Total Grain Bed Depth

[jimgsp]

Hello,

I am a new to BeerSmith 3.

I would like to calculate the total, maximum grain bed/water depth achieved during a single infusion mash in a specific clyindrical MLT. I know the formulas for calculating the dry grain depth in a cylinder, and the the formula for calculating water volume in a cylinder. The combination of these two numbers are inaccurate due to the depth of dry grain vs. wet grain.

Is there a number in BeerSmith that represents the total, maximum depth of the grain bed/water for a specific recipe in a specific vessel?

Is there a formula for this calculation?

Thanks!

[dtapke]

Is this what you're asking about? (bottom middle "mash volume needed")

[brewfun]

BeerSmith doesn't model grain bed depth. Your grain bed depth will change over the course of a mash.

Are you looking at extraction efficiency and wort velocity? If so, then your initial strike volume, minus absorption, is the effective bed depth.

Volume (V) = (Pi)r²h. So, h = V/((Pi)r².

A gallon takes up 231 sq.in. If you know your absorption rate, subtract that from your strike volume. Also, subtract any foundation water (under the false bottom). Convert your remaining strike water into sq.in.

Calculate your false bottom area in sq.in. Divide the remaining strike water volume by the false bottom area. The result is the height in inches. This is also your column inches for determining wort velocity.

[jimgsp]

  - dtapke
Thanks for the reply. Unfortunately, this is not the volume I am looking for.

 - brewfun
Thanks for the reply. I am looking for an estimated total, maximum depth of wet grain plus 1?-2? of water above the bed. The purpose is that I am designing an immersion coil for heating the mash in a 2 BBL mash/lauter tun. I would like to estimate the maximum height in the tank for a given recipe to give me a range of adjustability in placement of the coil.

I called it an immersion coil for clarity, but it is actually a hydronic coil. I run a small dedicated hot water vessel that feeds the coil inside the mash tun. It works well, but currently I can?t set the optimum location in the tank before mash-in. I am attempting to correct that.

Hope this makes sense.

Thanks.

[dtapke]

Makes sense, sounds interesting.

Although brewfuns calcs sound great, personally I would go off the mash volume needed then drop it the corresponding depth in gallons to what you're looking for. Seeing as you would need measurements in inches/cm of your kettles to allow for the calculations you need to do it within beersmith, and the program doesn't take measurements into account this would be impossible for beersmith to calculate. it seems like it would be pretty easy to estimate based off the volume required number. Say i needed 15.5g of mash tun space, i would drop said "immersion coil" just below the corresponding "gallon" mark in my kettle, adjusting the top of the coil to the 15 gallon mark.

with my kettle i know that .72"=1 gallon, therefore my mash would take up ~11" of space at 15.5G i would set the coil in at 10.75" and call it as close as i could get. Best of luck to you, as brewfun stated, the height of your mash is going to change throughout the brew so I can't imagine ever having it perfectly accurate.

[brewfun]

I am looking for an estimated total, maximum depth of wet grain plus 1?-2? of water above the bed.

When a calculation doesn't help, I'll default to a pretty good rule of thumb.

Generally, the maximum water & grain a mashtun can hold is equal to 70% of the total volume in quarts (above the false bottom).

If you calculate the cylinder volume and divide by 231 the again by the height, you have the gallons contained in each inch.

If your mashtun were 28" wide and a total of 36" high, it would hold about 96 gallons. Using my above RoT, you could cram about 269 lbs in with water.

Your solution is probably to convert the water additions into weight and a corresponding weight per inch of the mashtun.

Let's say that you're using 140 lbs of grain to make a batch. The maximum grain weight (269#) divided by the height (36") is 7.47 lbs/inch. Nevermind that you'll use a false bottom or that you might have deadspace. We only care about the weight per inch, at this point.

If you're a traditional mash thickness guy, then you're using 1.33 quarts water per lb, which is 9.92 quarts per inch. Convert to weight and you have 20.7 lbs per inch. Add the two together and you get 28.17 lbs/inch.

This means that a 140# grist with traditional liquor should stand about 19" above the false bottom. If you're aiming for your coil to float somewhere around halfway, the coil center should be at about 9.5" off the false bottom.

There will be a minor amount of displacement from air, but it will not change the overall depth by much.

As with most pro brewing, staying away from volume measurements and using weight for all liquids leads to more accuracy, no matter what temperature. It also leads to less waste and more profit.

[jimgsp]

Thanks again dtapke & brewfun.

I really appreciated your efforts! Given the detailed information you have provided I am confident that I can find an estimated adjustment for a given total grain weight & water addition. I will work on this over the weekend and give you some feedback.

I have used Brewer?s Friend and BeerTools extensively in the past and recently decided to switch to BeerSmith as I though it would be a better fit for small batch commercial production. I am running (2) BCS-462?s as well; one in the brewery and another in the cellar. If you are interested in our total system design check us out on Facebook. GSP Craft Brewing.

