It's been some time since I've last brewed. You see, I broke my ankle 3 weeks ago and have been relegated to crutches as my only means of getting around. That being said, I've not been spending any time lifting carboys or carrying around 6 gallons of hot wort. The last time I brewed was on May 7th! So much for the summer plans of brewing weekly.
At this point, the kegs are running dangerously low and I need to heal up so that I can crank out some Bitter and Porter to fill the pipeline again. The upshot is that the beer I made on May 7th, an American Pale Ale, hasn't been touched since I pitched the yeast on 5/8. With a little lifting help that beer will be in a keg by day's end. As always, this is one of my favorite parts of the whole beer-making process because I'll have an entire hydrometer to sample and get a first glimpse of how the beer turned out.
Now more about the beer...
Summer Pale Ale, brewed on May 7th, 2011
Grain:
8.25# 2-Row
1.68# Dark Munich
1.16# Crystal 40° L
Hops:
12 AAUs Cascade (60 min)
1 oz Centennial (7 min)
0.5 oz Cascade (3 min)
0.5 oz Cascade (0 min)
Yeast:
Wyeast 1056 - American Ale
Mashed at 152° for 60 minutes with a thickness of 1.66 qts/lb. LA has moderately hard water so I used 3.5 gallons of distilled water mixed with 5 gallons of de-chlorinated tap water. I hit my mash temp on the nose and I chalk it up to good pre-heating of my mash tun. I had a problem hitting my mash temps and then realized that preheating takes more than just a couple pitchers of hot water 10 minutes before the strike. I pre-heat for 45 minutes, adding water as fast as I can heat it on the stove.
After chilling the wort I read an OG of 1.054, one point short of where I was aiming. Started yeast in 3/4 pitcher of chilled wort and pitched the next day. Over the first 4 days of fermentation the water bath measured between 66°-67°.
So it's been chugging away for just short of 6 weeks. At this point in writing the beer is kegged, under pressure, and cooling in the fridge. Final gravity came out to a dry 1.009. Down from 1.054, that puts the ABV at ~5.9%. The color is a nice, golden copper. So far so good in keeping to the style guidelines. There was a bit of stirred up yeast in the beer at the end of the siphon, but it's just due to the 1056 and it's nothing 2 weeks of chilling won't clear up nicely.
The taste? A big hop flavor! The ounce of Cascade in the last 3 minutes of the boil give it those classic citrus notes. The Centennial works well to add some complexity. The beer is crisply bitter, but not overwhelming. I could see it walking the line with an IPA, especially with it's subtle alcohol flavor, and the calculated IBUs--46 by Tinseth--are at the high end of the spectrum for a Pale Ale. All the same I think I can easily tack on the old "West Coast" title and call it a day. The malt profile is simple. The Munich works nicely to deepen the base flavor, and the crystal 40 is just doing it's crystal 40 thing--offering a caramel sweetness.
I'm quite excited about this beer. It's the same recipe as the "Estate Pale Ale" I made last fall to experiment with wet-hopping using home grown hops. I used the same bittering addition and just dumped in a jumble of fresh Columbus, Cascade and Centennial continuously throughout the last 10 minutes. I think this beer will see an improvement in the hop character--the flavor hops are more organized. Very present, but more orderly so one can more easily identify the different hops.
I'm looking forward to the next couple weeks. With any luck, I'll get some help and I will be able to sneak in a brew day. In the meantime, it'll take some willpower to let this pale rest and get ready. It's about time that there were some fresh beer on tap around here.
Friday, June 17, 2011
Friday, June 10, 2011
Bad Memory
Throughout my entire schooling, I've never been very good at remembering the minutia. This, I believe, is why I was never any good at history despite how much I enjoy it. I also think that this gives rise to my success in mathematics and physics: I never really remember anything, but rather how to derive it. In working over the derivations I piece together a larger world in which I can swim about and see the landscape that disparate topics create when viewed from afar. With this in mind, I recently came across a very nice, straight-forward derivation of Schrödinger's equation that I'd like to share, plus my LaTeX could use some practice...
For Uniform Dynamics, time evolution is described by a unitary operator:
\[
|\psi(t)\rangle = U(t,t_0)|\psi(t_0)\rangle
\]And we can consider the derivative with respect to time of a state $|\psi\rangle$ at time $t$ as an operator $G$ acting on $|\psi(t)\rangle$:
\[
\begin{align}
\frac{d}{dt}|\psi(t)\rangle & = G|\psi(t)\rangle \\
\ & = \frac{d}{dt}U(t,t_0)|\psi(t_0)\rangle \\
\ & = \frac{d}{dt}U(t,t_0)\lbrack U(t,t_0)^\dagger U(t,t_0) \rbrack |\psi(t_0)\rangle \\
\end{align}
\]So, because $U(t,t_0)|\psi(t_0)\rangle=|\psi(t)\rangle$ we can say that $G = \frac{d}{dt}U(t,t_0)U(t,t_0)^\dagger$, and, keeping normalization constant,
\[\begin{align}
\frac{d}{dt}\langle\psi|\psi\rangle & = 0 \\
\ & = \lbrack\frac{d}{dt}\langle\psi(t)|\rbrack|\psi(t)\rangle + \langle\psi(t)|\lbrack\frac{d}{dt}|\psi(t)\rangle\rbrack \\
\ & = \langle\psi(t)|G^\dagger|\psi(t)\rangle + \langle\psi(t)|G|\psi(t)\rangle \\
\ & = \langle\psi(t)|G^\dagger + G|\psi(t)\rangle
\end{align}\]Therefore $G^\dagger = -G$, meaning that $G$ is Anti-Hermitian and we may write it as $i$ times a Hermitian operator, say $H$:
\[H = i\hbar G\]Here the $\hbar$ is just a constant which could be absorbed into $H$ but we need it for convention and for keeping the units squared away. Using this knowledge paired with our first consideration of the time rate of change of a given state we have ourselves what we're looking for:
\[\begin{align}
\frac{d}{dt}|\psi(t)\rangle & = G|\psi(t)\rangle \\
\ i\hbar\frac{d}{dt}|\psi(t)\rangle & = H|\psi(t)\rangle
\end{align}\]We can call $H$ the Hamiltonian, and it works out that it has units of energy, as well as the basis states being the eigenstates with energy eigenvalues. Perfect! It is working through guided derivations such as this one that really helps me keep the pieces organized, rather than just memorizing an equation and how to use it.
