Back sweetening - The Honey-Oechsle equation

"Three is the magic number" as the saying goes, and that is right for honey too. I always use 7.2 kg of honey for 20L must because I know I will have a gravity of 1.120 or Oechsle value of 120 degrees. The ratio between Oechsle value and honey concentration, which I call the honey factor, is then equal to 0.3333, and hence the inverse of this factor is exactly 3. 

Using this factor, it then becomes very easy to calculate how much honey to use to reach any target Oechsle value.

Now, this factor can also be used when adding fruit juice, by expressing all the sugar content of the juice as honey. This calculation also takes into account the additional volume. In the end the honey factor is eliminated. As the examples show, you can either calculate the new Oechsle value when adding a fixed volume of juice/extract, or you can calculate how much juice/extract you need to reach a target Oechsle value.

Finally you can use the same set-up for calculating how much honey to use for back sweetening. This time you will need the inverse honey factor and the density of the honey. I usually use the value 1.35 g/ml for the density which is used to calculate the volume increase. As before, examples illustrate how you can either calculate the new Oechsle value when adding a fixed mass of honey, or you can calculate how much honey you need to reach a target Oechsle value.
  

These calculations work great in Excel and they are a great help if you, for example, want to add honey to a target Oechsle value and be spot on first time :o)

Limitations

What are the limitations? The equations do not take into account that the gravity is lowered due to the content of alcohol. If all has been converted to ethanol, the density should not be lower than 0.970, i.e. a correction of 3% would be needed. But 3% is likely well within the error of all values going into the equations, and it would not improve your result significantly.

The inverse honey factor are of cause dependent on the water content of the honey. As a mead maker you will of cause be using high quality honey where the water content is only 15-17%, i.e. within a quite narrow range. Hence, this variation in sugar content will also be small.

The biggest contributor to error is, as I see it, the density of honey. I do not have data showing the variations in density in various honeys. Never the less, the density is used to calculate the added volume, and this volume will always be small compared to the volume of the must, i.e. a large error will not influence the new Oechsle value very much.

Mixing volumes might not be exactly equal to the sum of the individual volumes, but again the correction would be smaller than the error of other values.