Tidal Calculation Time for High and low Tides

Discussion in 'Clock Construction' started by Jim DuBois, Sep 11, 2013.

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  1. Jim DuBois

    Jim DuBois Registered User
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    I have a large library of books regarding clocks and clock making, the history of clocks, and many many illustrations photos and the like. That said, I was recently asked about constructing a clock that would show high and low tides each day for a specific location on the east coast of the US. The clock would need be built in a classical fashion, i.e. late 18th or very 19th century regulator style.

    Calculating the time of the tides, both high and low, is not the largest problem I am having per se. How those calculations would be done on a mechanical clock is a bit less obvious to me, and, I did not find any details in any of my books on clocks that do calculate the tides. No drawings that I have found, no details on how others may have accomplished this. I am assuming "kidney cams" of about 29 1/4 days duration would need be plotted and made for both high and low tides reflecting the calculations for the specific location...but what I don't know on this subject would fill several books.....extreme accuracy or perfection is not required or expected for this effort. Plus or minus a few minutes per day would be wonderful.

    Any suggestions from the group on where I might find more information? I do have access to one local clock that does have a tidal dial and part of a mechanism that calculates the tidal information. Unfortunately, it is missing a lot of parts so it adds more to my confusion than assists me.

    Any other ideas? Anything would be better than what I have right at the moment.Thanks in advance for any assistance and best regards to all....T
     
  2. Tinker Dwight

    Tinker Dwight Registered User

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    First, you might want to do 29.5 instead of 29.25.
    I've seen a more analog ish tide that accounted for both the
    phase of the moon and the inclination.
    It did the same for the sun as well. It did this
    with cams that had both lunar, daily and annual cycles.
    Each cam drove a piston for a fluid display with a scale.
    The simpler methods I've seen just show the times of high and
    low tides and not the amplitudes.
    Since you want to show it for a particular location, I'd think you'd
    want to first get a couple of years of tidal logs and then apply
    an FFT to it to determine the amplitudes and phase of the frequencies.
    From there you could create the cams running at the right timing to
    recreate the desired effects.
    Tinker Dwight
     
  3. Jim DuBois

    Jim DuBois Registered User
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    Dwight, thanks for the response. You are of course correct about the period of of the lunar month (29 days, 12 hours, 44 minutes). Fat fingered typist hit wrong key and didn't proof read well. I do have the data to calculate at least roughly the cams for each lunar month duration, a cam for high tide and one for low tide. I am not certain that I need the expected tidal heights. Too much information I think, but I could be wrong. What I would like to see is how others have done this in the far past. Calculating the gearing is not an issue but the whole set up I have envisioned is a bit Rube Goldberg in nature...there has to be a better way....and I will bet someone has done it better in the past......

    Where this starts getting really messy is here "Semi-diurnal tides have two high and two low waters per tidal day. They are common on the Atlantic coasts of the United States and Europe." "Why does a full moon cycle last almost 14 lunations rather than just the 12.37 lunations of a year? This would be the case, if the moon's orbit kept a constant orientation with respect to the stars, but the tidal effect of the Sun causes the orbit to precess over a cycle just under 9 years. In that time, the number of full moon cycles passed becomes one less than the number of sidereal years passed."

    Needless to say I am well past my original inclination to make this perpetual..... At this time I am hopeful for the mechanism to be reasonably accurate for a year......I may want to even reconsider that over some single malt ....

    The average duration of the anomalistic month is:
    AM = 27.55454988 days[SUP][3][/SUP] The synodic month has an average duration of:
    SM = 29.530588853 days[SUP][4][/SUP] The full moon cycle is the beat period of these two, and has a duration of:
    2.png

    and it sort of goes down hill from here.....
     
  4. Tinker Dwight

    Tinker Dwight Registered User

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    This reinforces the idea of the FFT. Of course, there is
    the weather noise to deal with. Maybe you need to work with
    a Chinese calendar. ;)
    You might also look a the web page:
    http://co-ops.nos.noaa.gov/harmonic.html
    Tinker Dwight
     
  5. Tinker Dwight

    Tinker Dwight Registered User

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    Also look at products pull down and
    find Harmonic Constituents.
    Combining the larger ones for your location
    can give you a reasonable tide table.
    Tinker Dwight
     
  6. Tinker Dwight

    Tinker Dwight Registered User

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    I was looking at a number of the cycle rates and
    it looks like many of them can be compensated
    with a differential that will get them quite close.
    At least for the ones that are close to 12 hours.
    Play with some of the ratios and what compensation
    would work.
    Tinker Dwight
     
