Total sugar extraction as function of water input into the mash tun

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Johan Dingler

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So I'm preparing to brew an imperial stout. This is the second time i'll brew this recipe. I wanted to conduct a long two hour boil this time instead of the standard 1 hour. If I want to end up with the same amount of wort in my fermentor, obviously i'll have to have about a gallon more of pre boil wort compared to the last time I brewed this recipe.
Last time i went from about 7 gals pre boil to 6 gals in the fermentor, and this time i plan to go from about 8 gals pre boil to 6 gals in the fermentor. Logic tells me that this time my OG should be higher, since the extra gallon of water I'm dragging from the mash tun will contain some amount of sugar, and my final volume will be the same. However, according to the formulas I use, this is not the case, and the OG would be exactly the same. What am I doing wrong?

Formulas:
1) First I calculate my pre boil SG by getting the amount of sugar I can extract from each malt: SystemEfficiency*Malts'sPPG*MaltPounds/PreBoilGallons. I do this for each malt and then add them all up.
2) I take the pre boil SG and scale it up to the final volume: preBoilSG*(preBoilVol/postBoilVol)

I reckon since in the first formula I divide by preBoilVol and in the second formula I multiply by it, and this is the variable I'm changing, the OG ends up being the same in my calculations. How can I take into account the sugar that this extra gallon of runnings from the mash tun will bring into my wort?? Is it taken into account as an increase in mash efficiency???

Hope i was clear and thanks!
 
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How can I take into account the sugar that this extra gallon of runnings from the mash tun will bring into my wort?? Is it taken into account as an increase in mash efficiency???

Yes, the reason you get a higher OG by running off more and then boiling more is that by running off more, you're increasing mash efficiency, i.e. getting more of the total potential sugars/dextrins out of the mash tun and into the kettle.

Further reading...
http://sonsofalchemy.org/wp-content/uploads/2020/04/Mash_Efficiency_and_Brewhouse_Efficiency.pdf
 
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