In light of Phil's gravity confusion on another thread, I thought I'd post up how I went about formulating my last recipe, an APA. This is how I go about 95 % of my beers:

First up I decide the target gravity and the rough malt bill:

Then the volume: 28 litres
Then the expected efficiency: 78 %

To work out how the expected efficiency affects the quantity of grain you use you need to do a bit of maths. In brewing texts it is generally accepted that pale malt has a potential extract of 1.037 SG per lb per US gallon (3.8 litres). Notwithstanding fluctuations in quality of malt, I find it easiest to round up the entire grain bill to 1.036 SG lb/gal including all the crystal and roast malts etc.

First I convert this to metric: 1.036 = 36 GU

36 x 3.8 = 136.8 GU per lb per litre

136.8/0.454 = 301.32 GU per kilo per litre

So this is my basic unit for potential extract in every brew: 301 GU/kg/l

Now apply the efficiency: 301 x 0.78 (78 %) = 235 GU/kg/l

In other words I expect to get 235 Gravity Units for every kilo of malt for every litre of wort.

*Crystal malts and particularly roast malts have lower potential extract, so when I do a brew with a lot of roast malt etc, I dial my expected efficiency back a bit - you need to get a feel for this, but it is easier than working out potential extract for each grain and applying the efficiency one by one...*

Now to work out the quantity of grain:

28 litres x 1.050 = 1400 GU

1400 GU/235 expected extract = 5.96 kg of grain

So:

73 % Pils Malt - 4.35 kg
9 % Munich - 0.537 kg
9 % Oat Malt - 0.537 kg
9 % Caramalt - 0.537 kg

After mashing and sparging I collected 32.8 litres at 1.045, equal to 1476 GU when I was aiming for 1400 GU. This means my extract efficiency was 1476/5.96 kg = 247 GU/kg/l

247/301 = 82 %

Once I boil this down to 28 litres I will have an OG of 1.052.

Also included in the recipe are loads of citra, galaxy and amarillo and the new Danstar BRY-97 American Ale yeast.

This ^^ is all quite geeky stuff that I love, when clearly you can get good results using different methods (including guesstimation!). I also do all my calcs for the mash and hopping rate by hand and can post this stuff up if it is of interest to anyone....

I *can* do all this by hand (and alot of it in my head - the bjcp written exam actually tests your ability to do so). But I like the convenience of using software to mve things about during recipe formulation, and then the added aspect of inventory management.

Ali

BJCP National Judge
BJCP Assistant Regional Director (North-East/Europe)
American Homebrewers' Association International Subcommittee
Organizer, National Homebrew Competition
CBA UK Competition and Training Coordinator

Can't agree more. Even if you forget the maths a day after you learn them, at least you have the right intuition built up, which comes in handy when troubleshooting problems. Thanks for the great write-up!

If you want to improve the accuracy a bit at the expense of simplicity, the varying GU contributions from each malt can be taken into account using a weighted average. It looks like this:

Where ax represents the GU/kg/L of each malt, and bx is the mass (in kg) of malt you want to add. I've written the equation with three malts, but follow the pattern to add as many as you like. The jist of the equation is that it comes up with an average GU/kg/L figure, but gives priority to the malts that make up a greater percentage of the grain bill.

If you work in terms of percents rather than weights, the equation gets a lot simpler:

Effective GU/kg/L = (a1*p1+a2*p2+a3*p3)

where px is the percent of each malt, written in fractional form. So 55% would be written as .55, for example.

Just uploaded the homebrewed homebrew calculator spreadsheet I've made for myself and Ariel. Find it here, and feel free to copy the template to a new sheet and edit as you please. I guess this is a bit counter to the moral of Mark's post, but since it's an Excel spreadsheet, at least you can see the equations behind the numbers. Tell me if you spot any errors too!

EckersKlein wrote:Can't agree more. Even if you forget the maths a day after you learn them, at least you have the right intuition built up, which comes in handy when troubleshooting problems. Thanks for the great write-up!

If you want to improve the accuracy a bit at the expense of simplicity, the varying GU contributions from each malt can be taken into account using a weighted average. It looks like this:

Where ax represents the GU/kg/L of each malt, and bx is the mass (in kg) of malt you want to add. I've written the equation with three malts, but follow the pattern to add as many as you like. The jist of the equation is that it comes up with an average GU/kg/L figure, but gives priority to the malts that make up a greater percentage of the grain bill.

If you work in terms of percents rather than weights, the equation gets a lot simpler:

Effective GU/kg/L = (a1*p1+a2*p2+a3*p3)

where px is the percent of each malt, written in fractional form. So 55% would be written as .55, for example.

-Eric

Nice! I'll try that equation for the malt bill on my next brew, though I suspect I'll prefer my method for its simplicity.