Estimating %alcohol

I have found 3 ways of estimating the final alcohol percentage in alcoholic beverages. 

I:
The first is just based on the concentration of sugar added to the must. I have used the calculations for recipe 1. The calculations can be seen below.

Honey	7.50	kg
Sugar content	85%
Sugar	6.38	kg
Convesion factor	17.0	g/L/%
Total volume	20.0	L
Theoretical ABV	18.8	%
Actual ABV	15.5	%
Residual sugar	1.11	kg
Concentration of residual sugar	55.3	g/L

The sugar content of the honey is estimated so far since I do not have a refractometer. When I get hold of one I will be able to measure the water content in % by mass. The sugar content will then be calculated at 100%-%water.

All the parameters can easily be measured or calculated except one - the conversion factor. This is an experimental factor that can only be set from experience. The number 17 g/L/% has been found by searching the internet. It means that for 1 % of alcohol by volume (ABV) to be produced on 1 L of must, then 17 g of sugar is needed. 

There are some reasoning behind this figure, though. The classical equation for conversion of sugar to alcohol is

C6H12O6     ->    2 CH3CH2OH   +   2 CO2

  Glucose                     Ethanol            Carbondioxide

  (sugar)                      (alcohol)     

i.e. 1 mol of sugar becomes 2 mols of ethanol. The molar mass of glucose is 180 g/mol and the molar mass of ethanol is 46 g/mol. Hence for every 180 g of glucose, 2*46=92 g of ethanol is produced. Put in another ways the mass yield is 92g/180g*100% = 51% 

Now, 1% of ethanol by volume can be converted to mass by multiplying with the density 0.79 g/ml which becomes 7.9g ethanol / L of must. If the conversion yield was 51% then the sugar needed would be 7,9g/0.51 = 15.5 g sugar / L of must. 

Well, yeast also need energy for multiplying and life processes to perform the conversion, so the use of sugar needed will be higher. The literature that I have found so far states figures from 17 g sugar/L up to 19 g sugar/L. I have chosen to start with 17 g/L and adjust later when I have measured the ethanol content.

ABV after ended fermentation depends on the alcohol tolerance of yeast or the time when the fermentation is stopped by for example addition of sulfite. I selected the port yeast because of the higher tolerance and I have no intentions of stopping the fermentation :o)

I also calculate the residual sugar. Wines have somewhere between 1-3% sugar left (10-30 g/L). I want my mead to be a bit sweet, so I figured about 50 g sugar / L would suffice. 

II:

Once you get started preparing the mead the density can be measured with a hydrometer. The density (or gravity) is measured relatively to water and is therefore without unit. The typical scales are Oechsle, Baume, or Brix. I prefer hydrometers where the density is measured in Oechsle since it is pretty much the same as relative density.

When the must is ready for yeast addition, the density is measured with a hydrometer. The relative density is typically defined at 20C but the yeast is added at 25C, so the density is typicaly a bit higher than what is actually measured initially. SG is the term used for the density or "Specific Gravity" at any time point. The initial measurement before the yeast is added is called Original Gravity or OG. Afterwards SG can be measured at any time to follow the fermentation. When fermentation stops, either naturally as when the alcohol tolerance of the yeast is reached or when sulfite is added the measured gravity is called Final Gravity or FG. The difference between the starting point and the ending point (OG-FG) is a measure of how much sugar have been converted.

To estimate the ABV I use the simplest estimate where ABV and (OG-FG) behave linearly, i.e. one can be converted to the other my multiplying a constant. The constant that I have found is based on beer so it might not be quite adequate, but it is a best estimate so far. The constant I use is 1/0.0075 so the calculation becomes

ABV = (OG-FG) / 0.0075

If I can get access to measure the alcohol content very precisely for example by gas chromatography, I will adjust the constant to match the OG-FG measurement.In that manner I can estimate ABV more precisely though only for a narrow range of high OG musts.

III:
I found a so called advanced calculation to calculate ABV. It looks like this

ABV =(76.08 * (og-fg) / (1.775-og)) * (fg / 0.794)

The relation between (OG-FG) and ABV is no longer linear, and ABV depends on both OG and (OG-FG).
If OG is fixed at various levels, ABV can be plotted against (OG-FG)

All lines goes through (0.0) and they are all ALMOST linear, so the difference between each line can be estimated by the slope. This is the exact same slope that is used in the constant of the simplified expression above (which is actually 1/slope).

If we put OG in a table against the respective slope and convert it into constant used above, we get the following

OG	1.14	1.12	1.1	1.08	1.06
slope	157.40	149.66	144.53	139.71	135.16
Constant	0.00635	0.00668	0.00692	0.00716	0.00740
Selected	0.0065

As it can be seen from the table above the lower OG (starting density) is, the closer the constant get to 0.0075 as used above. Since most meads that I will produce are probably in the OG range of 1.12 to 1.14, a constant of 0.0065 is more adequate to use as a general constant. 

Hmm, if this is so, the alcohol tolerance level will be reached much earlier than expected and I will end up with a very sweet mead. I am quite curious to know how different the constant will be compared to one used so far (0.0075). More on that later if I get to measure the actual alcohol content.