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?
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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