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  1. #1

    Default Bob temperature compensation

    I hope this isn't a stupid question, I have only recently got interested in Horology and last year began building a clock. It has a one second pendulum driven by an electronic interpretation of a Hipp Toggle. I have plenty to learn.
    So the question is about the pendulum and bob. I bought 1 metre of 8 mm dia Invar and had a bob made from steel 8" high x 2" dia. With the bob supported at the bottom I had to extend the invar rod with steel (1.5" 8mm steel stock and the rest steel 4ba threaded rod.)
    I understand that ideally the bob should be supported half way up it's height. But have I inadvertently incorporated approximate temp comp for the bob with the 4" of steel at the bottom of the rod ?
    It SEEMS to me that with the bob expanding upwards, its centre point will go higher, but be lowered by the same amount due to expansion of the steel element in the rod ??

  2. #2
    Registered User Jim DuBois's Avatar
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    Default Re: Bob temperature compensation (By: rogerj)

    Well, the bob will expand at a different rate that will your steel extension even if both are of identical steel. That is due to the mass of both being dissimilar as well as the rod will heat or cool lagging the mass of the bob most likely. The steel extension being in contact with the material of the bob will stay more or less at the temperature of the center of the bob. But, that said, we may well be splitting hairs with worrying about what will be a small percentage of changes in length...the length of the steel piece as well as the length of the bob. Also, temperature compensation was much more important before most of us moved to decent heating systems. A clock in a jewelers store in the northern US in 1880 might see temperature shifts of 40-50-60 degrees F from no heat overnight during winter to sometime in the day a full blast of the old pot bellied stove. Today, most clocks don't see a shift in 24 hours of more than a degree F or so. Also, some of this will depend on how accurate you want your clock to be. Usually in most clocks timekeeping errors in the pendulum with an Invar shaft will be overshadowed by errors in the train, outside vibrations, changes in humidity/air pressure, and so forth. While a Hipp toggle can assist in making a very accurate clock I would test the rate of the pendulum as you have built it and see what it does over time. If you should put a recording thermometer in the case and measure the temps over several days at the same time checking the rate you may find you don't really have a problem with the pendulum assembly.

  3. #3
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    Default Re: Bob temperature compensation (By: rogerj)

    Quote Originally Posted by rogerj View Post
    I understand that ideally the bob should be supported half way up it's height. But have I inadvertently incorporated approximate temp comp for the bob with the 4" of steel at the bottom of the rod ?
    Basically the answer is yes. Including a high expansion material support tube on the rating nut and extending to support at the center of the bob is an accepted method of providing temperature compensation. invar doesn't have a zero coefficient of expansion it is approximately 10% that of steel so a 100 cm. rod of invar would expand as much as 10 cm. of steel. Aluminium is a good candidate for temeprature compensation due to its' large coefficient.

    Phil

  4. #4

    Default Re: Bob temperature compensation (By: Phil Burman)

    Thanks for the helpful replies..
    My Invar supplier only sold 8mm rod in one or two metre lengths. It was expensive and at the time I ordered it I thought I needed a bit more than one metre (was it 46" ?) but two metres would be far too expensive and lots of waste..I regarded the inclusion of the plain steel extensions as a disadvantage. Recently I started to think about getting the bob drilled from the bottom to the halfway point and changing to centre support.
    Fortunately I then had the thought that prompted the question in the OP and it would seem that the mod would have gained me little if anything. I appreciate the finer points raised but the clock is finished and keeping time to standard I had hoped for so I'll leave well alone.
    Roger

  5. #5

    Default Re: Bob temperature compensation (By: rogerj)

    I thought I would add another question to my older thread as its directly related to the above Q&A's.
    The clock generally kept good time but did show variations particularly with temperature so I had added a small 12 watt heater (a resistor), controlled by a digital stat with a 1 degree differential in the case.
    Recently, with the assistance of a friend, I was able to monitor the clock closely with a Raspberry Pi and the the minute by minute variations, due tho the stat cycling at times, could clearly be seen. (Not in the overall rate but in the minute by minute analysis)
    So I wanted to experiment more. I changed the heater to 36 watts and the stat to one with a 0.1 degree differential set to 24C. Although this worked and the rate was within a second a week, the very short term jitter (seen in computer analysis) in the rate was alarming and yesterday at 8.15 GMT I switched the heat off and opened the case door for half an hour. The ambient was 20C and the rate, as expected, IMMEDIATELY slowed to losing.
    Ambient has stayed close to 20C throughout, just dropping to 18C overnight and the pressure stable at around 1023 Mb.
    I've attached a graph of the rate which shows that the clock has now lost about a second in a day and shows no sign of changing at the moment.
    I can't see how the pendulum is over compensated and anyway the effect would not be immediate surely.
    The question is then, Can this losing rate be entirely explained by the increased air density of 4C cooler air ? If yes, how is compensated for in pendulum design.

