GB2575926A

GB2575926A - Aerodynamic bob and bob-stem combination for omnidirectional pendulum

Info

Publication number: GB2575926A
Application number: GB1911209.3A
Authority: GB
Inventors: Olenici Dimitrie; John Goodey Thomas
Original assignee: Individual
Current assignee: Individual
Priority date: 2019-08-06
Filing date: 2019-08-06
Publication date: 2020-01-29
Also published as: GB201911209D0

Abstract

A bob 1a for an omnidirectional pendulum that minimizes air resistance equally in all directions is formed in a rotationally symmetric lenticular shape having a convex upper surface 3, a convex lower surface 4, and an intermediate circumferential edge portion 5, and includes a construction 2 for attachment to a suspension member for holding the bob with the central plane of its edge portion oriented horizontally. A rod shaped stem member may be fixed to the bob by the attachment construction so as to extend upward from the bob upper surface along its central axis AX, with a wire attachment construction being provided at its upper end so that the bob-stem combination can be suspended from a suspension wire. Optionally the edge portion may be sharp; it may be formed with holes; and its surfaces may be dimpled, thus further minimizing air resistance Figure 23.

Description

TITLE OF THE INVENTION

AERODYNAMIC BOB AND BOB-STEM COMBINATION FOR OMNIDIRECTIONAL PENDULUM

FIELD OF THE INVENTION

The present invention relates to a bob for a pendulum that operates omnidirectionally and to a bob-stem combination for such a pendulum, and more particularly relates to such a bob and such a bob-stem combination that provide improved aerodynamic characteristics.

BACKGROUND ART

The first scientific observation of a pendulum was probably performed in 1583, when, while in church at the Cathedral of Pisa, Galileo Galilei watched a chandelier as it swung on a chain, and noticed that, no matter how big the swings were when the lamp was first swung, or how small the swings were as the lamp came nearly to a standstill, the time that it took to complete each oscillation was effectively the same. He also established by experiments that the period of a pendulum depended only (to first order) upon the length of the cord from which the pendulum bob was suspended. This was dubbed the law of the pendulum. The chandelier observed by Galileo was probably the most exotic pendulum bob that has ever entered into consideration in a scientific experiment.

Galileo suggested the idea of employing a pendulum as a timekeeping device for a clock, and later workers in the field (Huygens and others) implemented this concept. These pendulums were all unidirectional pendulums that were set up so as only to oscillate in a single direction (i.e. along a single preferred azimuth), or in any case, whose small residual motions in other directions were ignored. Various other applications of pendulums for scientific purposes were developed, but for three hundred years the only scientifically useful pendulums were operated unidirectionally.

Then in 1851 Leon Foucault built his famous pendulum by suspending a spherical 28 kilogram bob from the dome of the Pantheon in Paris with a 67 meter long wire. This pendulum was omnidirectional; that is, it was free to swing in any direction, i.e. along any desired azimuthal line. The following three effects were observed:

(1) The amplitude of the pendulum swing steadily diminished over the hours;

(2) From effectively rectilinear oscillations at the start, the pendulum motion gradually developed (or deteriorated) and its path became an elongated ellipse whose minor axis increased over time;

(3) The direction of the major axis of that elongated ellipse rotated in the clockwise direction with a period of approximately (sidereal period of the rotation of the Earth) / (sine of the latitude of Paris). This was dubbed the Foucault precession, and it was considered to demonstrate the absolute rotation of the Earth with respect to the fixed stars.

PROBLEM TO BE SOLVED BY THE INVENTION

The attenuation of the amplitude of the pendulum - effect (1) above - is an undesired factor, because the observation of the more interesting effect (3) is rather impeded as the amplitude becomes smaller. However, it appears that neither Foucault nor any of the very numerous following pendulum experimentalists took any substantial practical steps to reduce such amplitude attenuation, apart from making their pendulum bobs larger and heavier, which is of course effective because the surface area of the bob, which determines its air resistance, varies as the square of its linear dimensions, whereas the energy stored in the bob at any particular angular displacement varies according to its mass, which varies as the cube of its linear dimensions.

Friction at the suspension point at the top end of the pendulum setup is usually negligible. The diminution of the pendulum amplitude is usually substantially entirely due to the effects of air friction, to a minor extent air friction upon the suspension member (sometimes a rod, and more usually a wire), but mostly air friction upon the bob. With a unidirectional pendulum in a clock, the pendulum amplitude is maintained by the mechanical escapement which steadily replaces lost energy, but with an omnidirectional Foucault pendulum maintaining the amplitude without affecting the motion is not an easy proposition. Expedients that have been adopted include raising and lowering the suspension point in synchrony with the pendulum swing (Professor A.B. Pippard tried this) and mounting an electromagnet directly below the suspension point (this position will be termed bottom dead centre or BDC) and energizing that electromagnet in synchrony with each approach of the bob. However, both of these systems inevitably introduce unpredictable precession effects of their own, and therefore compromise any scientific conclusions deduced from the pendulum motion. Such devices may be convenient for pendulums for public exhibition, but vitiate use for serious scientific investigation. The employment of a Charron ring for zeroing the minor axis of the elliptical pendulum motion likewise eliminates any scientific meaning.