For Uniform Dynamics, time evolution is described by a unitary operator:
\[
|\psi(t)\rangle = U(t,t_0)|\psi(t_0)\rangle
\]And we can consider the derivative with respect to time of a state $|\psi\rangle$ at time $t$ as an operator $G$ acting on $|\psi(t)\rangle$:
\[
\begin{align}
\frac{d}{dt}|\psi(t)\rangle & = G|\psi(t)\rangle \\
\ & = \frac{d}{dt}U(t,t_0)|\psi(t_0)\rangle \\
\ & = \frac{d}{dt}U(t,t_0)\lbrack U(t,t_0)^\dagger U(t,t_0) \rbrack |\psi(t_0)\rangle \\
\end{align}
\]So, because $U(t,t_0)|\psi(t_0)\rangle=|\psi(t)\rangle$ we can say that $G = \frac{d}{dt}U(t,t_0)U(t,t_0)^\dagger$, and, keeping normalization constant,
\[\begin{align}
\frac{d}{dt}\langle\psi|\psi\rangle & = 0 \\
\ & = \lbrack\frac{d}{dt}\langle\psi(t)|\rbrack|\psi(t)\rangle + \langle\psi(t)|\lbrack\frac{d}{dt}|\psi(t)\rangle\rbrack \\
\ & = \langle\psi(t)|G^\dagger|\psi(t)\rangle + \langle\psi(t)|G|\psi(t)\rangle \\
\ & = \langle\psi(t)|G^\dagger + G|\psi(t)\rangle
\end{align}\]Therefore $G^\dagger = -G$, meaning that $G$ is Anti-Hermitian and we may write it as $i$ times a Hermitian operator, say $H$:
\[H = i\hbar G\]Here the $\hbar$ is just a constant which could be absorbed into $H$ but we need it for convention and for keeping the units squared away. Using this knowledge paired with our first consideration of the time rate of change of a given state we have ourselves what we're looking for:
\[\begin{align}
\frac{d}{dt}|\psi(t)\rangle & = G|\psi(t)\rangle \\
\ i\hbar\frac{d}{dt}|\psi(t)\rangle & = H|\psi(t)\rangle
\end{align}\]We can call $H$ the Hamiltonian, and it works out that it has units of energy, as well as the basis states being the eigenstates with energy eigenvalues. Perfect! It is working through guided derivations such as this one that really helps me keep the pieces organized, rather than just memorizing an equation and how to use it.
LaTeX!
So I just figured out how to use LaTeX in Blogger, check it out:
\[
\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}
{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}
\]
\[
\begin{align}
\nabla \times \vec{\mathbf{B}} -\, \frac1c\, \frac{\partial\vec{\mathbf{E}}}
{\partial t} & = \frac{4\pi}{c}\vec{\mathbf{j}} \\
\nabla \cdot \vec{\mathbf{E}} & = 4 \pi \rho \\
\nabla \times \vec{\mathbf{E}}\, +\, \frac1c\, \frac{\partial\vec{\mathbf{B}}}{\partial t} & = \vec{\mathbf{0}} \\
\nabla \cdot \vec{\mathbf{B}} & = 0
\end{align}
\]
Wednesday, June 1, 2011
How I Brew
I brew my beer simply, without much for fancy equipment. I use a converted Gatorade cooler as a mash tun. I have some propane tanks and a turkey fryer. I batch sparge, and heat my strike water on the kitchen stove. I keg because I don't like dealing with bottles. I always make 5.5 gallon batches and my saccharification rest is almost always 60 minutes. Mostly, I brew modest beers that I like to drink and don't wreck either my palate or my motor functions with huge flavors and high gravities.
My favorite beer to brew, and the one I brew most often, is an English Special Bitter (a pint of which is pictured above). The recipe is simple, and the style is balanced nicely between sweet malts, hop bitterness (not too much hop flavor) and just enough esthers and diacetyl from the yeast to keep it interesting. It's got plenty of flavor and it's not too strong, making it a great beer for a session. I think that the entire bitter family of styles (ordinary/special/extra special) offer the best day-in day-out drinking because of their simplicity and mildness. From a homebrewing perspective, a special bitter is a dream because of small size--it's cheap to make a batch and the turn around is super fast. When I make a bitter, I'm pulling off pints only 12 days after I pitch the yeast.
I've brewed this beer more than any other, and I think that my recipe is finally pinned down:
Grist:
8.25# Marris Otter
0.75# Dark English Crystal (~135 °L)
Hops:
9.4 AAUs East Kent Goldings (60 min)
0.5 oz Fuggles (5 min)
Yeast:
Wyeast 1099 - Whitbread
I conduct a thick mash of 1 qt/lb and rest for 60 minutes at 150°, and try to ferment as close to 60° as possible. After about 8-9 days in the fermenter, it's right into the kegs to cool and carbonate. I really enjoy how simple this recipe has become. When I first drafted it up a couple years ago it had biscuit and other crystal malts in there, but this makes the best beer, and it is a staple at my house. It's not flashy, it's not huge, but it is descriptive of how I like to brew my beer.
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