What is the formula for calculating how much sugar sugar syrup contains?

[ugcheleuce]

Hello everyone

If I feed the bees 1 litre of sugar syrup from a jerry can of sugar syrup that was made with 1 litre of water plus 1 kilogram of sugar, how much sugar did I feed the bees with that 1 litre of sugar syrup? Surely not 1 kilogram... since 1 litre of water plus 1 kilogram of sugar does not equal 1 litre of sugar syrup (assuming the sugar is all actually dissolved and not simply floating about in the syrup).

What is the formula for calculating this?

For example, today I fed my bees 3 litres of sugar syrup that was made from 2.5 kilograms of sugar per one litre of water. I would like to know how many kilograms of sugar did I feed the bees today.

Thanks
Samuel

==
Added: Googling gets me this handy spreadsheet based on this handy list of calculations, but it refers only to so-called 65% syrup, and I have no idea what that is.

 

[ugcheleuce]

Okay, to answer my own question, if I understand correctly (and please correct me if I'm wrong), it works like this:

You need to find out what the brix degree value of your sugar syrup is. Then you use a brix look-up table to find out how much sugar the syrup has.

The brix degree value is the percentage of sugar (by weight) that is mixed into a solution (by weight). If you add 2.5 kg of sugar to 1 kg of water, the total weight would be 3.5 kg. So, 2.5/3.5*100 = 71.4% (or: 71.4 degrees brix).

Here and here are some brix look-up tables for gallons (presumably US) and pounds. I could not find a brix look-up table for kilograms and litres.

Google says "1 pound per US gallon = 119.826427 grams per liter", and the USDA look-up table says that my 71.4% solution has 8.074 pounds of sugar per US gallon, so that means that my solution has 0.9 kg of sugar per litre. That seems rather little...

 

[Erichalfbee]

Far too complicated for me....
Are you planning to feed more?
If you are make up another 2.5 Kg in 1 litre. Note the volume. Relate that to the 3 litres you need information on. Arithmetic much easier that way

 

[ugcheleuce]

If you are make up another 2.5 Kg in 1 litre. Note the volume. Relate that to the 3 litres you need information on. Arithmetic much easier that way...

Easy in hindsight. Not if you already have the finished syrup.

 

[ugcheleuce]

What is the formula for calculating this?

The formula is rather complex because it involves constants from a look-up table, but here is a pre-calculated table of common values:

kg sugar...l water...% sugar in syrup...kg/l sugar in syrup
1..........4.........20.................0,22
1..........3.........25.................0,28
2..........5.........28,6...............0,32
1..........2.........33,3...............0,38
3..........5.........37,5...............0,44
2..........3.........40.................0,47
3..........4.........42,9...............0,51
4..........5.........44,4...............0,53
2,5........3.........45,5...............0,55
1..........1.........50.................0,62
2,5........2.........55,6...............0,70
4..........3.........57,1...............0,73
3..........2.........60.................0,78
5..........3.........62,5...............0,81
2..........1.........66,7...............0,89
2,5........1.........71,4...............0,97
3..........1.........75.................1,03
4..........1.........80.................1,13
5..........1.........83,3 ...the tables don't go that high

Assuming that brix equals percentage weight of sugar of weight of sugar plus water, assuming USDA brix look-up table, and assuming 1 pound per US gallon = 0.12 kilograms per litre

 

[user 6228]

you use this

http://www.brewersfriend.com/brix-converter/

 

[REDWOOD]

Try This
Sorry unable to upload file

 

[ugcheleuce]

You use this:
http://www.brewersfriend.com/brix-converter/

The specific gravity given by that converter is roughly the same as the USDA table gives. However, the converter only gives volume of sugar per volume, and not weight of sugar per volume. Beekeeping books tell you to feed X kg of sugar per hive, not X litre of sugar.

 

[Luka22]

If I understood your question right, then I had the same one a few weeks ago. I was wondering that if the bees need up to 20kg of Stores for winter, how many kg of sugar do I need to feed/buy.

So I looked again at an article in the BBKA from last year about winterfeeding.

