time base calibration

a 10MHz frequency reference locked to GPS is a standard instrument

why? the period should only depend on the length of the pendulum and gravity

-Lasse

Only to a point. The solution of the differential equation relies on sin x = x , which is true for small angles, to a certain level of approximation. I don't know at what angle it starts making a big difference, but different angles defineately have different periods. For a measurement as fine as the one proposed, surely it would make a measureable difference.

Bill, Just look at the specification of your clock. If you clock is more accurate than those 7us/2s, then you will be able to measure it. There are some ovenized oscillators being as accurate as 0.01ppm for not that much money. I expect them to be built into those not really cheap counters. Another difficulty is the rotation of the pendulum and its thermal expansion.

Rene

--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net

Sounds like you have set yourelf quite a task. When you want a really good vacuum you should consider cryo-pumping the vessel. That will involve liquid gas coolants (nitrogen and helium). This would also assist in keeping the temperature of the pendulum stable and thus the amount of variation due to length changes.

To do the very finest timing you would look at atomic clocks but only if you need timing accuracy well sub nano-second. Of course if you weren't going for that sort of accuracy then there are other laboratory time standards that could be employed.

If you only needed to swing the pendulum just before making the measurements you could use some sort of magnetic haul which released at the precise maximum amplitude of swing.

If you do manage to do the experiment I am sure we would be interested in the results.

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snip

I did a search a couple of months ago for a 10KHz GPS module, ISTR that they are no longer produced

Martin

It doesn't, at least not the way you think ;-p

You're overlooking the fact that you're doing this experiment sitting on a planet in a stable orbit around the sun, rotating around itself. Which means that you have to sum multiple forces to find the resulting net effect on your pendulum:

Sun gravity Moon gravity Earth gravity daily centrifugal force yearly centrifugal force

And that's before we consider that the gradients of the various gravity fields combined will not just accelerate, but also _elongate_ the pendulum differently depending on its current direction.

Sorry to burst your bubble, but: if you must ask, the answer is that you quite certainly can't do it to the required level of precision and stability.

That's going to be among the smaller problems you encounter in this project. Getting electronics to be stable over relatively long times may seem tricky at first sight, but it doesn't hold a candle to getting the *mechanical* aspects of this handled to the same kind of accuracy. Electronic oscillators that are stable to well within 100 microseconds in a second (on average) exist all around you: they're called "quartz clocks". Just think about it: good wrist watches aren't off by more than a couple seconds a month. That's about 1 ppm.

There's a reason why Newton's Gravity constant is still so shamefully imprecise, and why the institutions that can reliably handle this kind of thing all tend to have the word "national" or "federal" in their name. The reason is that precision measurements of gravitation are *hard*.

Some other points to keep in minds:

• pendulums, if they're any good, have rather small amplitudes and velocities. Now think how far such a thing would move in roughly 100e-6 seconds, and how thick your typical optical interruptor's beam is. So how many iterations would it take to get a significant reading? What is the relation of this time to the length of one day?

• You worry about temperature drift of an electronic oscillator. Do you have any idea how much worse this is for the length of the arm in a pendulum?

I got several Rockwell GPS receivers from Timeline Inc. several years ago. They still have them listed on their website ($69):

Don

and the correct answer is ? Do you have a value for the actual gravity deviations ?

Tides are one real illustration of the effects of gravity summs, and tide tables are widely available.

-jg

I did a search for Trimble GPS and found their Mini-T GPS. 10 MHz and 1 PPS.

Don

You would think so, except that we are on a planet that is also affected by the Sun, and being accelerated about as hard by its gravity as the pendulum is.

You have to look at the tidal forces (proportional to 1/r^3) instead of the straight gravity (1/r^2). The effective force will be down by a factor of about r_Earth/r_orbit, which is a factor of a few times

10^-5, putting you in the nanosecond range.

If your original calculation were correct, then it would be easy to measure. The trick is you don't measure one swing, you count a few thousand of them and see how long that takes. After about an hour, you would be off by about 1 second (at 600 microseconds/2 second swing).

