Take a hundred grams of solution. Its volume is its mass over its density.
The water in it is 100 − °Bx grams, which on its own would occupy its mass
over the density of water. The difference is the volume due to the sugar.
Dividing by the grams of sugar gives the volume per gram, which is the same
number as litres per kilogram.
Nothing is looked up. SG(°Bx) is platoToSg, the ASBC fit this
package uses for every gravity, and ρ_water is the reference density from
corrections.ts. The results (0.6162 at 10 °Bx, 0.6180 at 20, 0.6197 at
30, 0.6215 at 40, 0.6249 at 60) match the figures quoted in the beverage
literature. We derive them so the package can show its working.
It rises with concentration, so it takes an argument
A gram of sugar in a thin solution fits into the spaces between water
molecules. In a heavy syrup there are fewer spaces, so it takes up more
volume. The spread is only 1.4 % across the usable range, so the answer is
always close to 0.62, but computing it at the actual concentration costs
one line and means no number in this file is copied from elsewhere.
Beyond the brewing range
The Plato fit is quoted for 1.000–1.130 SG, and a 60 °Bx syrup is 1.29. It's
still within a few parts per thousand of published sucrose tables, which is
much smaller than the couple of per cent error from assuming volumes add
(see proofAndSweeten).
Litres of volume a kilogram of dissolved sucrose takes up, at a given °Bx.
Take a hundred grams of solution. Its volume is its mass over its density. The water in it is
100 − °Bxgrams, which on its own would occupy its mass over the density of water. The difference is the volume due to the sugar. Dividing by the grams of sugar gives the volume per gram, which is the same number as litres per kilogram.Nothing is looked up.
SG(°Bx)is platoToSg, the ASBC fit this package uses for every gravity, andρ_wateris the reference density fromcorrections.ts. The results (0.6162 at 10 °Bx, 0.6180 at 20, 0.6197 at 30, 0.6215 at 40, 0.6249 at 60) match the figures quoted in the beverage literature. We derive them so the package can show its working.It rises with concentration, so it takes an argument
A gram of sugar in a thin solution fits into the spaces between water molecules. In a heavy syrup there are fewer spaces, so it takes up more volume. The spread is only 1.4 % across the usable range, so the answer is always close to 0.62, but computing it at the actual concentration costs one line and means no number in this file is copied from elsewhere.
Beyond the brewing range
The Plato fit is quoted for 1.000–1.130 SG, and a 60 °Bx syrup is 1.29. It's still within a few parts per thousand of published sucrose tables, which is much smaller than the couple of per cent error from assuming volumes add (see proofAndSweeten).