Linear Recipe Scaling. Fact or Fiction?

[Biscuits]

As a 1 - 3 gallon brewer, I find myself scaling recipes often and I was always told that you can simple scale the recipes linearly. Too easy, right?

Well, after some batches that missed OG by .01 or more, I started looking into software to help me figure out where in my brewing process I was going wrong. Long story short, I came to the realization that scaling recipes isn't a linear function.

The main reason I have found for this is the change in mash water volume based on grain weight due to brew system losses (boil off, mash tun loss, kettle loss, etc).

I wish to open this theory for discussion, as I know there are a plethora of members on here with a much more qualified brain than mine to settle this issue once and for all.

I am providing the following example to substantiate my theory and provide a base of discussion.


Original Recipe: Summer Citra Cerveza

Recipe Type: All Grain

Batch Size (Gallons): 5.5
Original Gravity: 1.040

Boiling Time (Minutes): 60



Ingredients:

5 lbs 2 Row
3 lbs Flaked Corn
1 lbs Flaked Barley (fluffy white head)


0.5 oz Cascade pellets 60 min of boil
0.5 oz Centennial pellets 20 min of boil
1.5 oz of Citra pellets at 150f of whirlpool

Now, removing process variables, like water pH, yadda, yadda, yadda...and going solely on numbers here. This recipe, on my system (BIAB), would produce a preboil gravity of @ 1.036 and I would do a full volume mash with 7.86 gallons.


If I scale in half (2.75 G) linearly the recipe would be:

2.5 lbs 2 Row
1.5 lbs Flaked Corn
.5 lbs Flaked Barley (fluffy white head)


0.25 oz Cascade pellets 60 min of boil
0.25 oz Centennial pellets 20 min of boil
0.75 oz of Citra pellets at 150f of whirlpool

This changes cuts everything in the recipe right in half, except the water. Instead of 3.93 gallons, my water calculates out to 4.71 gallons, which is @ 0.78 gallons more than the half way mark, which would result in a lower pre-boil gravity of @ 1.030...which would, assuming the same boil off rate, result in a lower OG.

This goes even further if you cut it in half yet again.

So, I open it up to your thoughts here. While a linear scale is a decent rule of thumb, depending on how far down you scale, it begins to fall way off track...have we been giving bad advice or am I just wrong and missing something?

 

[laredo7mm]

If you do a one hour boil on each batch and have the same boil off on each batch, then you are reducing the half sized batch by a larger percentage.

Using your numbers and a 1 gallon boil off:

Start with 6.5 gallons at 1.036 and boil off 1 gallon gives you 5.5 gallons at 1.043.

Start with 3.75 gallons at 1.030 and boil off 1 gallon gives you 2.75 gallons at 1.041.

Looks close enough for me.

You are reducing the full sized batch by 15.38% and the half batch by 26.67%.

 

[jddevinn]

How are you calculating your water? Your boil volume should be your finished volume + boil off rate x boil time. So the half batch preboil volume should be half of the "full" batch preboil volume.

The efficiency of the mash may change with batch size. This will need to be reflected in the scaling.

 

[doug293cz]

How are you calculating your water? Your boil volume should be your finished volume + boil off rate x boil time. So the half batch preboil volume should be half of the "full" batch preboil volume.

The efficiency of the mash may change with batch size. This will need to be reflected in the scaling.

If the boil off volume is the same for the large and small batches, then:

Small Batch Pre-Boil Vol = Boil Off Vol + (Large Batch Pre-Boil Vol - Boil Off Vol) / 2​

Mash efficiency equals conversion efficiency times lauter efficiency. For the case of equal and non-zero undrainable MLT volumes, the small batch lauter efficiency will be lower than the large batch lauter efficiency. However, since the small batch needs more total water, that will raise the lauter efficiency. These two effects counteract each other, so lauter efficiency could go either up or down depending on specifics. A thinner mash for the small batch (due to more total water) could also lead to higher conversion efficiency, since thinner mashes tend to convert faster than thicker mashes.

Any interest in a calculator that would sort (most) of this out?

Brew on

 

[Biscuits]

How are you calculating your water? Your boil volume should be your finished volume + boil off rate x boil time. So the half batch preboil volume should be half of the "full" batch preboil volume.

The efficiency of the mash may change with batch size. This will need to be reflected in the scaling.

