Buoyancy contribution to uncertainty of mass, conventional mass and force

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.