The following project is the hard work of Ron Lebar. We are continuing to update it as and when Ron is able to let us have a report of his progress. If you need any further information about the clock please contact Ron by email at info@alphaentek.com or True Point at our contact email address.

I am building a prototype mechanical clock, with advanced specification. The instrument will include a calendar display using a rotating brass disc which is already made. This will utilise Trochoidal wave reducers instead of gears and will keep track of the Gregorian calendar until the year 2399 (if it survives that long).

Appearance: The design is for a single main dial clock, with centre seconds hand. The brass chapter ring is 250 mm outside diameter, 154 mm inside diameter.  Numerals are Mayan, pierced through the dial and optionally backlit.

 Three hands are counter-balanced within the mechanism for less frontal clutter.  The seconds and minute hands are aluminium to minimise rotating mass.

 The glazed case will be approximately six foot high without its adjustable feet, twenty inches wide and one foot deep. Most of the mechanism will be visible through the dial aperture or the sides. Rear panel is meranti,  frame is oak.

 Glass shelves allow the clock to double as a display case. It will be dust tight, the door locked, the dial glass screwed shut. 

Power sources: The free pendulum power will be provided by a small battery, maintained by a mains trickle charger. This should last for at least a year without the mains connected. The pendulum will send a timing pulse to the clock once a second. Mains will also provide optional dial and case illumination.

 The clock itself is essentially a slave mechanism, entirely mechanical apart from the electro-mechanical escapements. Movement driving power will be two springs, wound by a temperature sensor mounted behind the rear panel.

 Temperature Sensor: The sensor consists of thirty (30) vertical one metre long acetal rods, each six millimetres in diameter. These are capped at each end by substantial aluminium sections. The lower one is attached to the rear panel. The upper is connected to a one hundred to one lever system.

 Acetal has a coefficient on linear expansion (C.L.E.) of one hundred and thirty (130) parts per million (PPM) per degree Centigrade. Meranti wood has an approximate C.L.E. of three point one (3.1) PPM.

 The differential movement of the sensor is thus over 125 microns  for a one degree centigrade change in temperature. Magnified by the levers this becomes twelve point five millimetres. Six such changes, up or down will rotate the spring arbour double acting ratchets one full turn.

 Running train ratios are chosen so ten (10) turns of the spring will provide power to the minutes hand for four hundred days.

 If main springs are fully wound the sensor levers will be disconnected and diverted to wind the chiming mechanism, a lower level of priority.

 It may be decided to add barometric pressure and humidity sensors to provide additional power. Particularly for the seconds hand train.

 Design: The design is intended to be accurate, reliable and self powering. With that in mind, minimising friction has been a priority. 

The main usage of power in mechanical clocks, is the constant acceleration and stopping of the entire main gear train. Equivalent to taking a car journey by alternately stamping on the throttle and the brake. What would the MPG be and how long would the car last?

 It says a lot for the quality of construction of clocks that they can last centuries despite this non-stop 'stop-go' cycle. This cycle is the main cause of the loud tick of a pendulum clock.

 Atmos and anniversary clocks solve the problem by using a torsional pendulum. This swings much slower, for a given size. So the escapement operates less frequently, less power, less noise.

 The idea was to isolate the running train from this perpetual stop-start cycle and have it running steadily. This should then require less power. To do this an approach was taken that is similar to switching regulation, also efficient (explanation available if required).

The design has two running trains, one for the seconds hand and one for the minutes This division enables the clock to be set without winding the seconds hand round thousands of times. There are no slipping clutches, drive is solid and direct. Similar to a radio controlled clock in this respect. 

The seconds train runs sixty times faster than the minutes, power is proportional to that speed. The same approach is however applied to both trains.

The escapement underwent some mental evolution, originally a pin-wheel design was chosen. Thinking about it revealed a problem, The pins being parallel to the axis require robust support. Hence high rotating mass, concentrated at the fast moving circumference.

 Finally a star wheel was chosen, with least mass at the periphery. Made from thin, fully hardened spring steel. This will be driven a spring, wound by the running train seconds shaft (rear shaft).

 The escape wheel in turn will be coupled to the seconds hand shaft (front shaft) by another spring. The elasticity of each spring will be set, in conjunction with the driven mass, to give a 'time constant' of one second.

 With this arrangement the front and rear shafts will be turning at a constant rate of one revolution per minute. In between the light star wheel will rotate gently in one second steps. It should be interesting to watch.

 The minute hand will be driven in a similar way, so will move from one minute to the next over a period of one second.

 Gear train: The 'gears' will be Trochoidal drives, with all wheels rotating in the same direction.. A drawing of how they work will be included soon. It must be mentioned that these are untried. Tools to make them do not yet exist and must be made.

