I. Water
Water is water, right? Not at all. Beer is mostly water, and it’s composition can have a huge impact on the final brew.
Is my water good for brewing? The first basic test is to taste it. If it tastes ok, then it’s probably good to brew with. If not, you may want to consider another source.
Get a copy of your water report. If you use bottled water a lot, get a copy of the report from them – it may not be as pure as you think. Many cities have their water reports available on line. Those that don’t will usually mail you a copy.
Pure H2O? Despite what some water venders may tell you, their water is not pure H2O, or even close to it. Pure lab grade water is way expensive (on the order of $20 per gallon, if I remember right) and comes with a “do not drink” warning.
Chlorine – usually 2-3 ppm (parts per million) in drinking water
Detectable at about 0.1 ppm, and objectionable to 50 ppm.
General rule – remove as much as possible.
Boiling or letting the water stand overnight will remove chlorine gas.
Only the charcoal filter will work for chloramines, which are the more common chemical for chlorination water.
I don’t do anything and it still turns out ok.
Effects of too much chlorine – plastic and/or medicinal flavor & aroma
Good things in water: Low concentrations of nitrogen-containing ions. Also iron, manganese, copper, and zinc which are needed by the yeast for healthy fermentation.
Define ion: A molecule with a net charge – either extra electrons or too few.
Define ionic compound: An ionic compound is one in which two (or more) elements come together, and an electron is transferred from one to the other. An example is table salt (NaCl). Sodium (Na) and chlorine (Cl) can combine. An electron is transferrend fro the Na to the Cl (for reasons that are way beyond the scope of this class) forming positive sodium ions and negative chlorine ions. These ions will combine in regular patterns, forming the salt crystals we use in cooking.
Define pH: (water contains many OH- and H3O+ ions, in varying proportions)
Mathematical definition of pH: pH = -log[H+], where [H+] is the concentration of the hydronium ion, also sometime written as H3O+
In practical terms, pH < 7 is an acid, and pH > 7 is a base (and no, 14 is not the limit)
Hardness and alkalinity – hardness is a measure of the cations (positively charged ions) in the water, usually calcium and magnesium.
The Anion (negatively charged ion) determines if the hardness is permanent or temporary. If the anion is bicarbonate, then the hardness is temporary and can be removed. Boil the water and a white solid, CaCO3, will precipitate out. Siphon the water off the white precipitate.
If the anion is sulfate (SO4), the hardness is permanent, and can’t be removed by boiling.
If Ca is less than 100 ppm and the Mg is less than 30 ppm, you’re ok and don’t need to change it. Otherwise, consider diluting the water with distilled. Especially for pale beer.
Alkalinity – is a measure of how well buffered the solution is – able to resist changes in pH when acids or bases are added. Essentially, how much calcium carbonate would I have to add in order to have it buffered this amount? (expressing it as equivalent CaCO3).
Water with a high alkalinity tends to have a high pH (although the reverse is not necessarily true).
Why are we concerned about pH?
Mash enzymes work best in certain pH ranges.
pH influences how husk tannins are dissolved.
Ions to be concerned with
Calcium (Ca++): 50-150 ppm is optimum for mashing.
Can be added as: gypsum (CaSO4*H2O)
Calcium carbonate or chalk (CaCO3)
Calcium chloride (CaCl2*2H20)
If water is high in sulfate, add the chlorate or carbonate form
If water is low in sulfate, it’s ok to use gypsum
Magnesium (Mg++): 10-20 ppm recommended as a yeast nutrient.
More than 30 may give a sour taste (good if you’re doing a Flanders Red)
Sodium (Na+): No effect on mash chemistry, but it has a flavor.
70-150 ppm, it will accentuate sweetness, especially if chloride is also present.
Above 200 ppm, a salty flavor is noticeable.
To add – don’t use iodized; iodine is toxic to yeast.
Carbonate (CO3--): will counteract the effects of calcium in the mash.
Should be less than 50 ppm for pale beers.
Bicarbonate (HCO3-): Same effect as carbonate, but with twice the buffer capability.
Chloride (Cl-): No direct effect on mash reactions. If greater than 250 ppm, it can enhance sweetness. High concentrations can hamper yeast flocculation.
Sulfate (SO4--): Accentuated hop bitterness and dryness. At greater than 400 ppm this may be too astringent.