The question of the shape of the pendulum bob requires further attention. For an omnidirectional pendulum, in order to avoid unwanted aerodynamic effects that may disturb the precession, the bob should be rotationally symmetric about the vertical axis (the axis of the suspension rod or the suspension wire), in order for the pendulum to function neutrally with no dependence upon the azimuth of pendulum oscillation. Following this logic, spherical bobs and vertically oriented cylindrical bobs have often been employed in conventional Foucault pendulums. Examples of such bobs are schematically shown in Fig. 1(a) and Fig. 1(b), which relate to the prior art.

However, the drag upon a sphere or a cylinder in an air flow transverse to its axis is relatively high, as can be seen from the summary of drag coefficients shown in the table of Fig. 2, which relates to the prior art. The comparison between the drag coefficient of a sphere (0.47) and that of a streamlined body (0.04) is stark. (The drag coefficient of a cylinder in an air flow transverse to its axis is similar to that of a sphere.) Essentially this is due to the fact that a quite extensive volume of low pressure is created downstream of the sphere or cylinder. Accordingly, with a spherical or cylindrical bob, the swinging amplitude diminishes rather quickly, so that the Q factor of the oscillating system as a whole is poor.

As a related factor, the motion of a spherical or cylindrical pendulum bob through the air inevitably causes turbulence behind it. Air flows around cylindrical bodies at various Reynolds numbers are schematically shown in Fig. 3, which relates to the prior art. The Reynolds number at which a Foucault pendulum operates is generally around 8,000 to 10,000, depending upon various factors such as the length and the amplitude of oscillation. Typically a Karmann vortex street develops behind the bob as it moves; this phenomenon is schematically shown in Figs. 4(a) and 4(b), which relate to the prior art. These vortices create high drag upon the bob, Moreover, the Karmann vortices break away alternately from the downstream side of the bob in opposite directions and usually have varying sizes, and this phenomenon inevitably engenders repeated unpredictable sideways jerking of the bob as it moves, thus to some extent discounting the scientific merit of precession observations.

There is also the problem of disturbance of the pendulum motion by air currents. The greater the air resistance of the pendulum bob, the more sensitive its oscillations will be to perturbation by air movements coming from the side. This phenomenon can seriously deteriorate the scientific value of experiments, because a pendulum is fundamentally a device for accumulating very small effects over many cycles - indeed, that is the very reason that pendulums so often are used for delicate scientific experimentation.

Lenticular pendulum bobs oriented vertically have often been used in clocks and have been effective for reducing air resistance. An example of such a bob is shown in Fig. 5(a), which relates to the prior art. However these are always unidirectional pendulums, so that the problem of the lenticular bob shape turning somewhat sideways to the motion and acting as a crude aerofoil to generate sideways lift does not arise since the bob cannot rotate in yaw. With an omnidirectional pendulum, however, such an effect may well come into play, and of course would completely stultify any experiment. A vertically oriented disk is a variant of the above lenticular shape, and in fact such a pendulum bob was utilized by Allais in some of his experiments. An example of such a bob is shown in Fig. 5(b), which relates to the prior art. However, the same problem in connection with generation of aerodynamic lift arises with this disk-shaped bob in the same way as with a vertical lenticular bob, and in fact may be more troublesome because, when the disk is at a slight angle, the air flow past it is more confused and turbulent.

Therefore there has been an unsatisfied demand for a bob for an omnidirectional pendulum, which can reduce the effects of air resistance and the effects of air current disturbance. And accordingly it is an objective of the present invention to provide a bob for an omnidirectional pendulum, which can reduce the effects of air resistance. Moreover, it is another objective of the present invention to provide a bob for an omnidirectional pendulum, which can reduce the effects of air current disturbance.

SUMMARY OF THE INVENTION

According to a first aspect of the present invention, the objectives of the present invention as described above are realised by a bob for an omnidirectional pendulum, formed in a generally lenticular shape that is rotationally symmetric about a central axis, and having a convex upper surface, a convex lower surface, and an intermediate circumferential edge portion delimiting between the convex upper surface and the convex lower surface, and further comprising a means for attachment to a suspension member that, when the suspension member hangs vertically and suspends the bob, holds the bob with its convex upper surface facing upwards and its convex lower surface facing downwards, and with the central plane of its circumferential edge portion being oriented substantially horizontally.

This bob is capable of moving through the air with less resistance than has been the case for the prior art, because it is generally lenticular in shape and has the convex upper surface, the convex lower surface, and the edge portion delimiting between them. Furthermore, this bob is suitable for application to an omnidirectional pendulum because it is rotationally symmetric and is held to be generally horizontal, and accordingly it can oscillate indifferently in any desired azimuthal direction.

Moreover, according to a specialization of this first aspect of the present invention, the circumferential edge portion of the bob may be formed as rounded. On the other hand, according to an alternative specialization of this first aspect of the present invention, the circumferential edge portion of the bob may be formed with a sharp angle. In either of these cases, the air flow past the bob easily can be shed from its trailing edge, so that the air resistance is kept low.

Yet further, according to a specialization of the first aspect of the present invention, the circumferential edge portion of the bob may be formed with at least one through hole extending between the convex upper surface and the convex lower surface, substantially parallel to the central axis of the bob. This through hole may be utilized for attachment of a thread which may be burnt in order to release the bob.

