Rule of 86: Where does the 86 come from?

[bob_day]

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

[Gary R]

Bob,

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

Hope this helps.

[Grade "A"]

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!!!

[bob_day]

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?

[Father & Son]

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-Maple-Syrup-Producers-Manual-Ohio-State_W0QQitemZ270257130506QQihZ017QQcategoryZ378Q QssPageNameZWDVWQQrdZ1QQcmdZViewItem

Jim

[ennismaple]

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".

[Gary R]

Bob, sorry I didn't just type this out earlier. I bought the bible directly from Ohio State. It is a wounderful book that answer's many questions.


The rule of 86 is outdated. It came about when the standard brix of syrup was 65.5 brix. It is calculated by dividing the weight of sugar in a gallon of 65.5 brix syrup (7.2115 pounds) by the weight of sugar in a gallon of 1 percent sap (0.0836 pounds) The answer is 86.26 gallons of 1% sap needed.

Sorry, I don't know how many pounds of sugar are in a gallon of 66.7 brix syrup.

Happy sugar'n

[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.

[ennismaple]

Sorry, I don't know how many pounds of sugar are in a gallon of 66.7 brix syrup.

Happy sugar'n

1 USG = 11.33 lbs

I generally get around 8lbs of granulated sugar from a gallon of syrup.

[Beweller]

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.

[bob_day]

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.

[Beweller]

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.

[maple flats]

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.

[OGDENS SUGAR BUSH]

I am with you MAPLE FLATS

RICH

[KenWP]

Okay guys I need some help. I bought a sap hydrometer today at the local CO OP and did not even think about the fact the directions come in french only. Do I have to use a column of sap greater then the length of the hydrometer to test the sap. Any help wit this would be appreciated greatly. I have no problem with the graph that came with it to calibrate it due to the temprature of the sap being tested. Numbers are the same in both languages.

[dano2840]

you need enough liquid to make it float, a 2 inch tube 6" high will work

[Gary R]

Ken, The numbers might look the same but the scale, F vs. C is different;) Do you have a short or long stem hyd.? Short might fit in a 6" tube, but a long needs almost a whole 5gal. bucket full to float. You'd probably need about a 16" tube for the long one.

[KenWP]

Thanks it is a long one I figure since its probbably 10 inches from the bottom to where the number one is on the grid. Now to use it I have to find 5 gallons of sap or a real skinney bucket.

[Thompson's Tree Farm]

Ken,
When I was a kid, my dad soldered 2 tin cans together to make a cup. Just cut both ends out of one of them and soldered it to the top of the other. They were a kinda long skinny can...might have to use 3 shorter ones.

[KenWP]

Now that makes sense. I have lots of small cans in the shop for my bolt bins.

[maplwrks]

If you testing sap---Drop the hydrometer into a bucket of sap to check?

[jtthibodeau]

Ken,
When I was a kid, my dad soldered 2 tin cans together to make a cup. Just cut both ends out of one of them and soldered it to the top of the other. They were a kinda long skinny can...might have to use 3 shorter ones.

Great idea from your Dad, TTF. I was trying to think which can would work best. All I could think of was 2 or 3 tomato paste cans. Then it can to me. I believe the sauce can from a Chef Boy-r-dee pizza mix is just about the right size in diameter and the length may be ok for a short hydrometer. With my luck, their probably made with paper or plastic now.

[ennismaple]

We use a SS thermos - works great and easy to clean!

[buxtonboiler]

I just did the same thing, bought the hydrometer without a cup. I made a cup out of 1.25 inch copper pipe. I made the pipe 2 inches longer than the meter and soldered (lead free) a copper end cap on it. I also used a 12 inche piece of .25 inch copper tube soldered on for a handle. Works Great.

[3% Solution]

buxtonboiler,
You is the man, didn't really want to buy a large cup like that just for puts'n around a couple of times during the year.
I think a piece of PVC pipe would do the trick too!!
Thanks for getting the wheels turning!!!!

Dave

[maple flats]

Good idea, but experience tells me you would be better off if you had a piece of 1.5 or better 2" copper. This is because of how quickly the syrup cools even with pre heating. I didn't realize how fast it cooled until I got a cup with a thermometer mounted in the side. This is important because the results are only accurate if the temp is right. My cup with a thermometer came with a chart to read the reasults bassed on the actual temperature. Look up accucup from The Maple Guys.

[maple flats]

Or the pvc would be better because it insulates to hold temp longer.

[3% Solution]

maple flats,
Was looking to check small amounts of sap.
If I don't have a 5 gallon bucket full I can't check it.
Was interested how much sweeter it is coming out of the EEU.

Dave

[maplesyrupstove]

sap tester 1 1/4 PVC pipe x 13" long with a flange on the bottom.syrup tester stainless steel 2"x8 1/2" long with 3/16 handle.The syrup tester was heavy and hard to hold,so I made one more.SS 1 1/2" x8 1/2" with 1/2" handle and the wife likes it.Big handle is easier to hold. Darrell

[BackwoodsBill]

Great idea from your Dad, TTF. I was trying to think which can would work best. All I could think of was 2 or 3 tomato paste cans. Then it can to me. I believe the sauce can from a Chef Boy-r-dee pizza mix is just about the right size in diameter and the length may be ok for a short hydrometer. With my luck, their probably made with paper or plastic now.

try asparagus cans the tall kind that the whole stalk asparagus comes in 2 of those stacked should be plenty
Bill!

[3% Solution]

Hey guys,
Made an 1-1/2" pvc cup for checking sap.
Had the pipe, just needed the cap.
Sets on the shelf nicely.
The only things is the glue and cleaner in the bottom, but that little bit of sap can be tossed.
I think it's going to work!!!
Let cha know!!

Dave

[KenWP]

If you used PVC and primer its safe once it driesand is washed out the first time.

[3% Solution]

KW,
I washed it out twice and once let the bleach and water set in it for a while too.
It still has a strong glue and cleaner smell to it.