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by Shawn Carlson
Jan, 2000

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Every Sunday morning I enjoy a walk along a two-mile stretch of the world's most sensitive gravimeter. The sun's and moon's gravitational tugs on my body amount to only a few millionths of the earth's, and yet that tiny force acting over the Pacific Ocean regularly raises the sea level so high as to batter my path with waves. But isolating these feeble forces inside a laboratory tasks even professional instruments. That's why I was astonished to learn that Roger Baker of Austin, Tex., has developed a device that can gravitationally track the position of the sun and moon--for about $100.

One of my favorite truisms of science asserts that yesterday's discovery is today's calibration and tomorrow's noise. That is particularly applicable here. Last January I described another Baker invention that can detect micropulsations in the earth's magnetic field. But even these minute magnetic effects would swamp the gravitational forces that we are trying to measure here. In fact, eliminating all the spurious influences is by far the most challenging part of this project, and success depends on experience. Only expert gadgeteers should attempt it.

In Baker's apparatus, a small but powerful magnet delicately floats between two permanent magnets. A clever optical device senses small movements caused by gravitational shifts, seismic activity, thermal expansion, a stomping toddler and so on. A control circuit counters the motion by fine-tuning the current through an electromagnet. Changes in this current thus track forces acting on the floating magnet. The float is weighted to make it insensitive to high-frequency motion. But it does capture slowly oscillating signals from earthquakes (with undulations of a few tens of hertz) and the changing position of the moon as the earth turns on its axis. In fact, Baker originally designed the instrument as a vertical-motion seismograph.

 

Figure 1: SENSE AND CONTROL CIRCUIT(top) detects tiny movements of the flag and adjusts the current in the feedback coil to compensate. To use the instrument as a seismograph, add the filters as shown. The temperature control circuit (above) can maintain the sensor's temperature to within one hundredth of a degree Celsius. Click image to enlarge.

The optical sensor accounts for much of the instrument's sensitivity. To monitor the float's position, it uses an opaque flag to block some of the light from an LED and keep it from reaching a phototransistor a few millimeters away. When the float and flag move, the light signal changes quickly; shifts in position on the order of a nanometer have a discernible effect.

Radio Shack sells ceramic magnets in sets of five for about $2 (part no. 64-1888). You'll need two sets for a total of 10 ring magnets. Stack six of them into two groups of three and epoxy them to bolts. The seventh magnet will serve as the float; the other three are unneeded. Baker keeps the float from moving sideways by attaching it to a steel razor blade. The sharp edge of the razor will abut a brass plate on the side of the instrument support. Two miniature rare-earth magnets (Radio Shack part no. 64-1895) behind the plate fix the razor's edge to the brass. A smear of oil along the blade creates an almost frictionless hinge that allows the float to swing up and down but not side to side. Finally, Baker attaches a one-ounce lead fishing weight to lower its natural frequency and the small opaque flag to sense its position.

Although you can build the gravimeter frame out of any nonmagnetic material, Baker recommends using window glass because of its low cost, low thermal expansion and ease of assembly. He cuts the plates with a carbide-wheel glass cutter so that the pieces fit together without gaps and then braces the structure with triangular glass supports. He glues them all together with silicone cement. Mistakes are easy to fix because the parts can be readily separated with a razor blade.

Figure 2: BAKER'S GRAVIMETER shown in horizontal cross section, can register extremely small movements caused by gravitational pulls. (In practice, the device is mounted vertically.)

For the electromagnet, Baker winds a coil utilizing two of the unused ceramic magnets as guides. Wrap a pencil with masking tape until the magnets slide onto it snugly. Cover the magnets with more masking tape and position them about one magnet diameter apart on the pencil. Then tape one end of 30-gauge enameled magnet wire (Radio Shack part no. 278-1345B) to the edge of one of the disks and begin wrapping the wire between them. Keep a few ounces of tension on the wire and continuously coat it with 24-hour epoxy as you go. Don't stop until the coil's edge is about two millimeters below the edges of the magnets. After the epoxy sets, warm the assembly in an oven at a low setting to melt away the masking tape adhesive, then separate out the bare coil. The finished coil will be about 0.5 centimeter long and 2.7 centimeters in diameter. Its DC resistance should be about 10 ohms.