If the boil off volume is the same for the large and small batches, then:

Small Batch Pre-Boil Vol = Boil Off Vol + (Large Batch Pre-Boil Vol - Boil Off Vol) / 2​

Mash efficiency equals conversion efficiency times lauter efficiency. For the case of equal and non-zero undrainable MLT volumes, the small batch lauter efficiency will be lower than the large batch lauter efficiency. However, since the small batch needs more total water, that will raise the lauter efficiency. These two effects counteract each other, so lauter efficiency could go either up or down depending on specifics. A thinner mash for the small batch (due to more total water) could also lead to higher conversion efficiency, since thinner mashes tend to convert faster than thicker mashes.

Any interest in a calculator that would sort (most) of this out?

Brew on

To answer both of you, I use use pricelessbiab to calculate water volume, so technically I use a formula you created or helped create doug293cz.

I see your point about the mash thickness being the possible equalizer here, but in this scenario, both mashes would be full volume BIAB so, sure one mash would be slightly thicker as far as qt/lbs, but neither would be anywhere near 1.25 or even 1.75 qt/lb...so I guess, the question is...

How thick does the mash have to be before you start seeing a noticeable difference in conversion efficiency?

And yes, there is interest...which is why I am asking...I am trying to modify mine to automatically account for the necessary changes when scaling recipes.

 

[doug293cz]

To answer both of you, I use use pricelessbiab to calculate water volume, so technically I use a formula you created or helped create doug293cz.

I see your point about the mash thickness being the possible equalizer here, but in this scenario, both mashes would be full volume BIAB so, sure one mash would be slightly thicker as far as qt/lbs, but neither would be anywhere near 1.25 or even 1.75 qt/lb...so I guess, the question is...

How thick does the mash have to be before you start seeing a noticeable difference in conversion efficiency?

And yes, there is interest...which is why I am asking...I am trying to modify mine to automatically account for the necessary changes when scaling recipes.

I didn't "create" the formulas, but I did derive them independently. I created a mash/sparge simulation spreadsheet, that I provided to @pricelessbrewing , and he incorporated the formulas into his nifty on-line calculator. When I asked about interest in a calculator, I forgot that priceless has incorporated an auto recipe scaling function in the latest version of his calculator. I suspect it might take into account all the factors I mentioned in my previous post, but I haven't played with that new functionality yet. so can't say for sure.

Kai Troester discusses mash thickness effects here.

Brew on

 

[Biscuits]

Awesome, thanks for the link doug293cz.

 

[SteveH aka shetc]

Have you seen this calculator? http://biabrewer.info/viewtopic.php?f=5&t=1869

 

[Biscuits]

Have you seen this calculator? http://biabrewer.info/viewtopic.php?f=5&t=1869

I don't have permission to that site so I cannot access the link to the calc.

 

[jddevinn]

If the boil off volume is the same for the large and small batches, then:

Small Batch Pre-Boil Vol = Boil Off Vol + (Large Batch Pre-Boil Vol - Boil Off Vol) / 2​

Mash efficiency equals conversion efficiency times lauter efficiency. For the case of equal and non-zero undrainable MLT volumes, the small batch lauter efficiency will be lower than the large batch lauter efficiency. However, since the small batch needs more total water, that will raise the lauter efficiency. These two effects counteract each other, so lauter efficiency could go either up or down depending on specifics. A thinner mash for the small batch (due to more total water) could also lead to higher conversion efficiency, since thinner mashes tend to convert faster than thicker mashes.

Any interest in a calculator that would sort (most) of this out?

Brew on

OK, maybe I'm a bit dense today but ignoring specific volume changes of water at different temperatures the only volume change is what is boiled off so the final volume can only be:

Final Volume = Preboil volume - boil off volume

Final Volume = Preboil volume - boil off rate x boil time

I now see that y'all are talking about a full mash BIAB volume, not initial boil volume. I don't BIAB (so take this with a grain of salt) but to me it does not make sense to adjust the preboil volume and boil time to make up for efficiency differences. IF I wanted to do a full volume mash (I don't partially because of this) I would calculate my water based on the boil off volume + 0.12gal water per lb of grain for absorption (and adjust based on your system) and then adjust the grain amounts for the efficiency differences in the mash, keeping the boil off time the same.

 

[SteveH aka shetc]

I don't have permission to that site so I cannot access the link to the calc.

Become a member (it's free) then you will get access.

