Buoyancy contribution to uncertainty of mass, conventional mass and force

Abstract

The conventional mass is a useful concept introduced to reduce the impact of the buoyancy correction in everyday mass measurements, thus avoiding in most cases its accurate determination, necessary in measurements of "true" mass. Although usage of conventional mass is universal and standardized, the concept is considered as a sort of second-choice tool, to be avoided in high-accuracy applications. In this paper we show that this is a false belief, by elucidating the role played by covariances between volume and mass and between volume and conventional mass at the various stages of the dissemination chain and in the relationship between the uncertainties of mass and conventional mass. We arrive at somewhat counter-intuitive results: the volume of the transfer standard plays a comparatively minor role in the uncertainty budget of the standard under calibration. In addition, conventional mass is preferable to mass in normal, in-air operation, as its uncertainty is smaller than that of mass, if covariance terms are properly taken into account, and the uncertainty over-stating (typically) resulting from neglecting them is less severe than that (always) occurring with mass. The same considerations hold for force. In this respect, we show that the associated uncertainty is the same using mass or conventional mass, and, again, that the latter is preferable if covariance terms are neglected.

A Cost Saving Method for Determining Air Density in Weighing

“…However, effects of possible covariances in the calculation of the air density values using the artefact method in a mass laboratory should be better understood and included in the calculations before the method is widely applied. Hints and considerations can be taken from [9].…”

Development of a comprehensive software application for realization and dissemination of the mass scale

“…For this reason the covariance matrix Ψ m,∆m is evaluated. This contribution is described in the paper by Malengo and Bich [7], and plays an important role in the uncertainty evaluation, as it considers the air buoyancy uncertainty already contained in the uncertainty of the mass reference.…”

Guide to the expression of uncertainty in measurement — Part 6: Developing and using measurement models

“…By implication, it can be necessary to consider the corresponding measurement models as a single multi-stage measurement model. An instance arises in mass and force measurements, in which covariances between volume and mass at the various stages of the dissemination chain must be taken into account to evaluate correctly the contribution of the buoyancy correction to the uncertainty associated with the output estimate of the current calibration [118].…”