The optical position sensor requires some care. You can use an ultrabright red LED (Radio Shack part no. 276-066B) and a phototransistor (part no. 276-145A), but you'll need to eliminate the outer cases to bring the active elements as close together as possible. Grind the casings down to the chips and then polish the ends with a fine-grit polish. A combination of toothpaste and elbow grease applied against the back side of a piece of soft wood works well. Install the circuit elements into their frames with silicone cement [see illustration below]. Next, blacken three small pieces of aluminum foil with a felt-tipped marker. Carefully epoxy two of them to the LED so that they form a narrow horizontal slit; Baker says his slits are about half a millimeter wide. Use the third piece to block the bottom half of the phototransistor. This trick sharpens the device's sensitivity because it causes the signal to crash rapidly to zero as the flag cuts across the narrow beam of light emerging from the slit. Assemble the rest of the instrument as shown.

Figure 3: GRAVIMETER is shown atop its metal housing. In operation, the device is slid inside the cylinder, an iron pipe wrapped with mu-metal to block the earth's magnetic field. The resistors glued to the outside of the housing act as heaters to keep the instrument's temperature constant.

Like almost all delicate instruments, Baker's gravimeter will produce spurious results if its temperature changes. Baker solved that problem by controlling its temperature. He installed the detector inside a metal sleeve, which he kept at about 10 degrees Celsius above room temperature by employing twenty 50-ohm 1Ž2-watt resistors as small heating elements. Baker sensed the temperature using a Radio Shack thermistor, the output of which he compared with an adjustable set-point voltage, determined by a potentiometer. A circuit turns on the current through the resistors whenever the thermistor signal is below the set point and turns them off when the signal climbs above it. This setup, simple though it is, can keep the temperature constant to within a few hundredths of a degree C. The metal sleeve also serves to shield the apparatus from the earth's magnetism. It consists of an iron water pipe, three or so inches in diameter and eight inches long, wrapped with layers of thin foils made of mu-metal or permalloy interposed with sheets of a nonmagnetic material such as cardboard. You can purchase mu-metal foil through the Society for Amateur Scientists for $30 per square foot. In any case, the shield needs to extend at least two pipe diameters beyond both the top and bottom of the detector to attenuate magnetic fields that enter through its open ends.

To monitor the forces on the detector, you'll need to connect it to a computer. Baker uses the WinDAQ analog-to-digital converter, which runs from the Windows operating system. The WinDAQ/ Lite sells for about $100. Macintosh aficionados should check out the Serial Box Interface from Vernier Software. There are, of course, other options. For this application, the computer should display the data like a chart recorder, showing the shifting voltage across the coil versus time.

 

Figure 4: OPTICAL SENSOR which can detect nanometer shifts in position, consists of an LED (left) facing a phototransistor, with an opaque flag that cuts the light beam between them (right). The beam passes through a narrow slit in the aluminum foil.

Install the instrument vertically on a stable base and set it on a concrete foundation as far from car and foot traffic as possible. Turn on the power and let the heater warm up. Then remove the insulation from the top and adjust the screw that raises and lowers the upper magnet while watching the output and find the location at which the signal from the phototransistor just barely turns on. This is an extremely tricky operation. At this point, a slight movement would turn the signal completely on or off. The float will naturally bob up and down at a frequency of about one second, which should be apparent on an oscilloscope. Replace the insulation.

For fine adjustments, rest a ceramic magnet on top and move it around until the signal from the phototransistor just dims. The instrument should now record for weeks with only occasional adjustments to the outer magnet necessary to maintain its high sensitivity. If you are really observing extraterrestrial gravity, you should see a slowly varying sine wave that is in phase with your local tides. The detection will be less ambiguous if you live far from the shore so that secondary effects, such as swelling of the beach, do not account for the signal. Ambitious graviteers can carry out a Fourier transform on the data and look for excess power at around a period of 24 hours and also at 28 days.

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