Math Equation I Need Help With

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hafmpty

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OK. So, I'm trying to figure out the water:grain ratio in my stainless BIAB basket when it is installed in my kettle. There is space OUTSIDE the basket and space inside the basket. The basket will obviously have grain AND wort, while the space outside the basket will only be wort.

Basically what I'm trying to figure out is an easy(ish) way to calculate the water:grain ratio INSIDE the BIAB basket, NOT the total water:grain ratio in the entire pot. Is there a way to figure this out? And if so, is there an Excel calculation I can write where I supply certain numbers (i.e. amount of grain, water, etc.).

I want this because if possible, I'd like to target a particular water:grain ratio in the basket for the mash and then at the end of the mash add the remaining water (if any) to get my full volume before removing the basket.

How can I figure this out?

The BIAB Basket is shaped like a D (see picture). Here are the measurements:

BIAB Basket Height - 13"
BIAB Basket Diameter - 11"
BIAB Basket Segment Depth - 9"
Total Space Available - ≈4.68gal according to this calculator:
http://www.mathopenref.com/cylindervolpartial.html

The Brew Pot is a 7.5gal Blichmann Boilermaker G2. It's internal dimensions are:

Pot Height - 14.75"
Pot Diameter - 12.3"
According to Blichmann when this pot is full to the brim there is ≈7.4gal of space available.

There is a "step" at the bottom that reduces the diameter to 9.25". This step is ≈5/8" tall.

If it helps, when I have the BIAB basket installed there is ≈.4375gal of water underneath the basket (i.e. Foundation Water).

Make sense? If not...I can supply other measurements/numbers/info/explanations/etc.

BIAB Basket Profile-01.png
 
Does the basket move up and down at all, like does it float on the water as you add water into the pot?

Assuming the answer to the above is a no, and the basket height is fixed, then I think you would just need the height of the water in the pot, from the bottom of the basket. Then plug that height into your segment calculator you linked to get the volume of water.

Does that help?
 
Does the basket move up and down at all, like does it float on the water as you add water into the pot?

No, the basket doesn't move up and down. It's stainless mesh welded to a stainless frame.

As for "does that help" well...sort of. Can you use my example below to see if I'm thinking about this correctly?

I'm going to be brewing a 3gal batch that will start with ≈5.35gal of water in the kettle. This is the amount I need to have a starting boil volume of 4.6gal factoring a 12% grain absorption volume (.75gal).

There will be 6lbs 3oz of grain. Using the assumed grain volume displacement of .11gal per pound (some use .08gal per pound)...this means that the grain will displace .68gal of space.

With this grain bill, I would need to have 3.09gal of water in the BIAB basket to get the targeted 2qts/lb. This means the water and grain will take up 3.77gal of space in the BIAB basket. Using the calculator, I figured that I would need the basket filled to 10.45" inches. Adding the height of the foundation space (1.125"), I would need the kettle to be filled to about 11.575".

So...is this correct? And is there a way to make this an easy calculation via Excel?
 
I would say most definitely you can make it easy. But I'm still not quite sure exactly what you want.

According to here: http://www.mathopenref.com/segmentareaht.html
The area of a circle segment is:
Equation-1.gif


And volume is just that * length of the segment.

So are you just trying to solve for h?

Edit: this mathopenref website formula images don't seem to display well for me (as in, they're blank), even when I post them here. Same for you or can you see it?
 
I'll be happy to work this out for you. I'm uncertain on the dimensions of the BIAB basket.

Is it D shaped for the full height of the basket? You say that it is 11" in diameter and 13" high but with a segment depth of 9". Does that mean it is only D shaped for 9"?

I usually solve problems like this with autocad, it's a simple problem.
 
Is your segment diagram of the top view of the basket? I was assuming it was oriented like the picture in the mathopenref link you posted. If so, that makes it a lot simpler I think.
 
I think I understand what you are trying to do, but IMHO I think you are missing a key fact. The enzymes in the mash dont care about the water/grist ratio in the basket vs. in the kettle. They will move throughout the liquid in the entire kettle. Although most BIAB brewers don't always care as much about water/grist ratios as non-BIAB guys, since you do just use the kettle volume for strike water volume calculation purposes. The basket doesn't absorb anything, so it can be ignored. After the mash, add your "sparge" or top up liquor.

My apologies if I totally missed the mark here.:confused:
 
A more fundamental question than the basket volume, is why are you concerned with hitting a particular water to grain ratio? Why not just do a full volume mash?

