Of torsion balances and construction cranes

The torsion balance in NIST’s quantum measurement laboratory includes two sets of four cylinders. As shown in the illustrated overhead view below, the quartet of test masses lies on a disk that is suspended by a thin strip of metal inside a vacuum chamber; the four source masses sit on a rotating carousel just outside the chamber. The source masses exert a small but measurable gravitational torque on the test masses. By rotating the carousel and measuring the gravity-driven twist of the metal strip, NIST physicist Stephan Schlamminger and his team calculate the value of the gravitational constant G. Because of the feebleness of gravity, the constant has proved stubbornly difficult to determine (see the article by Clive Speake and Terry Quinn, Physics Today, July 2014, page 27 ).

In preparing for his latest torsion balance measurement of G, Schlamminger identified a troublesome source of noise: When the experimenters rotated the carousel of source masses, they would inadvertently cause the metal strip from which the test masses hang to twist and untwist every few minutes. Schlamminger set out to find the optimal way to move the source masses so as to minimize the periodic twisting of the strip. Treating the system as a pendulum, he used a Laplace transformation, which is typically used to solve differential equations, to get snapshots of the inner disk’s twisting. Then he determined when and how to counteract the pendulum motion with discrete movements of the source masses.

Schlamminger’s results indicated that to achieve maximum damping, he needed to rotate the carousel between the two positions used to perform the G measurement, and to do so at a frequency of nearly one twist–untwist period. The source masses would shift as the strip was changing the direction of its twist. When Schlamminger and his colleagues put his equations to the test, they found that each maneuver reduced the amplitude of the torsion pendulum by nearly 150 microradians. Via 15 maneuvers executed in just over an hour, they lowered the amplitude from 1830 μrad to 1.5 μrad, a dissipation of energy that would take months to occur on its own.

Whereas metrologists may find the damping method surprising, Schlamminger realized that operators of construction cranes would not. As a postdoc, his adviser had told him about the “crane operator’s trick,” a series of precisely timed jolts to a tower crane’s trolley to stabilize a swinging load. Suspecting that journal readers would like to learn about construction equipment in addition to torsion balances, Schlamminger applied his derived equations to the pendulum motion of a crane’s load. The equations predicted that for transporting a load initially at rest, a crane operator should apply a velocity that opposes the direction of the trolley and then apply the opposite velocity a pendulum period later—a strategy similar to the one that dampened the NIST torsion pendulum. He also laid out tactics for other crane scenarios. Schlamminger and his colleagues published solutions for both cranes and torsion balances last month in the American Journal of Physics.

Schlamminger and his team are capitalizing on their dampening method as they collect data for their gravitational constant measurement, which they hope to obtain within the next several months. The metrology community is curious to see their result because of the particular torsion balance they are using. It came from the International Bureau of Weights and Measures in France, where researchers attained values of G that are several standard deviations higher than those from other experiments. (See the red points in the plot above. The vertical line designates the internationally agreed-on value.) The Committee on Data of the International Science Council will soon reevaluate its recommended values for G and other fundamental constants. (S. Schlamminger et al., Amer. J. Phys. 90, 169, 2022 .)