Calc for non-boiling water in stepped mash?

[hardrain]

Hey all, I can't find anywhere on the internet a calculator that will allow me to use non-boiling water for a step-up during my mash.

For example, instead of 1.5 gals of boiling water to raise my mash temp, how much of 185F water do I need?

I'm unsure if it's a linear dynamic, can I just take (if I'm using 185F water) ... 185/212 = .87. If i need 1.5 gals of water to hit my second step, is that just (1.5 / .87) = 1.7 gals of 185F water?

I ask because I have a tankless water heater that I can use to do this, which I like better than boiling water separately.

Thanks!

 

[helibrewer]

The fancy formula is:

0 = (m Cp deltaT) for water + (m Cp deltaT) for the grain
m = mass in kg
Cp = heat capacity in kJ/kg/K
delta T = change in temperature (T final - T initial)

You can use C for temp since it is delta T and 1C=1K

The Cp of water is 4.19kJ/kg/K and grain is 1.6kJ/kg/K
1 gallon of water = 3.79kg
212F = 100C
185F = 85C

In your case you would solve this equation for m of water and convert back to gallons

 

[pricelessbrewing]

As far as I'm aware, there is no prebuilt calculator to do this currently.

The formula above is correct however it's probably more involved then most brewers can deal with, and the conversion for gallons of water to kg of water is only true at room temp. I'm not sure of the heat capacity of grain, as I'm sure it varies based on variety, type of grain, and moisture content of the grain. Moreover you'll need two terms for the water (existing water in mash, and new water addition, then combine terms and simplify).


The traditional formula (from palmer) is shown here

http://howtobrew.com/book/section-3/the-methods-of-mashing/calculations-for-boiling-water-additions

Palmers formula says you need approximately 1.82-1.88 times the amount of 185F water as 212F water.

 

[hottpeper13]

In John Palmers How to Brew first edition on page 170 has all the formulas for figuring out everything, and I use them for every brew. The addition formula for step mashes needs the temp of the addition to work , hence 185 would be your constant. Mine is 209 because that is the temp after going thru the pump and lines.