Is Brix linear?

[OneLegJohn]

I have 11.7 gallons of syrup at 72 brix. How much 61.6 brix syrup to I need to mix in to get to 66.5 brix? Is there an online calculator out there?

[maple marc]

OneLeg,

The easiest way to solve a problem like this is by allegation, using a Pearson's square. If you have a copy of the North American Maple Producers Manual (second edition), see page 300. Here is a link with another example:

http://maple.dnr.cornell.edu/pubs/confections/Confection%20Notebook%20section2.pdf

See page 17

Using this method, you need 13.13 gallons of the light syrup.

Math is amazing! Have fun.

Marc

[Beweller]

Brix is weight percent sugar (or sugar equivalent). The calculation is linear if use WEIGHTS of syrup.

Do a sugar balance. You will find you need a huge quantity of the 66.1 percent syrup. After all, a kg of 66.1 syrup is short only 6.9 grams of sugar to become 66.5 percent syrup.

66.1% 1.3230 sg
66.5% 1.3254 sg
72.0% 1.3598 sg

[Beweller]

Oops! I interchanged two digits. Sorry, not quite so much 61.6% required.

[Beweller]

Back again, with the correct concentrations. I find you need 13.58 gallons of the 61.6% syrup.

The non-linear affect is not large for this case.