Brew on :mug:
 
Anybody got any links to good reading on water/grist ratios and why they matter or what they affect?
 
Is it D shaped for the full height of the basket?

Yes it is. 13" tall with that segment "missing" for the entire height.

Is your segment diagram of the top view of the basket?

Yes. It is the top view.

quick'n'dirty spreadsheet.

Awesome! Thanks. This helps me see how I’m doing on my own spreadsheet. I’m on the right track. But I seem to be missing something. Don’t know if it’s me or what. I think I’m confusing the amount of space that will be taken up in the basket with grain & water together with just water needed to get me to a particular water:grain ratio. In my spreadsheet, the amount of space the grain displaces is not factored into the amount of water needed in the basket. Am I thinking about this right?

The enzymes in the mash dont care about the water/grist ratio in the basket vs. in the kettle.

You are correct and I know that. I’m just curious to see how “thick” my mash is going to be in the basket. The thicker the mash, the more difficult it will be for the enzymes to make their way through the grain during recirculation…right? Plus, I’m just curious. :)

A more fundamental question than the basket volume, is why are you concerned with hitting a particular water to grain ratio? Why not just do a full volume mash?

I will 99% of the time, but I’m also interested in some of these figures. Helps me think of experimentation, consistency, etc.
 
Anybody got any links to good reading on water/grist ratios and why they matter or what they affect?

#RTFP

http://amniconbrewing.tumblr.com/post/94488735099/rtfp

I'd like this to become one of the homebrewing acronyms alongside RDWHAHB.

All kidding aside, check out the Brewing Network's show "Brew Strong." They've done a few shows on the mash and talk about this very topic. Really helpful information.

In addition, check the relevant sections in John Palmer's book How To Brew.
 
If you are thinking of experimenting with water/grain ratios, you really don't want to do that in a setup like yours. The concentrations will not be anywhere near uniform throughout the mash vessel, so you won't be able to draw any valid conclusions about the effects of the ratios.

Brew on :mug:
 
If you are thinking of experimenting with water/grain ratios, you really don't want to do that in a setup like yours. The concentrations will not be anywhere near uniform throughout the mash vessel, so you won't be able to draw any valid conclusions about the effects of the ratios.

Brew on :mug:

You're right. I was thinking more in terms of duplicating batches. Brewing a beer with a higher water:grain ratio, meaning the water will flow through the grain a bit better, with the end result being that I remove some of the wort to get the proper pre-boil volume. That...versus mashing "thicker" but having the proper amount of wort.

That's the kind of thing I'm thinking. There's also, as I mentioned before, a part that is just curious to know what I'm working. It's a number which means it's a factor and a factor I want to understand. To be able to do that first requires me to be able to figure it out...which I'm struggling with...thus asking for help. :)
 
#RTFP

http://amniconbrewing.tumblr.com/post/94488735099/rtfp

I'd like this to become one of the homebrewing acronyms alongside RDWHAHB.

All kidding aside, check out the Brewing Network's show "Brew Strong." They've done a few shows on the mash and talk about this very topic. Really helpful information.

In addition, check the relevant sections in John Palmer's book How To Brew.
Palmer seems to be focused primarily on fly sparge process brewing, and what is appropriate when fly sparging can be sub-optimal when batch sparging or or full volume (no sparge) mashing. Water to grain ratio is one item where what is best for fly sparging is not applicable to the other methods. Kai Troester has shown that higher water to grain ratios lead to better mash efficiency with batch or no sparge than the lower ratios used with fly sparging.

Brew on :mug:
 
Kai Troester has shown that higher water to grain ratios lead to better mash efficiency with batch or no sparge than the lower ratios used with fly sparging.

Maybe we should add #RTFT to the acronyms too. :)

Great article. I read that a while back. It's helpful for me to remember this...especially as I'm working with these numbers and water:grain ratios that will be pretty high at times with BIAB brewing.

BTW...I've got most of my BIAB brewing equipment purchased/made. I made the transition from 10gal 3V brewing to 2.5gal 1V BIAB brewing because of back issues. I really enjoy running numbers and messing with things so there is definitely part of that curiosity that is driving this.

Anyway...not to be dissuaded, I'm still going to be working on this. I'm a "visual" learner, so I'm drawing pictures (in my mind and on paper) seeing how this all works. Keep the info coming as you figure it out. I appreciate everyone's thoughts and input.
 