Still further, according to another specialization of the first aspect of the present invention, the circumferential edge portion of the bob may be formed with a plurality of through holes extending between the convex upper surface and the convex lower surface, each of these holes being substantially parallel to the central axis of the bob. Any one of these through holes may be utilized for attachment of a thread which may be burnt in order to release the bob, and accordingly the bob can be released from any of a plurality of starting azimuths, without any requirement for the bob itself to be repositioned in yaw. Furthermore the presence of these holes tends to generate microturbulence in the air flow over the bob, which further reduces the drag of the bob.

Even further, according to a further specialization of the above described specialization of the first aspect of the present invention, the through holes may be substantially equally circumferentially spaced around the circumferential edge portion of the bob. This is important in order to preserve the rotational symmetry of the bob and thus to enhance its characteristics for operating indifferently from a plurality of release azimuths.

Moreover, according to another specialization of the first aspect of the present invention described above, at least one of the upper surface and the lower surface of the bob may be formed with dimples. And also, according to another specialization of the first aspect of the present invention described above, both the upper surface and the lower surface of the bob may be formed with dimples. The presence of such dimples encourages microturbulence in the air flow over the bob, thus further reducing the drag of the bob.

Yet further, in any of the cases described above, it is desirable for the ratio of the axial thickness of the bob to the outer diameter of the circumferential edge portion thereof to be between 15% and 35%. And it is more desirable for the ratio of the axial thickness of the bob to the outer diameter of the circumferential edge portion thereof to be between 20% and 30%. Moreover, it is yet more desirable for the ratio of the axial thickness of the bob to the outer diameter of the circumferential edge portion thereof to be between 20% and 25%. These constraints on the dimensions of the bob have been found to be appropriate for minimizing drag upon the bob.

The attachment means may be constituted by an attachment hole that opens from the convex upper surface of the bob and extends along the central axis. And this attachment hole may be constituted by a blind hole that does not open to the convex lower surface of the bob. Alternatively, this attachment hole may be constituted by a through hole that opens to the convex lower surface of the bob. Moreover, this attachment hole may be formed with a smooth internal surface. Alternatively, this attachment hole may be formed with a female thread. These configurations of the attachment hole are respectively suitable for mating with a suspension member whose lower end is smooth, or whose lower end is formed with a male thread.

And, according to a second aspect of the present invention, the objectives of the present invention as described above are realised by: a combination of: a bob according to any of the versions described above; and a rod shaped stem member whose lower end is fixedly attached to the bob by the attachment means so that the stem member extends upward from the convex upper surface substantially along the central axis, and comprising a wire attachment means for attachment of a wire at its upper end remote from the bob.

The bob-stem combination can be conveniently attached to the lower end of a suspension wire by this wire attachment means. The use of a thin suspension wire keeps the air resistance of the entire construction low.

According to a specialization of the second aspect of the present invention described above, the attachment means may be constituted by an attachment hole having a smooth interior surface that opens from the convex upper surface of the bob and extends along the central axis, and the lower end of the stem member is formed to be smooth and is fixedly attached in the attachment hole by adhesive. Adhesive is a convenient means for attaching the lower end of the stem member in the attachment hole.

And, according to another specialization of the second aspect of the present invention, the attachment means may be constituted by an attachment hole, having an interior surface formed with a female thread, that opens from the convex upper surface of the bob and extends along the central axis, and the lower end of the stem member may be formed with a male thread and may be screwed into the attachment hole. Screwing is another convenient means for attaching the lower end of the stem member in the attachment hole.

According to another specialization of the second aspect of the present invention, the attachment hole may be constituted by a blind hole that does not open to the convex lower surface of the bob. In this case the lower surface of the bob is left completely smooth, which is beneficial from the point of view of air resistance.

And, according to an alternative further specialization of the second aspect of the present invention, the attachment hole may be constituted by a through hole that opens to the convex lower surface of the bob. In this case, the lower end of the stem member is presented at the lower surface of the bob, which means that it is easy and convenient to attach a flag member to this lower end of the stem member.

According to a yet further specialization of the second aspect of the present invention, there may be further included a locking nut that is engaged onto the male thread of the stem member above the bob, and that is screwed against the convex upper surface of the bob. In this case, the attachment of the stem member in the hole in the bob is securely guaranteed. Moreover, the convex upper surface of the bob may be formed with a recess that receives this locking nut. This makes the upper surface of the bob-stem combination smoother, which is beneficial from the point of view of drag reduction.

Alternatively, the attachment hole may be constituted by a through hole that opens to the convex lower surface of the bob, and there may be further included a locking nut that is engaged onto the male thread of the stem member below the bob, and that is screwed against the convex lower surface of the bob. In this case, the attachment of the stem member in the hole in the bob is securely guaranteed. Moreover, the convex lower surface of the bob may be formed with a recess that receives this locking nut. This makes the lower surface of the bob-stem combination smoother, which is beneficial from the point of view of drag reduction.

In the above specializations of the second aspect of the present invention, there may be further included thread locking material, provided between the male thread and the female thread. This is a further method for ensuring that the attachment of the stem member in the hole in the bob is securely guaranteed.

BENEFICIAL EFFECT OF THE INVENTION

The first aspect of the present invention as described above provides a bob for an omnidirectional pendulum, which reduces the effects of air resistance and the effects of air current disturbance. Moreover, the second aspect of the present invention as described above provides a bob-stem combination for an omnidirectional pendulum that is adapted to be suspended from a suspension wire, which reduces the effects of air resistance and the effects of air current disturbance.

