Help the MM Build a LONG Period Pendulum

There’s a [thread=255059] thread [/thread] running re this subject and, as always, I was about to continue some weird-ass simian hijack. I never know when to start a new thread but I’ll give it a go.

I’m a designer and machinist and a notion like this says BUILD ME! in no uncertain terms. So I want a Foucault pendulum in my back yard that will knock down pegs, just like at the museum. The ideas from the thread got me thinking of long period pendulums so that lateral displacement with each swing will be substantial. But does that small displacement of CM give me less stability of swing; less angular momentum or whatever it is that I’m trying to have a lot of?

I’m thinking of a 15’, or so, high structure with teflon bearings of a ball and cup nature. Do I go with high mass, low mass, bigger CM displacement with a shorter period. Help!

We’re currently re-landscaping the backyard yard and one of the features will be a 18’ mosaic compass rose. You can probably guess where I want to put the pendulum.

The one that used to hang in the Smithsonian had a cable length of 52 feet

According to the Indiana State Museum, “Foucault suspended a ball of 61 pounds on a steel wire 220 feet long from the dome of the Pantheon in Paris.”

The Science Museum of Virginia’s “pendulum weighs in at 235 pounds (107 kg) and is 95.8 feet (29.2 meters) long — one of the longest in North America.”

I don’t think 15 feet will be long enough.

:smiley:

15 feet will be plenty. Heck, a six inch Foucault pendulum could work, for a while.

A little brainstorming…
You want the largest mass possible. I know that makes construction harder, but the inertia of a large mass will diminish the relative effect of confounding factors like friction and air resistance. A ton or two isn’t overkill, and yet is well within the capacity of common industrial parts that won’t break the bank: jacketed steel cable, fixtures, etc. If it’s more than a lark, consider going even higher.

Since it’s outdoors, wind and weather will be major issues. Don’t expect your pendulum to run for days, but it should make a nice demo for the duration of a backyard barbecue or party.

Make sure your stand is as inflexible as possible. Vibration and flexing will kill the effect surprisingly rapidly Reinforced concrete towers with deep concrete footings wouldn’t be overkill. (Soil isn’t a terribly firm substrate) Try to design the suspension to prevent torsion (though freely rotatable bob might add to its ‘play value’ when it’s not being a physics demonstration. No. Wait. That could get dangerous…

Do consider the million ways a reckless kid might find to mangle themselves on your creation. Even a 100lb bob could be dangerous if a kid decided to lie down in its path or play chicken with it. It wouldn’t present the positive menace of an otherwise sedate 1-ton bob, but Screaming Banged-up Kid [band name!] is not the soundtrack of my fondest memories.

Give artistic consideration to the form and nature of the bob: maybe a 454 engine, an interesting piece of industrial iron from a junkyard, or a '72 Caddy pimpmobile (actually, no, they were 18.5-22.5 ft long), but remember that an assymmetric bob will be deflected by the its own passage through the air. The bob’s path and orientation remain (relatively) unchanged compared to the rotation of the earth between it, so its assymetric air resistance will be a constant displacing force that won’t “average out” over time.

Personally, I like the idea of a giant multi-ton concrete disk, ponderously but unstoppably gliding a scant inch or two over the ground, with ineffable mystery and majesty, but it would also pose distinct problems:

  1. the wider your bob, the more you have to worry about its edges scraping the ground at the extremes of its arc. A 15’ pendulum swinging over a 18’ rose would subtend about 72 degrees so it would make a 36 degree angle with the ground at the ends of its arc. For a 3-5ft radius disk, this woulld require the center to be to be a couple of feet in the air, which would shorrten the effective length and ruin the effect I’m imagining (sigh) Giving it a curved bottom (ideally, a surface section of a 15ft sphere) might help, but … no, it’s a write off. Forget it.

  2. I presume you’ll want it to mark its passage in some way. A disk would be the worst shape, because it would maximally obscure the area under it. That’s why many pendulums have pointed bottoms to knock over pegs, conical buckets that slowly leak a trail of sand as they operate, or a flexible probe or string dangling to delicately trace a path in a sand bed underneath).

