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On Gravimetric Measurements of Total Dissolved Solids
07 May, 2021
On Gravimetric Measurements of Total Dissolved Solids

#### by Jonathan Gagne

A while ago, I read an interesting idea from Robert Mckeon Aloe on Matt Perger's Telegram channel about measuring the total dissolved solids of a live espresso shot with the Decent DE1 machine, by comparing the output gravimetric flow measurements with a bluetooth-connected Acaia scale, to the input flow above the puck at the shower screen as predicted by the DE1. I think this is a really good idea in principle, but when I read this I immediately expressed worries that I didn’t think it could be done accurately yet because of the systematic inaccuracies with which the DE1 currently estimates flow rate.

The idea is simple; the flow rate at the shower screen tells you what volume of water is incoming per unit time, and the Acaia scale measures how much total mass is falling into the cup per unit time. The key here is that this total mass is not only made up of water, but it also includes dissolved chemicals (what we usually refer to as total dissolved solids, or TDS), oils, dissolved CO2 and undissolved solids in suspension. Using the well-known mass density of water, one can calculate how much of that total weight is made up of water, subtract that and obtain the weight per unit time of everything else. This is not exactly a live measurement of TDS, because of all the other stuff in there, but it might very well be a good tracker of TDS if the dissolved solids make up most of the non-water mass.

Basically, Ray Heasman at Decent uses a purely empirical and very complicated model that takes the voltage of the DE1's vibratory pumps as an input, and predicts how this relates to the flow of water at the shower screen. This is quite crazy, because the answer depends on so many factors, and changing a single tube in the machine can throw off these predictions. Even worse, the answer is different when the pressure changes, and the properties of the user's electrical grid can also affect this. Somehow, Ray managed to pull this off by gathering enough data and building a predictive model that works reasonably well within typical espresso settings. I think that this is quite a feat, and it shows how much real geekery is going on under the hood of this fantastic machine.

Because the flow model depends on so many parameters, it is not rare to see the flow rate being off by 10-20% on the DE1. Therefore, I thought we could not reconstruct something useful and repeatable in terms of a live TDS curve during a shot that is based on the difference in output weight minus input flow of water. Worse, the measurements provided by the Acaia scale are very noisy, especially when estimating the change of weight per unit time. After a shot is done, it is possible to smooth the gravimetric data to make a useful comparison, but doing so live in an accurate way would be extremely hard (although probably not impossible). Readers could be tempted to also worry about the Acaia readings lagging behind (as I was), but because water is incompressible at 9 bar, the should be no lag in terms of the flow measured at the bottom of the espresso basket and that at the top of it, and the only sources of lag that remain are (1) the freefall of the fluid (about 0.136 seconds for a 91 mm fall in my case) and (2) any lag in the Bluetooth data transfer to the DE1, which I suspect is also not too significant.

Things would get much worse if one would attempt predicting the average extraction yield by summing up the TDS curve at every moment in time, because the inaccuracies would pile up, resulting in a very large measurement error. After having this discussion with Robert, I kind of forgot about the idea, maybe a bit too fast.

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