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Dr. Slack

Thu May 29 2014, 08:54AM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

I'm making a gravity measurement device. It's been a long term, low level project that I've been brewing for years in my head, but have decided it's time to start cutting metal, and go public with it.

It's not really intended to be an accurate determination of G, I will be happy if I get one sig fig of agreement, delirious if I get two. It's more of a philosophical exercise. How philosophy? Even as a young man, I didn't really get the feeling that I knew my neighbourhood. I thought perhaps that I could travel round the world by human power, walk, cycle, to the extent that there was land at any given longitude to do it on. But that takes resources, a year or two out, and money, and was never really going to happen. So yes, I regard my neighbourhood as a little wider than most would.

So, an alternative exercise, build a small desktop apparatus that will measure the gravitational attraction of a small local weight, and the sun and moon all at the same time. There, I'm holding at least the locally important bits of the solar system in my hand, so to speak.

Some orders of magnitude. If I take a pendulum, and hold a 1kg weight within 100mm of it (about the best concentration of mass I could get, given structure and heat-shield enforcing a minimum separation), then the pendulum would deflect about 1n radian. The tidal effects of the sun and moon (according to Wikipedia) are about 50n and 100n radians respectively at the equator in the line of centres. Once they have been multiplied by sin and cos of latitude (one for distance from earth's axis, and one because the pendulum resolves force parallel to earth's surface), that's a few tens of n radian each. If I sense a 300mm long pendulum position with a capacitive sensor, built from the pendulum itself with perhaps 0.3mm spacing to 20x15mm plates round it, then the output per n radian will be an order of magnitude above the 1Hz bandwidth noise floor of a reasonable amplifier for 1v AC drive, 10kHz initially for easy sound-card use, maybe go up later. If I put a volt from plate to pendulum, then the electrostatic attraction will swing it about 10n rad, which shows that drive level stability and symmetry is not a big issue.

Ground heave due to solar heating is the big stability problem, as I am measuring the angle of the pendulum to the local angle of the ground. Although the mass signal is very small, I can control the position of the mass, perhaps rotating it around the test mass once per minute. The moon's position will vary on a 28 day period, also easily separable from a 24 hour period effect. But without digging myself a deep hole, or setting up in a deep mine tunnel, the second harmonic of diurnal heave will be indistinguishable from the solar tidal effect. I'll choose a concrete floor in the middle of my property for the first setup, and see how I get on.

I've already had a quick look-see at the sensor, with a few electrodes of copper tape stuck on the outside of a test-tube, and a test mass of a bit of old brass rod hung inside with a fine steel wire. I decided to see how bad magnetic attraction to the steel wire was as I waved a magnetron ceramic magnet around, and was astonished to find my bit of brass rod was so magnetic I could actually see the deflection if I looked carefully. It's very old brass, so presumably has high levels of ferrous impurities. So, main lessons, think about the magnetic properties of everything used in the build, and measure them (gravity probe B found some magnetic BeCu clips in an early prototype of the spacecraft). When I whizz the weight around the tube, I want to be able to convince myself that the pendulum is responding to gravity, and not to magnetic fields or temperature gradients. But I can generate those two without generating a gravity signal, which will put an upper bound on the susceptibility of the apparatus to those.

The first job, now I'm actually building real stuff, is not a better pendulum, but a remote operated micro-leveller, capable of monotonic resolution to sub 1u radian. This will allow me to zero the level signal to at least 10% of full scale. And the first measurement will be its stability.

Of course, what I'm making is also a seismograph. It'll be interesting to see how noisy traffic on the local road, and the kids thumping up and down stairs, will be.

I'll start posting dimensions, perhaps POVRAY renders or photos of the proposed kit, diagrams, more accurate calculations as time goes on. But don't expect any rapid developments.

Does anybody know of a mine, or really deep decommissioned nuclear shelter, that I could use in a couple of years when it's finished?

Ash Small

Thu May 29 2014, 10:02AM

Registered Member #3414 Joined: Sun Nov 14 2010, 05:05PM
Location: UK
Posts: 4245

Regarding the 'magnetic properties' of your 'old piece of brass', I found this on the internet, Neil:

"So while brass isnâ€™t magnetic, it can interact with magnetic fields. This happens because the movement of a magnet (or the brass could be moving instead) sets up an electrical current in the brass. This current has its own magnetic field which interacts with the magnet. The effect is best felt with strong neodymium magnets"

Sulaiman

Thu May 29 2014, 05:18PM

Registered Member #162 Joined: Mon Feb 13 2006, 10:25AM
Location: United Kingdom
Posts: 3140

I thought that brass is actually diamagnetic
so a tiny bit of paramagnetic material may be needed to counteract the diamagnetism?

Temperature control and/or two dissimailar metals ("gridiron style, e.g.

)
are vital to maintain accuracy.

although your pendulum is static, some insight may be gained from;
(assuming your measurement system uses ac)

GPS disciplined clocks tend to have short-term jitter,
get a Rubidium oscillator from eBay.
(I compared my Rubidium oscillator with a friend's GPS disciplined oscillator using Lissajous figure on a 'scope)

Have you looked at 'Time Nuts" ?

(some of the links lead to pendulum clocks, different but relevant)

" A man with one clock knows the time, a man with three clocks is never sure."

Patrick

Thu May 29 2014, 08:51PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

i need a pic....

Dr. Slack

Thu May 29 2014, 10:13PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

Yeah, pictures.

