# A musing upon how to apply the "Golden Ratio" to Hop additions

Discussion in 'General Brewing Discussions' started by Silver_Is_Money, Mar 24, 2021.

1. ### Silver_Is_Money Active Member

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#1
Last edited: Mar 24, 2021
I could easily be wrong here, but to date this might actually be the worlds first ever attempt at the application of the "Golden Ratio" to hop additions.

For the specific case of using two hop additions via the application of the Golden Ratio whereby to determine ideal bittering and flavor/aroma additions:

Nature is rife with examples of the "Golden Ratio". The golden ratio is a multiplicative ratio consisting of two numbers for which the first number times (itself - 1) equals 1.

1.6180339... x 0.6180339... = 1 (This being the "Golden Ratio")

We need help, so lets cheat a bit:

0.3819661 + 0.6180339 = 1 (The highlighted value being the "Golden Ratio" quick_solver/cheat factor)

Example:
Lets shoot for 30 IBU's
Lets add them at 60 minutes and 15 minutes (whereby some prefer 10 or 20 minutes (or other) to 15, with this being your choice)

How many IBU's should we add at 60 minutes?
How many IBU's should we add at 15 minutes?

IBU's for 60 minutes: 30 x 0.6180339 = 18.54 IBU's
IBU's for 15 minutes: 30 x 0.3819661 = 11.46 IBU's

Proof that this cheater method meets the criteria of the Golden Ratio:

(1.6180339 × 11.46 IBU's) + (18.54 × 0.6180339 IBU's) = 30.00 IBU's = TRUE

To make this process far more simple use these "close enough" truncated fractions:

1.618 x 0.618 ~= 1

0.382 + 0.618 = 1

For three hop additions, say at 60, 30, and 10 minutes, the golden ratio becomes 1.618 x 1.000 x 0.618 = 1

Who will assist in deriving a simple method whereby to make the Golden Ratio work for 3 hop additions?

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2. ### Silver_Is_Money Active Member

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#2
Upon further musing:

0.618... divided by 1.618... = 0.382 = the cheat factor

3. ### Craigerrr Well-Known Member

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4. ### Silver_Is_Money Active Member

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#4
For three hop additions the "cheat factor" becomes: 0.309023486...

Example:
We want to add 40 total IBU's to a batch in 3 additions (at say 60, 30, and 10 minutes, with this up to you) via the "Golden Ratio"

Method:
40 x 0.309023486 = 12.36093944 = IBU's for hop addition #2
12.36093944 x 1.618 = 20.000000014 = IBU's for hop addition #1
12.36093944 x 0.618 = 7.639060574 = IBU's for hop addition #3

Proofs:
(12.36093944 x 0.618) + 20.000000014 + (7.639060574 x 1.618) = 40
20.000000014 + 12.36093944 + 7.639060574 = 40

For simplicity the three hop additions cheat factor can be rounded to: 0.309

5. ### Silver_Is_Money Active Member

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#5
Last edited: Mar 24, 2021
It appears that for 3 hop additions via the 'Golden Ratio' the 1st addition will always deliver half of the total batch desired IBU's.

6. ### Silver_Is_Money Active Member

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7. ### Silver_Is_Money Active Member

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#7
Last edited: Mar 24, 2021
Even the quantum mechanical search for the ever elusive "Theory Of Everything" seems to intricately involve the Golden Ratio.

https://quantumgravityresearch.org/golden-ratio-in-nature-overview/

So I've simply asked myself: If nature itself, right on up to the quest for the theory of everything seems to be entwined around the application of the Golden Ratio, how about attempting to apply it to hop additions?

8. ### Silver_Is_Money Active Member

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#8
Should the very time sequence itself for determining when to add hop additions be related to the golden ratio? Hmmm???

9. ### HighVoltageMan! Well-Known Member

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#9
Last edited: Mar 24, 2021
I see that architecture has a golden rule of 1.618. I planned to build a new barn using old architecture designs, I kept playing with the dimensions until it looked right. After I built it, I ran across the golden ratio rule and realized I used it unknowingly.

You may be on to something, but I'm not sure how it could be used in brewing. Hops? Grain? Mash thickness? As long as it comes out as beer, you win.

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10. ### Silver_Is_Money Active Member

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#10
Last edited: Mar 24, 2021
A two story home with these rough dimensions seems as if would be a close fit to the 3 factor Golden Ratio:

48.5 Ft. wide
30.0 Ft. deep
18.5 Ft. Tall (from ground level to the roof line, allowing for 8 Ft. ceilings & small basement windows)

48.5 x 30 = 1,455 Sq-Ft per floor, and 2,910 Sq-Ft overall (not including the basement)

Whereby:
48.5 corresponds to ~1.618 x 30
30.0 corresponds to 1.000 x 30
18.5 corresponds to ~0.618 x 30

11. ### Hawkbox Well-Known Member

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12. ### Silver_Is_Money Active Member

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#12
I'd be interested in hearing how others compute as to how many IBU's each addition should nominally contribute for the case of 2 and 3 hop additions added exclusively during the boil. And also hearing as to what your preferred 2 or 3 hop addition times typically are for a 60 minute boil. Exclude IPA's please.

13. ### west1m Well-Known Member

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#13
Wouldn't that picture look more like this if following the Golden Rule?

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14. ### Craigerrr Well-Known Member

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#14
I don't tend to follow the rules with hops so much to be honest

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15. ### Herm_brews Well-Known Member

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#15
Rule breaker

16. ### Head First Well-Known Member

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#16
When it comes to math calculations I stay with the KISS rule. When blending hop bittering with multiple hops I stick with even numbers. Making 10gal batches I stay with multiples of even ounces. So no worries for 8 to 10 IBU's off 1 way or another. Aroma hops used properly will mean more to flavor than bittering hops. I guess I am more of a simple cook than one to worry about formulas. To get the flavors I want I think I will stick with trial and error. There are lots off ways to enjoy a hobby. Maybe you should work with grain calculations too. Brew on!

17. ### Silver_Is_Money Active Member

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#17
Last edited: Mar 28, 2021
First I must say that clearly no one is capable of breaking any rule that has been quite literally just conceived, and as such is merely a "potential", until multiple split batch attempts, with one applying the rule and one stabbing in the dark as is the current means, with this effort likely spanning years, 'perhaps' revealing benefit (or clearly perhaps not). Second I will say that to my knowledge this is one of perhaps only a scant few, to perhaps in reality zero other attempts at systematically quantifying hop additions with respect to specifically their staged IBU contribution, and it appears almost certainly to be the first ever attempt to utilize the mathematics of the Golden Ratio whereby to do so. Lastly, whenever anyone is first to reach for the potential of advancement or enlightenment there is always the full anticipation of both ridicule and opposition. I was fully therefore anticipating it at the onset. I look forward to other attempts at forecasting hop additions, such that someday a website like Brewers Friend may be able to assist with fully quantified hop additions, rather than looking at their contribution through the rear view mirror.

18. ### Hawkbox Well-Known Member

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#18
I break all the rules, I'm a rebel.

19. ### Head First Well-Known Member

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#19
I wish you luck on your quest. Science is presently finding that hops are not even close to being properly calculated. The idea of helping them out is a very good idea if that is your thing. Cheers!

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20. ### Donoroto Well-Known Member

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#20
Ok, I oppose and ridicule this. With that out of the way, this is something I want to try, as it may hold promise, and in the worst case I'll still end up with beer.

In each of my next few brews (@AHarper 's Mannekin Pis excepted) I will modify the hops bill to (try to) follow the Golden Ratio.

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