gravity calculations

[bringitonhome]

Does anyone know how to express the ratio of gravity to gallons of water as an equation, so they can be manipulated?
For example, if my efficiency is low, I'd rather boil down more to hit my target gravity than hit my target volume.

Since specific gravity already is a ratio, it's throwing me off.

This is a scenario came up with from the brew i did this weekend:
if my target OG is 1.035 for 5 gallons, I need to extract 35x5=175 "points" of sugar.
if my boil volume was 7 gallons, i would expect 175/7 = 25, or 1.025 BG.
My BG came out to be 1.021, so I had only extracted 21x7=147 points.
Therefore, in order to hit the target OG, I would have to boil down to 147/35=4.2 gal.

Is this correct?

Incidentally, I didn't take this into account, and just did my normal boil and ended up with ~5 gal @ 1.030

 

[Ecnerwal]

Congratulations!

You have a lower-alcohol beer brewing, and your math skills are working. Don't you wish your math teacher had told you THIS was what you'd need it for? Would they get fired for doing so in today's climate?

If you kept some on hand for these occasions, you could also add DME to bring the pre-boil gravity up to spec.

 

[menschmaschine]

It looks like your efficiency was lower than you expected.

Not that this will help you now, but I believe the equation you're looking for is:
C1V1=C2V2

C = Concentration, V = Volume. "Concentration" can be anything including SG (last two digits), IBUs, ABV, etc.

 

[Ecnerwal]

In the particular form you wanted,

C1V1=C2V2

solves to

V1=C2V2/C1

Where 1 is post-boil and 2 is pre-boil. But you had worked that out in practice yourself.

 

[wildwest450]

Don't you wish your math teacher had told you THIS was what you'd need it for? Would they get fired for doing so in today's climate?

Screw the math teacher and buy yourself some brewing software, making beer is supposed to be fun not a freaking math problem.

 

[A4J]

Screw the math teacher and buy yourself some brewing software, making beer is supposed to be fun not a freaking math problem.

LOLLERS!! Thank god for Brewsmith cuz I brew on my days off and I hate having to think on my days off.

 

[BrewWhat]

I use beersmith.
I don't like math, it will figure my effiency and a whole bunch more for me. It was good enough that I downloaded the 30 day free trial version and ended up paying the $21.50 for the full access version. It's also cool that it has access to 350+ recipes as add-ons.

 

[billtzk]

You seem to be aware that total gravity doesn't change regardless of whether you dilute or boil down. If you are low on your starting gravity pre-boil, you can manipulate the fermentables rather than the volume to hit your target. That would be my preference over producing less beer in this situation. (More beer = good, less beer = bad, IMO.) You could add DME or LME before you boil in order to hit your final volume at your intended gravity.

Using your example, you wanted 175 points but only got 147 so you need to add enough DME to make up 175 - 147 = 28 points. Points are also called gravity units.

(Total Gravity (target) - Total Gravity (pre-boil)) / extract per pound per gallon = extract lbs

DME has a potential of 1.045 per pound per gallon, or 45 Gravity Units per pound.

(175 GU - 147 GU) / 45 GU per lb = .62 lb

So adding about 10 ounces of DME prior to boil would let you hit both target OG and volume.

If you ended up with more points than you need pre-boil to hit your intended volume and OG, you could just tolerate a higher than intended volume of beer (good IMO), or you could throw away some of your wort prior to the boil (bad IMO).