Calculate hop utilization when scaling batch/recipe from 3 gallon to 50 gallons

Would like to brew multiple 3 gallon (pilot) batch sizes before brewing at 52 gallons.
If the pilot batch turns out good I would like to then brew the same recipe at batch size of 52 gallons.

I'm hoping for a formula or general rule of thumb to scale the recipes (hop utilzation) so bitterness stays as close to the same in both batch sizes.

My understanding is once I scale to a larger batch > (x) times the size that's when I will start to see a degregation in bitterness in a larger batch size.
If I scale up from 3 gallons to 52 gallons that would around 17.6 times the size from the pilot batch at 3 gallons.

In each case specific mash/boil/fermentation vessels will be used in proportionate to the batch size.
Appreciate any help I can get here. 

Thank you, Aryan

Without experience on the 52 gallon system, its pretty difficult to say. If you have a recipe you've made at that scale, just deconstruct it to the 3 gallon size, first.

That way, you'll be matching the pilot recipe to a known large batch in determining a lot of variables, including bitterness.

Thank you I like your suggestion to work backwards from 52 galons batch to the pilot to gather the data on the variables which change.
So on all future batches regardless of the recipe I should then have a rule lof thumb for % loss in bitterness etc to apply as a template to other recipe/pilot batches.

This will be my first 52 gallon batch so I have not yet worked out a recipe where bitterness is just right.
I wonder what homebrewers who start microbreweries do on thier first large scale batch when taking a homebrew recipe and brewing it large scale, same method were talking about here suppose?

You could also check this out:

http://beersmith.com/blog/2014/06/11/scaling-beer-recipes-for-commercial-use-with-beersmith/

Exactly what I needed. Thank you so much -

Not a problem.

amills said:

I wonder what homebrewers who start microbreweries do on thier first large scale batch when taking a homebrew recipe and brewing it large scale, same method were talking about here suppose?

Click to expand...

Learning a new brewery is pretty much the same at any scale. The first batch or two are just simple "hip pocket" recipes that you know by heart and what it's supposed to taste like. Ideally, they also have really wide target areas.

One of my favorites to start with is a 35 IBU American Pale Ale. Just Pale Malt, 10% C-40 and two hop additions. It might not be an exciting beer, but the simplicity takes the ingredients out of all the other variables you're trying to nail down. American Wheat is another one I use a lot, for the same reason.

With simple recipes at first, if the gravity, color or bitterness are a little bit too much in one direction or another, you still have a very drinkable beer AND insight.