You're right. I was thinking more in terms of duplicating batches. Brewing a beer with a higher water:grain ratio, meaning the water will flow through the grain a bit better, with the end result being that I remove some of the wort to get the proper pre-boil volume. That...versus mashing "thicker" but having the proper amount of wort.

That's the kind of thing I'm thinking. There's also, as I mentioned before, a part that is just curious to know what I'm working. It's a number which means it's a factor and a factor I want to understand. To be able to do that first requires me to be able to figure it out...which I'm struggling with...thus asking for help. :)

I can see where you might have a case that using the full volume of water for mashing would lead to not having enough volume to cover all of the grain in the basket, which would lead to mash inefficiencies, and poor batch to batch consistency when that happened. So, you do need to know if the water will be sufficient to cover the grain, and for that you need to know the volume of the submerged part of the basket.

If the optimal amount of water would leave some of the grain above the water/wort level, then the best solution would be to target a higher pre-boil volume, with higher boil off, so that you can get all the grain submerged.

Brew on :mug:
 
I can see where you might have a case that using the full volume of water for mashing would lead to not having enough volume to cover all of the grain in the basket, which would lead to mash inefficiencies, and poor batch to batch consistency when that happened. So, you do need to know if the water will be sufficient to cover the grain, and for that you need to know the volume of the submerged part of the basket.

That was originally what got me thinking along these lines. Basically wondering, what's the biggest beer I can brew with my kettle and basket and still get decent efficiencies, consistency, etc. That took me to this whole discussion.
 
Could I get a mod to put an end to this? You're ruining the hobby bros, math hurts muh head! :p;):p
 
Now, I may be wrong, but wouldn't it be easier to figure out the volume of water that the basket displaces then subtract that from your total water volume?
Also, since the basket is mesh (I assume), wouldn't the water:grain ratio of the total kettle be more important? I mean, any water around the basket should equalize with whatever water is in direct contact with the grain.
Right?
 
i'm not sure when exactly the book Brewing Better Beer by Gordon Strong was written, but he seems to be concerned with any deadspace in the mash tun when it concerns water:grist ratio. i guess if you're recirculating, that should help push the enzymes and starches around. But still, as the OP stated, the thicker the water:grist ratio in the basket, the harder it will be for these to come in contact with each other.

in other words, i just don't understand when people give the advice: "why even worry about it?" if it's a problem with a solution, why can't we just help the guy like he's asking?

also, you do know that you two don't have to click on a thread whose title is "Math equation i need help with," right? you two should be flagged for unnecessary comments in a technical thread:

Could I get a mod to put an end to this? You're ruining the hobby bros, math hurts muh head! :p;):p

I think this thread needs a warning. Something like this........... (Yes, I know the word 'explode' is misspelled, but it's still funny...)
 
I don't know if I understood your question correctly but the D shape as you've described it has an area of 83.23 square inches.

at 13 inches tall that gives a volume of 1081.99 cubic inches. Google tells me that a gallon of water at room temp takes up 231 cubic inches.

I don't know if any of this helps.
 
I don't know if I understood your question correctly but the D shape as you've described it has an area of 83.23 square inches.

at 13 inches tall that gives a volume of 1081.99 cubic inches. Google tells me that a gallon of water at room temp takes up 231 cubic inches.

I don't know if any of this helps.

Thanks. Yeah, I've got that so far. I'm still working through the rest of the numbers.
 
Thanks. Yeah, I've got that so far. I'm still working through the rest of the numbers.

Ok, using the generally accepted grain displacement of 0.08 gal/lb, the volume (water + grain) of a mash at a water to grain ratio of R qt/lb is:
Mash_volume [gal] = ((R qt/lb / 4qt/gal) + 0.08 gal/lb) * Grain_weight [lb]
Mash_Volume [cu-in] = Mash_Volume [gal] * 231 cu-in/gal
"Mash"_Water = (R [qt/lb] / 4 [qt/gal]) * Grain_Weight [lb]​
Now we calculate the height the mash will occupy in the basket as:
Mash_Height [in] = Mash_Volume [cu-in] / 83.23 [sq-in]​
So, the total height of water in the vessel (to cover the grain in the basket) needs to be at least:
Min_Fill_Height [in] = Mash_Height [in] + Distance_Vessel_Bottom_to_Basket_Bottom [in]​
The total volume in the vessel will then be:
Total_Volume [cu-in] = Min_Fill_Height [in] * Pi * (Vessel_Diameter [in] / 2)^2
Total_Volume [gal] = Total_Volume [cu-in] / 231 cu-in/gal​
The "excess" water to fill the space around the basket will then be:
"Fill"_Water [gal] = Total_Volume [gal] - Mash_Volume [gal]​
And the total strike water volume will be:
Strike_Volume [gal] = "Mash"_Water [gal] + "Fill"_Water [gal]​
Does this give you what you are looking for?

