Basic Clock Design

[Martin KyteParticipant @martinkyte99762]

In fact I don't event think you can see it from here.!!

;0)

[Michael GilliganParticipant @michaelgilligan61133]

Posted by Michael Gilligan on 20/04/2016 23:44:54:

… a rhetorical question:

What do we mean by 'basic clock design' ?

If a "clock" doesn't keep time, then it is mere decoration … a shiny motor and gearbox that serves no useful purpose.

To my mind; a 'basic clock' is the simplest possible construct that keeps good time.

.

I posted ^^^ on page 6 of this thread.

Would anyone care to discuss that point ?

MichaelG.

[Martin KyteParticipant @martinkyte99762]

Yes, I would like to comment on that Michael.

One assumption

We are talking about any clock that varies by less than say 5 mins per week. Anything else is either not working properly or isn't really a clock. (That would probably be my definition of basic)

Probably the least important thing about any clock we are likely to make is actually telling the time and I don't mean how well it goes or not. If we want to know the right time we check we use anything from digital watches, radio controlled clocks or the television. It's nice when our clock runs well and is in agrees with GMT within a minute or so but we don't get irritated if its 5 mins out. In fact within a quarter of an hour is often good enough to know that its just about tea time.

We make clocks because we like making clocks.

Some of us do it for the challenge of making something that runs well and to understand the mechanism.

Others because it looks nice.

In the age of atomic clocks all the mechanical clocks are to a greater or lesser degree ornaments when they have been completed.

Once you have completed your mechanical clock you set it by your wrist watch, you don't do it by astronomical observation. If you really want to test it you don't build another just like it as a regulator you use quartz stabilized oscillators to measure the variation.

It's a real challenge to make something that is good to a second or two a day which was as good as George Graham got and he was considered one of the best of his day.

So if we do it for something that looks intriguing, because we enjoy the journey or because we are looking for the challenge of precision or intellectual understanding, but lets not pretend it's because we want to know the time.

regards Martin

[BazyleParticipant @bazyle]

What is 'good time'. Before TV soaps five minutes either way was good enough most of the time, as the church bells got you to the service on time. Only the monk who rang the bells needed a better clock.

For Model Engineers the making of the mechanism should be the primary enjoyment and if it actually runs it is bit more useful that the steam engine they made but it doesn't need to be a precision timepiece as there are so many other sources for that
For the beginner a nicely structured series from ME showing the stages and explaining methods enhances the modeller's skills too.

[Michael GilliganParticipant @michaelgilligan61133]

Martin and Bazyle

Thanks for responding … I don't intend this to be a debate with a 'winner' but I would like to see a range of opinions [no pun intended].

Perhaps a good baseline for a "Basic Clock Design' is Benjamin Franklin's.

MichaelG.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Martin Kyte on 03/05/2016 10:05:59:

The addition of oil to the escapement reduces the drag on the pendulum caused by the pallets moving across the teeth of the scape wheel and thus causing the pendulum to "speed up".

I had considered that but "speeding up" the pendulum or, more correctly reducing the slowing down, by reducing the drag surely results in a greater amplitude not a shorter period?

Russell.

Edited By Russell Eberhardt on 03/05/2016 13:34:31

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Michael Gilligan on 03/05/2016 10:06:11:I'm struggling a bit, Russell … but see if this makes sense:

Although I mentioned SNR, I suppose that in the case of re-oiling the escapement we are really talking about a small non-random message [lubrication >> less wasted energy >> more impulse] buried in a larger 'carrier'.

Yes, of course, but why is the "noise" unidirectional? I imagine it must be the result of a non-linear effect somewhere. Stiction perhaps??

Russell.

[Martin KyteParticipant @martinkyte99762]

As I said previously for small angular swings the pendulum amplitude has very little effect on the period. Thats why most clocks are designed with small swings so the pendulum is isochronous. It's motion is a series of accelerations and decellerations. The period is affected by drag because that is the biggest factor in changing the angular velocity at the vertical (max velocity position). In effect for less friction the average velocity goes up. Crudely put the velocity is higher in the central portion of the swing where velocity is high. This effect dominates the effect of slightly increased arc so the period is shorter and the clock speeds up.

regards Martin

[John HaineParticipant @johnhaine32865]

Um, sorry to disagree with that Martin. Viscous drag creates a force in phase with the velocity, dissipating energy but not affecting the rate. By contrast a force, from the escapement for example, which not in phase with the velocity (so for example applying an impulse slightly later or earlier than BDC) does affect the rate.

[duncan webster 1Participant @duncanwebster1]

The period of a pendulum swinging with a small arc is almost independant of amplitude. If viscous drag affects amplitude, and I'd imagine a 'sticky' escapement wheel gave rise to less impulse and so a smaller arc, then drag will affect period.

