How much DME addition for a partial boil?

[gatomalo]

Over the weekend I was helping a buddy with a Tank 7 clone and his first partial mash. I made the switch from extract brewing straight into full boil, all grain so I'm not really familiar with DME additions - his recipe called for 5lbs of Pilsen DME.

The question I have is how do you calculate how much DME you need for a partial boil?

We mashed nearly 10# of grains, but needed to get to 1.082 OG. We didn't have the time or experience to figure it out on the fly so he just threw in 5# of Pilsen. Needless to say we overshot our OG to 1.093.

I've seen calculations for gravity x pre-boil volume, but every example I see is full pre-boil volume (6.5 gal). Obviously adding water will alter the gravity, so I'm not sure how to go about this.

Thanks!

 

[PlinyTheMiddleAged]

gatomalo,

All you have to do is count points of sugar - it sounds complicated, but it's actually pretty easy:

Look at where you want to end up at - take your target gravity, subtract 1, multiply by 1000, and multiply by your target volume. This gives you the "amount of sugar" you want in the end.

Next, look at where you are before you start boiling - take your pre-boil gravity, subtract 1, multiply by 1000, and multiply by your pre-boil volume. This is the "amount of sugar" you have. If the amount you have is less than the amount you want, then you have to add some. In your case you want to add DME.

A typical sugar content for DME is 42 ppg (points per pound per gallon - a pound of DME will raise the gravity of a gallon of wort by 0.042). So multiply the number of points you are short by the target volume and divide by 42. This will tell you how many pounds of DME to add.

The problem looks like:
((OG-1)x1000xVpost-(SG-1)x1000xVpre)xVpost/DMEppg

Let's say you wanted 5 gallons of 1.082 wort and had 6.5 gallons of 1.060 wort pre-boil. Let's also assume that your DME supplied 42 ppg. You would need
((1.082-1)x1000x5-(1.060-1)x1000x6.5)x(5/42)=2.4 lbs of DME.

Basically, you want 410 points of sugar but only have 390 in your kettle, so you have to add 20 points to your 5 gallons.

Sounds complicated, but it's pretty simple.

*** There's an error in the above equation! Please see post #9 for the corrected equation ***

 

[gatomalo]

So going with a 3.5gal pre-boil volume (which we would top off to get to 5gal... this comes out to 23.8 lbs of DME... which is not correct.

Would I have to account for boil-off and make an assumption of how much water I'd have to add in order to hit 5gal?

Part of me is embarrassed that, having a Masters in engineering, I couldn't rack my brain around this... But I'll blame it on a late night brew session after having a couple.

 

[PlinyTheMiddleAged]

Oh - I missed that you were adding water to top up to 5 gallons.

In the end though, you still just count sugar. Adding water is just adding zero sugar.

Do you have all of your measurements - pre-boil gravity and volume and your post-boil gravity and volume? If you give that, then we can work through the correct amount of DME to add (and find out where you or I went wrong with our calculations).

 

[gatomalo]

I was using your SG number but my volumes to get the 23.8#.

Checking my notes, heres what we had:
Preboil SG was 1.051 and V was 3.5 gallons
Enter 5# DME
Postboil SG was 1.093 and V was 5 gallons

 

[gatomalo]

In the end though, you still just count sugar. Adding water is just adding zero sugar.

Well more water will dilute the concentration of the sugar solution. So there has to be a balance.

FWIW I would have simply done a full boil simply to avoid this situation of not knowing how to control the outcome. I was helping a friend so it wasn't my call. I'm still left scratching my head tho.

 

[PlinyTheMiddleAged]

I was using your SG number but my volumes to get the 23.8#.

Checking my notes, heres what we had:
Preboil SG was 1.051 and V was 3.5 gallons
Enter 5# DME
Postboil SG was 1.093 and V was 5 gallons

Well, something isn't right here. I suspect that your post boil gravity measurement is incorrect.

Pre-boil, you had (1.051-1)x1000x3.5 or 178.5 points of sugar. To that you added (assuming 42 ppg for you 5 pounds of DME) 42x5 or 210 points for a total of 388.5 points of sugar. Post-boil, you have (1.093-1)x1000x5 or 465 points. That can't happen.

Well more water will dilute the concentration of the sugar solution. So there has to be a balance.

Yes, you are correct about that. There is a balance. If your pre-boil measurements are correct, then after adding 1.5 gallons of water, your post-boil gravity must have been 1+((1.051-1)x1000x3.5/5+210/5)/1000 or 1.078.

You could also look at what 5 lbs of DME would add to 3.5 gallons of your 1.051 wort and then dilute that to 5 gallons - you should get the same answer as above.

The 388.5 pts of sugar from above would make 3.5 gallons of wort with a gravity of 1+(388.5/1000/3.5) or 1.111. If we dilute this to 5 gallons, we get (1.111-1)x3.5/5+1 or 1.078.

 

[pmoneyismyfriend]

1 lb of base malt has an o.g. of .005
1 lb of lme has an o.g. of .006
1 lb of dme has an o.g. of .008

I use the recipe builder from Brewersfriend.com

When my preboil gravity falls short of the mark, I add dme in the amount calculated by the difference. In your case being short by .011, I would have added 1.375 lbs of dme. The numbers will vary, depending on your preboil volume and your target fermenter volume. Brewersfriend.com has a lot of calculators, you can input your preboil volume, target to the fermenter, boil off, temperature adjustments (hydrometer)...

 

[PlinyTheMiddleAged]

My apologies!!!! I did find an error in my original post.

Ok. Let me try again.

((OG-1)x1000xVpost-(SG-1)x1000xVpre)/DMEppg = weight of DME needed

So, going back to your problem,
OG = 1.082
Vpost = 5
SG = 1.051
Vpre = 3.5
DMEppg = 42
((1.082-1)x1000x5-(1.051-1)x1000x3.5)/42=5.5 lbs

If your preboil gravity measurement was correct, then you only needed 5.5 lbs to get you to your desired gravity. So, you were close. Sorry again about the mistake in my initial post. I'd go back and fix it, but then your responses wouldn't make sense. I hope I don't mess anyone else up!