 This is to eliminate the rubbing friction of counter rotating gear teeth. Replaced by simple rolling resistance, a couple of orders of magnitude less.  A greater ratio in a single step should be possible.

 Free Pendulum: A one-point-two metre Invar rod with a four inch bronze bob near the bottom. Conventional thermal compensation, a wheel that does not need re-inventing.

Pivots: A twelve mm horizontal pivot rod, forty mm long, lies front to back  at the top. In two bronze blocks, with twelve point one mm holes. A central seven mm vertical drilling allows the six mm pendulum rod through, with clearance.

 Near the top of the pendulum rod is a two mm left to right cross drilling. Through this is pressed a two mm silver steel rod, which sits in a groove in the top of the pivot rod. This supports the pendulum rod, allowing it to find its own front to back angle.

 This is to prevent differential stress on the two jewelled pivots. In each end of the pivot rod are stepped vertical drillings. The upper larger part holds a cup sapphire with its cup down, held against the step by a pre-loaded spring.

In the bottom of the bronze blocks are matching drillings, these take upward facing diamond cones, to mate with the cup sapphires. These are adjusted by a screw, to just lift the pivot rod out of contact with the bronze support blocks.

 The whole arrangement is designed to only allow 50 microns of movement in any direction to protect the pivot jewels if the clock receives a shock. Also to ensure even weigh distribution between the jewels if the clock is not level.

 Pendulum Sensor: Just below the bob is the sensor, this will detect the centre point and amplitude of the swing. Two horizontal steel rods, one each side. Partly within a pair of coils wired in a Wheatstone bridge arrangement.

 The rods vary the inductance of the coils differentially, at the pendulum's rest point both coils are the same. They are energised by a push-pull ten Kilocycles per second (10Kc/s) signal, giving a one millisecond resolution.

 As the pendulum moves away from centre the bridge is unbalanced, giving an output. The phase of that output indicates which way the pendulum has moved, the amplitude indicates how far it has swung.

 Circuitry processes this signal and decides if the motor needs energising and which way. As the pendulum reaches its exact centre of swing the motor is given a pulse, in the correct direction, if the swing is not sufficient.

 The duration of this short pulse will be tailored to gradually restore the swing to optimum. If the circuit detects the pendulum has stopped a series of stronger pulses will be applied to restart the clock. An alarm will indicate a time error.

 As the pendulum reaches its centre, regardless of any signal to the motor, a pulse will be sent to the seconds escapement. Also to the minutes escapement at the sixtieth second.

At the hours and quarters this pulse will also be sent to the chiming mechanism, which will decide what to do in response. At midnight it will be sent to the calendar train, which will also decide what to do.

 Seconds, minutes, hours and date signals will also be available as an external output for any other slave clocks.

 Motor: About half way up the pendulum rod are two horizontal rod magnets, left and right with like poles together. These are partly engaged within coils, similar to the sensor.

 These coils are wired in series anti-phase. A pulse in either direction will attract one magnet and repel the other, providing motive force to the pendulum.

To take account of the leap century at 2400 it would require another reducer which is probably overkill. The chapter ring, already made in rough form, and uses Mayan numerals which are a few centuries older than Roman numerals, but look intuitive and modern. It will be based on a one second, just less than one metre, free pendulum. This requires bearings designed to minimise friction, as does the rest of the clock. The running train will be powered entirely by small atmospheric changes.

The pendulum will weigh around 4 Kilogrammes. My thought is to support it on two conical diamonds sitting in sapphire cups. The movement will be minimal; the swing at the bottom end will be 15 mm on average.

The bearing structure will be supported against over-travel in all directions and spring loaded to absorb any applied shock. My initial thought was a 6mm diameter silver steel cross shaft, with the cups set in each end, facing down. These ends will rotate in steel (or brass) blocks reamed to 6.1mm, giving a 50 micron radial clearance.

The diamond styli will sit in the lower part of these blocks, facing up, with their tips contacting the sapphire cups. They will be adjusted in height until the shaft is centered in the gap; this is checked by electrical contact being broken.

Axial clearance will be set to 50 microns, so if the clock gets a jolt, the pendulum assembly can only move

50 microns in any direction. As downward thrust can fracture the jewels, the diamonds will be held up by springs, preloaded to just take the assembly's weight at rest, (an idea inspired by a 'shockproof' watch balance).
 

Excessive movement of the lower end will be restricted by strong support rings around the shaft, 'just' clear of the bob above and below. Swing will be 15mm total on average, so not a lot of clearance is needed.