BRIEF DESCRIPTION OF THE DRAWINGS

Fig. 1 relates to the prior art, and is a pair of perspective views, schematically showing a spherical pendulum bob and a vertically oriented cylindrical pendulum bob;

Fig. 2 relates to the prior art, and is a table taken from Wikipedia according to their Creative Commons licence, schematically showing various shapes and their drag coefficients;

Fig. 3 relates to the prior art, and is a set of views taken from Wikipedia according to their Creative Commons licence, schematically showing air flows past cylinders at various Reynolds numbers;

Fig. 4 relates to the prior art, and is a pair of views taken from Wikipedia according to their Creative Commons licence, schematically showing Karmann vortex streets in air flows generated by cylinders;

Fig. 5 relates to the prior art, and is a pair of perspective views, schematically showing a vertically oriented lenticular pendulum bob and a vertically oriented disk-shaped pendulum bob;

Fig. 6 is a schematic perspective view showing a horizontally oriented lenticular pendulum bob according to a first embodiment of a first aspect of the present invention;

Fig. 7 is a plan view of this lenticular bob;

Fig. 8 is a sectional view of this lenticular bob taken in a vertical sectional plane including its central axis AX;

Fig. 9 is a side view of a rod-shaped suspension member and a suspension mechanism, for suspension of this lenticular bob;

Fig. 10 is a partial sectional view of the central portion of the bob and of the lower end of the suspension member when it is attached to the bob, taken in an axial sectional plane similar to that of Fig. 8;

Fig. 11 is a sectional view analogous to the views of Fig. 3 and taken in an axial sectional plane similar to that of Figs. 8 and 10, schematically showing the air flow around this bob according to the first embodiment of the present invention and the corresponding suspension member lower end as they move;

Fig. 12 is an axial sectional view of a stem member that is an essential component of a bob-stem combination according to a first embodiment of a second aspect of the present invention;

Fig. 13 is a partial enlarged axial sectional view, showing the upper end of this stem member and the lower end of a wire to be attached thereto;

Fig. 14 is similar to Fig. 10, and is a sectional view of the central portion of a bob according to the first embodiment of the first aspect of the present invention and of the lower end portion of a stem member when the stem member is attached to that bob, taken in an axial sectional plane similar to that of Figs. 8 and 11;

Fig. 15 shows partial sectional views of a first set of possibilities for alternative methods for fixing the lower end of the suspension member to the central portion of the bob;

Fig. 16 shows partial sectional views of a second set of possibilities for such alternative fixing methods;

Fig. 17 is an axial sectional view of a pendulum bob according to a second embodiment of the present invention, taken in an axial sectional plane similar to that of Fig. 8 for the first embodiment;

Fig. 18 is an axial sectional view taken in an axial sectional plane similar to that of Fig. 17, schematically showing the airflow around this bob according to the second embodiment of the present invention and the corresponding suspension member lower end as they move;

Fig. 19 is a plan view of a pendulum bob according to a third embodiment of the present invention;

Fig. 20 is an axial sectional view of this bob according to the third embodiment of the present invention, taken in an axial sectional plane similar to that of Figs. 17 and 18;

Fig. 21 is a plan view of a pendulum bob according to a fourth embodiment of the present invention;

Fig. 22 is an axial sectional view of this bob according to the fourth embodiment of the present invention, taken in an axial sectional plane similar to that of Fig. 20;

Fig. 23 is a view from below of a pendulum bob according to a fifth embodiment of the present invention; and

Fig. 24 is an axial sectional view of this pendulum bob according to the fifth embodiment of the present invention, taken in an axial sectional plane similar to that of Fig. 8.

DESCRIPTION OF THE EMBODIMENTS

Embodiment One

A Bob Embodiment

Structure

Fig. 6 is a schematic perspective view showing a lenticular pendulum bob 1a according to a first embodiment of a first aspect of the present invention which consists only of a bob, Fig. 7 is a schematic plan view of this bob 1 a, and Fig. 8 is a schematic sectional view taken in a plane that includes the central axis AX of the bob 1a. The pendulum bob 1a shown in these figures is shaped in a generally lenticular form, i.e. as a flattened rotationally symmetric body, and with a central hole 2 being formed extending along its central axis AX. In this first embodiment, the central hole 2 is a blind hole that is formed only partway through the bob 1a from above, and its inner cylindrical surface is formed to be smooth. This bob 1a is formed with a convex upper surface 3 that is interrupted at its centre by the opening of the central hole 2, with an uninterrupted convex lower surface 4, and with a rounded circumferential edge portion 5 that delimits between the upper surface 3 and the lower surface 4. If the bob 1a is made from lead which is a cheap and dense material, then this rounded circumferential edge portion 5 can be relatively easily formed, and is not very susceptible to damage.

Fig. 9 is a side view showing an elongated suspension member 6 (not itself a part of this aspect of the present invention) whose lower end portion 7, during use of the above described bob 1a, is attached to the bob 1a and suspends the bob 1a, and also schematically showing an omnidirectionally pivoting suspension mechanism 8 (likewise not itself a part of the present invention), to which the upper end of the suspension member 6 is attached and through a centre of pivoting (not particularly shown) of which the suspension rod 6 passes. The details of this suspension mechanism 8 are not shown and will not be discussed herein because they are not particularly germane to the present invention: Kamerlingh Onnes, Longden, and Allais have suggested various omnidirectional pendulum suspension constructions that may be appropriate.

