Scaling Down Hops in Recipes

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We've got several 31 gallon beer recipes and we would like to scale them down for our setup - which produces about 11 gallons of fermentable wort. I've searched this site for information on scaling and learned that the hops schedule does not scale in a linear fashion. We know we can plug the recipe into brewing software and let it do the scaling. But we're curious about the math that the brewing software uses. For scaling hops, there must be some non-linear function. Can anyone provide us with that function?
 
Can anyone provide us with that function?
No, simply because differences in equipment are too complex to model with a simple function. If you want that level of accuracy you need to have a sample of your beer and/or wort tested by a lab.
 
I've searched this site for information on scaling and learned that the hops schedule does not scale in a linear fashion.

I'm intrigued. For the case of identical Wort SG's and boil times and addition times, as well as for using the exact same hops, why not?
 
Actual thermal loading and convection effects (i.e. agitation) that vary depending on size, shape, and type of heat source of the specific kettle.

It's one of the reasons why the predictions delivered by the formulas we use (all three of them) are at best guesstimates that can easily be off by -50%/+100%
 
Actual thermal loading and convection effects (i.e. agitation) that vary depending on size, shape, and type of heat source of the specific kettle.

It's one of the reasons why the predictions delivered by the formulas we use (all three of them) are at best guesstimates that can easily be off by -50%/+100%

Thank you all. The takeaway I'm getting is that I should just scale the recipe linearly since the margin of error is so great. But I am curious if Vale71 can point me to the three formulas used to guesstimate.
 
It must be noted that none of the people behind these formulas ever used pellet hops while developing their formulas. And to presume 10% more IBU's than whole/leaf for pellets is pure speculative fantasy guesswork, and not science.
 
You mean like the formulas themselves, right? ;)

Yes!!!

My conception ( which has not been tested and verified, so is also in the realm of pure speculation) is that due to having been virtually pulverized, the IBU's released by pellets are variable to the boil time significantly differently from whole/leaf. I speculate that if both types are boiled for 90 minutes or more roughly the same IBU's are liberated for identical weights and AA's, but for near flame out additions 50% more IBU's are liberated by pellets, and the scaled differential between the two forms IBU contribution with respect to remaining boil time runs linearly differently along these "boil time" lines. This is the unique pellet hop IBU modification which I incorporated into the IBU calculator found within 'Mash Made Easy' some time ago.

My intuitive assumption is that for pellets the lupulin glands are in a state whereby they will be exposed to release their acids and oils much sooner within the boil than for whole/leaf, but ultimately there is only so much of a percentage of the acid that can be isomerized and liberated. Even if my speculative 50% scaling to zero percent differential between them with respect to remaining boil time proves to not be correct (as it likely will be) I'm confident that some scale differential as to IBU liberation exists between the two forms with respect to remaining boil time, and the actual scale merely needs to be discovered and verified. And that this is a better approach than to presume that across all remaining boil times precisely 10% more IBU's will be liberated by pellets.
 
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Per Michael L. Hall, Ph.D. (a man who has researched the science of IBU's extensively) it was Gregory J. Noonan who first proposed that pellets could be anywhere from 0% to 50% stronger than whole/leaf with regard to IBU contribution, with this being boil time dependent. So my approach does have precedent from one of the early IBU researchers. The difference being that Noonan derived a "step ladder" chart for bumping up (or toning down, depending on how you are looking at it with respect to remaining time of boil) the contribution differential over chunks of time whereas I have smoothed this step ladder into a continuous value changing line and removed the numerous time laddered plateaus thereby. My advantage is the use of a computer....
 
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My conception ( which has not been tested and verified, so is also in the realm of pure speculation) is that due to having been virtually pulverized, the IBU's released by pellets are variable to the boil time significantly differently from whole/leaf.

Have you seen the experiment and data that was discussed in the Nov 1, 2018 BBR podcast (link)? see pp 12-14. The author was active over in /r/homebrewing (link) about a month ago.
 
I'm still listening to the podcast and reviewing the corresponding PPT data as I'm typing this, but the podcast has already confirmed that pellets liberate their IBUs much more rapidly than whole/leaf. And that by about 40-45 minutes of boil they are nearly maxed out as to what they will ultimately deliver, and wherein additional boiling doesn't raise the measured IBUs much more at all. Pellets are truly a different beast, and most programs from the past are clearly failing us when utilized with pellets. My intuition and Gregory Noonan's experience and observation are on the right track, and the 10% more IBUs rule for pellets is bunk. But there is clearly room for even more improvement with respect to IBUs from pellets, just as I stated. Thank you for posting the links.
 
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