The Foucault Pendulum
at the
University of Louisville

Introduction.

In 1978, a Foucault pendulum was installed in the Administration Building, now called Grawemeyer Hall, at the University of Louisville. This apparatus demonstrates directly that the platform to which it is attached is in a state of rotation. Since the platform in this case is the Earth itself, the rotation of the planet can be detected. The motion becomes apparent as the plane of oscillation of the pendulum appears to rotate relative to the surrounding structure. However, since there are no forces acting on the pendulum to produce an actual rotation, it is concluded that it is the support structure itself which is in motion. The effect varies with latitude, and is predicted to produce a complete rotation of the plane of oscillation in about 38.7 hr at Louisville, KY. The period of oscillation of the pendulum itself depends primarily on the length of the pendulum. The observed period of swing is 9.4 s, corresponding to a length of a simple pendulum of about 72.1 ft. This is consistent, to within the error in the period (+/- 0.05 s) of the declared length of 73 ft 5 in. Moreover, as will be explained below, the radius of swing of the pendulum is not uniform, and so only approximate agreement with results for a true simple pendulum is to be expected.

This report is written to provide a record of some of the history of construction of the pendulum, and to give instructions for its continued maintenance.

History of the Foucault pendulum project.

In 1977, the Administration Building had been completely renovated. In the early days of U of L on Belknap campus, this building had been pressed into service beyond its planned functions and many interior changes had been made. During the presidency of Dr. James Grier Miller, an extensive renovation had restored the building to its original appearance inside as well as outside. The first floor had been reopened in the center so that one could look from the gound floor to the top of the dome in the rotunda. The terrazzo floor of the ground floor had been covered over with a vinyl tile. When that was removed, it became apparent that there was set into the ground floor a stone compass rose, replicating the ironwork in the dome above.

In mid-1977, Mr. John M. Houchens, former Registrar, who had an interest in Foucault pendula, proposed to Dr. John A. Dillon, Jr., then Vice-President for Academic Affairs, that a Foucault pendulum be installed to add to the building a feature which would be of interest to visitors. Dr. Dillon enthusiastically agreed, and arranged for funding from a combination of private donations and restricted University funds. Some consideration was given initially to having the pendulum constructed by an outside firm, but it was realized that the expense would probably exceed the funds available. Dr Dillon enlisted a group of persons from within the University whose knowledge and skills would enable them to make and install a Foucault pendulum, together with its drive and controls. The design which was adopted is similar to one used by the California Academy of Sciences, but all details were developed independently here. Dr. Walter Moore, a retired Mathematics professor was a skilled machinist and continued to work part-time as an Instrument Maker in the Physics Shop. He would machine the pendulum bob and other metal parts which would be required. Profs. Verne Baxter and Samuel Bell from the Department of Electrical Engineering would provide the circuitry and sensing apparatus to control the magnet which was needed to maintain the steady swing of the pendulum. Mr. John Takeuchi, from the Office of Facilities Management would provide the design for the portions of the pendulum installation, other than the bob itself, which would be on public display. Dr. Roger Mills, also of the Office of Academic Affairs and a Physics professor, was responsible for the design of the drive magnet and of the pendulum mount. He also was to coordinate the work of the members of the working group.

Plans for modification of the structural iron work supporting the dome to accommodate the pendulum mount were prepared by a licensed engineer in the firm of Senler Campbell and Associates, and the work was performed by a crew from Steel Fabricators, Inc. (SFI), a Louisville firm. The iron needed for the magnet was donated to the University by SFI. Heavy welding for the mount platform was performed by SFI and, after some additional machining by Dr. Moore, the platform was raised into position and installed some 72 feet above the ground floor level by a crew from SFI.

The pendulum bob and its fittings were machined by Dr. Moore from a single brass casting, made in a local foundry from a pattern designed and prepared by Dr. Moore. The weight of the casting was not accurately determined, but it was estimated to be between 170 and 180 lb. Dr. Moore constructed a crane to enable placement of the casting in the lathe, and the crane was later used to move the finished bob into position in the Administration Building. The size of the spherical central portion was unusual, and made it necessary for Dr. Moore to fabricate special tools in order to complete the turning of the bob.

