- Title Pages
- Preface
- Introduction
- Chapter 1 Better accuracy from simple pendulums
- Chapter 2 A short history of temperature compensation
- Chapter 3 Scaling the size of a pendulum
- Chapter 4 Finding a pendulum’s axis of rotation
- Chapter 5 Does a pendulum’s axis of rotation shift with amplitude?
- Chapter 6 Some practical properties of quartz
- Chapter 7 Putting Q in perspective
- Chapter 8 The Allan variance and the rms time error
- Chapter 9 Transient temperature effects in a pendulum
- Chapter 10 Transient response of a pendulum to temperature change
- Chapter 11 Dimensional stability of pendulum materials
- Chapter 12 Variations on a Riefler bob shape
- Chapter 13 Bob shape
- Chapter 14 Rate adjustment mechanisms
- Chapter 15 Spring suspensions for accurate pendulums
- Chapter 16 James’ suspension spring equations
- Chapter 17 Barometric compensation with a crossed spring suspension?
- Chapter 18 Solid one-piece suspension springs
- Chapter 19 Stable connections to a pendulum’s suspension spring
- Chapter 20 Stability of suspension spring materials
- Chapter 21 Pendulum rod materials
- Chapter 22 The heat treatment of invar
- Chapter 23 The instability of invar
- Chapter 24 Position sensitivity along the pendulum rod
- Chapter 25 Fasteners for quartz pendulum rods
- Chapter 26 Effect of the pendulum rod on Q
- Chapter 27 Correcting the pendulum’s air pressure error
- Chapter 28 Pendulum air movement: A failed experiment
- Chapter 29 Pendulum air movement: A second try
- Chapter 30 Time error due to air pressure variations
- Chapter 31 Effect of the clock case walls on a pendulum
- Chapter 32 An electronically driven pendulum
- Chapter 33 Sinusoidal drive of a pendulum
- Chapter 34 Photoelectronics for pendulums
- Chapter 35 Check your clock against WWV
- Chapter 36 Electronic correction for air pressure variations
- Conversion Table
- Index

# James’ suspension spring equations

# James’ suspension spring equations

- Chapter:
- (p.121) Chapter 16 James’ suspension spring equations
- Source:
- Accurate Clock Pendulums
- Author(s):
### Robert James Matthys

- Publisher:
- Oxford University Press

In 1983, K. James published two useful but rather complicated equations whose purpose was to help design the suspension spring. The equations show the effect that different spring lengths, widths, and thicknesses will have on the pendulum. The two equations are quite helpful, as the suspension spring is without doubt the most complicated part of a pendulum, despite its apparent physical simplicity. The first equation calculates the maximum stress in the spring, which occurs at the spring's top end at the maximum angle of swing. The second calculates how much the pendulum will speed up due to the inherent torque exerted by the suspension spring on the pendulum rod. In this chapter, the second equation is used to show that the suspension spring exerts a temperature effect on the pendulum's timing that is roughly as big as the thermal expansion of the pendulum rod. Anywhere from 16% to 84% of a pendulum's total temperature sensitivity is due to the suspension spring, with the actual amount depending on the spring's dimensions, modulus of elasticity, and suspended weight.

*Keywords:*
suspension spring, pendulum, equations, maximum stress, temperature, thermal expansion, pendulum rod, modulus of elasticity, suspended weight

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- Title Pages
- Preface
- Introduction
- Chapter 1 Better accuracy from simple pendulums
- Chapter 2 A short history of temperature compensation
- Chapter 3 Scaling the size of a pendulum
- Chapter 4 Finding a pendulum’s axis of rotation
- Chapter 5 Does a pendulum’s axis of rotation shift with amplitude?
- Chapter 6 Some practical properties of quartz
- Chapter 7 Putting Q in perspective
- Chapter 8 The Allan variance and the rms time error
- Chapter 9 Transient temperature effects in a pendulum
- Chapter 10 Transient response of a pendulum to temperature change
- Chapter 11 Dimensional stability of pendulum materials
- Chapter 12 Variations on a Riefler bob shape
- Chapter 13 Bob shape
- Chapter 14 Rate adjustment mechanisms
- Chapter 15 Spring suspensions for accurate pendulums
- Chapter 16 James’ suspension spring equations
- Chapter 17 Barometric compensation with a crossed spring suspension?
- Chapter 18 Solid one-piece suspension springs
- Chapter 19 Stable connections to a pendulum’s suspension spring
- Chapter 20 Stability of suspension spring materials
- Chapter 21 Pendulum rod materials
- Chapter 22 The heat treatment of invar
- Chapter 23 The instability of invar
- Chapter 24 Position sensitivity along the pendulum rod
- Chapter 25 Fasteners for quartz pendulum rods
- Chapter 26 Effect of the pendulum rod on Q
- Chapter 27 Correcting the pendulum’s air pressure error
- Chapter 28 Pendulum air movement: A failed experiment
- Chapter 29 Pendulum air movement: A second try
- Chapter 30 Time error due to air pressure variations
- Chapter 31 Effect of the clock case walls on a pendulum
- Chapter 32 An electronically driven pendulum
- Chapter 33 Sinusoidal drive of a pendulum
- Chapter 34 Photoelectronics for pendulums
- Chapter 35 Check your clock against WWV
- Chapter 36 Electronic correction for air pressure variations
- Conversion Table
- Index