To get technical, the small amplitude argument relys on the approximation sin(X) = X, wheras sin(X) actually is X-X^3/3! + X^5/5! and so on ad infinitum. For small values of X, X^3 and so on are even smaller, but not zero

[John HaineParticipant @johnhaine32865]

The fractional loss in rate of of a pendulum is (amplitude squared)/16 compared to the "theoretical" rate due to the cubic term in that expansion – the remaining terms are negligible. As long as the amplitude remains constant you can adjust this out. If the escapement gets "sticky" (not sure what that means) yes, it will reduce the amplitude and potentially cause the clock to gain relative to its adjusted rate. But it may affect other things too especially the timing of the impulse relative to the swing which could have a larger effect, one way or the other.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by John Haine on 03/05/2016 20:05:42:

If the escapement gets "sticky" (not sure what that means) yes, it will reduce the amplitude and potentially cause the clock to gain relative to its adjusted rate.

As I said earlier, that is what I would expect to occur. However Harrison wrote, "In the case of Mr
Graham’s clocks, with a small pendulum amplitude and the other poor characteristics described earlier, most
especially when the oil is foul, a touch of fresh oil will cause the pendulum amplitude to increase and the clock to
thereby go faster." That is the opposite of my understanding of the theory but seems to be borne out by experience.

Russell.

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by John Haine on 03/05/2016 16:09:11:

By contrast a force, from the escapement for example, which not in phase with the velocity (so for example applying an impulse slightly later or earlier than BDC) does affect the rate.

Changing the phase of the impulse cannot itself change the rate. The impulse as a function of time can be broken down using the Fourrier series and will only consist of the fundamental frequency and its harmonics. It contains no unrelated frequencies so it can only change the rate as a result of changing the amplitude of the swing.

Russell.

edited to correct for erratic "d" key

Edited By Russell Eberhardt on 03/05/2016 20:58:00

[John HaineParticipant @johnhaine32865]

Oh dear. Do we have to get into Airy's laws here? When you change the impulse phase it changes the fundamental's phase and this changes the rate. This is all in Rawlings or Woodward. If you put a drop of oil on the escapement the amplitude may increase but this could cause the clock to go faster through escapement error which could be larger than circular error. In the case of Harrison's pendulum clocks it seems that the escapement error, circular error, and barometric error are all carefully balanced to optimise stability.

[Michael GilliganParticipant @michaelgilligan61133]

Here's a real treasure:

Harrison's Manuscript version of 'Concerning Such Mechanism …'

**LINK**

… I doubt if it adds much to our understanding, though.

MichaelG.

Edited By Michael Gilligan on 04/05/2016 00:44:43

[Martin KyteParticipant @martinkyte99762]

"dissipating energy but not affecting the rate"

So you reduce the kinetic energy and you don't affect the velocity John? Surely if the pendulum is moving more slowly through it's arc it will take more time. Conversely if it's retarded less it will take less time. (OK I know I'm ignoring the change in arc but the argument is that factor is negligible). With air resistance the pendulum must travel slower over its entire swing compared with no air resistance. If we take the distance traveled by the bob to be the same the period will be less in the second case. I suggest that this is the dominant factor for small arc pendulums.

I can see that what I might term the 'conserved' energy will not affect the rate. With no losses you just get an energy exchange from gravitational potential to Kinetic energy which is just a fancy way of saying that the period is independent of the mass of the bob.

In the case of the oil on the pallets I would suggest a bigger impulse will increase the velocity slightly causing the same effect. If my analysis is correct then air resistance would be the dominant effect as it acts for a greater part of the arc.

I know this has zero to do with the design for a basic clock but my understanding seems to be improving with this discussion at least.

regards Martin

[John HaineParticipant @johnhaine32865]

Martin, yes, you do reduce the peak velocity during a swing, but that means that the bob doesn't rise so high as it reaches the extermity of its swing as the reduced kinetic energy is traded into reduced gravitational potential energy. Overall, a non-impulsed pendulum at small amplitudes is very nearly isochronous as it runs down.

With an escapement to supply the energy lost and keeping the amplitude constant, the rate (compared to the natural rate of the pendulum) depends on both the amplitude (through circular error) and the escapement characteristics, in particular the phase offset of the mean impulse from the centre of the swing. In fact the escapement "error" is very nearly (phase error)/2Q. If the phase error arises because the escapement action is somewhat asymmetric relative to the swing, it will vary with amplitude, and may act with or against the circular error. Woodward in MORT describes a Brocot spring driven clock where the circular error reduced as the spring ran down, reducing the amplitude; but this was compensated for by increasing escapement error. In "Clock B" the circular error seems to be nearly compensated by the suspension cheeks, and the escapement error and circular error are traded against barometric error and variation of amplitude with air pressure to give overall a very stable clock.

[Martin KyteParticipant @martinkyte99762]

I agree with you but the period is not independent of drag. It's a damped system and the period will increase with increasing air resistance.

As you know Isochronous just means it is independent of amplitude not that it is not independent of other factors.

Martin

[John HaineParticipant @johnhaine32865]

Martin, again sorry to return to this. I'm spending quite a lot of time at the moment simulating Harrison clocks and it was easy for me to do some simulations. Here is the period and amplitude of a seconds pendulum with a Q of 5000, zero circular deviation, coasting down from an initial deflection of 3 degrees.