 

[ajdelange]

Any brewer, professional or amateur, who has ever moved on to new equipment will tell you that his old, time tested recipes are going to result in different beers on new equipment. As in transitioning from 5 gal to 50 gal is going to involve new equipment perhaps it is better to focus on the changes in process imposed by the new gear rather than on the fact that you are now mashing 100 lbs of grain with 32 gal of water rather than 10 lbs of grain with 3.2.

But just size does cause differences. The pressure at the bottom of a three foot high kettle is higher than the pressure at the bottom of a 1.5 foot high kettle and the temperature is therefore different. Similarly, the pressure at the bottom of a 1.5 bbl fermenter is higher than that at the bottom of a carboy and the yeast behave differently.

 

[doug293cz]

If the boil off volume is the same for the large and small batches, then:

Small Batch Pre-Boil Vol = Boil Off Vol + (Large Batch Pre-Boil Vol - Boil Off Vol) / 2​

Mash efficiency equals conversion efficiency times lauter efficiency. For the case of equal and non-zero undrainable MLT volumes, the small batch lauter efficiency will be lower than the large batch lauter efficiency. However, since the small batch needs more total water, that will raise the lauter efficiency. These two effects counteract each other, so lauter efficiency could go either up or down depending on specifics. A thinner mash for the small batch (due to more total water) could also lead to higher conversion efficiency, since thinner mashes tend to convert faster than thicker mashes.

Any interest in a calculator that would sort (most) of this out?

Brew on

OK, maybe I'm a bit dense today but ignoring specific volume changes of water at different temperatures the only volume change is what is boiled off so the final volume can only be:

Final Volume = Preboil volume - boil off volume

Final Volume = Preboil volume - boil off rate x boil time

I now see that y'all are talking about a full mash BIAB volume, not initial boil volume. I don't BIAB (so take this with a grain of salt) but to me it does not make sense to adjust the preboil volume and boil time to make up for efficiency differences. IF I wanted to do a full volume mash (I don't partially because of this) I would calculate my water based on the boil off volume + 0.12gal water per lb of grain for absorption (and adjust based on your system) and then adjust the grain amounts for the efficiency differences in the mash, keeping the boil off time the same.

Nothing I said is specific to BIAB or no-sparge. It applies equally to single batch sparge, multiple batch sparge, or no-sparge. Fly sparge is... well, complicated.

Let's look at the case of scaling a recipe from 10 gal to 5 gal using the same equipment (i.e. MLT undrainable volume and boil off rate stay the same.) Let's assume:

Target post boil volumes are 11 gal for a 10 gal batch and 5.5 gal for a 5 gal batch
Grain bill for a 10 gal batch is 24 lbs
Boil off rate is 1.2 gal/hr for both batch sizes
One hour boil
MLT undrainable volume is 0.125 gal for both batch sizes
Process is single batch sparge with equal runnings volumes
Conversion efficiency is 95%​

For the 10 gal batch our total water volume (strike + sparge) will be:

11 gal + 0.12 gal/lb * 24 lbs + 0.125 gal + 1.2 gal/hr * 1 hr = 15.21 gal​

and the pre-boil volume will be:

11 gal + 1.2 gal/hr * 1 hr = 12.2 gal​

If we did a linear scaling on the grain bill, then for the 5 gal batch the total water volume would be:

5.5 gal + 0.12 gal/lb * 12 lb + 0.125 gal + 1.2 gal/hr * 1 hr = 8.27​

and the pre-boil volume will be:

5.5 gal + 1.2 gal/hr * 1 hr = 6.7 gal​

The only volume that scales linearly is the post boil volume.

If we do a mash + sparge simulation on the 10 gal batch with the parameters above, we get the following results:

Strike volume = 9.11 gal
Sparge volume = 6.1 gal
Pre-boil volume = 12.2 gal
Pre-boil SG = 1.0546
Lauter efficiency = 82.36%
Mash efficiency = 78.24%
Post-boil volume = 11 gal
Post-boil SG (OG) = 1.0606​

The doing the same simulation for the five gal batch with 12 lb of grain:

Strike volume = 4.92 gal
Sparge volume = 3.35 gal
Pre-boil volume = 6.7 gal
Pre-boil SG = 1.0505
Lauter efficiency = 83.68%
Mash efficiency = 79.49%
Post-boil volume = 5.5 gal
Post-boil SG (OG) = 1.0616​

We see that the lauter efficiency (and thus mash efficiency) is slightly higher for the smaller batch. This is because the ratio of total water to grain weight is slightly higher for the smaller batch. Higher water to grain ratio means more sugar being rinsed from the grain bed. Also due to the higher water ratio, the pre-boil SG is lower for the smaller batch. But, since the boil off ratio is higher for the small batch, the OG comes out a little higher for the smaller batch. Thus from a theoretical standpoint, the grain bill shouldn't scale linearly with batch size.