In this example, the suspension member 6 is a rigid cylindrical rod. Fig. 10 shows the situation when the cylindrical lower end 7 of this suspension member 6 is attached to the bob 1 a. This lower end 7 of the suspension member 6 is formed to be smooth, and is secured in the hole 2 by adhesive

9. Thereby, the lower end 7 of the suspension member 6 is solidly and immovably fixed into the bob 1a, so that the suspension member 6 as a whole is constrained to extend along the axial line AX of the bob 1a. In this state, the suspension member 6 likewise constrains the bob 1a so that it is held oriented in a position in which its axial line AX runs along the central axis of the suspension member 6, i.e. with its central plane that includes its circumferential edge portion 5 extending orthogonally to the suspension member 6 which itself extends coaxially with the bob axial line AX. And, since the suspension member 6 is a rigid rod, accordingly the combination of the bob 1a and the suspension member 6 is constrained so that their common axial line AX passes through the centre of pivoting of the omnidirectional suspension mechanism 8.

And, in the state of the apparatus in which the suspension member 6 is hanging vertically downward from the suspension mechanism 8 and is bearing the weight of the bob 1a which is hanging at its lowermost point, i.e. when the bob 1a is at BDC, the omnidirectional suspension mechanism 8, by being capable of freely pivoting in any required direction, allows the bob 1a to be free to move in any horizontal direction in the horizontal plane (i.e. in either of two mutually orthogonal horizontal directions and in any vector combination thereof), while on the other hand the bob 1a is prevented from moving vertically either upward or downward, due to its own weight and due to the rigidity of the suspension member 6. Moreover, when the bob 1a is hanging downward at BDC, the suspension member 6 and the suspension mechanism 8 constrain the bob 1a so that so that it is maintained generally horizontal, i.e. with its central plane that includes its circumferential edge portion 5 being oriented substantially horizontally.

Operation

When this bob 1a according to the first preferred embodiment of the present invention swings to and fro together with the suspension member 6 as the suspension mechanism 8 pivots, the air flow around it follows a pattern generally like that schematically shown in Fig. 11, which is an illustrative sectional view taken in an axial sectional plane similar to that of Fig. 8.

Beneficial Effects

As shown in Fig. 11, the air flow in the case of this bob 1 a according to the first preferred embodiment is much smoother than the air flows around the prior art bodies shown schematically in Figs. 3 and 4. This is principally because the air flow lines at the rear of the bob 1 a as it moves come closer together than in the prior art cases before breaking away from the bob surface, so that the region L1 behind the bob 1a in which negative pressure is created is much smaller than in the prior art, and also because generation of a Karmann vortex street is eliminated or greatly diminished. The consequence of the above facts is that the drag effect of air resistance is reduced, so that the Q factor of the overall oscillation system is enhanced and the attenuation of the amplitude of the pendulum motion proceeds more slowly. Moreover, since Karmann vortices are much smaller or absent, accordingly they do not very greatly retard or disturb the movement of the pendulum as they successively break away on alternate sides. Furthermore, for reasons similar to those described above, the pendulum motion is much less susceptible to disturbance due to air currents coming from the side.

It has been found that the balance between pendulum mass and air resistance is favourable when the ratio of the axial thickness T of the bob to the outer diameter D of its circumferential edge portion 6 is made to be between 15% and 35%, is more favourable when this ratio is made to be between 20% and 30%, and is even more favourable when this ratio is made to be between 20% and 25%. There is some analogy between these findings and the results for air resistance versus fineness ratio of the bodies of historical rigid airships such as Zeppelins, but in the case of a pendulum (whether unidirectional or omnidirectional) it is not possible for the front end of the body around which the air is flowing (i.e. the bob) to be formed to be bluff or blunt as was found to be optimal in the case of a rigid airship (refer to the cross section labelled streamlined body shown in Fig. 2). This is because any pendulum bob is required to be capable of oscillating both to and fro, with its leading edge and its trailing edge interchanging roles every half swing, and accordingly its axial cross section needs to be bilaterally symmetric.

Therefore, by providing the bob cross sectional shape with a relatively narrow rear end, it is possible to reap the associated benefits described above, but this implies also providing a relatively narrow front end. Moreover, in the case of an omnidirectional pendulum, the cross section needs to be bilaterally symmetric and the same in any axial sectional plane, in order for the pendulum to swing to and fro indifferently in any desired azimuthal direction.

A Combination Embodiment

Figs. 12, 13, and 14 illustrate a first embodiment of a second aspect of the present invention which consists of a combination of a bob and a vertically extending stem member attached thereto. This second embodiment is applicable when it is desired to suspend the pendulum bob from the suspension mechanism, not by using a rigid rod as in the case described above, but by using a flexible wire. The advantage of employing a rigid rod is that the bob is constrained thereby so as not to be capable of rotating around any of its three rotational axes (except insofar as allowed by the omnidirectional suspension mechanism), but the disadvantage is that the rod is necessarily quite thick because it must not bend at all, and accordingly it experiences substantial air resistance, so that the total air resistance of the bob-rod combination is not as low as could be desired. Accordingly, in practice, a rigid rod can only be employed as a suspension means for a pendulum that is relatively short, as was Allais's pendulum. On the other hand, if a wire is employed for suspension, then it may be very thin and may have a diameter of the order of one or two millimetres (provided that it is sufficiently strong to bear the mass of the bob), so that the air resistance due to the wire itself is very low. In this case the pendulum height can be as great as desired. However, the disadvantages of employing a wire for suspension are that the bob is relatively free to rotate about its vertical axis, i.e. in yaw, due to the wire twisting, and also that the bob may be capable of oscillating to and fro in both pitch and roll to some extent.

