From the HBD Archive
Subject: Mashing Formulas
Date: 2000-04-14 18:53:33 GMT

There were a couple of questions in HBD 3299 about decoction/infusion
amounts/temperatures. At the risk of trading in my library card for
employment at the local branch, here are all the formulas you need to
infusion/decoction mash. They can
be found on my web site and are the formulas used in my software. The only
credit I can take is for rearranging the basic formula to figure the others.

Basic Formula

The following formula will compute the final temperature of a mixture of
two masses at different temperatures.

Tf = (Hc1*M1*T1 + Hc2*M2*T2)/(Hc1*M1+Hc2*M2)

Where:

Tf = final temperature

Hc1 = heat capacity of first mass
M1 = wieght of first mass
T1 = current temperature of first mass
Hc2 = heat capacity of second mass
M2 = weight of second mass
T2 = current temperature of second mass

Rearranging this formula, and using a value of 1 for the heat capacity of
water, we come up with the following:

Infusion Formula - Amount of Initial Strike Water

The following formula will compute the mass of initial strike water
required to hit a certain mash temperature based on the temperature of
the initial strike water.

Ma = Hcm*Mm*(Tf-Tm)/(Tw-Tf)

Where:

Ma = required mass of initial strike water

Hcm = heat capacity of malt (about .4)
Mm = mass of malt used
Tm = current temperature of the malt
Tf = final temperature desired
Tw = temperature of initial strike water

Infusion Formula - Temperature of Initial Strike Water

The following formula will compute the temperature of the initial strike
water required to hit a certain mash temperature based on the mass of the
initial strike water.

Tw = (Ma*Tf-(Hcm*Mm)*(Tm-Tf))/Ma

Where:

Tw = required temperature of initial strike water

Ma = mass of initial strike water added
Tf = final temperature desired
Hcm = heat capacity of malt (about .4)
Mm = mass of malt
Tm = current temperature of the malt

Infusion Formula - Amount of Step Infusion Water Required

The following formula will compute the mass of the water required to
boost a mash from one temp to the next.

Ma = (Hcm*Mm+Mw)*(Tf-Tmash)/(Tw-Tf)

Where:

Ma = required mass of water to infuse

Hcm = heat capacity of malt (about .4)
Mm = mass of malt
Mw = mass of water already in mash
Tf = final temperature desired
Tmash = current temperature of the mash
Tw = temperature of infusion water added

Infusion Formula - Temperature of Step Infusion Water Required

The following formula will compute the temperature of the water required
to boost a mash from one temp to the next.

Tw = (Ma*Tf-(Hcm*Mm+Mw)*(Tmash-Tf))/Ma

Where:

Tw = required temperature of infusion water

Ma = mass of water infused
Hcm = heat capacity of malt (about .4)
Mm = mass of malt
Mw = mass of water already in mash
Tf = final temperature desired
Tmash = current temperature of the mash

Decoction Formula - Decoction Mass of Mash Required

The following formula will compute the mass of the mash that must be
decocted, heated and returned to the mash to boost it from one temp to
the next.

Md = (Hcm*Mm+Mw)/(1+((Tf-Td)/(Tmash-Tf)))

Where:

Md = required mass of decoction

Hcm = heat capacity of malt (about .4)
Mm = mass of malt
Mw = mass of water already in mash
Tf = final temperature desired
Td = temperature of decoction when added back to mash
Tmash = current temperature of the mash

Decoction Formula - Temperature of Decoction Required

The following formula will compute the temperature the decoction must be
when returned to the mash boost it from one temp to the next.

Td = Tmash-(Hcm*Mm+Mw)/Md*(Tmash-Tf)

Where:

Td = required temperature of decoction when added back to mash

Tmash = current temperature of the mash
Hcm = heat capacity of malt (about .4)
Mm = mass of malt
Mw = mass of water already in mash
Md = mass of decoction
Tf = final temperature desired

Fudge Factor

When adding either hot water or decoctions to boost your mash temp, you
must always take into account the amount of heat your mash tun will
absorb. Typically, this will only be 1 or 2
degrees fahrenheit, but will vary from system to system. After a little
trial and error, you will become familar with the temperature drop