  7. Tinker Dwight

    Tinker Dwight Registered User

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    #7 Tinker Dwight, Sep 12, 2013
    Last edited: Sep 12, 2013
    Hi Jim
    I don't know where you are specifically targeting so I chose someplace
    close to me. I looked at Monterey. Ca.
    I then ordered them by amplitude to show which ones it might be practical to
    leave out.
    I've added the worst case error on the right to get a good idea of which
    cycles were important and which one might be left off to minimize
    the number of cams. I assume you'd nee one cam for each cycle.
    Chart:

    1 M2 1.616 309.2 28.9841042 4.675
    4 K1 1.199 99.4 15.0410686 4.059 87%
    6 O1 0.753 91.8 13.9430356 2.860 62%
    2 S2 0.428 300.2 30.0000000 2.107 45%
    30 P1 0.374 95.9 14.9589314 1.679 35%
    3 N2 0.368 287.0 28.4397295 1.305 28%
    22 SA 0.157 205.6 0.0410686 .937 20%
    26 Q1 0.134 87.9 13.3986609 .780 16%
    35 K2 0.121 291.3 30.0821373 .646 14%
    21 SSA 0.090 283.2 0.0821373 .525
    11 NU2 0.072 292.9 28.5125831 .435
    19 J1 0.071 108.7 15.5854433 .363
    14 2N2 0.044 260.7 27.8953548 .292
    13 MU2 0.041 250.8 27.9682084 .248
    18 M1 0.038 109.9 14.4966939 .207
    15 OO1 0.036 121.0 16.1391017 .169
    17 S1 0.033 199.1 15.0000000 .133
    25 RHO 0.026 88.8 13.4715145 .099
    33 L2 0.023 343.9 29.5284789 .073
    27 T2 0.022 288.1 29.9589333 .052
    29 2Q1 0.016 96.5 12.8542862 .030
    16 LAM2 0.011 305.0 29.4556253 .014
    28 R2 0.003 299.8 30.0410667

    So what it shows is that to get a 61 percent error, I could get by
    with 3 cams.
    To get to 36%, I'd need 5 cams.
    Using no cams that have long term effects would be 6 cams
    and you'd get to 28% error.
    The first one that has a long term is the one with .0410686
    or 365.24 days for a cycle. If one left that one out and included
    only 7 cams, one gets 25% error, worst case.
    I guess now, you'd want to target how much error you want
    to allow and and how often you'd want to reset the cams
    to account for drift.
    For Monterey, I'd consider 5 cams at a 35% error to be possible
    target.
    Some, like the 15.0410686 and the 14.9589314 have a
    beat time of about half a year, might be combined with
    a half year cam to correct the beat. The only problem with
    that would be that eventually the beat cam would need to be
    replaced as it would not be able to be corrected by just
    changing the phase angle.
    Still, a few of these long term beats could be combined into
    one cam that might be useful for several years.
    Just using the minimum number of cams does have the advantage
    that if periodically reset, they hold the best error without having
    to replace cams.
    Tinker Dwight
     
  8. Jim DuBois

    Jim DuBois Registered User
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    Tinker Dwight,

    I think by now it is becoming apparent to the casual user why I am looking for examples of previous art that may have solved some of these problems. I have been looking at this a bit differently than your information above. My target for the calculations is Charleston SC. Strangely enough the one example of a clock with a tidal indicator that i have access to is also Charleston (actually Charles Town SC on the dial as it predates the Revolutionary War when the name was changed to no longer honor Charles)

    I have been looking at this as 2 cams for daily high and low tides, (these would actually rotate fully in one lunar month) with a lunar year cam as well as a 9 year cam. By connecting these via differential(s) the high and low tides would be subjected to moderate input modification by the lunar year and 9 lunar year cams. I am still cogitating over having both a lunar and a sun cam in the whole mess.

    I think I am getting a headache and may well need some liquid reinforcement of what I think I know.....
     
  9. Ralph

    Ralph Registered User
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    Jim,

    Have you looked at Brittens, Watch & Clock Maker's Handbook Dictionary and Guide. It has a topic Tidal Clock, with a graphic and some wheel counts.

    I'll scan the pages for you, if you don't have it.

    Ralph
     
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  10. Jim DuBois

    Jim DuBois Registered User
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    Ralph, no I do not have that book. Anything you can scan and send me on this subject would greatly appreciated.
     
