First decoction mash- check my calculations

I'm gonna try my first decoction mash (and second step mash) for tomorrow's Hefeweizen. Can y'all double check my process (and my math )? I'm intentionally pulling slightly larger decoction volumes than it says it needs to compensate for any temperature loss in the mash. I normally just do a straight single infusion somewhere between 147-160 (depending on the beer), and skip mash out. The one step mash I did was infusions from protein rest to conversion rest, still with no mash out. So I'm unsure on some of this stuff.

Using this formula from How to Brew: Vd=[(T2-T1)(0.4*G+2*W)]/[(Td-T1)(0.4Gd+Wd)]

I mash in for my protein rest, 122F, with 11.25 quarts at 132F. I hold this for 20 minutes. (numbers thanks to the Brewers Friend mash infusion calculator).

I want a next step of 150, so Vd=[(150-122)(0.4(9)+2(11.25)]/[(212-122)(0.4(1/(0.6+0.32))+2(1/(0.6+0.32))(.6))]=4.669. In other words, I pull off 5 quarts of thick mash, heat it to 150, hold it for 20 minutes, then boil for 20 minutes. Add slowly back to mash checking temperature the whole way. Will have both boiling and cold water on hand to adjust if necessary.

That’ll get me to conversion temp of 150. Hold for 45 minutes.

Next step is 168, so Vd=[(168-150)(0.4(9)+2(11.25)]/[(212-150)(0.4(1/(0.9+0.32))+2(1/(0.9+0.32))(0.9))]=4.2. So I pull 4.5 quarts of thin mash, heat to 160 for 20 minutes, then boil for 20, add back, again adjusting if necessary with boiling or cold water.

That’ll get me at 168 mash out. Hold for 10 minutes or so, then sparge and proceed as usual.

Am I missing anything?

Your protein rest is going to be pretty long when you consider the time that you're doing the decoction. Make sure the pH is in the park before boiling. Try not to scorch the grain when you start to cook it. Do what you have written, after a while you'll dial in the process. It will take a few batches. I tri-decoction. It has taken me a long time to gather up the best equipment for that process and to get to the point of producing a consistent and balanced product. You'll do fine.

Raise your protein rest temp to 131 or skip it entirely. Also, if you mash in a cooler, my experience is that calculations for decoction amounts go out the window. You need to pull and boil a lot more than any calculator I know of tells you to do.

Well, I'm rolling along. Before reading this I raised the protein rest to 126 (if I do this again I'll go higher) and also shortened it to 10 minutes, and pulled a little more than 5 quarts for the first decoction (rougly .75 quarts more than the math said). Added it back in, and nailed the 150 mark, so between the higher temp/shorter time and the bigger decoction pull, looks like you're exactly right about calculations. This is quite a bit easier than I expected, although the stirring seems a bit tough on the arms. I'm also mashing in a kettle. And my pH has been at 5.4 the whole time. A tad higher than I'd prefer, but that's still good in range, no?

Thanks for the help!

Second decoction (again a little over 5 quarts) got me to 167. And now it's back to brewday as usual. This wasn't that tough. Although I don't know if it's going to make enough of a difference to be worth the extra time it took.