Set-up of Mass Scales above 1 kg Illustrated by the Example of a 5 t Mass Scale

Abstract

To an ever increasing extent, weighing instruments for the determination of masses of more than 50 kg are designed as high-accuracy weighing instruments of accuracy class II rather than as medium accuracy weighing instruments of accuracy class III. Consequently, the masses required for testing must meet higher accuracy requirements. The uncertainty of a 5 t mass scale set up at the Physikalisch-Technische Bundesanstalt (PTB) is assessed on the basis of an analysis of the uncertainties which can be attained. This mass scale allows masses of 10 kg, 50 kg, 500 kg and 5 t to be calibrated with relative uncertainties of 5 × 10-8, 6 × 10-8, 3 × 10-7 and 1,5 × 10-7. With their aid, deadweights of up to 50 kN for force standard machines can be determined with relative uncertainties of 4 × 10-7.

Proposed new determination of the gravitational constantGand tests of Newtonian gravitation

“…The mass of the shepherd can be measured to 3 parts in 10' by the large-mass comparator of the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig [46]. This will probably be the largest error in the determination of G (although it of course will have no effect on the tests of the inverse-square law, the equivalence principle, or G /GI.…”

“…It is one of only two physical standards still based on material objects rather than atomic properties. Moreover, mass comparisons, including the recent PTB work, are made in air, and are therefore subject to uncertainties from buoyancy, surface deposits, and unexplained sources [46]. Our experiment will be performed in vacuo (like all determinations of G since Braun's work at the turn of the century [47,48]) and are therefore also subject to outgassing uncertainties [49].…”

Buoyancy contribution to uncertainty of mass, conventional mass and force

“…is the counterpart of the corresponding term ρ a (V r − V t ) in equation ( 5), and thus represents the sought buoyancy correction C cb for conventional mass, and the last term in the RHS derives from equation (7). Equation ( 8) is the model for conventional mass comparisons, and thus constitutes the counterpart to equation (5). Corrections ( 6) and ( 9) vanish for ρ a = 0 and ρ a − ρ 0 = 0, respectively, or for ∆V = 0 .…”

“…Unfortunately, in common practice the covariance term (note that it is always negative) is ignored, which engenders errors and confusion. Formula (38), which might be compared with formula (16) in [5], has a nice physical interpretation. In the uncertainty u 2 (m ct ) about conventional mass, the contribution (ρ a − ρ 0 ) 2 u 2 (V t ), specific of the buoyancy correction to conventional mass, is added to u 2 (m t ), whereas ρ 2 a u 2 (V t ), specific of the buoyancy correction to mass, is subtracted.…”

“…At each step of the traceability chain, the unknown standard is compared to a reference by means of a comparator. Following an earlier attempt to address the issue [5], it was shown for both mass [6] and conventional mass value [7] that along this chain the air buoyancy effect plays an opposite role in the correction of the measurement, depending on the role of the standard, i.e., depending on whether the standard is the unknown (during its calibration), or the reference (when used in the subsequent step). However, to the best of our knowledge the interplay between mass and conventional mass value along the dissemination chain has never been elucidated, with the consequence that a consistent propagation of uncertainties back and forth between these two closely connected quantities is lacking.…”