    The red line/arrow indicate when the case temp was changed abruptly and the rate beforehand was typical of the preceding three days. The other two red lines are at midnight.
    Attached Thumbnails Attached Thumbnails Click image for larger version. 

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  6. #6
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    Default Re: Bob temperature compensation (By: rogerj)

    Air density is a tiny factor. Cooling would cause the air to
    be denser. This would not slow the clock, it would speed it
    up by increasing friction, shortening the natural swing.
    It might be an issue with your heating method. It is difficult
    to get a uniform temperature without using an outside chamber.
    You'd tend to get a very stratified temperature because of
    the losses through the case.
    You can buy that aluminum covered foam insulation cheaply
    and make a chamber. A small muffin fan can keep the temperature
    even inside.
    Tinker Dwight

  7. #7

    Default Re: Bob temperature compensation (By: Tinker Dwight)

    Thank you for your thoughts Tinker. Can I add that that the total arc of the pendulum is 2.5 degrees and it is under the control of an opto/electronic Hipp Toggle. Although I can't rule out a change of arc, and hence circular error, the time between impulses remains unchanged at 52 seconds. (Admittedly it can only change in 2 seconds increments.
    I absolutely accept what you say about the temperature control I tried for just thee days. it was disaster for all the reasons you gave and that's why the trial was stopped. I have already made another heater from an old cpu cooler with a 2" fan, plus reduced the wattage back to 12 for another trial sometime..
    However the denser air making it run slower (while the barometric pressure remains the same) has confounded me..but that's not surprising being new to this.
    So what I am asking is, what WOULD cause a pendulum clock, which was keeping good time, to instantly start losing a sec/day when the air temp was abruptly lowered by 4dC. ?

  8. #8
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    Default Re: Bob temperature compensation (By: rogerj)

    Think about what the pendulum is doing.
    In a vacuum, it crosses the center with a set amount
    of energy.
    This carries the bob out some distance where it gains
    in altitude equals that energy. It takes some amount of time
    to slow to a stop and swing the other way. That
    time is what causes the rate.
    Each part of the cycle takes 1/4 of the total time.
    Now, we put it in air. Friction robs some of that energy
    as does moving some mass of air.
    The time it takes to reach the altitude, equal to the energy,
    is reduced. It slows the speed of the pendulum but that
    means it takes less time to swing out.
    There is a slight increase in time it takes on the return
    to center but not as much energy is lost as on the outward swing
    where it had a larger starting velocity.
    The pendulum is not making a large enough swing to make circular
    error an part of slowing the rate.
    It is the increased loss of energy that speeds up the cycle by reducing
    the natural swing distance.
    It isn't until the air gets really viscus like water that the bob's return trip
    from the end of the swing is so slow that the rate is slower.
    In air, the return speed is closer to the pendulums natural vacuum
    speed from a shorter swing. More time is shortened on the outward
    swing because of the greater loss of energy, from the higher velocity.
    It is another one of those counter intuitive things like how the center
    of gravity being lower with the same moment of inertia makes the
    pendulum speed up.
    As the viscosity goes up there would be some point that an increase
    in viscosity would slow the pendulum rate. A pendulum with big wings
    would be past that threshold. It would run with a slower rate.
    If plotted, rate against viscosity, you'd see it was a humped curve
    and not a straight line.
    I've never looked at the math but I suspect it is around where 1/2
    the energy is lost to the viscus fluid.
    A good heavy bob is not over that hump.
    Tinker Dwight

  9. #9

    Default Re: Bob temperature compensation (By: Tinker Dwight)

    The bob in this case is 8"tall x 2 " diameter and weighs 6lb so I presume there is no way it is over that hump.
    Can you confirm that in the circumstances I've described, where all environmental things I can think of remain the same, that you would expect the clock to speed up when subjected to the 4C temp drop ?
    Of course I'm also puzzled why, after an hour or two, the clock hasn't speed as the pendulum settled at a new shorter length as you would expect if the temp comp wasn't correct - which I'm pretty sure it's not..