Trochoidal wave reducers are a form of what is usually called a cycloidal reducer. A hollow ring has a cycloidal wave pattern cut on its inner surface with a set number of lobes, for example 60. Within it sits another ring, slightly smaller, with an inverted cycloidal pattern cut in its outer circumference. This pattern has one less lobe (59).

This ring has a central ball race, on an eccentric shaft. The inner ring is constrained to allow movement but not rotation. As the inner shaft rotates, the inner ring rolls around the outer.

When it has completed one rotation, having one less lobe, it will have rotated the outer ring by one lobe out of sixty, in the same direction as the input shaft.

Friction is very low, compared to gears, only rolling contact, no sliding. So it is easier to design a clock to use minimal drive power. The down side is no tools are available to cut the rather tricky lobes, so these tools have to be made. Also they can only reduce speed, as with a worm drive another technique is needed to step up speed.

I enclose a photo of the rough cut chapter and date rings.

The following photo is of the temperature sensor that powers the movement. It is in an unfinished state, the rods will have guides to keep them parallel.

The meranti back panel is now French polished, using an old technique of mine. Meranti looks good enough, once polished, to use for the entire frame, apart from oak corner pillars. It is a very stable wood, paler than mahogany, with a coarser and more open grain. It will not be stained, we like the lighter colour.

My polishing technique does not use grain filler, so the subtle natural  figuring is quite distinct, unlike some highly polished mahogany clocks I have seen. In the old days wood was almost ubiquitous. Builders often concentrated on displaying their superb craftsmanship and hard work in polishing. Rather than highlighting the natural beauty of wood, it is a matter of individual taste.

Next step is to mount the sensor and pendulum. The lyre for the 'chimes' will be on the lower back, visible behind the pendulum. Originally a choice between struck rods, solid hung bars, tubular bells and plucked reeds. A 'final' decision is to use plucked strings, a form of harp, based on a prototype instrument of mine from 2001. The plinth, containing the control system, will double as sound board and resonant chamber.

Date: 26/05/2014

I have some photos of the pendulum assembly, during machining. Not a complete set,  the jewels are slowing me down, due to the precision required.

Shortly I hope to send microscope photos of that part of the work. The first job for completion is to get the whole assembly swinging, so it can be timed.

I have a suspicion that the seconds shaft may need ring jewels and the star wheel pallets may also need to be jewelled. I will start with steel and see how friction and wear pan out.

Date: 29/05/2014

When the pendulum is finally sitting on the jewels it will be started. So its timing can be set and monitored while the rest of the clock is built. Most mechanical parts will be polished, including structural rods etc.

The date ring has been redesigned. It will be co-axial with the chapter ring and use a window, to show only the current day number and month. Date numbers will be Mayan, we will just have to get used to them, they are easier than Roman.

Date: 04/06/2014

The pendulum is now hanging and swings. The sensor and motor are not yet made. The coil winder has to be fired up and bobbins turned etc.

Date: 08/06/2014

The pendulum is finally swinging on its jewels but without a source of power. First time  it touched the spindle it started swinging, about an inch. After an hour it was still at about the same amplitude, but next morning it had stopped.

One of the diamonds was then adjusted, until electrical contact was broken and corrected the spindle azimuth. It then swung for four hours before declining to one third.

But still moving slightly several hours later.

This equates to a 'Q' factor of about 45,000 which is not bad in air. The sapphires and diamonds do the job well. Probably better than knife edges on agate, the usual standard.

The best 'Q' documented was 110,000 in a vacuum tank, in 1921. We are unlikely to match the Q of a quartz crystal, a vacuum tank is not pretty.
 

Date:  13/06/2014

A substantial design change has been made after testing the pendulum. It works fine and has a high 'Q' as already established, but there is a chance that the position sensor, plus the motor may compromise the thermal compensation and increase air drag. Also that the motor may have a slight effect on the pendulum's natural accuracy.

So a new pendulum bob is being made, combining the position sensor, swing sensor and motor. The pendulum will now be driven and sensed at the exact 'centre of oscillation' (CoO) . This is the one point where drive pulse energy will not affect or reflect from the pivot point.

Later, if you wish, I will add drawings and text on the design, including the new motor design and a means of accurately finding the 'CoO' for this design.

The likely effect of these changes will probably be very small (apart from slowing completion). But if I am to achieve the goal of beating a quartz clock everything must be taken into account.
 

Date 15/06/2014

Making the new pendulum bob will not be a waste. It is more or less a copy of the first one, so that the first is still available if the modifications fail to work well.

If the second bob is a success the first will probably receive the same modifications. There will then be two if it is decided to change to a dual pendulum. The case layout has room for this.

If this is done it will not be a hit and miss arrangement like the marvellous Shortt clocks or David Walters' beautiful creation (D)W5.