Don't forget, I'm measuring universal G, not local g

The odd mix of SI and imperial dimensions reflects the fact that I'm trying to source materials in their finished sizes to reduce the machining I have to do. When I find a one-stop metals website, I tend to design around what they have.

You may wonder about the very thick wall on the outer tube. I did some calcs a while back (I'll reproduce them here eventually) about what temperature gradient across the tube would be required to make it banana-shaped enough to disturb the verticality measurement due to differential expansion, and it's like micro-degrees. So, the tube's the thickest wall practical. Which also means I can drill into and tap the ends for fixing. While the sensitivity of angle to output increases linearly with tube length, the thermal banana problem increases as the square. Without any actual figures for likely temperature gradients, I feel 300mm is a reasonable first stab.

klugesmith

Fri May 30 2014, 01:28AM

Registered Member #2099 Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716

I'm eager to follow your progress.

Once read an account of a modern-day Henry Cavendish experiment.
Instead of measuring deflection
(in system with large time constant, hard to damp critically)
it employed some controllable force to oppose the big G effect
and a servo loop to maintain virtually zero deflection.
IIRC, that greatly reduced the settling time after the large masses were moved in or out.
Sorry I have not yet read your plan closely.

Good luck weighing the Earth.
-Rich

p.s. I agree with you that a result within 10% of the literature value would be gratifying.
Of all physical constants, G is the least accurately known.
Nobody knows for sure the value of the fourth significant digit.
In contrast, the product of G and the mass of Sun, Earth, etc. is known well enough to navigate space probes to precise landings on distant planets and moons.

Forty

Fri May 30 2014, 06:36AM

Registered Member #3888 Joined: Sun May 15 2011, 09:50PM
Location: Erie, PA
Posts: 649

Sulaiman wrote ...

" A man with one clock knows the time, a man with three clocks is never sure."

I keep reading that to myself in a pompous British voice and laughing.

I think I've lost it.

Patrick

Fri May 30 2014, 07:27PM

Registered Member #2431 Joined: Tue Oct 13 2009, 09:47PM
Location: Chico, CA. USA
Posts: 5639

Forty wrote ...

Sulaiman wrote ...

" A man with one clock knows the time, a man with three clocks is never sure."

I keep reading that to myself in a pompous British voice and laughing.

I think I've lost it.

a jaguar commercial for sure.

Dr. Slack

Sat Jun 14 2014, 02:49PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

The first bits of metal have arrived. The tubes are extrusions, or more likely pulltrusions. There are quite significant die-marks running their length, inside and out. That shouldn't cause me too much of a problem, as long as they are straight, which they seem to be to an eye and a straight edge at least. I've already established that the 1/2" tube will be a drive-fit in the 1" tube, perfect.

Next job is to build the electrode assembly, using the 1" pendulum bob tube as the basis for the former. One layer of strong 0.2mm polyester thread wrapped round it, then a 0.1mm layer of paper. This will give me a 0.3mm spacing from the electrodes to the tube, and I can pull the cotton thread out from one end when it's time to release it. Then once I've placed the BeCu foil electrodes on the paper spacer and run wires down from them, build up a very thin, and hopefully uniform shell of GRP, up to a diameter where it's a slip fit inside the 2" tube. Well, the worst that can happen is that it all goes horribly wrong, and I learn something about building electrodes, or wearing gloves with epoxy, or jigging things better, or something.

I still need to think how I am going to attach a thin wire to the middle of a 1/4" hole.

They were out of stock of the ball-races I wanted to buy to make the levelling platform. That's what the U section is for. New stock in two weeks.

Dr. Slack

Sun Jun 15 2014, 04:15PM

Registered Member #72 Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659

As you would guess from the tentative tone of the previous post, I haven't really got a clue about building the electrode assembly, or perhaps it's better called a construction.

I need a lathe.

Anyhows, I wrapped polyester thread round the 1" mandrel, then applied a careful single layer of masking tape. The O/D was now 26mm, compared to a previous 25.2mm (that's not 1" guys, but, what's the tolerance on a pulltrusion?), so that's a 0.4mm rather than 0.3mm gap. It's all pretty nominal, so that will do for a first cut. I then placed 4 carefully cut pre-bent bits of BeCu shim on, which I held in place with some small elastic bands.

Next was a couple of layers of decorators' pasterboard glass fibre scrim-tape. Unfortunately this stuff is 10% glass, 90% fresh air, so on reflection, I'm going to get large radius variations if I try to build this stuff up to any thickness. Then a layer of cloth cut from a pair or trousers discarded a decade ago (geez, does this man throw *anything* away?). Wrapped in a few turns of cotton thread to try to compress it own to some semblance of uniformity. I put the mandrel in an oven at 70C to cure the epoxy overnight.

I was now concerned that I'd used so much tension in wrapping the 'poxy cloth that my 'unwind the thread' release may not work. I was unwilling to continue building and risk it being stuck on. I had a construction that was far from uniform, so now was the time to see if the thread release worked, to pull it all apart and see what I had learned.

Well, the thread release worked perfectly. There's the electrodes on the bare mandrel, can you see the 400um gap? Inside, the epoxy has obviously leaked under the electrodes at the gaps. That's not in itself a problem, but I could do with a release layer there rather than something that will get stuck to the epoxy.

Next steps. Get some woven glass cloth. Much more dimensionally consistent than plasterboard scrim tape. Use polyester resin, lower viscocity than epoxy. Use plastic gloves, that stuff takes ages to wash off the fingers. Make a guide jig to set up the final diameter (a lathe substitute).

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