The period remains within a gnat's of 2 seconds until the end of the 10,000 second run. It would be 2s except that the value of pi used in the simulation is only correct to 9 decimal places. Adding circular deviation gives this.

Here you can see the period some microseconds short at the beginning but as the amplitude decays it rises asymptotically to 2s again. Here's a different Q of 3000 again with no circular deviation.

Again the period is almost exactly 2s within nanoseconds and unchanging with amplitude. To the extent that the period does change actually it decreases with lower Q (i.e. increasing air resistance)

You are correct that there is a very very small change of resonant frequency with Q but for most practical values of interest in a clock it is unmeasurable. It is much much smaller than circular deviation.

[Martin KyteParticipant @martinkyte99762]

No need for the apology John it's a discussion not a fight.

Very interesting plots. From plots 1 and 3 (Q = 5000, 3000) you show a variation of about 2.6mS/day which would over 100 days be a little over 1/4 of a second and that is with a small swing so a lot less velocity and therefore friction. For Harrisons error budget of a second in 100 days even this is a quarter of his allowance.

I totally agree that for all practical clock-making it's irrelevant but not to the boys who are chasing the ultimate mechanical clock (I don't include myself by the way). However for the synchronome the rate reportedly changes noticeably with the case door open from shut as the air is more constrained and less free to move out of the path of the pendulum when it's shut. (don't lets get started on bob shapes yet ;0) )

I stand by my original statement that Harrison in the RAS was using controlled circular error (suspension cheeks) to compensate for changes in the atmosphere, primarily air resistance and buoyancy. You are right to say that from your plots that circular error seems dominant but is 2.7 hours a little long for a practical pendulum to keep swinging in air? Maybe you could have a look at your numbers and simulate period against changing Q. Could you perhaps measure the slope of the period at 3 degrees amplitude in you original plots to give a number to the circular error factor at the working amplitude.

The initial reason I brought it air resistance up was as an example of how reducing friction could speed a clock up. It has however prompted this interesting discussion.

Could you maybe do your simulations again with a much larger swing as Harrison used where air resistance would be correspondingly greater. It's going to rise as some power of velocity.

Perhaps this link would help. You seem to be better at maths than me.

**LINK**

best regards Martin

[Michael GilliganParticipant @michaelgilligan61133]

John & Martin

I am very happy to observe and learn from your interesting discussion …

May I just offer a starting point for the modelling, taken from Harrison's text:

[apologies for the typography … there may be a 'copy & paste' problem]

[quote]

… if for an Example in this Point, the ?aid Crouch [or Communicator of the Force of the Wheel, by the Pallats to the Pendulum, and as for this Experiment, with- out the Pendulum upon a Table] be ?et to vibrate only ?o far, as not to cau?e the Pallats to touch or be concerned with the Wheel, it will be 10 Minutes before it comes to rest … 

[/quote]

This is from pages 8-9 of the transcript:

MichaelG.

 

Edited By Michael Gilligan on 05/05/2016 10:35:48

[Russell EberhardtParticipant @russelleberhardt48058]

Posted by Martin Kyte on 05/05/2016 10:02:58:

is 2.7 hours a little long for a practical pendulum to keep swinging in air?

Not really. I checked the pendulum of my regulator some time ago and swinging in free air it decayed to 37% of initial amplitude in about 1 hour. So that gives a Q of just over 10,000 and would still have 5% of initial amplitude after 3 hours.

Lots of interesting points being raised here. I need to contemplate a bit more but still haven't seen why a clock with a little oil added to a sticky escapement should speed up.

Russell.

[Russell EberhardtParticipant @russelleberhardt48058]

Michael, I think that extract is just saying that the low friction of the knife edge supports for the crutch/pallet assembly will allow it to swing freely for ten minutes on it's own.

Russell.

[Martin KyteParticipant @martinkyte99762]

Exactly Russell.

Maybe a clearer 'translation' is:-

As a relevant example, with the movement on a table, the escapement (with crutch attached, but without the pendulum) will swing freely on it’s knife-edges (at an amplitude low enough to avoid contact with the escape wheel) for 10 minutes, without coming to rest. The air (at that rate of oscillation and being so light a matter) may be supposed to cause stoppage in that length of time.

Thanks for a confirmation of realistic decay time too.

Martin

[Michael GilliganParticipant @michaelgilligan61133]

Russell,

I think it true to say that the performance of the oils available in Harrison's time was far below what we have available now … and that much of 'CSM' is about the [claimed] superiority of his escapement detailing over Graham's. [i.e. it's more about the escapement efficiency than the pendulum]

Mudge's remarks, and their context, [cited here] are quite telling.

MichaelG.

.

Edit: The two preceding posts were made whilst I was composing this [delayed by a Coffee break] so I had not seen them.  … Yes, I am quite aware that the quote concerns the escapement without pendulum.

Edited By Michael Gilligan on 05/05/2016 11:37:54

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