The equation requires 4 inputs. The padlock button on the right selects which parameter will be calculated. Extracted percentage = (Beverage * TDS) / Dry Coffee. The preset buttons at the top allow starting points and suggested parameter inputs for that brew type. Best viewed in Desktop mode.
This is a server side script run on cheap hosting so the response to the front end can be slow and laggy as it has to run the calculations and generate an SVG.
This calculation proposes and implements a modified absorption coefficient of coffee retained in puck / water retained in puck. Traditionally liquid retention ratio (LRR) has been calculated by dividing the dry mass of coffee by the water retained in the grounds/puck/slurry. Using this traditional LRR makes it difficult to reverse calculate the coffee retained in the puck and will also lead to any calulcation for a gross sum of inputs using LRR as a mulitiplier to be incorrect. Of 10 brews using 2 coffees from Origin, modified absorption values ranged between 2.4 and 2.8 with a mean of aproximately 2.6 and this has been used as a suggested starting absorption value for filter coffee. It should be noted that the modified absorption calculation will increase and decrease alongside extraction percentage as the higher the extraction percentage, the less dry coffee there is remaning to absorb water and retained water / dry coffee (or whats left of it) = modified absorption coefficient.
This chart uses volume of water at the temperature inputted to calculate extraction. The Speciality Coffee Association (SCA) use volume of water. The calculations for water volume are visible beneath in the greyed out area and can be adjusted by temperature. This means that the extraction will be correct for the temperature at which you measure the TDS, most refractomters do not like measuring much warmer than ~25C. SCA numbers are calculcated in volumetric calculation. The problem with volume calculations and any derivative numbers is that they are only applicable at a specific temperature. Extraction percentage calculated by volume at 93C will no longer by accurate by the time its measured at 20C in a refractometer as the volume of the water component of the beverage will have changed by that point. Water volume/mass conversion functions between 1-150C (Kell, George S, Journal of Chemical & Engineering Data 1975, 20, 1, 97-105 (Article) Publication Date (Print):January 1, 1975). If you're interested in the physics of water check out the work of Wojciech Sas who explains water density at pressure and temperature and the implementation of polynomials.
After some exploration it appears that the SCA brewing control chart uses volume as an input and also uses volume for its extraction calculations. That means the volume based scale from the traditional brewing control chart is offset to the side and does not have the same scale as a mass based calculation.
It is possible that a Volume input option will be implemented in future so as to facilitate SCA style calculations. It is reasonable to use volume for the measured assessment of TDS in a refractomter as this is what a refractometer does, checks refraction in a volume of liquid, that is why TDS increases as temperature drops because the mass of liquid is shrinking and the particles in suspension have a different expansion coefficient. With all these factors in mind it is a balance of mass/volume/temperature that allows correct TDS to be calculated. Feel free to contact me if you have any suggestions regarding the implentation of this in a user friendly interface.
Possibly modelling the diffusion of CO2 in water at specific temperatures using Fick's first law.
There is currently no preset for Immersion brews, partly because I don't like them and therefore havn't obtained the necessary experimental data to calculate the aborption coefficient.
There is very little prevention for the entry of out of bounds numbers so you can generate negative brew or coffee values and extract beyond 30%, if you get lost, click a preset to reset the graph.
All formulas used in the generation of this chart and data have been obtained using theoretical and practical tests by the author (with the exception of water mass/volume calculations) and are therefore copyright to the author. Further documentation and explanations will follow. Charts are all in SVG format and can be downloaded.