I like simple elegance in design, both electronic and mechanical. Both pendulums would be adjusted to exactly the same period and encouraged to synchronise.

The anti-phase swing should lessen the effect of any outside influence, including minor earth tremors.

Incidentally the low friction pivots have given us a surprise. I noticed that the un-powered pendulum never quite stops. Even if not touched for many hours.

Date 23/06/2014

The first pendulum uses the cup jewels you supplied, cups down. Supported on conical diamonds, point upwards, these in turn are supported on pre-loaded springs.

For the slave pendulum I wondered if steel points, about the same tip radius, would be sufficient instead of the diamonds. Probably more robust, so less protection needed. Not to save money.

The slave pendulum may be used to trip the seconds escapement pallets instead of the original idea of electro-magnets.

It could be used to directly kick round the seconds shaft as in (D)W5. This would save a lot of construction, but then that part of the clock would not be atmospheric.

I think the time has come to stop making changes and stay close to my original design. The second pendulum was always an option, but only to raise the 'Q' of the first.

The pendulum thermal compensation is based on the Riefler astronomical clock, pushing the bob from the bottom.

The bob thus acts as part of the compensation, which creates a potential theoretical delay problem. The bob will heat and cool slower than the invar rod.

In case it does matter the second pendulum will have a more theoretically correct form. Supporting the bob from its centre of mass, slightly more complex.

We can then compare the two when the clock is running.

Date: 26/06/2014

I have decided to drop the Riefler style compensation in favour of a more compact design. Based on Mr. Riefler's ideas but hopefully an improvement.

I had toyed with the idea of putting the primary pendulum in a partly evacuated plate glass enclosure within the clock case.

At one time I considered having a glass back and evacuating the entire clock case. But that caused problems sealing the mechanical drive shaft for the weather sensors.

However when researching the ideas, a problem reared its ugly head. It turns out that silicon rubber, used to seal fish tanks, is gas permeable!

So if that road is to be tried another transparent glass sealer must be found, still looking.

Regarding V bearings, is a slight pre-load advisable? To ensure the horizontal shaft stays in the V centre or will that increase friction?

I had considered the escape wheel not having a shaft at all. Just located between the seconds pinion and hand shaft kept in place by its very soft input and output springs.
 

Date: 21/07/2014

Enclosed are some photos, the faceplate, with rear brass action plate fitted. The centre boss carries the front V jewel, the rear jewel will be on the rear plate. The four support rods will carry various action parts, the chapter ring and the wooden escutcheon etc.

There is also an annotated photo of pendulum three's bob etc. This weighs just over 250 grammes, with its Invar rod and compensator.

The bob is supported at its geometric centre by the silica tube, which has a coefficient of expansion of 3.3 parts per million per degree Centigrade. The geometric centre is close to the centre of oscillation due to the stepped drilling, which makes the top half heavier. So the bob should cause very little thermal rate shift.

Thermal compensation is at the pivot, my method. I also include a photo of the 14 Kilogramme counter mass for the third pendulum. This is used because, as mentioned in the text already sent, pendulum three has no vertical movement correction. Although it is intended to correct one and two vertically.

The counter mass is 300 mm square by 19.5 mm thick. It consists of three six mm steel plates and a one point five mm brass plate, for cosmetic purposes and a bit more mass.

Two of the plates will be behind the back and two in front. To minimise stress on the wood. The two parts will be bolted together through the back with spacers to give clearance.

With oversize holes, lined with felt,  so that the mass does not touch the back, inside or out. Felt washers will act as dust seals both sides, as well as preventing contact.

The weight of the counter mass will be supported by springs on the inside and outside. The idea is the any earth tremors are isolated from the pendulums, all of which are referenced to this mass. Such tremors can be caused by passing heavy vehicles, as well as more distant seismic activity.

As an extra photos of the three pivot assemblies are included, for reference. If the third pendulum is a success I will probably need another couple of S8 jewels, to raise its Q.

Incidentally I include a microscope photo of the diamond tip obtained for pendulum two. This shows that the tip radius is not as well formed as the first two (already pictured). I will probably need to find a source of better, more expensive, diamond styli.

Date: 21/07/2014

Enclosed are some photos, the faceplate, with rear brass action plate fitted. The centre boss carries the front V jewel, the rear jewel will be on the rear plate. The four support rods will carry various action parts, the chapter ring and the wooden escutcheon etc.

There is also an annotated photo of pendulum three's bob etc. This weighs just over 250 grammes, with its Invar rod and compensator.

