Math Question

[SmellsLikeSyrupNH]

Does anyone know the formula to help figure out how much water has to be removed to get to a certain sugar % ?

Example:
If I have 200 gallons of 2% sap. How much water do I need to remove for it to get to 6%?

My brain is hurting today and I cant seem to figure that one out.

Thanks!

[DrTimPerkins]

https://mapleresearch.org/pub/m1013jonesruleof86/

[SmellsLikeSyrupNH]

Thanks Dr. Tim! I have the Rule of 86 down, or 87.1, but im not seeing where I get the formula I am looking for. Maybe I am just missing it...???

[wobbletop]

It's not linear. I don't know the formula.

200g @ 2%
100g @ 4%
50g @ 8%

so, 75g @ 6%

You'd need to remove (200-75) 125g of water to get to 6%.

[berkshires]

At low percentages like this the math is pretty simple (as long as you don't need an exact number). You want three times the sugar, so you need one third the volume. That means you want to arrive at 67 gallons. 200 - 67 = 133. So you need to boil off 133 gallons.

The reason why this is not exact is that you actually want to boil off 2/3 of the water. And your sap is only 98% water (by weight). To figure it out precisely you need to be able to convert back and forth between the weight of the components water, sugar) and the volume of the total with those two components combined

If you wanted to do the exercise, you would have to:

1 - determine the weight of each of your starting products
- the water in your 2% sap
- the sugar in your 2% sap

That in and of itself is not trivial.

2 - This step is easy - determine the weight of the final products.
- the water in your 6% processed sap
- the sugar in your 6% processed sap
This is simple algebra

You get these by taking the weight of the sugar (found in step 1) and assuming that it's 6% of the total weight. So if:
sugar weight + water weight = total weight
To get water weight, solve for N:
.06 X + N = X
N = 16.67 X

In other words, you want 16.67 times the weight of water in your processed sap as you you have sugar.

3 - This step is tricky: Combine the above weight of water and sugar (from step 2) and tell me the volume. That will be the number of gallons you want to wind up with.

4 - This step is trivial: Subtract your starting gallons with your final gallons, and that's how much water you have to get rid of.

The problem is that steps 1 and 3 involve converting between weights and volumes for sugar in solution, and this is not simply math, it involves knowing the physical properties of the two.

Dr Tim's lookup, presumably knows those properties and does that for you.

Cheers,

GO

[SmellsLikeSyrupNH]

WOW!!!

Thanks for that detailed response. I wasnt thinking of it in those terms. Really was just looking to get the data for my RO just so I could grasp it in my head. I really appreciate you taking the time to do all of this work in the message.

-Scott




At low percentages like this the math is pretty simple (as long as you don't need an exact number). You want three times the sugar, so you need one third the volume. That means you want to arrive at 67 gallons. 200 - 67 = 133. So you need to boil off 133 gallons.

The reason why this is not exact is that you actually want to boil off 2/3 of the water. And your sap is only 98% water (by weight). To figure it out precisely you need to be able to convert back and forth between the weight of the components water, sugar) and the volume of the total with those two components combined

If you wanted to do the exercise, you would have to:

1 - determine the weight of each of your starting products
- the water in your 2% sap
- the sugar in your 2% sap

That in and of itself is not trivial.

2 - This step is easy - determine the weight of the final products.
- the water in your 6% processed sap
- the sugar in your 6% processed sap
This is simple algebra

You get these by taking the weight of the sugar (found in step 1) and assuming that it's 6% of the total weight. So if:
sugar weight + water weight = total weight
To get water weight, solve for N:
.06 X + N = X
N = 16.67 X

In other words, you want 16.67 times the weight of water in your processed sap as you you have sugar.

3 - This step is tricky: Combine the above weight of water and sugar (from step 2) and tell me the volume. That will be the number of gallons you want to wind up with.

4 - This step is trivial: Subtract your starting gallons with your final gallons, and that's how much water you have to get rid of.

The problem is that steps 1 and 3 involve converting between weights and volumes for sugar in solution, and this is not simply math, it involves knowing the physical properties of the two.

Dr Tim's lookup, presumably knows those properties and does that for you.

Cheers,

GO

[TapTapTap]

Uhg! My head hurts from studying this. I think its because the sugars are soluble in water and behave by different rules than I'm used to. I expected this to work like the relationships in construction materials like soil, cement grout, and concrete where we can analyze their water to solids relationship with what's called a phase diagram. Using the phase diagram and knowing the specific densities of the solids (and of course water) allows you to figure out any mass-volume relationship of mixtures. I'm figuring out that's not the case with sugar dissolved in water.

[SmellsLikeSyrupNH]

LOL my wife has her Masters in Engineering and she worked it out last night, it made my head hurt too!!

[TapTapTap]

LOL my wife has her Masters in Engineering and she worked it out last night, it made my head hurt too!!

Your wife has all my respect. I've got the same credentials except that I'm apparently not able to extend my engineering skills to sap and sugars. Once you figure out sap and sugar then I guess you go from masters in engineering to a master engineer! Sadly, I'm not there yet.

[maple flats]

I work it a little differently. If I start with 100 gal of sap at 2% and remove some water I then in my head, which seems close enough, figure if I remove 50 gal of water I have 4% concentrate, if I remove 75 gal of water I have about 8% so in my mind if I remove about 62.5 gal of permeate I would then have about 6% concentrate (half way between the 50 gal and the 75 gal. removed). That should get you ver close, being exact only really matters when you finish off the syrup for the proper sugar % in the syrup according to your state. While NYS only requires 66% sugar, I produce mine to 66.9% because for quality I want to match Vermont's standards.

[berkshires]

Re-reading my post, I realized that for step two I had the question right but the answer wrong. Here's what it should have said:


2 - This step is easy - determine the weight of the final products.
- the water in your 6% processed sap
- the sugar in your 6% processed sap
This is simple algebra

So how do we get these?

We already know the weight of the sugar - it has not changed. We can calculate the total weight based off that because we know the sugar is 6% of the total.
S = .06(T)
T = 16.67(S)

So now we have the sugar weight and the total weight, but we still need the water weight.
We know that the total weight is simply the sugar weight plus the water weight:
T = S + W
W = T - S

Substituting our formula above, we get
W = 16.67(S) - S
W = 15.67(S)

So multiply our starting weight of sugar (from step 1) by 15.67 and you have the final weight of water.