An open letter to Tonk re: Hard Cider

Tonk you asked me a question to which my facebook reply was too lengthy to be allowed. So here I am posting it here for peer review.

edit: This is a winded and round about way to answer your question about how much brown sugar you need to add to boost your cider's alcohol percent

Hard Cider experiment
Goal: to make 18% Alcohol (by weight) hard cider to use in making Apple Jack.

-Prelude
I did an experiment which I thought was scientific and reliable; but it is neither:

I had exactly 2 quarts (1/2 gallon) of cider juiced from apples in my backyard with a specific gravity of 1.052

1. I took 1 quart (1/4 gallon) of water and boiled it with 2 cups light brown sugar. [1 quart water plus 2 cups light brown sugar resulted in about 1.15 quarts. The jug that contains the apple juice holds 3 liters which is 3.17 quarts. This jug was near full after combining the sugar water and cider, which means that 3.17-0.02 quarts remaining space-2 quarts cider leaves 1.15 quarts sugar water.]
2. I then combined the apple juice and sugar water and let the mixture cool back down to room temperature
   
3. The measured the gravity was 1.080.
   

So I assumed that for every 1 quart water boiled with 2 cups brown sugar raised the gravity by 0.028.

• I didn't put much thought into this assumption although I based the remainder of my experiment on it.
• [Update] What I now believe is that I should have measured the specific gravity of the sugar water before combining it with the apple juice.
• Had I measured the sugar water's gravity before combining it with the cider I believe it would have been 1.129
• Working backwards, if 2 quarts of 1.052 + 1.15 quart of X specific gravity brown sugar water = 3.15 quarts of 1.080 specific gravity, then (1.052*2)+(1.15*X) = (3.15*1.080) then the specific gravity of the light brown sugar water would have been X = 1.12869.
  

What is your opinion?

The Main Experiment
I wanted to make another cider 18% Alcohol by weight. I knew it had been fermenting for a day and a half so measuring it's gravity was worthless at that point, but I knew that the initial specific gravity was 1.060.

-side note: I don't care if I am unable to ascertain the final % alc. anyways, since I will be ice distilling the cider into apple jack; As long as the liquor doesn't freeze in a freezer it's good, or perhaps I am able to proof it] I also knew that the yeast had an alcohol tolerance of 18%, thus my goal.

Assumptions:

• I have 4 gallons of cider
• It had a starting specific gravity of 1.060
• I am assuming that this cider ferments to a final gravity around 0.990. I have done two previous ciders which fermented down to 0.992 and 0.990 respectively. Although this time I am using a different type of yeast, Lalvin EC 1118, I predict it will ferment similarly.
• The alcohol tolerance of this yeast strain is 18%.
  
• The calculation for % alcohol by weight is 105*(starting gravity-final gravity) = % alcohol by weight.
• My Goal would be to add sugar so that 18=105*(Starting Gravity-0.990) - Thus my starting gravity should be around 18/105+0.990=1.1614
• And I need to raise the gravity by 1.1614-1.060=0.1014
  
• And for every 1 quarts water plus 2 cups light brown sugar, the gravity increases by 0.028. [Wrong]
• Therefore I need to add 0.1014/0.028= 3.62*(2 cups light sugar and 1 quart water)
• Because it's easier to measure, I boiled together and added 3 2/3rds quarts and 7 1/3 cups light brown sugar
  
  

Results:
As yet to be determined but the air lock is indicating a healthy fermentation bubbling a couple bubbles every second.

Upon Further Review:
Like I previously stated, I believe some of my methodology was wrong. Estimates using my updated hypothesis are as follows:

• 4 gallons of cider*4 quarts a gallon = 16 quarts of cider at 1.060 starting specific gravity.
• The ratio of water to brown sugar mixture did not change, so it's gravity should be the same as well: 1.12869.
  
• Therefore, (16*1.060)+((1.15*3.66)*1.12869) = (16+(1.15*3.66))*[Starting Gravity]
  
• Thus, what I actually created was a starting specific gravity of 1.074
  

Side notes:

From rough estimations I found that 2.25 cups sugar is roughly 1 pound. I've also noticed that recipes call for upwards of 5#'s sugar for 5 gallons sugar. with 7 and 1/3rd cups of sugar, I added approximately 3 and a 1/4 pounds sugar for 4 gallons cider (also, I have a hunch that it's over 4 gallons of starting apple cider when I include a few 12 oz. concentrates I threw in there.)

This means that I just brought my cider up to about 105*(1.074-0.990)= 8.82% Alc. by weight, or /0.79 = 11.16 % Alc. by volume. Not bad when you consider your average beer is 5% Alc. by vol. but this is upsetting if you're trying to make a liquor.

TL:DR version
I tried to make my cider more alcoholic by adding sugar. It turned out not as alcoholic than I had hoped but there is still some time left to add more sugar. Should I add more sugar?