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1. ## Pendulum Length Formula

Hi
Several years ago I found a formula in an old Bulletin for finding the length on an unknown pendulum using a test pendulum and a 12 or 24 hour time period to calculate the correct length.
I remember that I used it on a Warterbury longcase clock with great success. I measured the test pendulum from the hanger to the bottom of the bob and ran the clock over night.
I then plugged the numbers in and came up the correct length. Cut the new pendulum, started it up and the beast was right on the money. It kept perfect time!

Now here is the problem, my wife packed away my old Bulletons and I no idea where that Bulleton is. I have a clock in the shop without a pendulum and need that formula. Does any one have that formula handy?

3. ## Re: Pendulum Length Formula (By: Smudgy)

Thanks for the link. The formula I was looking for is a relation equation based on the length of Test Pendulum verses time gained or lost during the running time of the test. And here it is, very helpful formula to have at hand:

Lc = Lt (1-E/R)squared.

Where
Lc = the Correct Pendulum length
Lt = the Test Pendulum lenght
R = the Running Time of the Test
E = the Error in Time after the Test

Reference is The August 1989 Bulletin Volume 31/4 Number 261 Page 321
Determining Pendulum Length By the use of the Computer
By R.C. Barclay (CO)

I used this in the past with great success. It saves a lot of time messing about with a theoretical pendulum length trying to get to be the actual length.

Thanks

Kim

4. ## Re: Pendulum Length Formula (By: Kim St.Dennis Sr.)

Hey Kim - looks like a great formula to have! Could you elaborate on E and R for me? What unit is used - seconds, minutes, hours (or does it matter as long as it's consistent)?

5. ## Re: Pendulum Length Formula (By: shutterbug)

Hmmmmmm; Thanks, KST! That's a keeper. I've copied that for my files. Great formula to have, as I will use it often.

6. ## Re: Pendulum Length Formula (By: Scottie-TX)

Hmmm - I can't seem to make it work right.

7. ## Re: Pendulum Length Formula (By: shutterbug)

I have not tried it. Just thot I'd put it to task next time I put one under test.
What premises did you use? Did you apply it to a theoretical movement, not regulated? Did you de-regulate a known BPM movement?

8. ## Re: Pendulum Length Formula (By: Scottie-TX)

Hi
The test works better with the more time the test is run. In the article by R.C. Barclay the time units is in minutes. He ran his tests for 24 hours (1440 minutes). The longer you run the test, the grater the accuracy of the results.
Barclay's Example:
Lt = Test Pendulum = 12 inches
Test Run Time = 24 Hours (1440 Minutes)
Test Error = 2 Hours (120 Minutes)

Lc = Lt X (1 - E/R) squared
Lc = 12 X (1- 120/1440) squared
Lc = 12 X (1-.083333) squared
Lc = 12 X (0.916667) squared
Lc = 12 X 0.84208
Lc = 10.0833 inches

I ran the figures through an Excel spreadsheet to check the numbers and they are correct.

About 10 years ago I had a Waterbury Longcase Mission Clock in the shop without a pendulum. I ran the test, and to tell the truth, I measured the pendulum from the top of the suspension spring to the bottom of the bob. Plugged in the test results and cut the pendulum to the measurement given.

Started up the clock and it did not gain or lose any time in a week!

The equation is relational and the pendulum measurement is not critical. You do not have to find the center of the bob. Just measure from the top of the suspension spring to a point on the bob that is easy to measure too and go for it. Whatever point you choose will occupy the correct spot on the arch of the pendulum when it is running.

Kim

9. ## Re: Pendulum Length Formula (By: Kim St.Dennis Sr.)

Ahhh! My formula had a parentheses error that threw it off. Your example works, and I tested it with a negative 120 as well. A test run of 24 hours seems reasonable to me