  11. Tinker Dwight

    Tinker Dwight Registered User

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    Looking at the tables for Charleston, you could do just
    the first lunar value and then the daily one.
    Your error would be 48% at worst for the amplitude.
    Charleston has a much more dominant lunar effect then
    Monterey has.
    Just use the 2.569 feet for the lunar and
    .39 feet for the solar. ( double the numbers for full swing )
    You can use the 27.5 or try to better match
    the 28.9841042 degrees per hour that the chart has.
    If you make a single lobed cam, it would need to
    rotate at 12.439083 hours. If you where going to
    use a differential, it might be better to do a double
    lobed cam. You could then use 25 hours for the major
    part. You'd subtract 5/41th of an hour would then correct it to an
    almost perfect lunar cycle. For practical wheels and
    pinions, a 10 and 82 from the hours.
    Almost forgot to mention, the shapes of the cam would
    produce a cosine at the output.
    Tinker Dwight
     
  12. Bill Ward

    Bill Ward Registered User
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    This doesn't have to be that complicated. The classical tidal dial is just extra information on the moon dial. You don't have to calculate, or even understand, WHY the moon's period is what it is, or all the factors that cause minor changes in the exact position of the moon, or how to model them mathematically (after all, this is a subject that caused Newton to tear his hair for his whole life!) You just need to know what the time offset is for high tide for the specified, individual port, vs the time of full moon. That is, you need to know the age of the moon for high or low tides. So, for example, high tide takes longer to get to a city way upriver (like London or Philadelphia) than it does for a city right on a big ocean. A big bay with a small isthmus to the ocean also delays the tide, as does a shallow approach to deep water. This delay is more or less constant, and you just look it up in a tide table (which used to be published in the port's newspapers, but can be found in an ephemeris, or on the internet).
    The usual display is just an image of water (waves) painted on the moon dial, seen through a hole in the main dial plate, sometimes with some rocks painted next to the hole, preferably with a mermaid sitting on the rocks. I did once see a Dutch tidal dial with a mermaid slowly getting dunked; what was quite cute was that she held her nose just before going under the waves. Sometimes it's just the legends "High Tide" and "Low Tide" painted on the edge of the moon disk, along with the age of the moon.
    Tidal dials were a specialty of the great 18thC trading powers, like Holland and England. The Horological Journal has many articles on them; contact the NAWCC Library to get some copies. Answers to research questions is a benefit of membership.
     
  13. Jim DuBois

    Jim DuBois Registered User
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    Dwight, Ralph, and Bill. I appreciate greatly the assistance you have provided. I had not thought to consider the Horological Journal. None of the issues I have started me toward that as a source of information for tidal works. Silly me, should have at least thought about it. And yes, NAWCC membership has many benefits, one of which is access to research assistance. I did not expect my original interest in tidal mechanisms to be as complex a subject as it has turned out to be. The published work of James Ferguson (thanks Ralph!) has provided at least a working model complete with tooth counts, dial indicators, and a bit of theory of operation, and the like for rough calculations. It is similar to one I have seen a long time ago, now lost to me completely. Dwight, I believe the information you have provided is to a degree of accuracy my little effort will not achieve, but it is interesting none the less and useful as it points out short comings and the degree of error in solutions such as Ferguson's. Tidal tables for Charleston has at least 50 different locations and comparing this location to that location shows a larger than expected discrepancy in tidal height as well as the time for high and low being different by multiple minutes, all "in Charleston" so to speak. Bill, if it caused Newton heartburn for a lifetime I am in serious trouble!

    thanks again to all....
     
  14. Bill Ward

    Bill Ward Registered User
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    Re-reading my post above, I realized I'd not explained the mechanism completely, or even coherently.
    In the simplest variation, high and low tide time is indicated by a 24-hour hand against the moving moon dial. There are two cycles per day, but if a 12-hour hand is used, some method must be provided to differentiate between AM & PM. As mentioned above, the tidal hand is offset a certain number of hours, depending upon the specific port. A minute hand is not usually provided. The classical tidal dial does not indicate how high the tide is, just its time.
    Hope this helps somewhat.
     
  15. Tinker Dwight

    Tinker Dwight Registered User

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    If Newton had only been able to do FFT's, he'd have found the
    many little components of the tidal action.
    Looking at the tables is also interesting because at Charleston, just
    using the lunar primary effect, one gets to a 55% accurate value
    while at Monterey, one only gets to a 39%.
    A Ferguson solution in Monterey would be almost useless while in
    Charleston it would be quite useful.
    I recall seeing a tide prediction machine at the Monterey Aquarium.
    I don't recall how many terms it use. It has been interesting to think
    about the various things that effect the tide and the amounts of interaction.
    Tinker Dwight
     
  16. Tinker Dwight

    Tinker Dwight Registered User

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    As the Ferguson clock indicates, the peaks of the tide shift by 50.5 minutes each
    day.
    Tinker Dwight
     
  17. Jim DuBois

    Jim DuBois Registered User
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    sorry these are hard to read...
     