Thanks again for your time & consideration.

[jimgsp]

 - brewfun

I have followed your logic as indicated here:

3.14 x 14? x 14? x 36? = 22,155.84 cu. ins.
22,155.84 / 231 = 95.9127 gallons per cu. in. (231 cu. ins. in a US gallon)
96 x 4 = 384 quarts
384 x .7 (70%) = 268.8 quarts
269 / 36? = 7.47 lbs. per cu. in.
1.33 quarts of water per lb. of grain x 7.47 lbs. per cu. in.= 9.9351 quarts per cu. in.
 
I believe that from the above math 1 cu. in. would contain 9.94 quarts and weigh 7.47 lbs

What I can't quite grasp is how you arrived at the following:

Convert to weight and you have 20.7 lbs per inch

Can you enlighten me?

Thanks!

[brewfun]

I believe that from the above math 1 cu. in. would contain 9.94 quarts and weigh 7.47 lbs
<snip>
What I can't quite grasp is how you arrived at the following:

Convert to weight and you have 20.7 lbs per inch

Can you enlighten me?

Thanks!

Happy to explain! It's a seldom discussed topic. It's how manufacturers determine mashtun size, based on grain depth and extraction requirements. Once the math is done, it's not brought up again! 

A quick, but significant correction: the weight is per linear inch, not cubic. In any cylinder, each linear inch of rise corresponds to both volume and weight.

The 20.7# is the weight of the water per inch, alone. The actual total is 28.17#/in.

You need the sum of water weight plus grain weight per linear inch upward.

Here's what I said in the previous post:

The maximum grain weight (269#) divided by the height (36") is 7.47 lbs/inch.
<snip>
If you're a traditional mash thickness guy, then you're using 1.33 quarts water per lb, which is 9.92 quarts per inch. Convert to weight and you have 20.7 lbs per inch. Add the two together and you get 28.17 lbs/inch.

95.91 gallons spill height, not per cu.in. That's across 36".

95.91 / 36 = 2.66 gal/in or 22.19 lbs/in, no grain. The way I calculated it, the displacement of grain after absorption is baked in.

[jimgsp]

Thanks again, Brewfun!

Here is what I understand now:

"If you calculate the cylinder volume and divide by 231 the again by the height, you have the gallons contained in each inch."
3.14 x 14? x 14? x 36? = 22,155.84 cu. ins.
22,155.84 / 231 = 95.9127 gallons = total height. (231 cu. ins. in a US gallon)
96 x 4 = 384 quarts

"Generally, the maximum water & grain a mash tun can hold is equal to 70% of the total volume in quarts (above the false bottom)."
384 x .7 (70%) = 268.8 quarts

"If your mashtun were 28" wide and a total of 36" high, it would hold about 96 gallons. Using my above RoT, you could cram about 269 lbs in with water."
269 / 36? = 7.47 lbs. per lineal in., water only

"If you're a traditional mash thickness guy, then you're using 1.33 quarts water per lb, which is 9.92 quarts per inch.
1.33 quarts of water per lb. of grain x 7.47 lbs. per lineal in.= 9.9351 quarts per lineal in."

"Convert to weight and you have 20.7 lbs per inch".
9.92 / 4 = 2.48 gal. per lineal inch
2.48 x 8.34 (weight of 1 gallon of water) = 20.7 lbs. per lineal inch, no grain

"22.19 lbs/in, no grain. The way I calculated it, the displacement of grain after absorption is baked in."
95.91 / 36 = 2.66 gal. per linear inch (1? depth in 28? dia.)
2.66 x 8.34 (weight of 1 gallon of water) = 22.18 lbs. per lineal inch, no grain

"Add the two together and you get 28.17 lbs/inch"
20.7 lbs. per lineal inch, no grain + 7.47 lbs. per lineal. in. water & grain = 28.17 lbs. total water & grain per lineal in.

I can't seem to understand how we get from 28.17 total lbs. per linial in. to 19" of depth. I thought that 28.17 was the total weight of combibed grain & water for 1" of depth given a 28" dia. For 19" of depth, the total weight would be 28.17 lbs. per linial in. x 19" height = 535.23 lbs. This is obviously wrong.

Can you once again explain what I am not grasping? How do we arrive at 19"?

"This means that a 140# grist with traditional liquor should stand about 19" above the false bottom. If you're aiming for your coil to float somewhere around halfway, the coil center should be at about 9.5" off the false bottom."

[brewfun]

Sure, Lets step through this, again.

"If your mashtun were 28" wide and a total of 36" high, it would hold about 96 gallons. Using my above RoT, you could cram about 269 lbs in with water."
269 / 36? = 7.47 lbs. per lineal in., water grain only. What I did was take the calculated "maximum" weight that the vessel can hold, when water is added. The reason is that if I calculated grain weight based on vessel space, a real-world test would cause the grain to expand and spill out of the vessel. Therefore, we calculate with water, even though the result applies to the grain only. The weight of the grain as added doesn't change, but it does increase in volume as it absorbs water.