  10. #10
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    Default Re: Bob temperature compensation (By: rogerj)

    The length to the mass is the main contributor to the rate.
    If it got colder and there was no compensation, I'd expect to see the
    rate faster.
    If your seeing slower, I'd expect it was a problem of over compensation.
    Do remember, unless tested, you don't know the exact temperature
    coefficient of any of the parts you've constructed with.
    It is always best to tweak the temperature compensation with the
    rate close first. The rate doesn't have to be supper exact for the first run.
    Both usually effect each other a little but should converge.
    Tinker Dwight

  11. #11

    Default Re: Bob temperature compensation (By: Tinker Dwight)

    To throw in another variable: denser air is by definition more bouyant, lowering the weight (though not the mass) of the bob. This is essentially "floating" the bob more. Less weight means less restoring force of g to center on the pendulum. Just another mean little trick things play on us precision pendulum guys.

    Johnny

  12. #12

    Default Re: Bob temperature compensation (By: John MacArthur)

    Morning all..well it is in the Uk...perhaps the best day of the year in prospect ! Too good to be staying indoors messing with clock so my little Austin 7 is going for a run with the club..
    As for the clock, it's remarkable what sleeping on a problem can achieve..It suddenly dawned on me that I've been looking at the wrong problem ..ie an explanation for why the clock slowed when I thought it would gain..In fact it resorted to being a normal clock and running at the speed it should do.
    It was the condition prior to dropping the temperature was the abnormal condition ! For whatever reason - and they don't really matter - with the crude temperature control and the air currents and wildly differing and moving temp layers I had had created (alluded to by Tinker in #6) that was no good and I had re-rated for that condition.
    Lesson learned.
    My experiment with small heaters was an attempt to avoid getting the temp comp correct this by keeping the temp constant. Mistake.

    I'm a fan of Synchronome master clocks and eventually decided to have a go at making something similar..There is nothing beautiful about way mine is made. Synchronome claimed within 2 seconds /week and the aim was to equal, or perhaps better that. When I first ran the computer prog with the original gentler temp control operating it achieved +/- 0.25 sec for a week with final loss of 0.16 seconds..
    This kind of thing can get obsessive, hence the "improved" (but useless) change to a higher temp.
    I'll start a trial without temp comp and discover what I need to do to improve the compensation.
    BTW @John..I looked at your web page and admired those beautiful clocks..Fantastic workmanship..

  13. #13

    Default Re: Bob temperature compensation (By: rogerj)

    [QUOTE=rogerj;BTW @John..I looked at your web page and admired those beautiful clocks..Fantastic workmanship..[/QUOTE]

    Thank you Roger. I'm nearly done with #4, and will (soon, I promise) post a thread of its construction.

    Johnny

  14. #14
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    Default Re: Bob temperature compensation (By: John MacArthur)

    You ask what the time difference would be for a 4°C temp change.
    Your bob is 8 inches long = 200mm in round terms.
    It is supported at the bottom. Assuming the invar is temperature stable so the lower edge remains exactly where it was relative to the hinge point.
    Using the elementary period equation for a pendulum (in MS Excel notation) for a single swing (half of the complete cycle).
    T = Pi()*SQRT(L/g)
    L=T^2*9.81/Pi()^2 where T=1 & g=9.81 m/s^2
    L=993.961mm the length for a 1 second pendulum.
    Simplifying it as a pendulum with zero weight rod then that is the length to the middle of the bob.

    Now the expansion of your bob for 4°C.
    dl = L*a*t where dl = change in length. L=0.1m (distance from bottom of bob to its center). a = alpha = coefficient of linear expansion of steel = 0.000 013 m/m°C
    dl = 0.1*0.000 013*4 = 0.000 005 m

    So the period of the expanded pendulum will be:
    T = Pi()*SQRT((0.993961+0.000 005)/9.81) = 1.000 003 secs
    There are 86 400 secs per day. So your clock will take 86 400*1.000 003 = 86 400.234 secs to do that.
    You clock will be 0.23 secs/day slow.

    Complete maths of a pendulum are given at the Trinity Clock site at Cambridge University. Right now the site is down but Google should take you there.

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    Default Re: Bob temperature compensation (By: tok-tokkie)

    Hi Tok, I don't think you can ignore the thermal expansion of the invar. Invar has a Coefficient approximately one tenth that of steel but the rod is approximately 10 times longer than the bob to its' centre, so I think the OP is right that the setup is approximately self compensating. However the time/temperature lag difference between the rod and the bob will make a mess of any short term (read several hours) variations.

    invar 0.00000113 m/m/deg C
    steel 0.00001200 m/m/deg C

    Phil

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