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  18. tok-tokkie

    tok-tokkie Registered User

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    #18 tok-tokkie, Sep 15, 2013
    Last edited: Sep 15, 2013
    There was a mechanical wrist watch that displayed the tide as well as the tidal cycle (spring to neap). Google does not find it for me now.

    As I recall it had a hand showing the state of the tide as it rises and falls. That would be lunar based.

    Then there was a rotating disk concentric with the hands but the pivot was off center. It was painted blue. It represented the tidal cycle - spring to neap tide. This would be solar based.

    I forget quite how you read the eccentric tidal range disk - it may have been at the 12 o'clock position showing where the tidal cycle was. I was a surfer then & thought it was a very elegant way of giving those two bits of information of much interest to me then. That watch shows the general state of the tide but the time is not precise but absolutely adequate for surfing.
     
  19. Ralph

    Ralph Registered User
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    Jim,

    They don't look bad. When you click the thumbnail, it opens the image. Clicking the image opens the image in a new window full size..... at least in Mozilla, it does.

    Ralph
     
  20. Jim DuBois

    Jim DuBois Registered User
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    Ralph, I was trying to blow up the Tidal dial drawing to better see the details of it...to little avail. I was able to mooch an original, printed in 1757, of "Sir Isaac Newton's Principles" by Ferguson. He devotes several pages as to the "whys" of tidal changes, but provides no details on the "hows" of how he best solves the variables. I have also picked up a couple of books that show a fair number of Tidal clocks, unfortunately neither provide any details on gearing. The two books, "Stretch, America's First Family of Clockmakers" by Fennimore and Hohmann, and "Timeless Masterpiece American Brass Dial Clocks" by Hohmann, show multiple tidal dial clocks, ranging from simple moon phase dials with H/L tides on the moonphase to some rather complex stand alone dials. I was surprised to see photos of maybe 10 or more Stretch clocks with the more complex dials. While there are photos of the driving gear trains on the movements, there is absolutely no photos or details of the mechanics on the aux dials themselves.....more to follow, if you don't have the 2 modern books they are both on Amazon for fairly cheap money, think under $75 each. And they picture many fine clocks in some detail I have not seen elsewhere...and the 3 books belong to a mutual friend.....I went ahead and ordered the 2 modern works, they are too good not to have on the shelf
     
  21. Jim DuBois

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  22. Tinker Dwight

    Tinker Dwight Registered User

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    It looks like these all use the first order of the moon's
    effect. I think the way one would read these is that the dial
    would give the number of hours to the next high tide.
    They'd most likely use the same ratios at the other
    clock used ( 24hr 50.5 minutes ). That time would be
    the same every where.
    The moon phase dial part is the typical ratchet wheel still used
    today except it turns a dial hand instead of the painted plate seen on
    many clocks today.
    Tinker Dwight
     
  23. Jim DuBois

    Jim DuBois Registered User
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    Tinker, that would be the way I see these examples. It is interesting to note how many of these clocks Stretch made, as well as the complex method he used to transfer motion from the hour tube to the moon phase and tidal dials. From a practical point of view he could have accomplished the same with a long spring loaded finger, a pivot point on the front of the movement, and a lever lifted by a pin on the hour wheel from the pivot to the spring finger. But, that might not have appeared nearly as sophisticated a solution to the people that comprised his customers....

    Maybe he did use some modification of the gear ratios from the hour wheel to the moon phase to better arrive at the true lunar month and better approximate the lunar day also...can't tell from the photos on hand if that is the case...
     
  24. Tinker Dwight

    Tinker Dwight Registered User

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    Hi Jim
    I just looked at these pictures a little more.
    These are just the normal ratchet moon phase
    dials. The hour shown would correspond to time
    the high tide would be expected relative to the
    hour phase of the moon. It has no special extra
    gearing, other than advancing the moon dial.
    Not as sophisticated as the other example in the book.
    I suspect they were not aware of the solar
    effect and how much it was when the clocks
    were made. Instead of dividing the dial into 24
    evenly spaces hour marks, one could slightly
    offset the hour marks around the dial and get
    a closer mark.
    Of course, with the ratchet 12 hour increment,
    such additions would be lost in the noise.
    As I said, I suspect these were to show high
    tide times, as this was the important time for
    shipping.
    I've been thinking of using a graphic LCD display
    and adding the equations to create a clock and
    tide display, showing the current tide and a cycle
    or two into the future.
    Newton would have loved to had such a clock.
    He was just at the wrong time. I'm still glade he was
    there when he was but if he only knew where his thoughts
    would have brought us to today.
    Tinker Dwight
     

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