I wish there was a good rule of thumb! For background, I'm a homebrewer who currently works as unpaid labor in a microbrewery. Nothing
scales linearly. My limited
experience is that as you go up in volume the contribution of specialty grains increases, and the hop extraction efficiency goes up. With that said, I'm talking 5 gallon
to 10 barrel
batches. In scaling a 5 gallon to 15 gallon batch, the relationship is close enough to linear as to be beyond my tasting skills. But beyond that, even I can taste the difference. The relative extraction efficiency of both specialty grains and hops definitely increases as the volume increases. Unfortunately, I do not yet have enough experience to give you a mathematical formula. I hope to give you a better answer, maybe in a year or so.