The hard part about answering this question involves determining IBUs in a beer. For the moment, let’s ignore the elephant in the room and pretend that that is not so difficult for homebrewers! The thing that makes scaling recipes fairly easy is knowing hop utilization. Assume that a 20-liter (a bit over 5 gallons) test brew is made using a single 30 gram hop addition at the beginning of the boil. The hops used have 8% alpha acids and the resultant beer ends up with 36 IBU. The reason for this test brew is to determine hop utilization and that is pretty simple given the data above.
Utilization (%) = liters wort x IBU in beer ÷ grams hops ÷ hop alpha acid content x 10
Utilization (%) = 20 x 36 ÷ 30 ÷ 8 x 10
Utilization = 30%
I have intentionally left out units of this not to confuse the meat of this question. Previous columns and articles in BYO have covered the unit cancellation in this calculation for those interested in units. The point is that hop utilization can be calculated with the information above in hand. Multiple hop additions make the process a bit more complex, but the basic method is the same.
Now let’s jump into a new brewhouse, run the same experiment and calculations. The new brewhouse is determined to have a better hop utilization, where the first hop addition has a 35% hop utilization. Scaling up recipes from the old brewhouse is pretty darn simple. You can use the equation above to run hop calculations, or apply a few simple scaling factors. The new brewhouse produces 60 liters (almost 16 gallons) of wort, so all hop additions are simply multiplied by 3. To account for the improved yield, the additions can be adjusted by 30/35 (0.86). Combining the two multipliers (3 x 0.86) results in 2.6 and this is all that is needed to scale up those 20-liter recipes to 60-liter batches.
I have to take a break at this point and do a little explaining. Why am I using metric in these calculations? Because it is the easiest way to do calculations involving units that are fundamentally metric, which really means just about everything in brewing. The United States, Myanmar (Burma), and Liberia are the only nations on the planet that have not officially embraced the metric system. When brewing calculations are performed with pounds, gallons, inches, and degrees Fahrenheit things are just more difficult. So metric calculations are in a sense lazy!
Another bit of explaining involves assumptions. Liquid volumes get routinely tossed about by homebrewers and it is important that we use the same basis for communication. A 20-liter (or 5-gallon-ish batch) of beer means different things to different brewers. From a brewing calculation standpoint, batch size really refers to a very specific volume and that is wort volume produced after wort boiling. All of the malt extract and hop acids extracted during the brewing process are present in this volume of wort.
When wort is transferred out of the kettle (or whirlpool) some wort (representing malt and hop goodies) is loss. When beer is racked more malt and hop goodies are lost. And when beer is packaged more hop and malt goodies are lost. However, volumetric losses downstream of the brew kettle do not affect brewhouse yield (malt efficiency) or hop utilization. So it is important to actually measure how much wort is produced in the brewhouse because wort volume is the basis of all brewing calculations involving malt and hops added in the brewhouse. Your hydrometer does not care about beer or wort volume and neither do methods that measure IBUs in beer, as both of these measure concentration.
Back to the question at hand, and we are left with that pesky thing called the IBU. If you happen to have access to a UV spectrophotometer it is not very difficult to analyze your beer and determine IBUs. But what if you cannot analyze bitterness, is there another way? Fortunately hop bitterness can be diluted and analyzed with sensory methods. If you use a consistent beer with a known IBU, like a big name lager beer, as your reference standard you can dilute your homebrews (I am assuming that most homebrews are not less bitter than big name lagers) and some pretty basic sensory methods to determine beer bitterness. Any readers who work in a lab and are cringing right now, please put a sock in it!
If you want to try this at home you need something to dilute your beer with. Carbonated water is the best thing to use because carbonation does affect the perception of bitterness and you don’t want big differences in carbonation to alter the results. And by using a bracketing method of dilution you can dilute your homebrew so some samples are more bitter than your standard and others are less bitter. Once you tighten your dilutions around the standard you can come up with a reasonable estimate of the bitterness level, and from that you can calculate hop utilization. Or better yet, calculate the differences in your two homebrew systems. Sorry if this answer seems to have a heavy dose of voodoo and crystal ball quality sprinkled on top! Think this through and I am sure you will discover that you can get your recipes scaled up without disappointment.