This second aspect of the present invention comprises a bob 1a which is substantially the same as that described above, and also comprises an upper stem member 10 shown sectionally in the figures. Referring to Fig. 12 which shows an axial section of the stem member 10 as a whole, to Fig. 13 which is an enlarged sectional view of the upper end portion thereof, and to Fig. 14 which shows the stem member 10 installed to the bob 1a, the lower portion 7' of this stem member 10 is formed to be smooth, and is secured in the hole 2 by adhesive 9, just as was the suspension member 6 when it was fitted to the bob 1a according to the first embodiment of the first aspect of the present invention described above. However, the upper portion 11 of the stem member 10 that projects above the bob 1a and is exposed to the air stream is formed to be much thinner than its lower portion 7' (ideally it is formed to be as thin as possible, provided that there is no chance of it flexing significantly), and its top end portion is formed with a small axial hole 12 and a side screw hole 13, with a grub screw 14 being screwed into the screw hole 13, so that a suspension wire W (not itself a part of the present invention, and only illustrated in Fig. 13) can be clamped in the hole 12 by the grub screw 14. The suspension wire W extends upward and is attached to an omnidirectionally pivoting suspension mechanism of a type similar to that described above (which is not itself a part of the present invention, and accordingly is not illustrated).

Operation

When this combination of the bob 1a and the stem member 10 according to this second aspect of the first preferred embodiment of the present invention swings to and fro as the suspension mechanism pivots, the air flow around it follows a pattern similar to that shown in Fig. 8, so that similar beneficial effects are obtained. Moreover, the stem member 10 constrains the bob 1a so that it is held oriented in a position in which its vertical axis AX runs along the central axis of the suspension member 6, i.e. with its central plane that includes its circumferential edge portion 5 extending orthogonally to the axial line AX and orthogonally to the stem member 10. Furthermore, due to the combined weight of the stem member 10 and the bob 1a, the suspension wire W is kept tightly stretched and substantially coaxial with the axial line AX, and accordingly the combination of the bob 1a and the stem member 10 is constrained so that their common axial line AX is coincident with the axial line of the wire W and passes through the centre of pivoting of the omnidirectional suspension mechanism. However in this case, because the suspension wire W is not actually a rigid body, some swaying to and fro of the bob 1a and the stem member 10 at the end of the suspension wire W in pitch or in roll may occur, due to slight bending of the lower portion of the suspension wire W where it enters the hole 12. The amplitude of this swaying depends upon how skilfully the pendulum is launched from rest without sideways disturbance, and its period depends upon the length of the stem member 10 and the transverse moment of inertia of the bob 1a through its centre of gravity. In many scientific applications, this swaying of the pendulum will not present any substantial problem.

In relation to each of the bob embodiments and variant embodiments described below, it should be understood that a combination of that bob embodiment or variant embodiment and a stem member of the type described above is also to be considered as being a combination embodiment of the present invention. However, for the sake of brevity, these other combination embodiments will not be further described herein.

Variants of the First Embodiment

In the first embodiments of both the first aspect and the second aspect of the present invention, the attachment in the hole 2 of the lower portion 7 of the suspension member 6, or the attachment in the hole 2 of the lower portion 7' of the stem member 10, respectively, may be implemented in various different ways. Some of these variants will now be described. These modifications are parallel in the case of the lower portion 7 of the suspension member 6 and in the case of the lower portion 7' of the stem member 10, and accordingly only cases related to attachment of the lower portion 7 of the suspension member 6 in the hole 2 will be described. Fig. 15 shows a first set of possibilities for this attachment.

First, the hole 2 in the bob 1 may be a through hole that opens all the way from the bob upper surface 3 to the bob lower surface 4, rather than being a blind hole as described above, with the lower portion 7 of the suspension member 6 being secured in the hole 2 with adhesive 9, in a manner parallel to that described above. Fig. 15(a) shows this possibility. In this case, an axial hole 15 may conveniently be bored in the lower end of the lower portion 7 of the suspension member 6, for mounting of a flag member F (not itself a part of the present invention) for operating a sensor of some type; this variation is shown in Fig 15(b). The flag member F may be secured in the hole 15 by adhesive, or by a combination of a male threaded portion on the flag member F and a female threaded portion in the hole 15; these details are not particularly shown. By the way, it goes without saying that a flag member may be added in the same manner to any of the embodiments described below in which the hole 2 in the bob 1 is a through hole, or, if the hole 2 is not a through hole, then a flag member may even be mounted to the bob 1 itself by forming a hole in the centre of the bottom surface 4 thereof. However these possibilities will not be further discussed herein.

Alternatively, the lower portion 7 of the suspension member 6 may be formed with a male screw thread 17, and the internal cylindrical surface of the hole 2 in the bob 1 may be formed with a matching female thread 18, with the lower suspension member portion 7 being fitted into the hole 2 by being screwed thereinto. With this fixing method, the hole 2 may be a blind hole as shown in Fig. 15(c), or may be a through hole as shown in Fig. 15(d).

