I need 8.5 gallons (into the fermentor) of the highest gravity wort I can get. My mash tun is a bit less than 8 gallons. The underlet volume is about 1 gallon. Total vessel volume is 11 gallons. I'm doing this in Thing1, see link in my sig.

Let's guess that I'll use 24 pounds of malt, divided into 2 x 12 pound mashes.

Assume that conversion efficiency is 100%, which is fair if the grind is fine enough, we mash long enough and circulate enough. This is not sparge efficiency as it does not include the extract that remains trapped in the malt post sparge.

I need 8.5 gallons into the fermenter. let's assume we lose 1 gallon during boil. That means we need 9.5 gallons after the second sparge.

Each sparge will retain 12 pounds x 0.06 gallons/lb of malt = 0.72 gallons.

The post 1st stage sparge volume will be 9.5 + 2 x .72 gallons = 10.94 gallons total water.

Mash 1. 12 pounds x 37 points/pound = 444 points total extracted. We sparge with 10.94 gallons of water, for a gravity of 444/10.94 = 1.0406. 0.72 gallons of wort stays in the grain, so post sparge we have 10.22 gallons of 1.0406 wort.

Mash 2. 12 pounds x 37 points = 444 points total extracted. We sparge with 10.22 gallons of the wort from mash 1. Ending gravity is 1.0406 + 444/10.22 = 1.084. We leave 0.72 gallons of wort in the grain, so our ending volume is 9.5 gallons @ 1.084.

Overall efficiency of these two steps is:

(9.5 gallons x 84 points) / (2 x 444) = 89.8%

Next we boil down to 8.5 gallons. The gravity going into the fermenter will be (9.5 gallons x 84 points) / 8.5 gallons = 1.0939

I would like a higher gravity than that, so let's repeat the calc for 30 pounds of malt.

Each sparge will lose 15 pounds x 0.06 = 0.90 gallons of wort. Starting sparge volume will be 8.5 gallons into the fermentor + 1 gallon boil off + 2x 0.9gallons lost to grain = 11.3 gallons.

Mash 1. 15 pounds x 37 points = 555 points. OG = 555 points/11.3 gallons = 1.0491 Post sparge volume is 11.3 gallons = 0.9 gallons = 10.4 gallons.

Mash 2. 15 pounds x 37 points = 555 points. OG = 1.0481 + 555/10.4 gallons = 1.1067 Post sparge volume is 10.4 - 0.9 = 9.5 gallons.

Overall efficiency of these two steps is:

(9.5 gallons x 106.7 points) / (2x 555 points) = 90%.

Next we boil down to 8.5 gallons. The gravity going into the fermentor will be (9.5 x1.1067)/8.5 = 1.119. This is perfect.

If we tried to mash 30 pounds at 100% conversion efficiency in one mash, the volume of wort retained would be 30 x 0.06 = 1.8 gallons. Assuming a post mash volume into the boiler of 9.5 gallons, the total sparge water would be 11.3 gallons, same as before.

30 pounds x 37 points = 1110 total points. OG = 1110 pnts/11.3 gallons = 1.0982. Final volume is 9.5 gallons. Mash efficiency = 9.5 x 98.2 / 1110 = 84% <-- This would never be attained in the real world.

This is all theoretical. Real gravity will probably be 80% of the calc numbers.

I'll be brewing this beer twice in the near future. I'll report back how it goes.