Instead of suspending it by a cable, you might consider some other suspension. for example, you could suspend it by a pantagraph -two parallel bars- mounted on a rotating bearing at the top. This would allow your bob to remain parallel to the ground, adding visual interest, and eliminating the “ground-scraping problem” I mentioned above. On the downside, anything that departs from the simplicity of a cable does detract from its simplicity and self evidence. Its path might look more like a machine-made effect than a diplay of raw physical forces

Well, I doubt I’ve helped much, but I’ll be watching your plans with interest.

As soon as I posted, I noticed that your title said “long period pendulum” not “long pendulum”

In that case, you’re out of luck. The period of a pendulum depends on two things: its length and the gravitational field. I’m afraid I can’t help you with varying gravity over your compass rose (if I could, I’d have that as a backyard garden toy) so for 15 ft pendulum, you’re stuck with T= 2pi Sqrt(L/g) = 4.3 seconds.

This won’t vary with the mass of the pendulum (remember Galileo’s mythical experiment proving that all masses fall a the same rate) how far it swings (the higher you raise it, the more directly downward it falls at first, so the faster it initially accelerate. It all balances out.) or pretty much any other factor. That’s why pedulums were used to keep time in grandfather clocks.

You make it sound so hard! [ST:TNG]Q: “Simple. Change the gravitational constant of the universe.” LaForge: “What?!”[/ST:TNG]

But seriously, it’s not so hard to do as it sounds. If you suspend the pendulum from the center (clearly this requires a rigid support and not a cable) and put an equal counterweight on the top end, you’ve essentially cancelled the gravitational force on the bob. This won’t make a good pendulum, though it will make a pretty good gyroscope. If you make the top mass a little smaller (or a little closer to the pivot) then you have a compound pendulum; the gravitational force now acts only on the mass difference (actually its moment) but the whole mass still provides inertia. This can give a much longer period than 2 pi sqrt(L/g) for a pendulum of a given diameter L (arbitrarily long, in theory, though at some point you have to start worrying about other forces, like bearing friction and wind).

Well, I think it had more to do with the pendulum being a relatively simple high-Q oscillator; clock designers could choose the mass and amplitude for their pendulum clocks, after all. And for a simple circular-arc pendulum clock the amplitude is usually maintained at a near-constant value to avoid the inaccuracy caused by the anharmonic terms in the potential.

Thanks for the replies, all.

I went up to Disneyland and DCA after posting this morning with my brother. He’s a designer too, and we figured out the problem with a teflon ball and cup bearing. The basic oscillation won’t be too affected. The pendulum will swing nicely in line with really low frction. Unfortunately, the friction of even a nice teflon-teflon bearing will probably overpower the effect of the Earth’s rotation beneath the system.

I’d love to hear other ideas. It’ll be hand powered. This is line with KP’s post. I only want the thing to run for a half an hour, or so.

Have you thought of the structure that is going to support this thing? Have you thought about how you will keep it swinging? Who will reset the pins? Your guests would have more fun just playing around with a conical pendulum…

Also, if you put a sundial in your garden, please make sure the gnomen points due north.

Just some suggestions…

  • Jinx

I’ve heard it said that a simple way of suspending a pendulum that also features very low enery dissipation is to use a solid metal rod rigidly clamped at the upper support. It should be made of some sort of “springy” metal - stainless steel would probably be a good choice.

My high school physics teacher threw together a Fioucalt Pendulum with spare parts that he operated during our Physics Final. In that time you could clearly see the shift. He just used a big pendulum weight, braided steel cable, and a universal joint to mount it to the ceiling. This was a standard high school classroom, so it wasn’t all that high – 8 or 9 feet.

Sorry to bump this, but my subscription got messed up and with it my ability to post.

We have a powered foulault pendulum in my office, which you can read read about here. Its not quite what you are talking about, but I have fairly detailed drawings available. E-mail me if you’d like to learn more.