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Hop Utilization

Alright, I’m having a hard time here… I’m trying to calculate how many ounces of hops to use to reach a KNOWN IBU. However, all the equations I come across are the other way around, i.e. you have a known amount of hops and you’re looking to determine the IBUs. I know it’s just a simple re-arranging of the equation, but my math skills have gone out the window, apparently, and I can’t figure it out.

For my equation, I’m looking to determine how many ounces of Chinook to use (AA 11.4%) at 60 minutes (start of the boil) to reach an IBU of 40. Hop utilization at 60 minutes for an OG of 1.050 is 0.231.

Help/thoughts?

Avery

Size of batch?

I enter the entire recipe into a recipe calculator then play with the amount of hops.

or this one
https://www.brewtoad.com/recipes/new

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Palmer How to Brew, chapter 5:

  • IBU = AAU * U * 75 / V

  • AAU = Weight(oz) * AA

So

  • IBU = Weight(oz) * AA * U * 75 / V

substitute numbers from above and assume (boil size) V = 5 to keep the math simpler:

  • 40 = Weight(oz) * 11.4 * .231 * 75 / 5

  • 40 = 39.5 * Weight(oz)

Rework the equation to solve for Weight(oz):

  • IBU = Weight(oz) * ( AA * U * 75 / V )

  • IBU / ( AA * U * 75 / V ) = Weight(oz)

substitute numbers from above and assume V = 5:

  • 40 / (11.4 * .231 * 75 / 5 ) = Weight(oz)

  • 40 / 39.5 = Weight(oz)

Double check using @flars method!

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See how simple this is? :dizzy_face:Sneezles61

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Thanks chertel! That’s exactly what I needed. I’ve been going over the chapter in Palmer’s for a while now, and just couldn’t figure it out. Like I said, my math skills are dwindling. And uncdeo, the batch size is 5 gallons, which I forgot to mention.

Thanks everyone!!

Many ways to do the math: desktop programs, web sites, apps on the phone, look up tables (like table 7 in chapter 5, mentioned above), and …

“Wheel of Beer is a wort gravity calculator. … The Hop-Go-Round calculates hop bitterness.”
Randy Mosher.com - Wheels Of Beer, Slide rule - Wikipedia

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Dont worry. Me same thing going over the math in the book from palmer. Me work lots with formulas. At my work. But reading. Stuff. Wondering where it starts or comes from. The numbers. So me using now brew software

tl;dr? skip to the bottom for “on the fly hop substitution”

What’s nice about

  • IBU = Weight(oz) * AA * U * 75 / V

is that it can be simplified for my brewing system. The portion of the equation

  • 75 / V

is constant for the batch size that I brew. So I rebuilt table 7 in chapter 5 to reflect this.

  • Ume becomes 3.465 ==> .231 * 75 / 5

and my calculation is

  • Weight(oz) = IBU / ( AA * Ume )

or

  • Weight(oz) = 40 / (11.4 * .3.465)

Practical application?

I ran out of magnum at 11.4 AA, but have Warrior at 15.7 AA.

  • Weight(oz) = 40 / (15.7 * .3.465)

For me, it’s also easy to see that 11.2 AA vs 11.4 AA doesn’t matter when I repurchase magnum.

Many ways to enjoy the hobby (sometimes it’s building equipment, sometimes is reworking equations). And yes, “there’s an app for that this”.

Hmm… here’s what the Taylor method gets (should be similar to Tinseth):

(40-1.5)/3.6/11.4 = 0.94 oz

The 1.5 and 3.6 are some magical equation constants that I determined on my own. As you can see, they seem to work pretty well. Anyway, all IBU calculators come out a little bit too high as compared with actual laboratory results, so you may find that you actually do need the 1.01 oz or even a bit more if you were to measure in a lab. But we’re all in the same ballpark.

Cheers.

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