Brewing water of famous brewing cities
City |
Ca++ |
Mg++ |
Na+ |
CO3-- |
SO4-- |
Cl- |
Pilsen |
7 |
2 |
2 |
14 |
5 |
5 |
Munich |
76 |
18 |
2 |
152 |
10 |
2 |
Vienna |
200 |
60 |
8 |
120 |
125 |
12 |
Dortmund |
225 |
40 |
60 |
180 |
120 |
60 |
London |
52 |
16 |
99 |
156 |
77 |
? |
Dublin |
118 |
4 |
12 |
319 |
54 |
19 |
Burton |
268 |
62 |
54 |
200 |
638 |
36 |
Notice the huge range in numbers, especially between Pilsen and Burton. Traditionally they weren’t anble to adjust the water chemistry directly. Styles and brewing techniques had to be adjusted to allow best use of the local water.
Classic beer styles associated with the cities listed in the table above:
Pilsen – pilsner
Munich – Hellas (a light lager. See the style descriptions for details)
Vienna – Vienna lager is an amber lager
Dortmund – export
London – Porter
Dublin – Stout
Burton – English Pale Ale
Brewing water of cities in the United States
City |
Ca++ |
Mg++ |
Na+ |
CO3-- |
SO4-- |
Cl- |
Antelope Valley |
25 |
12 |
3.4 |
? |
55 |
85 |
Helena Montana |
45 |
13 |
6.6 |
? |
17 |
7 |
Duluth, Minnesota |
? |
? |
7.6 |
? |
9 |
? |
Azusa, CA |
55 |
12 |
25 |
? |
33 |
37 |
Monrovia, CA |
69 |
15 |
10 |
? |
33 |
20 |
San Diego |
66 |
6 |
78 |
1 |
66 |
90 |
What can we see from this data? First, we see that most municipal water reports aren’t complete. Some are several pages with lots of data, while others are a single page with almost no useful information. We also see the same kind of variation that shows up among the European cities. It’s especially interesting to compare Azusa and Monrovia, which are only a few miles apart. Much of the difference is due to the fact that Azusa has wells, and Monrovia gets most of its water from the Colorado River.
Chemical adjustments – I won’t go into these in this class, since it’s probably beyond what most SCA brewers are interested in. For the full article, see the Zymurgy Great Grain Issue.
II. Grain
Types of grains
Barley – the most common.
Rye
Malted rye – distinctive flavor when used in small amounts
Huskless, with lower extract than barley or wheat
Wheat
Malted wheat – amer & german wheat beers and kolsch
Unmalted wheat used in Belgian brewing
High diastatic power, lots of extractable sugar
huskless
Oats
Corn
Rice
Uncommon grains that can be used: buckwheat, millet, sorghum, triticale, wild rice.
More exotic ones that should work, but for which there’s little data: adlay, amaranth, dinkel, fundi, kamut, kasha, quinoa, spelt, and tef.
The malting process – one line description: (see BJCP study guide, page 46)
“The process of malting is done to convert the large, insoluble starch chains of the endosperm to water soluble starches, and to activate both the proteolytic and diastatic enzymes that will reduce the proteins and starches into desirable components in the mash”
Start with seed barley – contains the embryonic plant and reserves of starch and protein.
Starch and protein are in long chains & tightly packed – not well suited to our purposes.
Starches are mainly 2 types:
Amylose – long straight chains
Amylopectin – many branches, like a bristle brush
Starches are long chains of sugars – our goal is to separate the sugars
(See Brew Chem 101, pages 28 and 29) – examples of the sugars produced from various sized chunks.
G = glucose molecule F = fructose
Amylose: G-G-G-G-G-G-G-G- up to ~1000
Glucose: G
Maltose: G-G
Maltotriose: G-G-G
Fructose: F
Sucrose (common table sugar): G-F
Raffinose: G-G-F
Maltose is the largest contributor to our brewing.
Malting: grain is made moist and kept warm. The plant is allowed to germinate, or have acrospire growth. See the diagram in the Zymurgy special issue page 39.
Degree of modification: The ratio of the size of the acrospire, compared to the size of the kernel is called the degree of modification. The malster chooses when to halt the growth according to the desired properties in the final grain. A greater degree of modification gives more enzymatic power for breaking down starches, but leaves fewer starches .