The pendulum was hung in the Spring of 1978 by Dr. Moore, Dr. Mills, and two students, Cyril Meyer and David Mattingly, from the Electrical Engineering Department. They were also involved in M. Eng. Thesis projects relating to the sensing and drive electronics.

Since air resistance tends to damp out the oscillations of the pendulum as it swings, it comes to a stop in about two hours after it is started at full amplitude. To overcome this tendency, a drive magnet is used to impart to the pendulum at each swing a small impulse which makes up for the energy lost in the swing. The magnet is activated by a pulse of electrical current controlled by electronic circuits connected to an assembly which makes it possible to determine the moment when the pendulum bob has reached the center of its swing. In the first years in which the pendulum was installed, the sensing device was located in a small floor level, the light ring. This feature also has in its top surface 360 red diodes which are used as indicators of the apparent precession of the plane of oscillation of the pendulum. The sensing itself was done using one of two light beams near the floor which would be interrupted as the tip of the pendulum passed through them. The design, installation, and maintenance of the electronic components which sensed the interruption of the light beam and initiated the current pulse to the magnet was done under the supervision of Prof. Baxter and Dr. Bell. They worked first with Mr. Mattingly and Mr. Meyer. When the first designs did not prove to be satisfactory, the results were improved by work done with the third E.E. student, Ms. Shayesteh Khosravi-Kamrani. The design was based on counting the interruptions of the light beam to regulate the position of the activated red light and of the active sensing light beam. Experience showed that the two periods were not commensurate, and so the events became unsynchronized after several days had passed. Thus it was necessary to reset the device manually and after only a few days of operation. Eventually, this requirement for constant attention became too burdensome, and it became necessary to replace the old sensing system.

In late 1988 and early 1989, a group from the Physics Department, Mr. Charles Cowan, Electronics Technician, Mr. Ron Smith, Instrument Maker, and Dr. Mills, redesigned the sensing device. The new sensing device is located now with the pendulum mount, and is described more fully below. The pendulum now will opereate for extended periods with no need for maintenance other than the resetting of the plastic pins on the old light ring.

The design of the light ring was the work of Mr. Takeuchi. The metal parts were made by Dr. Moore, and the wooden trim by Mr. Lee Tucker, a carpenter in the Physical Plant Department. A viewer will notice that there is a bridge at the northward side of the ring. This feature was included so that the flourish in the design of the compass rose would not be obscured. The red lights in the ring only simulated the position of the pendulum: there was no direct sensing. In order to make it possible for casual passersby to detect the motion of the plane of oscillation, plastic pins are set upright every ten degrees, an are knocked over as the pendulum "passes by". This also provides an opportunity for direct sensing by the viewer.

Description of the pendulum.

The entire bob is composed of several brass pieces, all made from the original casting. These can be disassembled to access the fittings which seize upon the aircraft control cable which is used to support the bob in its swing. The radius of the central portion of the bob is 11.5 cm (4.5 in), and the two caps are approximately frustrums of cones 12 cm (4.7 in) in height, and with greater and lesser radii of 3.0 cm (1.2 in) and 2.5 cm (1.0 in), respectively. The spindle is cylindrical, with height 7 cm (2.7 in) and radius 1 cm (.4 in). The mass of the assembled bob was not measured, but can be estimated (assuming a specific gravity of 8.5) from these dimensions to be 59 kg (a weight of 130 lb). [The statement made in the leaflet available (in March, 1990) at the pendulum site lists the weight of the bob as 178 lb. This is comparable to the weight of the original casting, and takes no account of losses due to machining.] The suspension cable, standard 1/8"D aircraft control cable, was tested in machines in the Civil Engineering Department and found to be capable of sustaining a weight of over 1200 lb, thus guaranteeing an ample safety margin.

