## Saturday, February 9, 2013

### Refractometer summary of equations

Over the past couple of weeks I've done a bit of work with refractometers and how to best utilize them.  Here is a collection of tables and formulas that have been useful to me, and hopefully will be useful to you.

OGR = original gravity in Brix (eg 9)
CGR = current gravity reading in Brix (eg 9)
OGH = Original gravity as measured with a hydrometer (eq 1.036)
CGH = Final gravity as measured with a hydrometer (eq 1.004)
S%W = Sugar percentage by weight (eg 4 would indicate 4%)
ABV = Alcohol by volume as a percentage (eg 4 would indicate 4%)

Alcohol by volume based on current refractometer measurement and original refractometer measurement
ABV =0.6967*(OGR-CGR) (extrapolated from physical model)

Sugar by weight based on current refractometer measurement and original refractometer measurement
S%W =1.128*CGR-0.128*OGR (extrapolated from physical model)

Alcohol by volume based on current refractometer measurement and current hydrometer measurement
ABV =1.421*FGR-357.4*FGH+357.4 (based on physical model)

Sugar by weight based on current refractometer measurement and current hydrometer measurement
S%W =0.7488CGR+68.55*CGH-68.60 (extrapolated from physical model)

Original Gravity based on current refractometer measurement and current hydrometer measurement
OGH =-1.728*FGH+0.01085*FGR + 2.728 (extrapolated from physical model)

Specific gravity based on current refractometer measurement and original hydrometer measurement
SGH =0.00628*CGR-0.0025*OGR+1.0013 (based on physical model)

Equations that are "based on a physical model" are algebraically derived from other equations.  These include the Balling Observation that 2.0665g of sucrose are required to created 1g of Ethanol.  They also use some basic analytical chemistry to convert from various units.

Equations labeled as "extrapolated from a physical model" are derived from the physical models as describe above.  Instead of listing complicated equations that are algebraically correct these equations are simplified linear fits to the physical equations.  In most brewing applications these should be just as accurate as their algebraic equivalents.  When compared to the physical model these linear fit equations were accurate to two decimal places, or 0.01%.

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