After a certain amount of germination, the grain is dried and kilned, in varying ways depending on the desired final product. (The BJCP study guide gives a good description of temperatures and kilning times)
Enzymes – are also created (to add to the ones already there) during malting
Alpha-amalyse and beta-amalyse – active at different temperatures.
Enzymes will attack and split up the starches during the mashing process.
The Lovibond color scale
Used to describe the color of the grain.
Pale malt is less than 5. Show examples of the various levels.
Black malt is greater than 400
Types of Barley
Pale malt: 2 row vs. 6 row
American 6 row – less starch but more husk weight than 2 row
More protinaceous substances – more hot & cold break
Could give problems with haze
Harder to find for homebrewers
More extract from 2 row (per kernel)
Barley provides most of the enzymatic (diastatic) power – to convert complex starches into fermentable sugars
Dried completely before kilning (minimum color development)
Specialty malts
Table 2 on page 11 of the Zymurgy special issue has a great list of types of malt the some of their properties.
These are kilned at higher temps than pale malt, when dry or having very low moisture content. They have more flavor and still have some diastatic power.
Examples:
Vienna, Munich, amber, brown, biscuit, mild, or victory (there are many more)
Caramelized malts
These are fully modified during the malting process and kilned at relatively high temperatures while still moist. This makes the starches turn to sugars, and then caramelize.
Specific types:
Belgian Caravienne – caramel toasted flavor with residual caramel sweetness.
Good in a bock or Octoberfest
Belgian Caramunich – darker & more robust version of Caravienne. Gives a soft smooth finish.
Special B – extremely dark caramel malt with intense toasted flavor; almost toffee-like
Don’t use more than 2-4 ounces in 5 gallons unless you’re very familiar with it.
Well suited for Scottish ales.
Dextrin and Carapils:
Similar to caramel malts, but kilned at lower temperatures to minimize color production. These are good for boosting the body of light beers. Generally used as 5-10% of the grain bill.
Roasted malts & grains
These are kilned at very high temperatures that carbonize the starches & sugars.
Examples: chocolate malt, black patent, roated barley (not malted prior to kilning).
They have no diastatic power and need not be mashed.
They impart a lot of color and flavor
Other types:
Kilned over an open fire – German smoked
Kilned over peat - scottish
White malt (1 L) – used for lightening beers (rare)
Melanoidin malt – for adding body (rare)
Sauer malt (German) – an acidified malt for pH adjustment
Honey malt – good for adding maltiness and body
Adjunct grains and other souces of fermentable sugars
Flaked barley, corn, wheat, rice, rye, oats
Rolled oats
Potatoes
Corn tortillas
Corn grits
Refined corn starch from the grocery store (add directly into the mash)
Use of various malts in your beer
Specialty malts – usually up to 10% of the grain bill. When doing a partial mash, it could be much higher.
Smoked or peat malt – a little goes a long way. Use very little.
Caramelized malt – gives a sweet maltiness, and contributes to body & mouthfeel. They are typically used as 5-15% of an all grain beer. These are the ones well suited to partial extract recipes.
When in doubt, taste the grain
Roasted malt: use sparingly – it’s easy to over do it.
Unmalted adjuncts – starches should be gelatinized prior to use (heating that makes the starches vulnerable to the enzymes by rupturing the cell structures protecting the starches)(Flaked adjuncts can be added directly into the mash since they have been gelatinized)
Flaked barley – foam stability and mouthfeel – I use this in my Otuell Ale, adding a bit of complexity to the flavor.
Beware the stuck sparge! When using lost of adjucts, add some 6 row or extra hulls.
Crushing
Malt must be crushed but not ground to a powder. We want access to the starch, but will need a good grain bed. There are mills made specifically for crushing brewing grains. When possible, use the mill at the shop where you buy your ingredients.
The mashing process
Water and grain are mixed – the enzymes are activated
Types of mashing: Note – detailed discussion of mashing techniques is beyond the scope of this class.
Step mashing versus single step mash – depends largely on grain bill
Infusion mash – add hot water to change temperature
Decoction mash – take part out, heat it, and add it back in to change temp.
RIMS / HERMS – for serious geeks only
Enzymes are active at different temperatures
Alpha-amalyse: attacks all portions of the starch to make longer chain sugars
Most active at higher mash temperatures (131 – 158F)
Produces the dextrins that give body.