The bob is supported at its geometric centre by the silica tube, which has a coefficient of expansion of 3.3 parts per million per degree Centigrade. The geometric centre is close to the centre of oscillation due to the stepped drilling, which makes the top half heavier. So the bob should cause very little thermal rate shift.

Thermal compensation is at the pivot, my method. I also include a photo of the 14 Kilogramme counter mass for the third pendulum. This is used because, as mentioned in the text already sent, pendulum three has no vertical movement correction. Although it is intended to correct one and two vertically.

The counter mass is 300 mm square by 19.5 mm thick. It consists of three six mm steel plates and a one point five mm brass plate, for cosmetic purposes and a bit more mass.

Two of the plates will be behind the back and two in front. To minimise stress on the wood. The two parts will be bolted together through the back with spacers to give clearance.

With oversize holes, lined with felt, so that the mass does not touch the back, inside or out. Felt washers will act as dust seals both sides, as well as preventing contact.

The weight of the counter mass will be supported by springs on the inside and outside. The idea is the any earth tremors are isolated from the pendulums, all of which are referenced to this mass. Such tremors can be caused by passing heavy vehicles, as well as more distant seismic activity.

As an extra photos of the three pivot assemblies are included, for reference. If the third pendulum is a success I will probably need another couple of S8 jewels, to raise its Q.

Incidentally I include a microscope photo of the diamond tip obtained for pendulum two. This shows that the tip radius is not as well formed as the first two (already pictured). I will probably need to find a source of better, more expensive, diamond styli.

Date: 23/07/2014

The first two styli have a good profile and do the job, even though they were not sold for the purpose, but as security engraving styli.

Are your pivots able to support a one Kilogramme pendulum, between two of them, supporting the S8 jewels?

I do not see the need for several Kilogrammes for a free pendulum. Just more stress on the pivots. Air resistance is accounted for, plus varying barometric pressure and humidity.

I was studying Mr. Fedchenko's write-up on his pendulum and clock. Very interesting, some of his ideas are similar to mine, but he made it all work well.

I will not be controlling air pressure, just allowing for it. That is why I like the ancient Mayan civilisation. They did not try to change things, just take them into account.

Date: 27/07/14

I have just ordered a bunch of fused quartz rods 8mm and 6mm from Ohio in the U.S.A. together with some fused quartz tubing to make the bob holders.

Shipment is over three times the material cost. This will be the most expensive clock components to date. Later if it works, I will try to import the material in bulk, by some other method.

I have decided the glass case plates will be bolted in, with visible brass bolts like the face plate in. No conventional glazing.
 

Date: 05/08/14

The one part of the clock not intended to be powered by the weather now will be. I am investigating the best type of photo-voltaic panel.
 
To charge the battery for the pendulums' drive, chapter ring back-light and case illumination. So no dependence on mains power.
 
I now have the fused quartz rods and tubes from Ohio, import duty was levied on them. Even more expensive than the wood for the case.
 
The coefficient of expansion of synthetic fused quartz glass is so small that compensation can probably be done electrically.
 
Using the same method as for barometric and humidity compensation. This may mean that the average peak to peak swing is greater than the
original specification of fifteen millimetres.
 
This is part of my original idea of taking an age old problem and making use of it.

Date: 09/08/14

The fused quartz rods are to replace the Invar rods for the two main pendulums. The fused quartz tubes will replace the silica tubes to support the bobs internally at the centre of oscillation.

The expansion of the rod and tube exactly cancel. Ensuring that the bob remains at the same position on the rod regardless of temperature.

The bob's expansion will cancel, due to support at the centre of oscillation. This should eliminate the need for any mechanical temperature compensation on both main pendulums.

The tiny expansion of fused quartz, 5.5 parts in ten million per degree Centigrade, can be dealt with electrically. Together with the other relevant variables, humidity and barometric pressure.

So weather parameters will not only power the clock. They will be measured and allowed for in the pendulums' drive.

A detailed explanation, with or without a schematic diagram.

Almost all studies of pendulums that I have seen use arithmetic and/or vector analysis. These methods are non-intuitive and do not really show what goes on.

Dividing a pendulum's motion into horizontal, vertical  and rotary components shows everything needed for a true analysis.

That is my opinion and is what has been tried in the drawings sent. Admittedly not including the rotary component, which cancels with two anti-phase pendulums.

By the way, the aspects of weather not made use of include wind and rain. I'm working on it.
 

Pendulum Control System.

Sensor and motor. Design information.

 Two versions of the sensor have been designed, inductive and capacitive. The inductive version is described here. Only an inductive version of the motor has been designed. A capacitive version is considered impractical.

