For centuries, accurate pendulum clocks were of strategic scientific and military importance. Environmental factors such as temperature and pressure affect the rate of a pendulum. Without temperature compensation, accuracy is limited to about 10 s per day. With it, however, a secondper month is possible. Barometric compensation is required for additional improvement. Indeed, highly accurate pendulum clocks, such as Shortt-Synchronome Pendulums, are placed in controlled partial vacuums to avoid this unsolved problem. We model the pendulum as a Duffing oscillator to account for the effects of circular deviation, buoyancy, virtual mass, and aerodynamic drag. The application of routine perturbation methods reveals a simple and elegant solution to the problem of barometric compensation, an arc of motion where a balance is achieved. The results are confirmed by comparison to experiment.

References

References
1.
Andrewes
,
W. H. J.
, ed., 1993,
The Quest for Longitude
,
Harvard University Press
,
Cambridge, MA
.
2.
Boucheron
,
P. H.
, 1985, “
Just How Good was the Shortt Clock?
,”
Bull. Natl. Assoc. Watch Clock Collect.
,
27
, pp.
165
173
.
3.
Moon
,
F. C.
, and
Stiefel
,
P. D.
, 2006, “
Coexisting Chaotic and Periodic Dynamics in Clock Escapements
,”
Philos. Trans. R. Soc. A
,
364
, pp.
2539
2564
.
4.
Kuroda
,
K.
, 1995, “
Does the Time-of-Swing Method Give a Correct Value of the Newtonian Gravitational Constant?
,”
Phys. Rev. Lett.
,
75
, pp.
2796
2798
.
5.
Cagnoli
,
G.
,
Gammaitoni
,
L.
,
Hough
,
J.
,
Kovalik
,
J.
,
McIntosh
,
S.
,
Punturo
,
M.
, and
Rowan
,
S.
, 2000, “
Very High Q Measurements on a Fused Silica Monolithic Pendulum for Use in Enhanced Gravity Wave Detectors
,”
Phys. Rev. Lett.
,
85
, pp.
2442
2445
.
6.
Kevorkian
,
J.
, and
Cole
,
J. D.
, 1981,
Perturbation Methods in Applied Mathematics
,
Springer-Verlag
,
Heidelberg-Berlin
.
7.
Jordan
,
D. W.
, and
Smith
,
P.
, 2007,
Nonlinear Ordinary Differential Equations,
4th ed.
,
Oxford University Press
,
Oxford, UK
.
8.
Landau
,
L. D.
, and
Lifshitz
,
E. M.
, 1959,
Fluid Mechanics
,
Pergammon Press
,
London, UK
.
9.
Drumheller
,
D. S.
, 1998,
Introduction to Wave Propagation in Nonlinear Fluids and Solids
,
Cambridge University Press
,
Cambridge, UK
.
10.
Batchelor
,
G. K.
, 1970,
An Introduction to Fluid Dynamics
,
Cambridge University Press
,
Cambridge, UK
.
11.
Matthys
,
R. J.
, 2004,
Accurate Clock Pendulums
,
Oxford University Press
,
Oxford, UK
.
12.
Rawlings
,
A. L.
, 1948,
Science of Clocks and Watches
,
2nd ed.
,
EP Publishing Limited
,
East Ardsley, UK
.
13.
Baker
,
G. L.
, and
Blackburn
,
J. A.
, 2009,
The Pendulum
,
Oxford University Press
,
Oxford, UK
.
14.
Matthys
,
R. J.
, 2011, private communication.
15.
Hunt
,
H.
, 2011, private communication.
16.
Heskin
,
D.
, 2007,
Sleeping in Oblivion
,
Soptera
,
Leicestershire, UK
.
This content is only available via PDF.
You do not currently have access to this content.