However, the actual difference in OG using linear scaling is only 0.001. In the real world, we would be hard pressed to detect this difference between two different sized brews, given all the variables that can contribute to batch to batch differences.

Brew on

 

[jddevinn]

Nothing I said is specific to BIAB or no-sparge. It applies equally to single batch sparge, multiple batch sparge, or no-sparge. Fly sparge is... well, complicated.

Let's look at the case of scaling a recipe from 10 gal to 5 gal using the same equipment (i.e. MLT undrainable volume and boil off rate stay the same.) Let's assume:

Target post boil volumes are 11 gal for a 10 gal batch and 5.5 gal for a 5 gal batch
Grain bill for a 10 gal batch is 24 lbs
Boil off rate is 1.2 gal/hr for both batch sizes
One hour boil
MLT undrainable volume is 0.125 gal for both batch sizes
Process is single batch sparge with equal runnings volumes
Conversion efficiency is 95%​

For the 10 gal batch our total water volume (strike + sparge) will be:

11 gal + 0.12 gal/lb * 24 lbs + 0.125 gal + 1.2 gal/hr * 1 hr = 15.21 gal​

and the pre-boil volume will be:

11 gal + 1.2 gal/hr * 1 hr = 12.2 gal​

If we did a linear scaling on the grain bill, then for the 5 gal batch the total water volume would be:

5.5 gal + 0.12 gal/lb * 12 lb + 0.125 gal + 1.2 gal/hr * 1 hr = 8.27​

and the pre-boil volume will be:

5.5 gal + 1.2 gal/hr * 1 hr = 6.7 gal​

The only volume that scales linearly is the post boil volume.

If we do a mash + sparge simulation on the 10 gal batch with the parameters above, we get the following results:

Strike volume = 9.11 gal
Sparge volume = 6.1 gal
Pre-boil volume = 12.2 gal
Pre-boil SG = 1.0546
Lauter efficiency = 82.36%
Mash efficiency = 78.24%
Post-boil volume = 11 gal
Post-boil SG (OG) = 1.0606​

The doing the same simulation for the five gal batch with 12 lb of grain:

Strike volume = 4.92 gal
Sparge volume = 3.35 gal
Pre-boil volume = 6.7 gal
Pre-boil SG = 1.0505
Lauter efficiency = 83.68%
Mash efficiency = 79.49%
Post-boil volume = 5.5 gal
Post-boil SG (OG) = 1.0616​

We see that the lauter efficiency (and thus mash efficiency) is slightly higher for the smaller batch. This is because the ratio of total water to grain weight is slightly higher for the smaller batch. Higher water to grain ratio means more sugar being rinsed from the grain bed. Also due to the higher water ratio, the pre-boil SG is lower for the smaller batch. But, since the boil off ratio is higher for the small batch, the OG comes out a little higher for the smaller batch. Thus from a theoretical standpoint, the grain bill shouldn't scale linearly with batch size.

However, the actual difference in OG using linear scaling is only 0.001. In the real world, we would be hard pressed to detect this difference between two different sized brews, given all the variables that can contribute to batch to batch differences.

Brew on

Alright, thanks Doug... I see what the disconnect in our water volumes was. I fly sparge so never really think about the amount of strike water.... I calculate it out and ensure I have at least that much ready but try to minimize how much extra as I bring it to a to a boil and chill to degass.

I suppose my thought process is if my original recipe was for 11 gallons, 24lbm with a 82.36% Lauter efficiency .

The first time I made a 5 gallon batch I would scale it linearly. I'd use 12lb grain, my normal mash thickness and then sprage. If when I measured the results I calculate that I have a 83.68% Lauter efficiency and overshot my preboil gravity I would modify the boil time of this brew to result in the correct OG and then modify my recipe by reducing the grains to match the target preboil with the efficiency for that batch size.