 Inductive Sensor

 Horizontal steel rods are mounted on the left and right sides of the pendulum bob Adjusted to the height of the Centre of Oscillation, these two rods form both the pendulum motor armatures and the sensor actuators. Their outer ends  are each encircled by two stationary co-axial coils.

The inner left and right pair of coils form the position sensor, the other pair are the motor stator. The sensor coils are  wired in series, energised by a 'push-pull' signal, at a frequency of ten thousand cycles per second (10Kc/s).

When the pendulum is vertical, at rest, the two coils are of equal impedance (balanced), so no signal is present at their junction (sensor output).

If the pendulum is displaced from rest, the coils are unbalanced. One coil's rod enters it further, raising its inductance and impedance. The other coil's rod is partially withdrawn, lowering its inductance and impedance.

A 10Kc/s difference signal is produced at the sensor output. Its phase depends on which way the pendulum has moved. Movement to the left is arranged to give a signal in phase with the master oscillator. To the righ gives an out of phase signal. This difference is decoded as direction information ('DVI').

A one bit digital memory (flip/flop) holds 'DVI' for use by the motor. The signal is also rectified, giving a DC Voltage. The peak level of this Voltage indicates the peak swing (VS). This value is stored in a peak hold circuit for use by the motor comparator.

As the pendulum swings back the swing signal decreases. As it reaches zero the appropriate motor coil, (determined by 'DVI') receives a Voltage pulse. The peak hold circuit is discharged, ready to measure the next swing

The amplitude and duration of the motor pulse are determined by comparing VS with a corrected preset value (VC). This value is adjusted by the environmental sensors to maintain the correct swing rate.

Using full wave decoding, the theoretical resolution of the swing centre detection is fifty microseconds. One part in twenty thousand of the 15mm peak to peak swing, for the one second pendulums.

This is .75 of a micron, in practice, due to circuit noise, processing delays etc. this high resolution is unlikely to be achieved.

Rate correction:

 What is normally called 'circular error' (CE) is a reduction of a pendulum's swing rate with increased amplitude.

As with the Pythagorean comma in music, it is not truly an error, but a factor, to be allowed for or used.

The idea of using 'CE' was one of the first to be considered when the clock was planned.

The value 'VC' is initially adjusted to give a peak to peak swing, measured horizontally at the centre of oscillation, of 15 millimetres. This arbitrary value was chosen to give a small 'circular error', it may need to be changed.

Air temperature, pressure and humidity are measured by sensors. The values obtained, suitably scaled, are added to 'VC'. The purpose is to adjust swing amplitude to correct the rate.

A rise in temperature will extend the quartz rod, 5.5 parts in ten million per degree centigrade, slowing the pendulum by the square root of that change. The temperature signal is inverted and summed with 'VC', reducing its value.

The swing amplitude is reduced, speeding up the pendulum. The two changes cancel.

Likewise a fall in temperature will tend to speed up the pendulum. In this case a change in the temperature signal will increase 'VC'. The swing amplitude is increased, slowing the pendulum. Again the changes cancel.

The same method is used to correct for rate changes caused by barometric pressure and humidity. The idea is to eliminate the need for mechanical compensation. 'Time' will tell if it works satisfactorily.

 The critical parameters are the relative linearity’s of quartz's temperature coefficient, the various correcting signals and 'CE'. These can only be truly determined by careful measurement once the system is operational.

Potential errors with pendulum rate compensation systems.

The coefficient of thermal expansion of pendulum (CTE) rod materials is only approximately linear, over a limited range of temperatures.

The non-linearity may be different, over different ranges for various materials. Thus compensation may not be truly accurate when using, for example, bi-metallic compensation.

Fortunately commonly used materials have 'fairly' linear 'CTE' around comfortable room temperature. This includes fused quartz glass.

So thermal compensation, using two materials with different 'CTE', works 'fairly' well. It is not 'exact' compensation, over the full range of temperatures a clock may encounter.

Other factors, not amenable to compensation, affect a pendulum's rate. Such as variations in pivot friction due to age, wear etc. In the case of spring suspension the spring material will suffer gradual fatigue.

The best thermal compensation methods achieve accuracies sufficient that the uncontrollable errors are the major component. The Shorrt clock from 1921, when carefully set up, is accurate within 220 microseconds per day, 80.03 milliseconds per year.

That is one second in over twelve years, assuming error is cumulative, which is almost certainly not the case. So all is not lost, greater accuracy than this is hardly ever needed.

Electrical compensation using Circular Error (CE) is a different case. The relationship between 'CE' and swing amplitude is not linear.

Like many nonlinear factors, it can be assumed approximately linear over a small range. As any curve can be approximated by a number of straight lines.

The trick in obtaining sufficiently accurate thermal compensation here is to apply a compensating non-linearity to the correcting signal.

