A partigyle brew

I’ve been planning to brew a Special Bitter for the AHA Club Only competition in January. I’ve never brewed an English-style Pale Ale before so my recipe was going to be based on Jamil’s Special Bitter recipe from Brewing Classic Styles.

I should have brewed it a couple of weeks ago when I had the opportunity, because now I’m thinking about trying to do a partigyle. Both BYO and Zymurgy have recently run stories on Barleywines, so I’ve been trying to formulate a Barleywine/Bitter recipe. My thought was that I would top off my mash with enough water for my Barleywine runnings and then my sparge water (I batch sparge) would be enough for the Special Bitter.

Here’s what I’ve come up with:
20 lbs. Marris Otter
2 lbs. white wheat
½ lb. Aromatic (@20L)
½ lb. Crystal 120L

First runnings planned to be 6 gallons, with a 90 minute boil and estimated volume to fermenter of 4.5 gallons.
To the boil I plan to add 1 lb. dark brown sugar to help with my OG and attenuation and the hopping would be:
1 oz Cascade (5.0%AA) FWH
2 oz. Columbus (12.5%AA) @60 minutes
½ oz. Chinook (10.0%AA) @ 15, 10, 5 & 1 minutes
½ oz. Cascade (5.0%AA) @ 15 , 10, 5 & 1 minutes

Shooting for around 1.098 OG and approximately 125 IBU and SRM of 15

For my second runnings, I plan to pour in 7 gallons of sparge water and top off with ½ lb. Crystal 60L. Planning for @7 gallons in the kettle with 5 ½ going into the fermenter.

The hops schedule for the Special Bitter is:
1 ¼ oz. Challenger (5.5%AA) @ 60 min.
¾ oz. Challenger ((5.5%AA) @ 20 min.
½ oz. EKG (4.5%AA) @ 20 min.
½ oz. EKG (4.5%AA) @ 1 min.
Shooting for an OG of 1.048, IBUs of 40 and an SRM of 11

I have never done a partigyle so I’m not sure how to estimate the gravity of my first and second runnings. I’m also struggling with how to estimate my post boil gravity based on my pre-boil gravity. I’m sure there is a simple algebraic equation for this calculation, but I can’t find it. My thought is I can make adjustments in the kettle if I need to raise or lower my gravity. If you have experiences with a partigyle or estimated post boil gravity, please chime in.