### Author Topic: Algebraic solution for sugar syrup p/p/g numbers?  (Read 9203 times)

#### nateo

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##### Algebraic solution for sugar syrup p/p/g numbers?
« on: June 09, 2012, 01:22:56 PM »
Math isn't exactly my strong suit. Based on a figure of 1.046 for 1 lb of sugar in 1 gallon of water, I should be able to figure out what concentration of sugar it would take to hit some arbitrary gravity, right? The weight of the water is confusing me. Also, the English units are confusing me.

Sugar = 46 pts per 1lb per 1 gal
Water = 0 pts per 1lb per 1 gal

Let's say I want a syrup solution that has 32ppg, starting with sucrose that has 46ppg. How would I figure that out to express it in % sugar concentration, so I can use a candy-making chart that gives sugar concentration for a given temperature?

Or would it be easier to do this in *Bx, where

1.032 = 8*Bx = 8g sucrose per 100g H2O

1 gallon of H2O = 8.33lbs = 3778g

3778g / 100g = 37.78

37.78*8g sucrose = 302g sucrose

302g sucrose / 454g =  66% sucrose?

Is that right? 66% seems like too low of a concentration.
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#### brushvalleybrewer

• Assistant Brewer
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• Centre Hall, PA
##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #1 on: June 09, 2012, 03:37:40 PM »
I believe you want 32/46 of a pound of sugar. I believe that would give you 1.032 SG, or 8.5 Brix (8.05 Plato).

One pound of sugar gives you 46 points per gallon (technically, that's a gallon of solution of sugar and water, which will actually require slightly less than a gallon of water, but since we're worried about how much sugar we need, let's ignore that for now). That means each 1/46 of a pound of sugar gives you 1 point per gallon. If you want 32 points, you need 32 times 1/46 of a pound of sugar, or 32/46 of a pound. That's 11.13 ounces.

To make such a solution, you would dissolve the sugar in something less than a gallon (say a half-gallon, for arguments sake). Then you would add water until the volume of the solution equals a gallon. If you start with a gallon of water, you will have a little left over when you are done.
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#### nateo

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• Denver, CO
##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #2 on: June 09, 2012, 03:50:05 PM »
Oh man, I should've mentioned my syrups have been ending up around 1 pint of volume, give or take. I'm trying to figure out what concentration of sugar in a pint, give or take some, would make 1.032 ppg.

I always start with 500g of sugar and 500ml of H2O, but I never end up with the same volume when I'm done, so when I go to brew I can't figure the sugar additions by weight. Since candy temp corresponds to a certain sugar concentration, roughly, I'm trying to figure out where I need to stop heating my syrup to hit a specific ppg figure.
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#### brushvalleybrewer

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #3 on: June 09, 2012, 05:39:46 PM »
Clue me, nateo... Are you making candy, like in Belgian Candy Sugar, or like in peppermint candy, or are you trying to make an invert syrup for an English ale? Not that it matters, you are just confusing me with the talk about sugar temperature.

If you only want a pint, follow the instructions above, then put it into a gallon jug and pour out a pint. Put the rest in the fridge until you need to brew again.
In a humble log cabin off an unregarded back road, somewhere, deep in the heart of Pennsylvania’s hill country, we find our intrepid hero — the Brush Valley Brewer.

#### nateo

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #4 on: June 09, 2012, 06:12:31 PM »
It's a candy syrup, like Belgian candi syrup. The whole sugar volume (a pound, give or take) ends up reducing to about a pint's worth of volume. I want to be able to dispense it by weight, but the amount of water left over in it varies, which changes the ppg number significantly, so I can't accurately predict gravity contribution when going by weight.
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#### tubercle

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #5 on: June 09, 2012, 06:37:11 PM »
A pint's a pound the world around - Alton Brown.

There is a difference in adding pound of sugar in a gallon of water and a pound of sugar & water that makes a total of 1 gallon like brushvalleybrewer pointed out. Understand the difference. Sigar has volume.
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#### nateo

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #6 on: June 09, 2012, 07:24:37 PM »
A pint's a pound the world around - Alton Brown.

There is a difference in adding pound of sugar in a gallon of water and a pound of sugar & water that makes a total of 1 gallon like brushvalleybrewer pointed out. Understand the difference. Sigar has volume.

OK, I know that, but how do I use that to solve my problem?
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#### brushvalleybrewer

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #7 on: June 10, 2012, 05:25:05 AM »

500g is a bit more than 1 pound.

500 mL is a bit more than a pint.

That's going to be way more than 1.032 SG.

I think that will be something more like 1.368 SG (95.2 Brix). Logic: 8 pints per gallon. 46 points per pound per gallon. 46*8=368 points per point per pint.

Are you looking for a 95% sugar solution? Is that the problem you are trying to solve?

Sorry if I'm being dense.
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#### nateo

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #8 on: June 10, 2012, 06:25:21 AM »
DME = 44 points per pound per gallon.
Lyle's Golden Syrup = 36 points per pound per gallon

It doesn't matter if you use a pound or an ounce, the ppg number is constant. If you dissolved a pound of DME in, say, a pint, you would also get a very high gravity number.