First of all it was about 2:1 for winter, which is meant for 2lb sugar to 1 pint water. Since sugar is sold in kg bags I wanted to know what it meant for kg/l. The article then explained how to calculate this into kg/l. (2 kg sugar dissolved in 1.25 litres of water to get a 61.5% concentration)

At the end of the article it stated the following:

Now to calculate the amount of syrup to offer. In approximate terms, 10 kg of sugar made into heavy syrup gives a volume of about 25 litres and weighs about 16 kg, providing 15kg of stores and being equivalent to 12 kg of honey (16 lbs of sugar made into heavy syrup gives about 23–24 lbs of stores and is equivalent to 20 lbs of honey).

I tried it out myself and realised that 2kg of sugar actually made 2.5l of syrup which meant that 10kg of sugar makes 12.5l of syrup and not 25l as the article states. Just recently I then found a table which shows x kg of sugar in x l of water results in x kg of stores(theoretically) and x kg of stores realistically. For example it shows that 10kg of sugar in 6.7 l of water, makes 12.7 l of syrup and gives 12 kg of stores theoretically and 9.6 kg of stores realistically.

And that was the answer I was looking for. I hope it helps you.

Here the website for the BBKA article:
http://www.wirralbeekeepers.co.uk/page42/

 

[ugcheleuce]

At the end of the article it stated the following:
10 kg of sugar ... [provides] 15kg of stores

Interesting that they distinguish between sugar and "stores". In my region the mass of feed necessary for winter is not given as kilograms of stores as stored in the cells but as kilograms of sugar as fed in the feeder. So when local beeks tell me to feed "15 kg", they mean "15 kg of cane sugar", not "15 kg of the stuff that bees seal up in the cells". I should actually query that...

I tried it out myself and realised that 2kg of sugar actually made 2.5l of syrup which meant that 10kg of sugar makes 12.5l of syrup and not 25l as the article states.

Thanks, yes, the table that I printed above agrees with it: the value for 61.5% is not states in the table but one can guess it will be about 800 g of sugar per litre of syrup, so 2.5 litres of syrup will contain [2.5 x 800g] = 2kg of sugar.

 

[Erichalfbee]

Easy in hindsight. Not if you already have the finished syrup.

Easy enough to make up just the small amount of 2.5kg in 1 litre.
If you don't need it add some thymol and store in fridge then you can keep it till spring feed not forgetting to reduce the concentration to 1:1

 

[Luka22]

Easy enough to make up just the small amount of 2.5kg in 1 litre.

Or as my table says. 3 kg sugar in 2 l water which will provide 2.9 kg of stores.

And yes, it is confusing when they talk about stores and sugar, if you don't know how much sugar makes x kg of stores, but to be fair, nobody could say how much kg of sugar your bees will need, because they don't know how much food they have stored already. So to say 20kg of stores would be needed is the only way. You then check the weight of your hive and you know how much kg is still needed for the 20kg and from there you can see how much syrup/sugar you will have to provide.

 

[ugcheleuce]

You then check the weight of your hive and...

I'm afraid I can't do the weighey thing... I don't have a scale, and my hives are all of different designs (and so of different weights). And... I use a top feeder, so unless the feeder is empty, the scale will weigh the remaining syrup as well.

 

[ugcheleuce]

Easy enough to make up just the small amount of 2.5kg in 1 litre. ... If you don't need it, add some thymol and store in fridge...

Huh, what? No, you mean, if the bees don't need it... then I'll just use it to sweeten my coffee.

 

[thebeeman]

Thick 2lb sugar to 1 pint of water gives 61.5% sugar concentration
Thin 1lb sugar to 2 pints of water gives 28% sugar concentration

 

[user 6228]

i 've had a look at those tables they show the specific gravity and the relationship to brix.

they dont give a Kg/L because that is the definition of specific gravity.What was your problem again?

 

[user 6228]

Okay, to answer my own question, if I understand correctly (and please correct me if I'm wrong), it works like this:

You need to find out what the brix degree value of your sugar syrup is. Then you use a brix look-up table to find out how much sugar the syrup has.