The aim at the outset was to produce a clock with a non-cumulative error of no greater than one millisecond per week. One second in over nineteen years, better than any production quartz clock.

 Quartz oscillators are, when carefully adjusted, very accurate at one temperature. The characteristics of a quartz crystal change, like any material, with temperature.

This thermal change, at room temperature, is much less in quartz than most metals, even INVAR. This is why a quartz clock can be more accurate than a more expensive mechanical clock.

A problem is that the common, lower frequency crystals used have a quadratic temperature coefficient of frequency. They are calibrated at their best temperature, usually around 25 to 28 degrees Centigrade.

Any change from this temperature, in either direction, causes a drop in frequency, following a square law.

For high accuracy, quartz oscillators are frequently placed in thermostatically controlled ovens, to eliminate temperature effects. Time standard clocks made after 1929 used this principle.

The best accuracy was around one part in ten million, just over 3 seconds a year. Regardless of room temperature. Not nearly as good as the Shorrt clock, which it never-the-less superseded. Newer is better?

Good makes of quartz watches use a similar principle, the metal case back conducts the wearer's stable body temperature to the crystal. This of course only works while the watch is worn.

Most current radio clocks use a crystal controlled mechanism which is periodically corrected (reset)  by radio signals from a national time standard. The accuracy between these resets depends on the quality of the clock.

National time standards are synchronised by atomic clocks. These expensive and power hungry devices have accuracy beyond the capabilities of any mechanical system (at present).

Date:  14/09/2014

I enclose photos of pendulum number three, the half second, second order device. This has a simpler leaf spring for shock protection. This is easier, due to it being one quarter of the mass and with a thinner rod.

Apart from that it now uses a similar pivot block to the two one second pendulums. Its rod is three millimetre INVAR, effective length is 248.5 millimetres. The bob is supported, at its centre of oscillation, by a quartz tube, adjusted for rate by a brass nut.

It pivots on two of your S8 sapphires, supported by the two tungsten carbide pivots you made for me. The brass part above the pivot is the temperature compensation.

It is looking good, the 'Q' can only be determined when the full assembly is together, in the case.

The counter-mass is too heavy to set up until the case is fully built. The glazed case will now be mostly meranti framing, as well as the back. The four full height pillars will be sapele, better for turning and of a matching colour.

Date: 19/09/2014

I have been researching the characteristics of a number of precision clocks. In particular the investigation of Shorrt # 42, probably the most accurate pendulum clock.

It achieves a relative accuracy of 200 microseconds a day, but as with all precision pendulum clocks is at the mercy of gravity.

This is far from the constant it was once thought to be, the earth is in a constant state of flux. Tiny changes in gravity limit the ultimate accuracy of a pendulum.

These changes cycle, but the effects do not always cancel out over time. I am going to experiment, when 'time' permits, with compensating for these changes electrically.

It may not prove practical, but nothing ventured, nothing gained.

Date: 11/10/2014

A conclusion has been reached regarding pendulum three's bell crank. The idea of using ball bearings as pivots will probably be less efficient.

We will go back to jewels at these points, but reduce the pivots from four to two. One for the crank centre and one for the coupling. The assembly is thus free to move fore and aft. So it becomes self levelling.

The spring plate for the pendulum coupling is now made. I will send a schematic drawing and photos soon. Also the arithmetic for the pendulum and crank ratios etc.

Also another two S8 cup jewels. This will mean the complete pendulum assembly will have sixteen jewels. Including the two tungsten carbide pivots you made for me.

That is four for each pendulum, two cups and two styli. Plus the same for the crank.

Date: 31/10/2014

You will see that the half second pendulum pivot has lost its angle bracket.

This was a decision to balance the assembly, using a lightweight 'cage' construction, rather than the original idea of a solid metal crank at the back.

This crank sits on the mounting plate (the last picture sent). It translates the minute vertical movements caused by pendulums one and two into a small swing at its base. It has a linear magnification of 8.75.

This should synchronise pendulum three (half second) to the other two and vice versa. The idea is to isolate the entire system from outside world mechanical influences.

In like vein we will probably dispense with the angle brackets for pendulums one and two. This should look neater and again improve balance.

Date: 4/11/2014

Pendulum three, the second harmonic pendulum (P3), is now swinging on its bell crank. It appears to have a reasonable 'Q' factor, but probably nowhere near as good as pendulum one.

This is to be expected, it is intended to couple with the other two, to their mutual advantage. On its own it is comparatively  lightly mounted, on the sheet metal bell crank.

It will be interesting to see what happens when all three swing together. I enclose a picture of P3 swinging, with the plate in a vice on our saw.

