There are fields of technology in which through “almost measures” a pure numeric value is accurately determinated. Let’s take a couple of examples:
In both cases, the value of the measures (weight or flow) carried out does not have great utility as such, but only if referred to the second measurement performed. The value of each measure can provide us (when measured in a traceable way) just “incidental” information, such as the total weight of pieces or the total flow getting out from the diluter.
- a balance “pieces counter” using two measures of weight (the single piece and the total to be counted) to produce, by calculating the ratio of the weights, the dimensionless “number of pieces”
- in an diluter using two flow measurements (gas to be diluted and diluted gas) to produce their ratio (dilution ratio) that would be the “mesurand” if it were not dimensionless.
By contrast, each traceability has a cost, also in terms of accuracy: being the two measurements in both above cases, very different (because of the number of pieces or of the dilution ratio), tey will require different meters and / or different traceability chain, with the effect that on the true measurand (the ratio) would combine the errors of two very different calibrations in addition to the measuring errors
Measuring equal capillaries in gas divider
Everyone knows the example of the target that explains the difference between precision (or repeatability) and accuracy:
Here is represented in scale (diameter / flow), the difference between the flows that correspond to the elements (orifices or groups of capillaries),in a gas divider which work together in accordance with the binary progression giving origin to different dilution ratios (see page “dilution techniques”). It ‘obvious, that, by shooting with the same weapon (or by measuring with the same instrument) the relative errors will be much higher on the smaller target.
Working with equal capillaries the situation may be shown as above picture : targets may seam small, but just increasing the applied pressures the flows bay grow all together in a wide range. Each capillary flow is measured with the same meter in the best resolution field, reading very similar values (then the linearity of the meter is not critical).
Our luck is that, before the construction of the diluter, the capillaries are individually accessible with characteristics already very similar and therefore they can be selected for comparison with one capillary of the lot. In practice … we are allowed the luxury to shoot only the big target and we are also not required for precision, but just for repeatability. We like to win easy !
Easy solutions, nearly always give the best results.
…but traceability is required for fiscal metrology, then…
Unfortunately, when the capillary type diluter is fully assembled, the capillaries are no longer accessible individually: we know that have been selected to be “almost equal” (if they were truly equal the relative accuracy of the diluter would be 0.0%). It remains only Possible to measure the groups of capillaries, returning to the situation of the targets drawn on the left and repeatability is no longer sufficient, but the a good accuracy is required.
Apart from our internal audits, aim at detecting any assembling macroscopic errors, at this point it is necessary the performance of a laboratory accredited for flow measurements. This laboratory has to perform flow measurements simultaneously on one input and the output, by applying a balanced pressure on both inputs. The test is repeated setting different dilutions and the dilution factor is calculated as flows ratio and compared with the set factor.
In fact, the laboratory do not need to try all dilution factors, but just the “main factors”, which correspond to fixed groups of capillaries: all other dilution factors do use in different combinations the same groups and then their errors can be calculated on the basis of the fundamental errors measured.
Since the flow deviations at the level of the main groups are known, composing which all the dilutions are produced, it is possible to calculate the dilution error for the dilution in progress: this error is easily canceled by “pointing” to a dilution to which adds the reverse error.