Author Topic: How to compensate for wooden pendulum arm expansion?  (Read 5518 times)

Offline dcunningham2

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How to compensate for wooden pendulum arm expansion?
« on: January 29, 2007, 08:40:39 PM »
It seems to me that the length of wooden pendulum arms would be quite sensitive to humidity and temperature changes.  In the case of metal arms, I understand there are various means to compensate for thermal expansion, either by floating the bob in mercury, or by constructing a grid from metals that have different coefficients of expansion.

In the case of wooden arms that swell with humidity, a simple method of compensating for expansion does not come to mind, at least not to this simple mind.  Is anyone aware of such a method?  

Also, I may be making a couple of assumptions that could be false -- please let me know if these are not correct:

1.  I'm assuming that while wood expands with humidity relatively more across the grain than with the grain, the expansion with the grain is still significant enough to adversely effect the timekeeping of a clock with a wooden pendulum arm.  Is this correct?  AHA!!  since wood swells differently across the grain that with the grain, a grid could be designed to take advantage of this effect, much like the varying expansion of different metals described above.

2.  I'm assuming that wood has a high enough thermal coefficient of expansion to be concerned about.  Is this correct?   Does it vary with the grain as with humidity?

Finally, are certain woods considered to be very dimensionally stable and more suitable for pendulum arms?
Dave Cunningham
dcunninghamatbluevardotcom

Offline dcunningham2

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Okay -- I have the answer
« Reply #1 on: January 30, 2007, 09:36:39 PM »
I think I have the answer, and I don't like it.

In researching this question, I've come to the conclusion that if you wanted to choose a dimensionally unstable material from which to constuct an unpredictably inaccurate pendulum, you'd pick wood.  Here's why:

Wood is anisotropic, meaning its structural properties vary in different directions -- 3 different directions in the case of wood -- longitudinally (along the grain), radially (across the rings), and tangentially (parallel to the rings)

As wood ages, it "seasons" so that its mechanical properties change over time -- this is beyond just the process of going from green to dry.

Furthermore, as wood is exposed to temperature and humidity cycles, it undergoes further "seasoning" that affect its properties beyond purely aging.

Finally, properties vary not only from species to species, but from tree to tree, as well as from how close the wood was to the center core of the trunk, and from how far up the trunk the wood was taken.

Other than that, it's fairly predictable.

Here are some generalized properties:

Thermal Expansion -- longitudinally, wood expands about one-third as much as steel for a given temperature increase -- about 1/2,000,000th of its length per degree Fahrenheit.  Not bad.  (I calculate that a 10 degree temperature change would result in only a 79 second error per year).  However, across the grain radially or tangentially, it expands more than aluminum or any metal.  I'm thinking, make the pendulum arm along the grain.

Expansion due to humidity (or "hygrosity") -- oh yes -- put it this way, if your pendulum is growing in front of your eyes, its not because it's glad to see you -- it could just be a humid day.  This may have something to do with the divine purpose of wood being to conduct water.  Wood will shrink or grow from 0.1 to 0.3 percent with humidity -- this is in the longitudinal direction, which is the least reactive direction.  It doesn't sound like much, but it means that wood is about 40 to 100 times more more dimensionally sensitive to humidity changes than to temperature changes.  Across the grain is much worse -- about 100 times more sensitive than with the grain.  If my quick math is correct, a 0.1% change in pendulum length would result in about a 43 second error per day.

What's the solution?  I'm thinking, quartz watch.  Actually, I'm thinking forget about temperature and focus on humidity.  A solution does comes to mind that I will describe in a subsequent post.

How do I know all this about wood?  Plagiarism and theft of intellectual property, that's how.  I discovered most of this information in a paper entitled, Properties of Wood from the Society of Wood Science and Technology.  It can be found at:

http://www.swst.org/teach/teach2/properties2.pdf
Dave Cunningham
dcunninghamatbluevardotcom

Offline rabbit

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    • http://flashpages.prodigy.net/rpirtle/index.html
humidity growth
« Reply #2 on: January 31, 2007, 07:58:13 AM »
very interesting stuff, Dave. i nominate you as our forum researcher.

i have one wooden clock outside, on my patio. it makes an excellent hygrometer. i can tell the exact time when the humidity went above 80% - the clock stops.
- rabbit