Alcohol content if additives after fermentation

I'm probably having a brain fart here, and this probably ought to go in the cider forum, but this area gets more traffic, so forgive me in advance...

Having issues determining alcohol content after adding stuff after fermentation.

For example:

I did 4 gallons apple juice, with an OG of 1.052 (yeah, I should have bumped that up a little, lesson learned)
FG on the 4 gallons was 1.002

no problem there, AC of 6.55%

Here's where I'm brain dead... I added a gallon of juice, a pound of sugar, and some flavoring to get me up to a little over 5 gallons, so I can keg a full keg, and get the flavor I am after.

After adding all the other stuff, my gravity is now 1.028.

Have I dropped the AC to 3.1%, or am I just not remembering basic math and need to do a weighted average, which I can't remember how to do right now (darn IPA that's too good to stop after 5)

Thanks in advance. I ought to know better...

 

OK, lets see if we can figure this out.

You had a gravity of 1.002 for 4 gallons (4x2=8 points). You added 'stuff' and made it up to 5 gallons at 1.028 (5x28=140 points). The sugar content you added was equal to 140-8=132 points. That is equivalent to 4 lbs of sugar.

You do realize that unless you killed the yeast, it will start working on this new sugar source.

What was your effective OG for the 5 gallons? You started with 1.052 (4x52=208 points). You added an additional 132 points. Total points = 208+132=340. For 5 gallons, your effective OG would be 340/5=68, or 1.068.

I'm assuming this is what you were after.

Alcohol would be ~5.2%.

An easier way to to calculate the alcohol would have been 6.55x4/5.

Again, remember these new sugars are probably going to ferment too.

 

I've cold crashed and kegged, and I keep my cider kegs pretty cool (37 deg), so no worries about any restart.
Suprised the 20 oz of flavoring and the gallon of juice added 3 equivalent pounds of sugar to the equation.

The 6.55*4/5 made the most sense to me.

Thanks!

 

That is interesting. By contrast, the 1 lb sugar + gallon of apple juice if you think in terms of the above 132 points is 132/100+1 or 1.132 ???? Hmmmmm Apple juice is usually 1.05 so.... .132 points - 50 is 82 points which is 1.082 (the amount your pound added to the gallon of apple juice). That must have been some sweeet sweeet pounda sugar! Am I doing this right?