Since the components of the mount are not readily accessible to view, a photograph showing the components is included as Fig.1. The structural members painted red are portions of the main framework supporting the dome. The white panels at the bottom are translucent panels of frosted glass or of plastic which are set into the iron straps which are bolted to the support memgbers to form the framework seen from below as the compass rose. The pendulum platform itself rests on supports attached to the structural members. The platform is held in place by its weight, and is not rigidly attached to the structural members. The platform in fact rests on Teflon discs on brackets, and the position of the platform can be adjusted along two mutually perpendicular directions so that the assembly can be centered relative to the compass rose in the terrazzo below. movement of the platform is accomplished by turning bolts mounted in the brackets, and which bear on the platform edge. One of these bolts is visible, somewhat out of focus, as the white object near the middle right-hand edge of the figure. A blackened cylinder appears below the platform and serves both to obscure overhead light from the hole within which the pendulum cable moves, and to locate the sensors for the light beam used to determine the moments at which the cable passes through the center of the swing. Two such beams pass through holes in the cylinder to photodetectors in the far side of the cylinder. A wire leading from one of these detectors can be seen next to the left side of the cylinder. The light sources are mounted so that they project beams at right angles. One of the mounts for the sources is seen next to the wooden block at the lower left of the picture. The cylindrical object at the center of the figure is the drive magnet. It is held against the platform by Z-shaped braces, and it can be centered independently of the platform by the adjustment of the setscrews in the Z-braces. A hollow rod to which is attached an iron disc is about the cable. It swings within the magnet and couples the support cable to the magnetic pulses of the drive. The cable itself passes up through a brass bushing (cut from the original casting) and passes up through a final brass fitting (also from the casting) where it passes through an irregular hole and is seized by set screws. The hole in the bushing is where the bending of the cable occurs. In order to avoid stressing the cable at a particular point which could result in fatigue or breaking of the cable, the hole in the bushing is flared toward the bottom, approximating an evolute to the surface traced out by the pendulum bob. The bending of the wire as the pendulum swings then is distributed over approximately an inch of the cable, resulting, as noted in the Introduction, in a shortening of the radius of the swing by about an inch from the center to the maximum of the swing. (The action of the magnet also causes a momentary displacement of the center of the swing, also a slight divergence from the description of an ideal simple pendulum.) The final fitting is held firmly in place by the weight of the pendulum bob. It does not move at all relative to the platform (or to the building itself). The report in the present leaflet that a ball-and-socket support is involved is unfounded. The only moving part in the whole assembly is the pendulum itself. The magnet power supply rests on the platform near the magnet, to the left. At the right, one can see the power supply for the electronics which respond to the light sensors controlling the actuation of the magnet. A third component box, not visible in this photograph, contains the coincidence circuits and the adjustment controls.

The magnet is cylindrical in configuration so that the swing is not biased in any particular direction. It was carefully machined and wound by Dr. Moore to achieve this configuration. The magnet is actuated near the end of each swing so that it attracts the disc near the top of the cable. The timing of the electrical current pulse which actuates the magnet is controlled by sensing devices in the pendulum environment. The electronics components in the light ring were intended to switch from one of these beams to the other so that the one most nearly at right angles to the plane of oscillation would be the active one. The pins are weighted to facilitate resetting, and this daily task is the only routine maintenance now required.