The brix degree value is the percentage of sugar (by weight) that is mixed into a solution (by weight). If you add 2.5 kg of sugar to 1 kg of water, the total weight would be 3.5 kg. So, 2.5/3.5*100 = 71.4% (or: 71.4 degrees brix).

Here and here are some brix look-up tables for gallons (presumably US) and pounds. I could not find a brix look-up table for kilograms and litres.

Google says "1 pound per US gallon = 119.826427 grams per liter", and the USDA look-up table says that my 71.4% solution has 8.074 pounds of sugar per US gallon, so that means that my solution has 0.9 kg of sugar per litre. That seems rather little...

the weight of sugar per litre of solution is brix*density(brix)

question how much sugar in 2L of 71.4% solution by weight?
71.4 brix in your table corresponds to 1.36 kg/L density

2litres of 71.4 brix therefore weighs 2*1.36 kg

weight of sugar in 2L = 0.714*2*1.36 kg

 

[ugcheleuce]

I've had a look at those tables they show the specific gravity and the relationship to brix.

Yes. The USDA file also has a column named "pounds solids per gallon", which I interpreted to mean "pounds of sugar per gallon of syrup". Is that correct?

They dont give a kg/L because that is the definition of specific gravity.

If that was the definition of "specific gravity", then I would thank you for giving me a simple, easy to understand definition of it. Most of these sites don't actually define it. Wikipedia says:

Specific gravity is the ratio of the density of a substance to the density (mass of the same unit volume) of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for liquids or air for gases.

Interestingly, if Wikipedia is to be believed, the word "apparent" in the term "apparent specific gravity" does not simply mean "it is believed" but has an actual, distinct scientific meaning. Then, the USDA table gives apparent specific gravity (ASG), and not specific gravity (SG). I assume that that is what you mean when you say "that is the definition of specific gravity".

However, ASG can't be kg/l. The ASG of water without any sugar in it is 1.0, which is not the same as "1.0 kg of sugar per litre of syrup".

Could you please clarify your comments on the relationship between specific gravity and kg-sugar/litre-syrup? And/or could you tell me if you think my interpretation of the column "pounds solids per gallon" actually means "pounds of sugar per gallon of syrup"?

 

[ugcheleuce]

The weight of sugar per litre of solution is brix*density(brix)

I'm trying to believe you but it seems odd that it would be so, since that would mean that there are different "densities" for litres and gallons and for pounds and kilograms, and isn't "density" a ratio?

Also, neither of the tables linked to in my post list a column for "density". Both have a column named "weight/gallon in air" but that doesn't seem to be the "density" that you're referring to because no multiplying of columns with each other yields the value in the last column.

Where do you get density from?

 

[user 6228]

I'm trying to believe you but it seems odd that it would be so, since that would mean that there are different "densities" for litres and gallons and for pounds and kilograms, and isn't "density" a ratio?

Also, neither of the tables linked to in my post list a column for "density". Both have a column named "weight/gallon in air" but that doesn't seem to be the "density" that you're referring to because no multiplying of columns with each other yields the value in the last column.

Where do you get density from?

density(x)=sg(x)*density(water)

density(water) ~ 1kg/litre

adjustments need to be made for temperature and pressure , which we can ignore for this sort of purpose

difference between ASG and SG is the boyancy difference between air and vacuum during measurement. We dont need great accuracy and the SG is relatively close to 1 i.e 1.3, therefore we can ignore this

(from wikipedia) Since the density of dry air at 1013.25 mb at 20 °C is 0.001205 g·cm−3 and that of water is 0.998203 g·cm−3 the difference between true and apparent specific gravities for a substance with specific gravity (20°C/20°C) of about 1.100 would be 0.000120. Where the specific gravity of the sample is close to that of water (for example dilute ethanol solutions) the correction is even smaller.

From the table converting from lb / gallon we get 0.967 kg/L
From the SG using density of water as 1Kg/L ignoring all corrections we get 0.971 kg/L
which is a difference of 0.4%
Close enough