Ineffizient Weizen

This was my first attempt at an all-grain beer.  I used a 48 quart cooler converted into a mash tun. I decided since I was going to make a wheat beer that I was going to do a decoction mash. Well this was all great in theory. When we first got started I noticed that I forgot to bring my hot liquor tank with me. I initially wanted to do a step mash and then a decoction for the last step of the mash. In order to accomplish what I wanted to do I needed two pots. I need one for my step mash and the other to heat sparge water while I preform my single decoction. Well instead of doing things the easy way with a step mash I had to use my mash tun and preform a quadruple decoction mash.This was the mash schedule I used

Mash schedule:
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• 4 vinyl guaiacol 15 min @ 113 (Infusion) 1.5 qt/lb at 119F heat up (this step produces the molecule the yeast use to produce a clove aroma)
• Protein 10 min @ 126 (Direct) 1/3 gallon ~ 1.2qt
• Sacch Rest 1 40 min @ 144 (Direct) .75 gallon ~ 3 qt added 4 qt of water
• Sacch Rest 2 40 min @ 161 (Decoction boiled for 20 minutes) ~1 gallon ~ 4qt decocted
• Sparge with 4.75 gallons of water heated to 170F

To calculate the amount of wort to decocte from the mash I used the equation
Wa = (T2 - T1)(.2G + Wm)/(Tw - T2)
where:
Wa = The amount of boiling wort added (in quarts).
Wm = The total amount of water in the mash (in quarts).
T1 = The initial temperature (F) of the mash.
T2 = The target temperature (F) of the mash.
Tw = The actual temperature (F) of the infusion water.
G = The amount of grain in the mash (in pounds).

Each time I would measure my temperature and then plug it into the formula and drain off the amount of wort I needed. I would slowly heat the wort to a boil and then add the boiling wort to the mash when it was time for the next temperature step. Everything was working fine, my temperatures were a little lower than I as shooting for, but that is OK.  I vorlaufed into my mash tun and then lautered into my kettle.  Once the first runnings were finished I dumped my sparge water into the mash tun, stirred and then let it sit for about 10 minutes.  Recirculated and lautered into my kettle until I had 6.5 gallons. The rest of my recipe is as follows

Stats:

• Anticipated OG: 1.051
• Anticipated FG: 1.013
• Anticipated SRM: 20 (light brown to med brown)
• Calculated IBU: 18.8
• Estimated ABV: 5.1%
• Boil time: 115min
• Boil volume: 6.5 Gallons
• Batch: 5 gallons

Grain Bill:
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• German Wheat Malt Dark – 5 lbs
• German Two-row Pils – 3 lbs
• Munich Malt 10L – 1 lbs
• Belgian Special B – 0.5  lbs
• Chocolate Malt – 2 oz

Total Grist: 9lbs 10oz

Hop Schedule:
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60min Spalt Select -  1 oz

Yeast:
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WLP300

The problems with this beer came from my very low mash efficiency. I think I ended at around 54% or something like that.  My reasons for a low efficiency are probably from the fact that I lautered too fast and I didn’t stir the mash enough during the different rest to extract as much sugar as I could.  For my next batch I’ll try these techniques and I will use a double sparge technique and hopefully it will increase my efficiency. My OG ended up being 1.031 and my FG was 1.006.
I made a starter 3 days before burew day using a half a cup of light DME and about a cup or water and pitched the yeast I harvested from my Hefeweizen.  It fermented at abour 70 degrees in primary for two weeks and then was bottled using about a half of a cup of table sugar for priming. I let it condition at 70 degrees for two weeks.

Tasting
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Appearance: Light brown with yellow hues when held up to the light and an off white head about two fingers worth. The head retention is not where I would have liked it and it fades to a ring around the glass.
Aroma: Banana, a small amount of clove, and roasted malt. Very nice and a lot better than what I was expecting especially since the yeast was almost 3 months old.
Taste: Banana and sweat roasted malt. Again better than I was hoping for with all things considered.
Mouthfeel: Effervescent like I wanted and not nearly as light as I figured it would be with such a low FG. It is pretty dry but that makes it really refreshing and easy to drink.
Overall: A lot better than I thought it it would turn out. It was not what I wanted but it is still good. I would like to brew this recipe again, maybe after I can nail down my all-grain technique.