Purpose:

To develop an improved mathematical model for volume determination of standardized weights by geometric measurement.

Methodology:

The new model eliminates an assumption considered in the current model published in the OIML R 111-1 recommendation, since it considers existing deviations from the assumed shape of the weights in the current model, specifically in the so-called knob and ring sections. These deviations might originate during the manufacturing processes of the weights.

Results:

An improved mathematical model for the calculation of the volume of standard weights by geometric measurement was deduced. Additionally, the model has the advantage of eliminating the risk of scratching the weights, which makes it possible to extend the use of the new model to higher accuracy classes.

Limitations:

The proposed model involves the possibility of making geometric measurements without surface contact of the weights, for example, with an optical comparator.

Findings:

An assessment of the current model against data previously published allows highlighting the relevance and higher accuracy of the new model, which makes it possible to calculate the density of standard weights, even for E class, through only geometric measurements.