lloyd retorted:
Not entirely. Absolute time is not particular interesting. We pick a
point in the earth's rotation and say (arbitrarily) "this the the
beginning of the day." So setting the new clock is not at all difficult.
What the new clock really gives us is increased accuracy in measuring
intervals of time, something that has real scientific value. Oh, and
we will know the accuracy of the staring of the next day with more
precision. That is probably of value to someone too.
Glen Moore noted:
http://sciencecentre.uow.edu.au/welcome.html
A 4m high Foucault pendulum is on the left of the picture.
1. The suspension is a braided stainless steel wire (to avoid fatigue)
2. The driver is a cylindrical electromagnet
3. The trend towards circular
motion is avoided with a ring near the top of the pendulum which the
suspension wire strikes each half swing.
4. The timing for the electromagnet is synchronised by the wire touching the ring.
5. The amplitude is over 1m.
Using a similar design I constructed a successful pendulum only 1m high for teaching purposes (at University of Wollongong).
Nisaba Merrieweather wrote:
<interesting stough deleted for Brevity, who has a
*lot* of deleted stough
at my house that she STILL hasn't picked up!>
I was also interested in an explanation of how a pendulum could swing
*outside* a larger system when it was built within that larger system of
materials taken from that larger system. How do you remove the reference?
....Panthéon in Paris, which was bloody closed when I dropped in there
several years back. I have a photo of the sign saying it was opened, with
closed and locked doors behind it.
Harumph!
<giggling> You do Grumpy Dwarf better than the original.
and:
<blank look> What do you think I was asking for?
Thanks for the info - sounds a bit beyond the aegis of the miscellaneous
contents of my back shed. Even though I
*am* planning on buying myself a
small blowtorch soon, which I expect to enhance my standard of living
considerably <grin>.
Nisaba
Pendulumless
