Formula to calc sparge water temp after 1st runnings

What is the formula to calculate the temp of the sparge water needed after the 1st runnings have been drained from the mash tun so that the sparge temp is 168? I'm familiar with the strike water temp formula -

Strike Water Temperature Tw = (.2/r)(T2 - T1) + T2

where:
r = The ratio of water to grain in quarts per pound.
T1 = The initial temperature (¡F) of the mash.
T2 = The target temperature (¡F) of the mash.
Tw = The actual temperature (¡F) of the infusion water.

Last batch, I measured the temp of the grain in my mash tun after mashing out and draining the first runnings as 161 degrees. I wanted to sparge with water hot enough to raise the temp to 168 and guesstimated 176 degrees. It got me close (164ish) and fortunately below 168, but now I'm curious if there's a formula that will relieve me of guessing.

I don't know if there is a formula but I always sparge with 170F water. But I also batch sparge if it makes a difference.

Try Green Bay Rackers Mash Calculators. I'd link it but I'm on a phone and I don't want to.

On a side note, sparging at 168 doesn't really do anything. Your efficiency will be the same whether you're at 164 or 168. Denaturing is pointless since the mash already converted all starches.

No formula, just heat it into the mid 170's and sparge. There is nothing particularly magical about sparge temps unless you are doing long fly sparges where continued conversion might make the beer drier than desired.

V = Vmash * (Target Temp - start temp) /
(Boil Temp - T start)


That's what i used for my decoction mash. If you change your boil temp, to the temp of your water, and set the volume of water to the volume of the sparge you want to do. Then all you do is solve for the "boil temp" in that equation.