The mutual engagement of the screw threads 17 and 18 may be secured with thread locking material, so as to secure the attachment of the lower suspension member portion 7 in the hole 2, i.e. in order to ensure that the threads 17 and 18 are securely engaged together. However, it is considered to be preferable to provide a locking nut, in order to secure this mutual engagement. Fig. 16 shows various possibilities for the provision of such a locking nut N. If the central hole 2 is a blind hole, then the locking nut N should be engaged upon the lower suspension member portion 7 above the upper surface 3 of the bob 1, and should be tightened down against the upper surface 3. An example of this configuration is shown in Fig. 16(a). This configuration may also be employed even if the central hole 2 is a through hole and the lower suspension member portion 7 passes all the way therethrough; an example of this configuration is shown in Fig. 16(b). In this case, the lower end of the lower suspension member portion 7 should be faired off flush with the lower surface 4 of the bob 1. But if the lower end of the lower suspension member portion 7 is formed to protrude somewhat below the lower surface 4 of the bob 1, then the locking nut N may alternatively be engaged upon this protruding portion of the lower suspension member portion 7 and may be tightened upward against the lower surface 4. An example of this configuration is shown in Fig. 16(c). As improvements upon these cases, the upper surface 3 or the lower surface 4 of the bob 1 against which the locking nut N is tightened may be formed with a recess R that houses the locking nut N, so that a smoother overall surface is presented to the air flow over the bob 1. Examples of such configurations are shown in Fig. 16(d) and Fig. 16(e).

Embodiment Two

Fig. 17 is an axial sectional view of a pendulum bob 1 b according to a second embodiment of the present invention, taken in a plane similar to that of Fig. 8 relating to the first embodiment. The difference between this bob 1 b according to the second embodiment and the bob 1a according to the first embodiment is that the circumferential edge portion 5b of this bob 1 b which delimits between its upper surface 3 and its lower surface 4 is formed with a relatively sharp angle, rather than being rounded as was the case with the first embodiment. And Fig. 18 is an axial sectional view similar to Fig. 11 for the first embodiment and taken in a similar sectional plane, schematically showing the air flow around this bob 1 b according to the second embodiment and the lower end of the corresponding suspension member as they move. It is seen that the sharp angle at the rear of the circumferential edge portion 5b acts further to shed the air flow behind the bob 1 b in an efficient and streamlined manner without generation of high drag. In other words, the region L2 behind the bob 1b in which negative pressure is created is much smaller than was the region L1 in the case of the first preferred embodiment shown in Fig. 11. It may be anticipated that no Karmann vortex street at all will be generated in the case of this second embodiment, provided that the axial thickness of the bob is not very great in relation to the outer diameter of its circumferential edge portion 5b. Accordingly the air resistance of this bob 1b is significantly lower than the air resistance of the bob 1a according to the first preferred embodiment described above.

It should be understood that it would not be very appropriate to manufacture this bob 1b from lead. This is because the sharp circumferential edge portion 5b cannot easily be made by a casting process, and lead cannot easily be machined accurately. Moreover, such a sharp circumferential edge portion 5b made from lead, even if it could be manufactured accurately, would be so soft as to be very vulnerable to damage caused by even a slight impact. However, brass (for example) is an excellent material for manufacturing a sharp-edged lenticular bob of this sort. The sharp circumferential edge portion 5b cannot very easily be made only by a casting process, but the manufacture of the entire shape of the bob 1 b by CNC machining of a rough-cast blank (or of a large disk-shaped brass mass) presents no substantial difficulty.

Embodiment Three

Fig. 19 is a plan view of a sharp-edged pendulum bob 1 c according to a third embodiment of the present invention, and Fig. 20 is an axial cross sectional view thereof, taken in a plane similar to that of Fig. 17. The difference between this sharp-edged bob 1c according to the third embodiment and the sharp-edged bob 1 b according to the second embodiment is that the sharp circumferential edge portion 5c of this bob 1c which delimits between its upper surface 3 and its lower surface 4 is formed with a through hole 19 that communicates between the upper surface 3 and the lower surface 4 of the bob 1c and extends parallel to its axial direction AX. Such a through hole 19 can advantageously be employed for attachment of a flammable thread (not shown) to the bob 1c, in order to secure the pendulum away from its BDC to some fixed object for release (termed a launch tower, and also not shown), as a preparation before starting the swinging motion of the pendulum. When the pendulum is to be released, the thread is burnt through with a flame. This burning-thread method minimizes disturbance during the release process.

Embodiment Four

Fig. 21 is a plan view of a sharp-edged pendulum bob 1d according to a fourth embodiment of the present invention, and Fig. 22 is an axial cross sectional view thereof, taken in a plane similar to that of Fig. 20. The difference between this bob 1d according to the fourth embodiment and the bob 1 c according to the third embodiment is that, rather than only one through hole 19 of the type described above being provided, a plurality of through holes 19 are formed through the sharp circumferential edge portion 5d of the bob 1d so as to communicate between the upper surface 3 and the lower surface 4 of the bob 1d and so as to extend parallel to its axial direction AX. Desirably, these through holes 19 should be substantially equally spaced around the circumferential edge portion 5d, so as to preserve the symmetry of the bob 1d around its axis AX. The launch tower may be provided at any position around the bob 1d corresponding to any one of these through holes 19, and accordingly these multiple holes 19 provide various possibilities for the azimuth in which the swinging of the pendulum is to be started, without any requirement for the body of the bob 1d itself to be rotated in yaw. Typically 72 such through holes 19 may be provided at intervals of 5° around the sharp circumferential edge portion 5d (for convenience, only sixteen holes 19 are shown in the figure). Since such a large number of through holes 19 are provided, accordingly they also act to engender microturbulence in the air flow over the bob 1 d, which further reduces the air resistance of the bob 1d.

