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:
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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.
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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.