Brew on :mug:
 
Last edited:
Does this give you what you are looking for

I think, if I'm tracking with you, that I'm on the right track with my calculations. I used .11gal per pound of grain in my spreadsheet. If I change that to .08, here's what I come up with:

If I want an 8lb grain bill to have a 1.5qt/lb water:grain ratio, I would need to mash in with 4.99 gallons of water.

If I went with a full volume mash w/ 5.56 gallons of water, I would end up with a 1.7qt/lb water:grain ratio.

Thoughts? Issues? Calculation errors?
 
This sheet is read only, and the formulas are not visible. Tried downloading a copy to see if that would give me an editable version, but no joy.

Brew on :mug:

I signed out of Google and used the following link and was able to edit. Try again?

https://docs.google.com/spreadsheets/d/1N0d1kfsOG1mqZJlX6w3mun6XjqITVXWJdQjfp6YXVSI/edit?usp=sharing

Sorry for the hassle. I'm not super familiar with Google Docs. If you PM me your email address, I'll send you my Excel file.
 
I signed out of Google and used the following link and was able to edit. Try again?

https://docs.google.com/spreadsheets/d/1N0d1kfsOG1mqZJlX6w3mun6XjqITVXWJdQjfp6YXVSI/edit?usp=sharing

Sorry for the hassle. I'm not super familiar with Google Docs. If you PM me your email address, I'll send you my Excel file.

Ok, I got a copy where I can see the formulas and make edits. I'm having some trouble following your calculation logic.

How did you determine that there is 0.4375 gal of foundational water below the basket? Is that the volume with the kettle filled to a depth of 1.125"?

Brew on :mug:
 
Then when done, measure it to check the math?

A plastic liner inside the screen, and add measured (1 or 2 gal)water to the bag part, then measure water down the outside of the bag till it hits the same level. Add another gallon to the bag, and repeat measuring how much down the outside. Then you will have a nice chart!

I'm not sure I would fill the bag without filling the outside as you go, a gallon or so at a time, due to the forces that would create on the screen. I'd remove the plastic before trying to remove the basket also!
 
How did you determine that there is 0.4375 gal of foundational water below the basket? Is that the volume with the kettle filled to a depth of 1.125"?

Yeah, that is a measured amount. I filled the pot until it was at the level of the bottom of the basket, just before it started coming up through the bottom mesh.
 
If the question to be answered is: Given a grain bill weight, target pre-boil volume, grain absorption/lb, basket dimensions, and basket position constraints, then what is the apparent water to grain ratio within the basket? Then I would proceed as follows:
  1. Calculate total water required to reach pre-boil target
    Total_Water [gal] = Pre-Boil_Volume [gal] + Grain_Absorption [gal/lb] * Grain_Weight [lb]​
  2. Calculate total mash volume
    Mash_Volume [gal] = Total_Water [gal] + Grain_Specific_Displacement [gal/lb] * Grain_Weight [lb]​
  3. Calculate depth of mash in kettle
    Kettle_Depth [in] = (Mash_Volume [gal] - Found_Volume [gal]) * 231 [cu in/gal] / Kettle_Area [sq in] + Found_Depth [in]​
  4. Calculate depth of mash in basket
    Basket_Depth [in] = Kettle_Depth [in] - Found_Depth [in]​
  5. Calculate volume of mash in basket (equals depth in basket times basket area)
    Basket_Volume [gal] = Basket_Depth [in] * Basket_Area [sq in] / 231 [cu in/gal]​
  6. Calculate volume of water in basket
    Basket_Water [gal] = Basket_Vol [gal] - Grain_Specific_Displacement [gal/lb] * Grain_Weight [lb]​
  7. Calculate apparent water to grain ratio in basket
    Ratio [qt/lb] = Basket_Water [gal] * 4 [qt/gal] / Grain_Weight [lb]​
Brew on :mug:
 
I still don't understand all the gyrations you go thru in your spreadsheet, but the answers appear solid. I programmed a spreadsheet with my method outlined above, and the answers match yours.

Basket BIAB Calculations.png

Brew on :mug:
 
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