Rule of 86: Where does the 86 come from?

[bob_day]

Gary, thanks much for your replies. I bought a quart (16 servings) of grade A dark amber maple syrup at a local supermarket the other day, and did some calculations: The syrup + container weighed 1364 grams; the container alone weighed 91g. So the syrup itself weighed 1273g, which means that a gallon of syrup would weigh 11.226 lbs. The Nutrition Facts label gave 53g as the sugar content per 1273/16 = 79.5625g serving. From those figures, the brix value is 53/79.5625 = 66.6 brix, and the weight of sugar in a gallon would be (4 x 16 x 53)/453.59 = 7.4781 lbs. Dividing 7.4781 by your figure of 0.0836 for the weight of sugar in a gallon of one percent sap gives 89.45.

Perhaps the rule should now be the "Rule of 89" !

[bob_day]

I think I've figured it out. The problem is this: We want to know how much we have to boil down sap that contains P percent sugar in order to get standard maple syrup. Equivalently and a little more precisely, how many gallons, Gw, of water do we have to add to one gallon of standard maple syrup to make "sap" that contains P percent sugar?

To begin with, we need some numbers:

From my previous post, a gallon of standard grade A dark amber maple syrup weighs about 11.226 lbs and contains about 7.4781 lbs of sugar.

Also, one gallon of water at 60 degrees F weighs 8.337 lbs.

We want P percent of the total weight of liquid (the sap) we get by adding Gw gallons of water to one gallon of standard syrup to be 7.4781 (the weight of the sugar). So we set:

7.4781 = (P/100) * (11.226 + 8.337Gw)

Solving, we get Gw = 89.70/P - 1.347

Since we're adding the water to one gallon of syrup, the number of gallons of sap, Gsap, we have is Gsap = 89.70/P - 0.347

An easy to remember approximation would be Gsap = 90/P, that is, the number of gallons of sap that contains P percent sugar we have to boil down to produce one gallon of standard maple syrup is about 90/P.