Beta-amalyse: works on the ends of the starch chain to make small sugars (maltose)
Most active at lower mash temps (113 – 149F)
Rapidly deactivated above 149F
Steeping for partial mash brewing
Add character to extract beers
See Zymurgy special issue, page 48, for a good discussion.
III. Hops
Reference: Zymurgy special issue 1997
History of hops (brief)
Note the SCA convention of using the presence of hops to define a beer vs. an ale (at least until lager brewing started).In most of the SCA period, a hopped beverage is a beer and unhopped is an ale.
There is some evidence that this distinction wasn’t used (at least in England) until the 17th century.
Before hops what was used to counteract the sweetness of the malt (and to generally add flavor)?
Birch, spruce, oak, ginger, gillyflower, black pepper, wormwood, capsicum, juniper berries, heather, bog myrtle, ground ivy, lemon & orange peel, cardamom, mace sage, date juice, honey, ginseng, gentian root, nettle, dandelion, pennyroyal, wintergreen, mint, garlic, horseradish, and more.
Hops are believed to have originated in Asia, where several varieties of the genus humulus grow wild.
Pliny the Elder (Roman) writes about hops in the first century AD.
Romans used hops for food, and probably used the cones medicinally.
As a medicine, hops have been used for: diuretic, preventative against kidney & bladder stones, remedy for dyspepsia, a mild laxative and to prevent premature ejaculation.
Pillows stuffed with hops were also used to aid sleep (possibly not until the 18th century)
Earliest unequivocal discussion of hops in brewing: St. Hildegarde in 1071 (a member of the Benedictine order and Abbess of Rupertsebrg in SW Germany). More info on her is in the Zymurgy special issue pages 9 & 10.
By 1101, hops grown in Bohemia (Czech Republic) were being shipped to the markets in Hamburg.
Use of hops moves to Northern Europe and Scandanavia – meeting resistance everywhere, sometimes for financial reasons, sometimes not.
What forms are available?
Plugs – leaf hops compressed into plugs of a certain size – not real popular
Not used commercially in US, therefore there’s limited availability
Pellets – most common among homebrewers, they are convenient
Less prone to oxidation & take handling abuse better
More consistent
Extracts – not applicable to homebrewers
Hop oil (essential oil) - not usually applicable to homebrewers
Some shops sell oils for adding dry hop aroma
Difficult to work with. Hard to get consistency
Whole hops – leaf hops in a bag
More prone to oxidation & can have lupulin variations within the bag
I like them as a filter in the boiler (and because they’re traditional)
Why use hops?
Longer shelf life
Better taste?
Alpha acids – the main thing we’re concerned with as brewers
Humulone, Cohumulone, and Adhumulone
The amount varies with the hop variety
During the boil, all 3 will isomerize into bitter configurations
The isomerized acids help with stability of beer head and have a bacteriostatic effect.
Isomer: a compound with exactly the same elements, and exactly the same number of atoms, as another compound, but whose atoms are arranged in a different order. Six isomers are created from the three alpha acids (enough detail – see page 51 of the special issue for more details).
Note: isomerization is very slow – it’s not 100% after even 4 hours of boiling.
Essential oils – responsible for flavor and aroma (0.5 to 3 % of total mass)
More than 250 chemical compounds in beer have been traced to essential hop oils
How to use hops
First wort hopping – add hops to the kettle as you start filling it – before the boil
This gives a nice flavor to the final beer.
Use low alpha, noble type hops.
Used in Germany at turn of the century
People (homebrewers) started doing it only recently (it’s been rediscovered)
See page 74 of the Zymurgy special issue for a detailed discussion.
Bittering hops – typically boil for 60 minutes or longer
Flavor/Aroma hops
Boil for a short time (2 -30 minutes)
Steep – add after the boil
Hop back – run the hot wort through the hops
Dry hopping – add directly to the fermentor.
Utilization – portion of alpha acids that become isomers
Factors affecting utilization: boil time (30-35% for a 90 min boil), wort gravity, wort pH, vigor of the boil, amount of hops added, and the type of hops product used.
