In Kibble balances, the absolute value of the local gravitational acceleration g at the mass weighing position should be determined at the 10−9 level, corresponding to a few µGal (1 µGal= 1 × 10−8 m/s2). The absolute value of g was measured in the BIPM Kibble balance laboratory during the 2009 International Comparison of Absolute Gravimeters (ICAG-2009), with a relative uncertainty of 4.2 µGal. The measurement result was obtained at the height of 1300 mm, horizontally centered with respect to the vacuum chamber.
For the BIPM site, a number of comparison reference values (CRVs) of past international comparisons of absolute g measurements (ICAGs) are available. These can be used to estimate the long-term stability of absolute g values at the BIPM Kibble balance. The measurement results show that the g value change was within 1 µGal over 8 years. This might be verified again in the future.
In Kibble balances, the g value has to be transferred from the measurement position to the mass weighing position, and hence the relative gravity changes in space, i.e. the horizontal gravity gradient (HGG) and the vertical gravity gradient (VGG), need to be known. The HGG and VGG at the BIPM were determined by a combination of the relative gravity mapping and the evaluation of the instrumental self-attraction.
A 3-dimensional (3D) spatial array of g values was measured by a relative gravimeter inside the laboratory. Predictions were made from this 3D gravity map, which agreed to the off-grid experimental gravity measurement within 1 µGal.
The self-attraction effect of the BIPM Kibble balance apparatus was modelled by using the mathematical analogy between the equations for the gravitational field and the electrical field based on an electrostatic finite element analysis (FEA). The gravitational field of individual construction segments of the BIPM Kibble balance was calculated and combined, yielding a total correction of (4.7 ± 0.5) µGal at the mean trajectory position.
|The relative g mapping at the central trajectory plane (z = 0) including the self-attraction effect
(unit: µGal). The value at the weighing position (0, 0) is set to be zero.
The time-varying contribution of g, known as the Earth tides, polar motion, and atmospheric mass redistribution, was modelled by a software package based on localized parameter determination. The long-term measurement showed that this calculation can achieve an uncertainty of about 1 µGal.
The present uncertainty on the determination of the gravitational acceleration g at the location of the test mass is 4.6 µGal, which is not a limiting factor for a determination of the Planck constant at the 10−8 level.
For further details see:
- Jiang Z. et al., On the gravimetric contribution to watt balance experiments, Metrologia, 2013, 50, 452-471.
- Li S., Bielsa F., Kiss A., Fang H., Self-attraction mapping and an update on local gravitational acceleration measurement in BIPM Kibble balance, Metrologia, 2017, 54, 445-453.