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Accurate Clock Pendulums$
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Robert J. Matthys

Print publication date: 2004

Print ISBN-13: 9780198529712

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780198529712.001.0001

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Scaling the size of a pendulum

Scaling the size of a pendulum

(p.13) Chapter 3 Scaling the size of a pendulum
Accurate Clock Pendulums

Robert James Matthys

Oxford University Press

Making a pendulum bigger or smaller involves more than just a linear scaling up or down of the pendulum's dimensions. If you want to make a larger or smaller pendulum than the one you have now, how should the dimensions change? It turns out that not all of the dimensions should change linearly with pendulum length. The free length of the suspension spring should be scaled directly proportional to the pendulum's length. James has shown that the vertical distance from the pendulum's axis of rotation up to the free top edge of the suspension spring is directly proportional to the spring's thickness. So the spring's thickness is then scaled directly proportional to the suspension spring's length (and incidentally, also directly proportional to the pendulum's length also). The suspension spring's width is adjusted to keep the static and bending stresses approximately constant for all pendulum lengths.

Keywords:   pendulum, suspension spring, pendulum length, linear scaling, dimensions, bending stress, static stress, axis of rotation

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