Wort pH – As pH goes up, so does utilization (don’t try adjustments though, the wort is too heavily buffered)
Boiling time – the longer you boil the more utilization you get
Gravity correction – as gravity increases, utilization decreases
Hop addition quantity – larger quantity gives lower utilization (due to the solubility limit of alpha acids in wort)
Factors affecting utilization (see Page 71 of special issue)
Factor |
influence |
Utilization |
Wort pH |
Increase pH |
Increased |
Length of boil |
Longer boil |
Increased then decreased |
Hop addition rate |
Higher addition |
Decreased |
Wort original gravity |
Higher gravity |
Decreased |
Foaming in kettle |
More |
Decreased |
Foam in fermenter |
More |
Decreased |
Age of hops |
Older |
Decreased |
Alpha acid content (%) |
Higher |
Decreased |
Trub volume |
Higher |
Decreased |
Cold break volume |
Higher |
Decreased |
Yeast strain |
? |
Yeast dependent |
Pressure boiling (higher temp) |
more |
Quicker |
|
|
|
Growing your own (page 25 of the special issue)
Grown from rhizomes (root cuttings) rather than seeds.
Lie dormant in the winter and emerge in the spring
IBU’s & HBU’s
AAU = Alpha acid unit
HBU – Homebrew bittering unit (same as the AAU)
AAU = HBU = (weight of hops) * (alpha acid content)
A 15 HBU beer could use 3 oz. of 5% or 2 oz. of 7.5%
Doesn’t take into account volume of wort or boiling time (utilization)
Think of 15 AAU in 5 gal & 15 gal
To be more precise (account for non standard condition) – IBU
A measure of the alpha acid present in the beer regardless of how it got there.
IBU = 1ppm of iso-alpha acid = 1 mg iso-alpha acid per liter of beer
Assuming (bad assumption) that all the iso-alphas in the hops become iso-alphas in the final beer:
IBU(ideal) = (weight in oz. / Vol in gal) * (7489/100)
7489 = conversion from oz/gal to mg/L
1/100 = convert from percentage to fraction
Add in the utilization (U%)
IBU = (0.7489 * Woz * A% * U%) / Vgal
Corrections to the utilization
U% = U%(boiltime) * F(boilgravity) * F(hopform) * F(hoppingrate) * F(boiltemp) * F(storageloss) * F(hopbag) * F(yeastflocculation) * F(yeastfiltration)
For most brewers, ignore all except the first two, and possibly the third
See the graphs & tables below – note that I picked out a single set of data from that listed in the Zymurgy special issue. They had data shown from multiple calculation methods. Utilization as shown in the graph is percent.
Miscellaneous
BATF (or whatever they’re called these days) says: a beverage must contain at least 7.5 ponds of hops per 100 barrels to be considered a beer for tax purposes.
Botanical name : humulus lupulis, or little wolf plant
IV. Yeast
Reference: Zymurgy special issue 1989
History of yeast in beer – it’s always been used, just not understood.
The nature of yeast as a microorganism not known until Anton Van Leeuwenhoek of Holland (1632-1723).
The nature of fermentation wasn’t well understood until 1836, when Cagnaird Latour first proposed that sugar fermentation was a result of yeast activity.
Basic microbiology
Yeast is a fungus
Sachromyces Cervisiae, ale yeast
Also called top fermenting yeast
Ferments at higher temperatures (55 – 75 deg F)
Often produces fruity or sweet smelling aromas (esters)
Sachromyces Uvarium aka S. Carlsbergensis
Need cooler temperatures, 46-56 deg F
Bottom fermenting
Tend to produce a “cleaner”, less estery beer
Other yeast genus’s are Dekkera and brettanomyces (Note: Vinny Cilurzo, of Russian River Brewing makes a rather good beer fermented with 100% brett)
Difference between a species and a strain – thinks of dogs. A Chihuahua and a St. Bernard are the same species, but different breeds with very different characteristics. It’s the same with yeast. All ale yeast is Sachromyces Cervisiae, but different strains have different characteristics.
Microbiology difference between lager and ale yeast – see “Brew Chem 101, page 30, in the fructose section. One can metabolize raffianose (a sugar) and the other can’t.
