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Thread: Rule of 86: Where does the 86 come from?

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  1. #1
    bob_day Guest

    Default Rule of 86: Where does the 86 come from?

    I've surfed all over the Internet to try to find out where the 86 in the "Rule of 86" comes from. Jones' formula seems to be ever quoted but never derived or explained, other than how to apply it. A curious mind wants to know! Does anyone here know how Jones came up with the 86?

    -- Bob Day

  2. #2
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    Bob,

    If you have the latest edition of "The Bible", page 141 explains it.

    Hope this helps.
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    I't did not make any sence to me also. I would think that if maple syrup is 66%-67% sugar (I think) that would be the number you would use to figure how much sap to make a gallon of syrup. If you took something that is 66% sugar and divided 86 by it you get 1.3, so it would take 1.3 gallons of syrup to make a gollan of syrup? I'm lost!!!
    Matt

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  4. #4
    bob_day Guest

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    Unfortunately, I don't have a copy of "The Bible", and the libraries near my area don't either. Could someone who has it possibly post the details of how the 86 is arrived at?

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    Here's a copy I think first edition on ebay. The starting price might be a little high though. Check around, you can get a second edition for close to the same money.

    http://cgi.ebay.com/NORTH-AMERICAN-M...QQcmdZViewItem

    Jim
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    It's an imperical relationship that is a valid approximation of gallons of sap vs syrup for sap % within a certain range. It is not a formula but is a "rule of thumb".
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    Default rule of 86?

    Bob,

    Yep. Your syrup has a specific gravity of 1.3610. Putting your numbers into my equations,

    67.09*1.3610/1.006 = 90.76,

    for 2 percent sap, 90.05 for 4 percent sap.

    Just a little difference, probably because we used a different sap specific gravity, and some uncertainty about the reference temperatures (mine was 20 C, 68 F).

    Considering what the rule is used for, it doesn't make a lot of difference whether we use 86 or 90.

    My point was to explain that the rule comes from the fact that sugar is conserved during evaporation.

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    I like to just use the 86 devided by the sap sugar % and accept it blindly as close enough for computing the gal of sap needed to make each gal of syrup. Some things facinate me to run the numbers but this is not one of them.
    Dave Klish, I recently ordered a 2x6 wood fired evaporator from A&A Sheet Metal which I will be converting to oil fired
    Now have solar, 2x6 finish pan, 5 bank 7x7 filter press, large water jacketed bottler, and tankless water heater.
    Recently bought another Gingerich RO, this one was a 125, but a second membrane was added thus is a 250, like I had.
    After running a 2x3, a 2x6, 3x8 tapping from 79 taps up to 1320 all woodfired, now I'm going to a 2x6 oil fired and a 200-425 taps.

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    Default Rule of 86

    If we want to make syrup containing, say, 100 grams of sugar, we must start with sap containing 100 grams of sugar. The sugar contant per 100 ml of liquid is the product of specific gravity, d, and concentration, weight percent, d*c. For a volume v, ml, total sugar is v*d*c.

    Equating the sugar in the sap with the sugar in the syrup, the ratio of the volume of sap to the volume of syrup is

    ratio = (d*c)syrup/(d*c)sap.

    The ratio holds true for any volume unit, ml, gal, bbl, etc.

    The specific gravity of sap is near 1.0, and for 66 wt percent syrup the specific gravity (68 F) is 1.3224. Thus,

    ratio = (66*1.3224/1.0000)/c = 87.3/c.

    If we chose 4 percent sap as our base line, d= 1.0139, we get

    ratio = 86.1/c,

    the "rule of 86". The exact number will depend on the terperatures and the center sap concentration used.

  10. #10
    bob_day Guest

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    Quote Originally Posted by Beweller View Post
    If we want to make syrup containing, say, 100 grams of sugar, we must start with sap containing 100 grams of sugar. The sugar contant per 100 ml of liquid is the product of specific gravity, d, and concentration, weight percent, d*c. For a volume v, ml, total sugar is v*d*c.

    Equating the sugar in the sap with the sugar in the syrup, the ratio of the volume of sap to the volume of syrup is

    ratio = (d*c)syrup/(d*c)sap.

    The ratio holds true for any volume unit, ml, gal, bbl, etc.

    The specific gravity of sap is near 1.0, and for 66 wt percent syrup the specific gravity (68 F) is 1.3224. Thus,

    ratio = (66*1.3224/1.0000)/c = 87.3/c.

    If we chose 4 percent sap as our base line, d= 1.0139, we get

    ratio = 86.1/c,

    the "rule of 86". The exact number will depend on the terperatures and the center sap concentration used.
    Your equations are true enough, but your calculation doesn't seem to account for the interdependency of density and sugar concentration when it came to the maple sap. But lets begin at the beginning and make 1 liter of syrup from sap containing 1 percent sugar:

    According to the USDA National Nutrient Database for Standard Reference, one gallon of maple syrup weighs 5152 grams, or 11.358 lbs, and is 67.090 brix. In standard terminology, that's 67.090 percent sugar by weight (some other carbohydrates are included in that, but "sugar" is the standard term to encompass all of the carbohydrates).

    From those numbers, one gallon of maple syrup contains 5152 * 0.6709 = 3456.5 grams of sugar. Since one gallon is 3.7854 liters, one liter of maple syrup weighs 5152/3.7854 = 1361.02 grams and contains 3456.5/3.7854 = 913.114 grams of sugar.

    Now lets figure out how many liters of one percent maple sap contain 913.114 grams of sugar. Or, in other words, how much water do we need to add to one liter of maple syrup so that the resulting mixture of syrup and water will be one percent sugar? (First, we need to know the weight of a liter of water, and Wikipedia says that's 998.21 grams at 68 degrees F.)

    Letting Lw represent the number of liters of water we need to add, we set 913.114 [grams of sugar] =
    0.01 [percent] * (1361.02 + Lw*998.21) [the weight of the solution]

    Solving this equation for Lw, we get:

    Lw = (913.114/0.01 - 1361.02)/998.21, or

    Lw = 90.112

    So, to make one percent maple sap from one liter of syrup, we need to add 90.112 liters of water. That means, the number of liters of sap we have is 91.112 liters.

    In other words, we have to boil down 91.112 liters of one percent maple sap to make one liter of maple syrup.

    Now lets figure it out for other sap percentages, P. Also, since it will make little difference for low sap concentrations, we can approximate the weight of a liter of maple syrup with the weight of a liter of water. Our equation becomes:

    913.114 = 0.01P * (Lw + 1)*998.21

    So, letting Ls represent the number of liters of sap we need
    to boil down,

    Ls = Lw + 1 = 91.48/P.

    Notes:

    1. If we start with different numbers for the weight and the
    brix of a liter of maple syrup and the temperature of the
    water we add, we will of course arrive at slightly different
    results -- but the difference won't be much for modern syrup.

    2. According to Gary in a previous post in this thread, the
    '86' in the rule of 86 is outdated, and was based on 65.5
    brix syrup, not on the 66 - 67 brix syrups of today.
    Last edited by bob_day; 09-09-2008 at 12:24 PM. Reason: to fix format

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