Just like in watches...

[Isaac]

Hey everyone, figured I'd pop back on the forums for a little bit after taking a break and building up my own watch collection.

A question I was pondering as I was looking at my watch collection is beat rate. A higher beat rate for a watch usually makes it more accurate, due to limiting positional variance. However, in a pendulum type movement of a clock, does a higher beat rate also translate to a more accurate movement (even though a clock is stationary and not subject to extreme positional variances?), or at the very least become easier to regulate precisely? This question applies to all types of pendulum escapement designs.

Curious as to your answers.

 

[Uhralt]

I can see no reason why a shorter pendulum should make a clock more accurate. The position of a pendulum clock is fixed, so that shouldn't be an issue. In fact, most precision pendulum clocks have a long pendulum with a beat rate of 1/sec. It is more the quality of the movement and the material and composition of the pendulum that determines accuracy. Also, a long pendulum is easier to regulate because a small change of the effective pendulum length by moving the bob up or down has a smaller effect on the speed of the clock than the same change with a short pendulum. 1 mm change in a 1000mm pendulum is just a 1% change in length, but 1 mm in a 20 cm equals a 5% change in length.

The formula for the period of a pendulum (one swing forward and one back) is: T= 2 pi x (square root of L/g)
With T=period in seconds, L the length in meters, g= gravity constant (9.8).
If you plug in the numbers for a 1 mm change in a 1-meter pendulum and in a 0.2 m-pendulum you will find that the period of the long pendulum changes from 2.006 sec to 2.005 sec, a 0.05% change. The short pendulum's period changes from 0.8971 sec to 0.8949 sec, a 0.245% change.

Uhralt

 

[svenedin]

Isn’t a short pendulum subject to more air resistance due to the faster speed?

High beat rate watches do have their own issues. The greater speed leads to more wear. They have a tendency to throw lubricants off the escapement and even when new thixotropic greases were developed I believe Omega actually reduced the beat rate of the co-axial for this reason.

 

[novicetimekeeper]

Shorter pendulums make fine adjustments harder. The rate of the Great clock of Westminster is adjust by adding and removing pennies to change the effective length of the pendulum. That sort of control is difficult to achieve on a short pendulum.

 

[DeanT]

a smaller arc on the pendulum decreases the error as the pendulum oscillation is not completely isochronal and the period does depend on the angle of the swing.