Bacteria
From the BJCPstudy guide:
Bacteria, specifically Lactobacillus delbrueckii, is used in the production of the Berliner Weiss style of wheat beer with an intense lactic sourness. Other microorganisms are also used in the production of some Belgian ales, specifically lambics. Lambics have varying degrees of sourness which is appropriate for their style. Yeasts of the Brettanomyces genus, and various bacteria generate these flavors. Bacteria are commonly divided into two broad classes based on a laboratory Gram stain. The Gram-negative bacteria involved in lambic production are Escherichia coli and also various species of Citrobacterand Enterobacter, but fortunately they cannot tolerate even moderate alcohol levels and do not survive in the finished beer. The Gram-positive bacteria involved are from genus Pediococcusand Lactobacillus. These microorganisms use a different pathway than that of Saccharomyces yeast known as a mixed acid fermentation pathway. It involves the esterification of the various alcohols to the corresponding carboxylic acids, thus generating the sourness (7).
From the Brewing Techniques archives (http://www.brewingtechniques.com/library/backissues/issue1.1/schiller.html)
Beer-spoilage bacteria can be introduced during any phase of brewing; however, they grow and multiply at a quick rate after the yeast has created an acidic, anaerobic environment. Genera causing beer spoilage and odors or flavors commonly associated with fermentation with these bacteria are Pediococcus (diacetyl or ropiness), Acetobacter (vinegar), Acetomonas (apple or cidery), Lactobacillus (di-acetyl and lactic acid), and Zymomonas (rotten apples). Like yeast, bacteria are also living chemical microfactories, though the products of these factories can be foul, even in concentrations of parts per billion. Bacteria from some or all of these genera are present where you brew. To convince yourself that these bacteria are in your brewery, leave some spare wort open to the air at room temperature without adding yeast. After the bacteria "ferments" your wort, take a small taste. Unless you are attempting some classic Belgian styles or enjoy bacteria-fermented beer, these microorganisms are best left in the environment from which they came.
Basic life cycle of yeast
Phase 1 – the lag phase. Yeast is adapting to the environment.
Phase 2 – the growth phase. The yeast will begin budding, creating new cells, until the right concentration for fermentation is achieved. All of the dissolved oxygen in the wort is absorbed during this phase.
Phase 3 – The low krausen phase of primary fermentation. The yeast begins anaerobic activity. This is when the foam cap on top of the wort developes.
Phase 4 – The high krausen stage. Most of the sugars will be metabolized.
Phase 5 – The late krausen stage. This is where lager yeasts will metabolize some of the fermentation by products produced – especially diacetyl. The yeast will start to settle out in this stage.
Yeast reproduce via budding
To remember: yeast cycle is meant to make more yeast, not to make beer.
Making a yeast starter – Grow your yeast culture up to the best size for healthy fermentation. This will be covered in a future collegium class.
Definition of terms
Flocculation – refers to the settling of the yeast after fermentation is complete.
Attenuation – A measure of the percentage of sugars that get metabolized.
Alcohol tolerance – Alcohol is toxic to yeast. When it reaches a certain level, it starts killing off the yeast. Alcohol tolerance refers to how high the alcohol levels have to be before this starts to happen.
Esters and ester production – These are the chemical compounds that give us the fruity and sweet aromas and flavors in ales. In certain strains, such as those for wheat beers, they will produce clove and banana flavors.
References
Zymurgy Special Issue 1989 – Yeast and Beer
Zymurgy Special Issue 1996 – The Great Grain Issue
Zymurgy Special Issue 1997 – The Classic Guide to Hops
Principles of Brewing Science, by George Fix
Advanced level information on the brewing process.
An Analysis of Brewing Techniques, By George and Laurie Fix
Advanced level information on the brewing process.
Brew Chem 101 – The Basics of Homebrewing Chemistry, by Lee W. Janson
A more basic level than the George Fix books.
New Brewing Lager Beer, by Greg Noonan
A classic in the homebrewing community. Loads of good information. The title says it’s for lager brewing, but there’s plenty of information that applies just as well to ales.
Designing Great Beers, by Ray Daniels
A good all-around reference book.
The makers of Wyeast, one of the most popular yeasts for homebrewing.
http://www.beertown.org/homebrewing/index.html
American Homebrewers Association – a nation wide organization of homebrewers started in Colorado in the 1970’s.
The Beer Judge Certification Program. This is the program used for non-SCA brewers to learn beer judging. The style descriptions and exam study guide both have some good information.
http://www.brewingtechniques.com/
One of the best homebrewing magazines made, which unfortunately went out of business a few years ago. The web site still has a bunch of their articles posted – very good info.
A good general reference. I used section 15.1 Understanding the mash pH for the classs.