Garetz utilisation as a fraction:
(7.2994 + 15.0746 × tanh((t − 21.86) / 24.71)) / 100, floored at zero.
Why the floor
Garetz published a table of utilisations, and this tanh is the curve people
usually fit to it. The fit crosses zero at 8.80 minutes and keeps going. At
5 minutes it gives −1.6 %, and at the couple of effective minutes a
whirlpool addition works out to, −2.9 %. Without the floor, those hop
additions would make the beer less bitter, and on a modern recipe with a
late charge and a stand they'd subtract from the total. None of the rows in
Garetz's table are negative. The negative values come from reading the fit
outside the range it was fitted over, so we hold it at zero there.
We use zero instead of extrapolating the low end of the table, because that
would mean inventing a curve Garetz didn't publish. A brewer who wants late
additions counted properly can use Tinseth with the temperature-corrected
stand model.
Garetz utilisation as a fraction:
(7.2994 + 15.0746 × tanh((t − 21.86) / 24.71)) / 100, floored at zero.Why the floor
Garetz published a table of utilisations, and this tanh is the curve people usually fit to it. The fit crosses zero at 8.80 minutes and keeps going. At 5 minutes it gives −1.6 %, and at the couple of effective minutes a whirlpool addition works out to, −2.9 %. Without the floor, those hop additions would make the beer less bitter, and on a modern recipe with a late charge and a stand they'd subtract from the total. None of the rows in Garetz's table are negative. The negative values come from reading the fit outside the range it was fitted over, so we hold it at zero there.
We use zero instead of extrapolating the low end of the table, because that would mean inventing a curve Garetz didn't publish. A brewer who wants late additions counted properly can use Tinseth with the temperature-corrected stand model.
Source: Mark Garetz, Using Hops (1994).