The new sensing assembly consists of two beams of light oriented to cross at the center of the swing of the pendulum. In contrast to the old design in which only one beam was active at a time, both of the beams are always on. This eliminates the need too switch from one to the other. The event which initiates the current pulse occurs when both beams are simultaneously interrupted. Even when the plane of oscillation happens to be parallel to one of the beams, this simultaneous event can occur only where the beams cross. The fact of the simultaneous event is detected when signals from light sensitive components combine in a coincidence circuit to activate a timing circuit which regulates the current to the magnet. In essence, the timing is reset at the middle of each swing, and so the cumulation of error in the older circuits can no longer occur. The circuits are normally powered for twenty-four hours each day. If the pendulum is interrupted in its swing by a viewer, or if there is a power failure, there may be a need to restart the pendulum swing, for the pendulum's drive magnet is effective only if the pendulum is swinging at or near full amplitude. On any of the lower floors, a light click should be heard near the end of each swing. This is due to the iron disc being drawn up into the slotted magnet, and it is a sure indicator that the magnet is functioning correctly. If the clicks are not heard, or if they are heard only when the pendulum is swinging to one side, the pendulum will need attention. A full swing is easily noticed, for it will carry the bob over the light ring on the ground floor by about six inches. As stated, if the swing is reduced in some manner so that the bob does not reach the light ring, it will probably need to be boosted for the magnet to again become effective.

Maintenance of the pendulum.

Mechanical maintenance of the parts of the pendulum will ordinarily be minimal. These consist of two types of problems: starting the pendulum, and alignment. There will, of course be a need to reset the plastic pins on a daily basis, but that task requires no instructions.

Starting the pendulum.

It may become necessary to restart the pendulum if it should be disturbed by touching, or if the power to the magnet is turned off long enough for the pendulum's amplitude to be damped to the point where the magnet can no longer be effective. Starting or boosting the pendulum swing is easily done. One simply pushes against the control cable toward the center of the compass rose. A gentle, short push is enough. The push should then be repeated when the swing again has the pendulum moving toward the center of the compass rose. Once full amplitude (enough to swing the bob four to six inches over the light ring) is reached, the position of the bob at the bottom of each swing, back and forth, should be observed. If the position relative to a point at the center of the compass rose is the same, the motion is planar, and no further correction is needed. If the position shifts from the swing away from the observer to the swing towards the obser, the bob is ellipsing, and the sidewise componene should be damped out. This is also easily done. One should observe whether the lowest position (or nearly so) of the bob shifts on the swing away to the right (left(, the observer should lightly rub the left (right) side of the cable with his or her hand until the shift no longer appears, or at least is reduced to a small fraction of an inch. Some ellipsing may recur naturally as the pendulum bob swings, but this will be small, and is not of importance. (Any sidewise motion of the cable at the bushing in the mount also tends to reduce ellipsing, so the natural tendence is for the swing to be nearly planar.)

Alignment of the pendulum assembly.

Once aligned, the major assembly itself should be secure (barring a deliberate attempt to dislodge the platform) against almost anything short of an earthquake. (If there should later be some concern about the fact that the platform is held in place only by its own weight, the addition of clamps to secure it could be easily done.) However, should the improbable occur, the following instructions for realignment should be adequate.

There are two mechanical adjustments which must be made if the platform should shift for some reason. The first is aesthetic, centering the swing over the lower compass rose. With the pendulum bob hanging at rest, the bolts contacting the edge of the platform should be adjusted so that the bob is centered over the pattern once again. Note that this adjustment has not needed correction during the first dozen years of operation of the pendulum. The second mechanical adjustment is more important. In order that the magnet can best serve its purpose, it is necessary to adjust its position so that it will give maximum boost on each end of the swing. Thus the magnet should be aligned so that its center coincides with the center of the swing. In order to do this the pendulum should be started so that its amplitude is just enough to cause the magnet to catch the iron disc on either side of the swing. This can be done at the floor level or at the platform level. The side of the magtnet where the magnet does not catch the disc is then too far from the center, and it should be moved ttoward the center by loosening the upper setscrews in the Z-pieces and adjusting the setscrews in the legs. The procedure should be repeated until the disc is caught by the magnet equally well on either end of the swing. The same procedure should then be applied after the plane of swing has been changed to one which is perpendicular to the first plane. Once done, the setting in the original plane should be checked once more to assure that the second adjustment (if any) did not disturb the first one. Securing the magnet in position with the upper setscrews should guard the magnet's position against any further shifts.

Alignment of the sensing system.

