Gravity Question for JZ's Special Bitter

[WingedArmada]

I'm getting ready to brew the Special Bitter from Brewing Classic Styles and I'm having a bit of trouble reconciling the gravity numbers. The stated OG is 1.047, but when I add up the yields based on the ingredients, I get 1.043. Could someone take a look at my numbers (below) and let me know if I've screwed up?

(I suppose the answer could be that yields are approximate and I simply need to take a hydrometer reading post-boil and manage my dilution appropriately to hit my target. However, since boil gravity plays into hop utilization and I'm going to have to re-clac for a 3-gallon boil, I'd like the piece of mind that my math is solid before proceeding.)

Thank you!

Recipe: I'm Not Bitter, I'm Thirsty (Brewing Classic Styles, pg. 119)
OG: 1.047

Extract:
English Pale Ale LME (3.5 L) 6.8 lbs.
Steeping Grains:
Aromatic (20 L) .5 lbs.
Crystal (120 L) .5 lbs.
Special Roast (50 L) .25 lbs.


So my calcs go like this:
Presumed volume at end of boil: 6 gallons (per pg. 34)
-Yield from LME: 36 ppg
-Yield from Aromatic: 0 ppg. (In "How to Brew" Aromatic Malt is under the "Kilned Malts - Need to be Mashed" category, so I'm assuming no contribution.)
-Yield from Crystal (120 L): 16 ppg. (Palmer; Table 10)
-Yield from Special Roast: 20 ppg. (This is a complete guess on my part)

Stated Original Gravity Points:
47 * 6 = 282 points

Calculated Original Gravity Points based on ingredients:
(6.8 * 36) + (.5 * 16) + (.25 * 20) =
244.8 + 8 + 5 =
257.8

Calculated OG:
257.8 / 6 =
42.9 =
1.043

[Nyakavt]

I don't have my book in front of me, but let me give this a shot. I'm fairly sure that JZ and Palmer would not recommend steeping a malt that must be mashed for fear of introducing starch into the beer. Are you sure this one doesn't recommend a mini mash?

Also, where are you getting the numbers for yield on these malts? It could be the calculated recipe has a different assumed yield, like 1.037 for LME. If we use a different set of assumptions you can get a calculated result very close to the recipe:

LME: 37
Aromatic: 36 * 0.7 (mash efficiency in the book is assumed at 70%)
Crystal 120: 34 * 0.7
Special roast: 33 * 0.7

37*6.8+36*.5*.7+34*.5*.7+33*.25*.7 = 281.9 points.

Source for malt yields:
http://www.homebrewtalk.com/wiki/index.php/Malts_Chart

[WingedArmada]

Nyakavt-

Thanks for your feedback.

I've been brewing for quite a while, but it's only since finding the BN that I've decided to kick off the training wheels of pre-packaged malt-and-grain kits and assemble my own ingredients based on a recipe. It could very well be that I'm just being a bit too high-strung regarding making the numbers work and what I should (and will) do is follow the recipe, make my own measurements and see how it turns out.