There are devices available that can keep a pendulum swinging over the same arc length while counting out thousands of cycles. Here's what they look like (although you might want a smaller version if there is limited room on your workbench):

--
David M. Palmer  dmpalmer@email.com (formerly @clark.net, @ematic.com)

egg on my face, now!

should say simpleton

I remember this , sort of, ( the 1/R^3) now from physics class 20-odd years ago. :-0

Should have just cut the lawn, I guess.

Thanks for all your interesting replies. Bill Chernoff

Not right here, no. I might have a book to look it up in, somewhere. But it's getting a bit late around here to start juggling those volumes. And of course it's getting seriously off-topic here in c.a.e :-)

Unfortunately, tides themselves are only rather indirectly related to the actual tidal forces. There's just too much geography going on in all those ocean floors and coastlines for a nice and simple relation between tidal force and tidal amplitudes at a given point on some coast.

It's not as far off-topic as you might think :)

This could make a very good student exercise (and I never thought of looking for a gravity-sum influence on a pendulum )

So far, I have sketched out something with two opto interruptors,

• comparator, with something like a CPLD, or a fast uC. The timing sense interruptor would be at vertical, and the

2nd sensor would be used to fire a impulse coil, to maintain the pendulum It should be relatively easy to get to between 100-1000ppm on a single swing, and then 100 swings can give ~1ppm

Accurate length compensation is the other physical problem, although even that could have a c.a.e compensation solution :) ( or an invar rod? )

So it looks like ~1ppm is not too hard - what's needed now is some accurate predictions of the actual Gravity effects time variances.

Of course, I was not intending to infer any direct phase relationship, but merely to use the tides as a physical example.

-jg

Any time spent not cutting the lawn is a good choice.

--
David M. Palmer  dmpalmer@email.com (formerly @clark.net, @ematic.com)

In my own shame-faced defence, if the planets weren't moving and spinning, I would be right. :-)

Bill (I can't believe they gave me that degree) Chernoff

And the guy who gave the derivation earlier is correct only for a point mass on a massless bar, with a frictionless pivot in a vacuum, for small angles. So there! :-)

What is the most accurate pendulmn clock, anyways?

Cool student project: when I was in school, one upper level student project was a seismograph, where they were trying to find buried pipes with home made geophones (I guess thats what you'd call them) and a big steel plate on the gound which was pounded with a big sledge hammer. I never heard waht the results were, but it sounded interesting at the time.

I had a look at the Trimble Mini T. At 1600$ not really comparable to the Jupiter. Or are they cheaper over there ?

Rene

--
Ing.Buero R.Tschaggelar - http://www.ibrtses.com
& commercial newsgroups - http://www.talkto.net

Physics of gravitation and mechanics is. The electronic and software issues would be on-topic, but those have mostly been covered already.

A little research and computation turned up the following for the ratio of tidal acceleration to plain gravitational acceleration:

a_tide / g ~= 2 * (r_E / d_SE)^3 * (m_S / m_E) = 2 * (6.38e6 / 1.5e11)^3 * (2e30 / 6e24) ~= 5e-8

The effect of the moon is a little more than twice as big. And that's on the equator. It drops from there to zero the closer you come to the poles.

The pendulum period scales with the square root of overall acceleration, so the effect is:

sqrt(g * (1 +/- 5e-8)) - sqrt(g) ~= +/- 2.5e-8 * sqrt(g)

I.e. it would take 25 ppb sensitivity to "see" the Sun's effect, 80ppb to see the combined effect of Moon and Sun (during "spring tide"). If you don't happen to be on the equator, you have to do even better.

Did I mention this is really hard? :-O

For a processor-based solution, you would have to know the temperature expansion coefficient of the pendulum material rather well. Determining that from scratch would be a serious effort in its own right.

The classic aproach is neither that nor invar, but a bi-metal self-compensating rod. But unless you happen to find an old grandfather clock in a backyard, that would be hard to come by.

Its +/- this figure, so overall the affect is twice this. But, as you say, the period depends on root g. So I'd say the affect is 50 ppb, or 100 ns on a 2 sec period. On top of this the plane of the swing will rotate as the Earth turns unless you're at the equator. All-in-all, the experiment needs to be done there.

[snip]

Peter