A more realistic Foucault pendulum
A more realistic Foucault pendulum lead image
In 1851, Leon Foucault began building pendulums. He realized they demonstrate Earth’s rotation, and his projects grew to include a 67-meter pendulum in the Pantheon of Paris, whose bob shifts about 2 millimeters in each back-and-forth swing. Now, many universities and science museums house Foucault pendulums as simple experiments — but the so-called simple pendulum isn’t so simple.
Natalia Nieves Salva and Horacio Ramon Salva developed a realistic model of a Foucault pendulum, which includes both the Coriolis precession — the bob’s gradual shift as a result of the Earth’s rotation — as well as the oft-ignored Airy precession, which can change the direction of the pendulum’s swing independent of the Earth’s rotation. Tiny imperfections in the support of a pendulum can introduce and amplify Airy precession.
“Airy precession was traditionally considered a secondary perturbation,” said Horacio Salva. “In our work, we treat it as a key factor in the model, sometimes even more significant than Coriolis precession. We believe it is responsible for many strange behaviors of the pendulum.”
While Airy precession is negligible in long pendulums, like in the Pantheon of Paris, it plays a large role in shorter demonstrations. Depending on orientation, Airy can either reinforce or counteract the Coriolis precession, the subject of the demonstration. The authors studied its effects using an iterative numerical algorithm, with which they considered up to 1.5 days of oscillation at a time.
“This work aims to demonstrate how crucial Airy precession is, as it can disrupt a demonstration of Earth’s rotation,” Horacio Salva said.
The researchers hope their model will help inform future demonstrations in classrooms and museums, and that educators will work to reduce Airy precession as much as possible.
Source: “Interplay between Airy and Coriolis precessions in a real Foucault pendulum,” by N. N. Salva and H. R. Salva, American Journal of Physics (2025). The article can be accessed at https://doi.org/10.1119/5.0208092 .
