Max hop bitterness to boil time?

[punkrocker1991]

Apologies if this has been discussed before, if so please point me to where I can find the answer(s).

The post here has me thinking Boil-off rate calculator

Is there a good source that talks about the point during the boil where the hops don't contribute any additional IBUs?

In other words, say I put in some Challenger 7.5% expecting a 60 minute boil, but instead boil for 120 to compensate for low boil off rate, will there be a point where the hops themselves have given all the AAs they can? I'm guessing there's a curve to be found somewhere that shows this. I've put some numbers into various IBU calculators that seem to show that there is a bit of a tailing off over time.

(Obviously then the concentration/overall wort volume comes into play, but am curious about the hops side.)

Do I need to just buy the For The Love Of Hops book? Will that lead the way?

 

[MHB]

Hops and bittering can get very complicated. Most of the readily available calculators won’t get you very close.

The conversion of Alpha Acid to IsoAlpha Acid then to Trans Iso degradation products.
There are also lots of variables, most important is the temperature usually assumed to be 100-100.5oC. The form the hops are in (flowers or pellets) can change the outcome by 10% (ish). The amount of motion in the kettle from boiling plays a part...
The following is a kinetic conversion from the equations in (well see attachment if you are interested). This is for pure isolated Alpha Acid in constant volume laboratory conditions but it gives you a very real idea of what will happen.
Might not give you an exact answer as it leaves out some bits that all added together people call "Utilisation". That’s really just a fudge factor that lets you compare the measured bitterness you got against the theoretical outcome.
On the same system using the same boil times and the same form of hops, the utilisation figure wont vary too much and lets you take a fair stab at what your bitterness will be.

As you asked, yes you have added a finite amount of AA (Alpha Acid). In the real world these are bound up in the hop vegetal matter and won’t go into solution instantly as they do with the extract in the lab model.
Temperature is a funny one too; there are two rates of reaction; AA > IsoAA > Trans IsoAA.
At higher temperatures the rate of break down is faster than the rate of formation. get too hot and IsoAA is almost instantly degraded (roundabout 200oC)

After years of studying hopping beer I have settled on the Goldilocks model.
Take your best guess, brew the beer, then adjust until its just right!
Mark

Vertical scale is IBU's, Horizontal is time in Minutes