Since the sensing system is mounted at the platform level, the alignment must be done at that position. Pieces of plywood which will fit over the iron work are stored in the upper part of the dome near the platform, and should be placed in position to assure safe footing when doing any work at this level. Care should be taken in handling the plywood pieces. The inner dome itself consists of a thin shell of plaster, and can be easily penetrated. Further, the plates of glass in the compass rose frame are not tempered, and break easily.

The sensing system is composed of two light sources, two detectors, and an electronic circuit which triggers a pulse when both light detectors simultaneously receive no light. There are also present two dummy sources. The latter are present only to preserve the symmetry of the pattern when seen from the floor below. The light sources include a high intensity light bulb mounted in a holder placed before a focussing lens. The resulting beam is oriented so that it enters the blackened cylinder below the platform through a one inch hole and proceeds through, unless obstructed, to a photodetector mounted on the opposite side of the cylinder. Since the bulbs are not built to strict uniform specifications, the variance of the position of the filament is accommadated by mounting the bulb holder on gimbals. The light source itself is clamped to one of the curved pieces of iron forming the upper compass rose, and can be shifted from side to side if need be. The focussing lens can be adjusted back and forth before the bulb so that the beam is focussed on the cable when it is in the center of its swing. Working sketches of the mount details have been prepared by Mr. Ron Smith. For convenience another picture of the mount is shown in Fig. 2 in which the coincidence electronics box is visible at the right (the box with the white top). A more detailed picture of the box containing the coincidence circuit is shown in Fig. 3. There is apparent in Fig. 3 a triangular configuration of LEDs on the box. When the beams are unobstructed, the LEDs are off. When the left hand beam, the one from the source shown in Fig.2, is obstructed, the LED labeled 1 lights. When the right hand beam is obstructed, the LED labeled2 lights. When both beams are simultaneously obstructed, all three LEDs will be lit. (The light bulbs have an average rated life of 3000 hrs when operated with 0.20A at 14V. In the light sources, the bulbs are operated at 11V to extend the lifetime of the bulb. It is estimated that at this level of use, the lifetime will be extended to 10,000 hrs. At the time of the writing of this report (3/90), the bulbs have operated for about 400 days (9600 hrs) before an interruption in service occured which made it necessary to change them.) Alignment of the lightsources consists of placing the light bulb in the holder, and focussing the beam on the cable. (A piece of rubber tubing has been attached to the cable at the level of the beam to make the focussing less critical, but this should still be done with some care so that there will be maximum occlusion of the beam when the cable swings through it. The bulb should be maneuvered in the mounting so that the LED which is associated with it is extinguished when the pendulum's cable is away from the center position. Except for assuring that the beams are as nearly perpendicular as possible, the two beams can be focused and aligned independently of each other. The coincidence event which initiates the timing of the pulse of current to actuate the magnet occurs when the cable obstructs both beams at the center of the swing, regardless of the orientation of the plane of oscillation.

Details of the electronic circuits have been prepared by Mr. CharlesCowan.

Afterthoughts

Aside from resetting the pins daily, the U of L Foucault pendulum requires little maintenance. If the swing should be disturbed, the pendulum is easily restarted. If upon restarting, it is not possible to hear the distinctive click near the end of each swing caused when the magnet seizes the disc, one should first check to see that the power to the magnet is on. If the power is on, and the clicks are still not audible, it is necessary to check the functioning of the light bulbs which provide the sensing beams. If one of these is burned our, it can be replaced following the procedure stated above. Since the cost of the bulbs is nominal, it would be sensible to replace both when either burns out since the remaining one will probably go before mucyh more time has passed. The first interruption of service which required replacement of the bulbs came after about 400 days of operation, but intermittent interruptions of the swinging were noted before that time. While these might have been due to mechanical interference (due, for example to a viewer touching the pendulum), it might be just as well to replace the bulbs on a regular schedule, perhaps yearly. It may be desirable to polish the pendulum bob when there are occasions of ceremony in the building.