Embodiment Five

Fig. 23 is an axial sectional view, similar to Fig. 8 and taken in a similar sectional plane, showing a pendulum bob 1e according to a fifth embodiment of the present invention. The difference between this bob 1e according to the fifth embodiment and the bob 1a according to the first embodiment is that the lower surface 4e of this bob 1 e is formed with a large number of dimples or indentations D which, in appearance, are somewhat similar in form to the dimples that are conventionally formed upon a per se known golf ball. These dimples D act to engender microturbulence over the lower surface 4e of the bob 1 e, thus further reducing its air resistance.

Naturally, as variations of this fifth embodiment, dimples D may instead be formed upon only the upper surface 3e of the bob 1e. Alternatively, dimples D may be formed upon both the upper surface 3e and also the lower surface 4e of the bob 1 e, and this acts further to reduce the air resistance of the bob 1e.

Claims

1. A bob for an omnidirectional pendulum, formed in a generally lenticular shape that is rotationally symmetric about a central axis, and having a convex upper surface, a convex lower surface, and an intermediate circumferential edge portion delimiting between said convex upper surface and said convex lower surface, and further comprising a means for attachment to a suspension member that, when the suspension member hangs vertically and suspends the bob, holds the bob with its convex upper surface facing upwards and its convex lower surface facing downwards, and with the central plane of its circumferential edge portion being oriented substantially horizontally.

2. A bob according to claim 1, wherein said circumferential edge portion of the bob is formed as rounded.

3. A bob according to claim 1, wherein said circumferential edge portion of the bob is formed with a sharp angle.

4. A bob according to claim 3, wherein said circumferential edge portion of the bob is formed with at least one through hole extending between said convex upper surface and said convex lower surface, substantially parallel to the central axis of the bob.

5. A bob according to claim 3, wherein said circumferential edge portion of the bob is formed with a plurality of through holes extending between said convex upper surface and said convex lower surface, each of these holes being substantially parallel to the central axis of the bob,

6. A bob according to claim 5, wherein said through holes are substantially equally circumferentially spaced around said circumferential edge portion of the bob.

7. A bob according to any one of claims 1 through 6, wherein at least one of said upper surface and said lower surface of said bob is formed with dimples.

8. A bob according to any one of claims 1 through 6, wherein both said upper surface and said lower surface of said bob are formed with dimples.

9. A bob according to any one of claims 1 through 8, wherein the ratio of the axial thickness of the bob to the outer diameter of said circumferential edge portion thereof is between 15% and 35%.

10. A bob according to any one of claims 1 through 8, wherein the ratio of the axial thickness of the bob to the outer diameter of said circumferential edge portion thereof is between 20% and 30%.

11. A bob according to any one of claims 1 through 8, wherein the ratio of the axial thickness of the bob to the outer diameter of said circumferential edge portion thereof is between 20% and 25%.

12. A bob according to any one of claims 1 through 11, wherein said attachment means is constituted by an attachment hole that opens from said convex upper surface of said bob and extends along said central axis.

13. A bob according to claim 12, wherein said attachment hole is constituted by a blind hole that does not open to said convex lower surface of said bob.

14. A bob according to claim 12, wherein said attachment hole is constituted by a through hole that opens to said convex lower surface of said bob.

15. A bob according to claim 13 or claim 14, wherein said attachment hole is formed with a smooth internal surface.

16. A bob according to claim 13 or claim 14, wherein said attachment hole is formed with a female thread.

17. A combination of: a bob according to any one of claims 1 through 16; and a rod shaped stem member whose lower end is fixedly attached to said bob by said attachment means so that said stem member extends upward from said convex upper surface substantially along said central axis, and comprising a wire attachment means for attachment of a wire at its upper end remote from said bob.

18. A combination according to claim 17, wherein said attachment means is constituted by an attachment hole having a smooth interior surface that opens from said convex upper surface of said bob and extends along said central axis, and the lower end of said stem member is formed to be smooth and is fixedly attached in said attachment hole by adhesive.

19. A combination according to claim 17, wherein said attachment means is constituted by an attachment hole, having an interior surface formed with a female thread, that opens from said convex upper surface of said bob and extends along said central axis, and the lower end of said stem member is formed with a male thread and is screwed into said attachment hole.

20. A combination according to claim 18 or claim 19, wherein said attachment hole is constituted by a blind hole that does not open to said convex lower surface of said bob.

21. A combination according to claim 18 or claim 19, wherein said attachment hole is constituted by a through hole that opens to said convex lower surface of said bob.

22. A combination according to claim 17, further comprising a locking nut that is engaged onto said male thread of said stem member above said bob, and that is screwed against said convex upper surface of said bob.

23. A combination according to claim 17, wherein said convex upper surface of said bob is formed with a recess that receives said locking nut.

24. A combination according to claim 19, wherein said attachment hole is constituted by a through hole that opens to said convex lower surface of said bob, and further comprising a locking nut that is engaged onto said male thread of said stem member below said bob, and that is screwed against said convex lower surface of said bob.

25. A combination according to claim 17, wherein said convex lower surface of said bob is formed with a recess that receives said locking nut.