"Convert to weight and you have 20.7 lbs per inch".
9.92 / 4 = 2.48 gal. per lineal inch
2.48 x 8.34 (weight of 1 gallon of water) = 20.7 lbs. per lineal inch, no grain Yes!

"22.19 lbs/in, no grain. The way I calculated it, the displacement of grain after absorption is baked in."
95.91 / 36 = 2.66 gal. per linear inch (1? depth in 28? dia.)
2.66 x 8.34 (weight of 1 gallon of water) = 22.18 lbs. per lineal inch, no grain This was offered for clarity, but seems to have become a red herring. All I was trying to do was show that just calculating the water weight will give you a different answer. Calculating based on water and grain together is the direction you want to go. I was going to omit this topic, but I'm pretty sure someone would have eventually pointed it out.

"Add the two together and you get 28.17 lbs/inch"
20.7 lbs. per lineal inch, no grain + 7.47 lbs. per lineal. in. water & grain = 28.17 lbs. total water & grain per lineal in. Correct. Your coil is meant for the mixed mash. So, in any cylinder, knowing the mash weight will lead you to the correct mash depth. Every mashtun can be calibrated so that you know how deep a properly mixed mash will be. If the mix is off, then the depth will change. That's an operation error though, not a mathematical one.

I ended with:

"This means that a 140# grist with traditional liquor should stand about 19" above the false bottom. If you're aiming for your coil to float somewhere around halfway, the coil center should be at about 9.5" off the false bottom."

Which created a new question for you:
I can't seem to understand how we get from 28.17 total lbs. per linial in. to 19" of depth. I thought that 28.17 was the total weight of combibed grain & water for 1" of depth given a 28" dia. For 19" of depth, the total weight would be 28.17 lbs. per lineal in. x 19" height = 535.23 lbs. This is obviously wrong.

Is it wrong? You're on the right track.

140# dry grain
1.33 qt/lb liquor

140 x 1.33 = 186.2 qt = 388.227 lbs

388.227 lbs liquor + 140 lbs grain = 528.227 lbs  << pretty close to your 535.23 lbs!

528.227 total weight / 28.17 = 18.75 inches (about 19" because mashes are not smooth  )

[jimgsp]

 - brewfun

Awesome! I have got it now. Thanks so much for you patients and detailed explanations!

I am sorry that it took this much work for you, but I can assure you that it was a termendous help for me. I spent my life-long career in engineering, and I am consequently cursed with a need to understand as completely as possible most aspects of brewing.

I am going to build a simple Excel spreadsheet to calculate this math to result in the hight of a grain bed with user input for the required parameters. I have ran the numbers on high and low grain bills for some my recipes and have the desired range for heating coil adjustment. Now that I understand the math, I can see numerious uses for this information.

Here is the calcs for my currect recipe:

GSP Craft Brewing Parameters
Mash tun: 25? dia. X 39? high
Current recipe:
150.83 lbs. dry grain
1.25 quarts per lb. liquor

3.14 x 12.5? x 12.5? x 39? = 19,134.375 cu. ins.
19,134.375 / 231 = 82.8327 gallons for total height. (231 cu. ins. in a US gallon)
82.8327 x 4 = 331.3312 quarts, water only

331.3312 x .7 (70%) = 231.9319 quarts, water only

231.9319 / 39? = 5.9470 lbs. per lineal in., grain only

1.25 quarts of water per lb. of grain x 5.9470 lbs. of grain per lineal in.= 7.4337 quarts per lineal in.

7.4337 / 4 = 1.8548 gal. per lineal inch
1.8548 x 8.34 (weight of 1 gallon of water) = 15.4993 lbs. per lineal inch, water only

15.4993 lbs. per lineal inch, water only + 5.9470 lbs. per lineal. in. grain only = 21.4463 lbs. total water & grain per lineal in.

151 x 1.25 = 188.75 quarts
188.75 / 4 = 47.1875 gal. x 8.34 (weight of 1 gallon of water) = 393.5436 lbs.
393.5436 lbs. liquor + 150.83 lbs. grain = 544.3738 lbs.
544.3738 total weight / 21.4463 = 25.3831 inches (about 26" because mashes are not smooth)

[brewfun]

(about 26" because mashes are not smooth)

Aye! 

Keep in mind that this is all about what's ABOVE the false bottom. The water in this calculation is in addition to what you need for foundation and dead space.

Good luck! Brew on!

[jimgsp]

Copy that!

[dtapke]

I enjoy this yet am curious how it proves in practice. You'll have to report back what your height ends up being, as my oversimplified method came with a slightly different answer.

BS mash tun volume needed for 151lbs grain at 1.25qt/lb is 58.98g

82.83 gallons in 39" of height equates to .47" per gallon

.47" times 58.98g = 27.7"