Infusion Volume for a Mash Step

A step mash holds the grain at several temperatures in turn — a protein rest, a saccharification rest, a mash-out — and the traditional way to move between them without a direct heat source is to add boiling water. This equation says how much. It is the same heat balance as the strike-water calculation, run in the other direction: instead of asking how hot the water must be for a known volume, it asks how much water is needed at a known temperature.

Read the numerator and the whole thing becomes obvious. $0.2G + W_m$ is the mash's thermal mass in quart-equivalents — the grain counted at a fifth of its weight because malt holds a fifth as much heat per pound as water does per quart, plus the water already there at face value. Multiply by the temperature rise you want and you have the heat required; divide by how much each quart of infusion water can give, which is $T_w - T_2$, and you have the volume. The same 0.2 carries the same imperial baggage as it does in the strike calculation, and for the same reason.

The constraint this equation makes visible is that step mashing by infusion runs out of room. Each addition thins the mash, so the second step needs proportionally more water than the first, and the third more again. A brewer who starts at 1.25 quarts per pound and steps three times will finish somewhere near 2.5, at which point the mash is a soup and there is no headspace left in the tun for a sparge. This is precisely why decoction exists: pulling a thick portion of the mash, boiling it, and returning it raises the temperature without adding any water at all, at the cost of an hour and a scorched pot. It is also why direct-fired and RIMS systems have displaced infusion stepping in most modern homebrew setups.

Practical notes that the arithmetic omits. Add the water gradually and stir continuously, or the addition will overshoot locally and denature enzymes in the hot spot even while the bulk sits below target. Let the mash equilibrate for a minute before reading the thermometer, because a stratified mash will read whatever the probe happens to be sitting in. And check the mash temperature before calculating rather than assuming it is still where you left it — a mash loses a degree or two over a rest, and starting the calculation from the temperature you INTENDED rather than the one you have is the mistake that compounds through every subsequent step.