Date: 5/11/2014

As promised a few photos, showing the mounting plate in various stages of dis-assembly. Plus some showing it with the bell crank and short pendulum mounted.
 

	1: Brass spring plate. This shows that the milled slots isolate the central rectangle. This area, which holds the pendulum mounting plate, is only connected by the series of L shaped strips. These act as springs, allowing some movement in any direction.
	2: Steel plate with bearings. The milled cups are part of four thrust bearings. Five balls in each stabilise the brass central rectangle, allowing movement in only one plane.
	3: Pendulum mounting assembly: This is screwed to the brass plate's central area, so can also move in one plane. The two main pendulum pivots are mounted on this plate, as is the bell crank transfer bearing.
	4: Front thrust bearing: An annular groove, milled in the mounting plate contains twelve steel balls. In conjunction with an outer race, they prevent the plate assembly tilting forward under the pendulums' weight.
	5: Thrust bearing with adjustable outer race and lock nut.
	6: With friction sleeve fitted. This, with a flat spring (not shown), damps fore and aft movement of the bell crank assembly.
	7: Two views of the front bearing. The top view also shows the gap between plates, caused by the rear bearings.
	8: Assembly with styli. This shows the assembly set up on our saw. The brass pillars carry the two diamond styli, clearly visible. The left pillar is mounted on the steel plate, part of the 14 Kg., spring supported, counter mass. This provides a stable reference for the entire system. The right pillar is on the pendulum mounting plate. Via its diamond it transfers the reaction thrust of the two main pendulums, to the bell crank and vice versa.
	9: Assembly with bell crank and pendulum three, which is swinging. Its 'Q' factor is fairly good. It should be a lot better when it can interact with the other pendulums. The knurled brass nut, to the right of pendulum three's pivot, adjusts the force on the transfer pivot.

10: Method of operation. assume only pendulum one is swinging. Its reaction is transferred, via its pivot, to the mounting plate. Taking just the horizontal motion, the plate will move, very slightly, left and right.

This will absorb energy from the pendulum, lowering its 'Q'. Now assume that pendulum two is also swinging, in exact anti-phase to one. Its reaction will tend to shift the mounting plate in the opposite direction.

The two reactions cancel, the plate does not move, no energy is lost. Each pendulum will see the mounting plate as having a high mass, the ideal condition for maximum 'Q'.

Two similar pendulums will naturally tend to settle into this stable anti-phase condition. Nature prefers stability. In addition, the effects of external horizontal movements tend to cancel.

However the vertical motion has not yet been taken into account. Assume the two pendulums have a peak to peak swing, measured on the horizontal axis, of 15 millimetres.

From the table of pendulum movements, the vertical movement is about 30 microns upwards, for each half swing. This movement is thus twice per full swing, the second harmonic.

As mentioned previously, this vertical movement is in phase, so the loss from each pendulum adds rather than cancels. Thirty microns is small but is still part of the equation.

In addition, it means that the pendulums are influenced by vertical earth movements. From passing heavy vehicles or distant seismic activity etc. They measurably affect precision clocks.

The horizontal movement, of a pendulum one quarter the length, is at the same frequency as this vertical movement. This suggests a way of providing some correction, although the waveforms are not the same.

The bell crank has two downward facing cup sapphires. These are supported on the two upward facing diamond styli. vertical movement of the mounting plate is transferred, via the right hand stylus, to the crank.

This causes a greater horizontal movement at the bottom of the crank. The half second pendulum's pivot is mounted here, so is affected by this movement.

Thus the horizontal swing of the half second pendulum is coupled to the vertical movement of the two one second main pendulums.

This should provide the same advantages, in terms of vertical movements, as the horizontal coupling of two pendulums. Will this, in practice, cancel the effect of earth tremors? 'Time' will tell.

Trying something unusual is not a waste of time, even if not successful. Failing to try, dismissing as not worth the effort, is the true waste of time.

All this tinkering has cost more in time and money than the original project. If a job is worth doing it should be done as well as it can be.

Date: 9/11/2014

Soon we are going to replace our old, defunct, table router. Then the meranti framework can be rebated to allow assembly and glazing.

We are toying with the idea of making the four full height pillars from polished aluminium rather than hardwood. This will mean the whole thing is very different in appearance from other tall clocks.

We do not want it to look like a 'retro' copy. Turning the 'twiddley bits' on the pillar ends is more difficult with metal, another challenge.

One shame, we have poor FM reception. With metal, the pillars will be the correct length, five feet, to make a multi-element half wave FM aerial. But they will be vertical. FM polarisation is horizontal!

We are also looking forward to mounting the pendulums in the case. Then the 'gear' trains need to be built.