Experts weigh in

Following our article on the new definition of the kilogram, Martin Vlietstra, one of our occasional contributors, provides some insight into how, in the 21st century, this standard is passed down to us, the general public.

Last year the definition of the kilogram was revised. Using the new definition, one can specify the mass of a bag of sugar to accuracy so great that a weighing device could detect a shortfall of a single crystal. Measuring to this accuracy requires some exceptional equipment – according to the US National Institute of Standards and Technology NIST *  a table-top Kibble balance designed to measure masses of the order of 10 g will set you back $50,000. (The original Kibble Balance, which cost millions of dollars, was designed to measure masses of the order of 1 kg). You will probably also need a PhD to understand the operating manual!

What actually are such balances used for? In practice, they are used to weigh calibration masses that are used in turn to calibrate other balances.  Often the highest precision calibration weights are stored in vacuums and are used only to calibrate further that are used in turn to calibrate commercial and laboratory balances. To this end, the International Organisation for Legal Metrology (OIML) has defined seven classes of weights which they have labelled E1, E2, F1, F2, M1, M2 and M3.  (See OIML recommendation R111 at https://www.oiml.org/en/files/pdf_r/r111-1-e04.pdf).  A Class E1 weight is accurate to within 0.5 parts per million and a Class M3 weight is accurate to within 500 parts per million or ±0.05%. A Class E1 weight would probably never leave the laboratory where it was calibrated while a M3 weight is suitable for use in commercial transactions.

It is well known that whatever you buy, you get what you pay for. In order to facilitate the specification of weighing device, the OIML has defined four classes of weighing devices, identified as  Class I, Class II, Class III and Class IIII devices #. Class II (high accuracy) devices have an accuracy of better than one part in 100,000 at the upper end of their operating range, Class III (medium accuracy) have an accuracy of one part in 10,000 and Class IIII (Ordinary accuracy) has an accuracy of one part in 1000. Class III scales are usually required for commercial transactions and for accurate medical measurements while Class IIII scales are suitable for medical clinics. In practice, this means that a Class III scale that is set to weight people up to 100 kg will have an accuracy of 0.01 kg and a class IIII scale an accuracy of 0.1 kg. One area where a hospital might use a Class III 10 kg scale (accuracy 1 g) would be to measure the amount of milk that a breast-fed baby takes in during one feed (the baby is weighed before and after the feed and before any nappy changes!), while Class IIII scales are suitable for use in a doctor’s surgery.

These days, very few weighing devices actually rely on weights – they are electronic and are pre-calibrated against the gravitational force. Pre-calibration brings in its own set of problems – the gravitational force is not constant around the globe. As you rise vertically, so the gravitational force decreases – at 9000 metres above sea level (the height of Everest), gravitational force will have reduced by 0.29%, but this is offset by an amount of 0.08% due to the decrease in air density (and therefore loss of buoyancy as per Archimedes Principle) leaving a net decrease of 0.21%.  The change in gravitational force due to the earth not being fully spherical is even greater – the combined effect of change in gravitational force and centripetal force (caused by the earth’s rotation), is about 0.5%. The solution to these problems is to re-calibrate one’s weighing device at regular intervals, something which, in many jurisdictions, is a legal requirement for weighing devices that are used for trade. The standard way to re-calibrate a device is to use a physical certified weight of the appropriate grade.

References

* see https://physics.aps.org/articles/v12/33

# see https://www.oiml.org/en/files/pdf_r/r076-1-e06.pdf

2 thoughts on “Experts weigh in”

  1. Just out of curiosity, how would these scales work if one was somewhere in outer space where the force of gravity would be close to zero? What other method could be used to measure mass where gravity is not present to too small to be useful?

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  2. @Daniel Jackson – depending on the circumstance, one could possibly make use of conservation of momentum (linear or angular).

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