Mash efficiency, etc, according to the Professor.

We recently came across a piece by blogging home/craft brewer (and, we're sure, diamond geezer) broadfordbrewer  Reading an account of a yummy sounding raspberry wheat brew, we were a bit confused by some of the calculations employed in estimating efficiencies. So, as we usually do when confused (and we usually are), we asked the Professor for help.

"Ah yes, Stringers," he smiled,  "I've seen the kind of thing you're referring to."  He laughed, "These homebrewers and their formulae, passed down like myths and fairy tales from who knows what original source!"

"Of course" , he continued, "you'd be wise to measure efficiency in terms of how efficient you are in getting stuff out of the grain, so you refer to laboratory extract, rather than simply the mass of the grain (which would include husk, other insolubles, dead mice, etc), as some homebrewers do. Why do they do that?"

He limped over to the blackboard, "See, Stringers, you may have come across something like this..."
Chalk squeaked.

Extract = (volume) x (specific gravity) x (ºPlato — expressed in decimal form).

"But this doesn't really make sense...  since we can convert specific gravity to ºPlato like this..."

 degrees = (SG x 1000) - 1000
ºPlato = degrees / 4 [approx]

"So why are both SG and ºPlato in this formula? Since we can convert one to the other, we're not adding any information by including both. Formally, they're measures of the same dimension, expressed in different units. Pretty much."

He continued, "We can substitute and rearrange, to show that..." 

SG x ºPlato = (250 x SG²) - (250 x SG)   He smiled, "approximately".

"You see ºPlato has disappeared. So, indeed, there wasn't any point in having it in the first place!"

We spoke up, "The maths always seems easier if we work with litre.degrees."

"For sure, yes", said the Prof,   "The product of volume and gravity in brewers degrees."
He flourished his chalk, "For instance..."
10 litres at SG 1.040 = 10 x 40 = 400 Litre.degrees.

"Yes", we said, "That kind of thing."

He commenced pacing, "The maltsters give laboratory extracts for the malts which you might  think of as the extract 1 kg would give in 1 litre. If that were actually possible. For decent pale malts this is probably around 300 (assuming a coarse crush / moisture as is)"

We nodded, he went on,  "That's to say, one kg of malt mashed under ideal conditions would give you 1 litre of wort with a gravity of something like 1.300."

"So, for an example homebrew mash:" He turned back to the blackboard.

Pale malt: 2.8 kg @ 293 L.deg per kilo = 820.4
wheat malt: 0.8 @ 296 = 236.8

He waved at the board, "I got these values for extract from a recent malt analysis, but you can look up typical values on the InterWeb , or you could call it 300 and wouldn't be far wrong."

He continued writing,
total potential extract 820.4 + 236.8 = 1057.2 litre.degrees

Turning to us, "What you actually get out of the mash might be 24 litres at 1.040 Specific Gravity, i.e..."
24 litres x 40 degrees = 960 litre.degrees

"So your mash efficiency is something like..."
 960/1057.2 = 0.908 = 90.8%

"Post-boil, you might end up with..."
 18L @ 1.044 i.e 18 x 44 = 792 and 792/1057.2 = 0.749
"That is..."
74.9%

"Which you might call brewhouse efficiency!"

He dropped his chalk and pushed his spectacles back up, "Got that Stringers?"

"Thanks Prof!"