Since I can't measure volume easily while I'm cooking the syrup, but I can measure temp, I was hoping to come up with a percent sugar solution that would correspond to a ppg figure, like, whatever concentration Lyle's is at would be fine.

It's just a pain to try to measure the volume while it's cooking, and then dissolve some in water and measure with a hydrometer once it's done.
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#### narvin

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #9 on: June 10, 2012, 07:06:54 AM »
Can you post this temperature -> sugar concentration chart?  It seems doubtful to me that this would be accurate at lower temperatures since you're making a syrup, not rock candy, but I guess it's worth a shot.
Thanks

#### nateo

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##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #10 on: June 10, 2012, 07:13:28 AM »
Can you post this temperature -> sugar concentration chart?  It seems doubtful to me that this would be accurate at lower temperatures since you're making a syrup, not rock candy, but I guess it's worth a shot.

I've not seen a chart for low temps. I know that H2O has a 0% concentration of sugar. If I can figure out some concentration for what the sugar should be, working backwards from 80% or 85% or whatever my syrup is at, based on temp, I should be able to figure out how much water I'd need to add, based on the weight of the syrup, to hit a given concentration.
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#### nateo

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• Denver, CO
##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #11 on: June 13, 2012, 10:01:47 AM »
I'm wondering if I'm thinking about this too hard. With a known quantity of sugar going into the syrup, I wonder if I could just do a simple dilution calculation to figure out the ppg figure.

I'm thinking something like [(points)*(sugar weight) + (points)*(water weight)] / (total weight)

So if I start with 500g sugar, and the end syrup weighs 750g, that'd be

(46 points)*(500g) + 0 points*250g / 750g = 30.6 points/pound/gallon
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#### morticaixavier

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• Underhill VT
##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #12 on: June 13, 2012, 12:58:45 PM »
I'm wondering if I'm thinking about this too hard. With a known quantity of sugar going into the syrup, I wonder if I could just do a simple dilution calculation to figure out the ppg figure.

I'm thinking something like [(points)*(sugar weight) + (points)*(water weight)] / (total weight)

So if I start with 500g sugar, and the end syrup weighs 750g, that'd be

(46 points)*(500g) + 0 points*250g / 750g = 30.6 points/pound/gallon

^ This. The sugar in the pint is the same as the sugar in your starting solution. The total points in that pint are the same as that in your original 500ml + of solution.

A pint's a pound the world around - Alton Brown.

as much as I love alton brown gotta call foul on this statement, and the attribution. I have no idea who said that originaly but it tweren't AB. also a pint of sugar syrup is not a pound. at 1.046 a pint is 1.046 pounds. a pint of honey weighs in at like 1.5 lbs. you can actually use this to determine gravity of a solution if you have acurate volume measurments and weight measurments.

(Pardon the spelling, I do not have integrated spell check at work  )
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#### Slowbrew

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• Posts: 2320
• The Slowly Losing IT Brewery in Urbandale, IA
##### Re: Algebraic solution for sugar syrup p/p/g numbers?
« Reply #13 on: June 13, 2012, 01:14:39 PM »
I'm wondering if I'm thinking about this too hard. With a known quantity of sugar going into the syrup, I wonder if I could just do a simple dilution calculation to figure out the ppg figure.

I'm thinking something like [(points)*(sugar weight) + (points)*(water weight)] / (total weight)

So if I start with 500g sugar, and the end syrup weighs 750g, that'd be

(46 points)*(500g) + 0 points*250g / 750g = 30.6 points/pound/gallon

^ This. The sugar in the pint is the same as the sugar in your starting solution. The total points in that pint are the same as that in your original 500ml + of solution.

A pint's a pound the world around - Alton Brown.

as much as I love alton brown gotta call foul on this statement, and the attribution. I have no idea who said that originaly but it tweren't AB. also a pint of sugar syrup is not a pound. at 1.046 a pint is 1.046 pounds. a pint of honey weighs in at like 1.5 lbs. you can actually use this to determine gravity of a solution if you have acurate volume measurments and weight measurments.

(Pardon the spelling, I do not have integrated spell check at work  )

My understanding of "a pint is a pound the world around" was that it was an American memory tool.  One pint in America is 16 fluid oz and 1 pound American is 16 dry oz.  Those are 2 different units of measure and are not equal but people can generally remember that one pound is 16 oz. so 1 pint is too.  The phrase wasn't meant to indicate they were equal, just that they were the same number.

None of this should be confused with the English pint though which is 20 fl. oz.

Just one of the many reason the metric system makes so much more sense.

Paul
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#### brushvalleybrewer

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• Centre Hall, PA
##### Algebraic solution for sugar syrup p/p/g numbers?
« Reply #14 on: June 13, 2012, 01:55:50 PM »
My understanding of "a pint is a pound the world around" was that it was an American memory tool.

It is also useful for relative magnitude. Rounding to one significant figure, a gallon of water weighs 8 pounds. A pint is 1/8 of a gallon, which would make a pint of water weigh a pound (to one significant figure).

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In a humble log cabin off an unregarded back road, somewhere, deep in the heart of Pennsylvania’s hill country, we find our intrepid hero — the Brush Valley Brewer.