Help me understand gravity and fermentability of fruit juices

I just got a cranberry apfelwein into the fermenter. This is only my 2nd apfelwein and I want to better understand the sugar/carb content and how it makes up the fermentability of the juice.

The apple juice I used had a sugar content of 26g/cup and a carb content of 29g/cup. I understand that 1lb of sugar in 1 gallon of water gives a SG of 1.046. Based on the sugar content of the apple juice, I would expect an OG of 1.042 (26g*16cups = 0.92 lb of sugar per gallon = 42.2 gravity points).

However, I measured the SG at 1.051. This is the same SG of the apple juice that I measured on my 1st batch. Am I missing something?

Also, the sugar content was 26g/cup and the carb content was 29g/cup. When I measure the SG, I assume I am also measuring the non-sugar carbohydrates. Do the 3g/cup of non-sugar carbohydrates really contribute 9 points? If I calculated them as sugars, I would get (3g*16cups = 0.11 lb per gallon = 4.9 gravity points).

I'm also wondering what the fermentability of the juice will be. Will those 3g of non-sugar carbohydrates be fermentable by wine yeast?

hi i don't tknow the answers to any of this but i figure if i show my calculations maybe i'll get partial credit...

if you prise yourself away from gallons, cups and lbs you can embrace the decimal system and use brix points for sugar content, which is pretty easily translatable to gravity. brix is of course just an estimate of sugar percentage (+ other dissolved solids) w/v (weight to volume), or grams sugar per 100 ml solvent:
for example: 10 grams sucrose in 100 ml = 10% w/v = (looked up on a chart) 1.040.
or, 26 g per cup: 1 liter is apparently 4.2 cups * 26 g = 109.7 g per liter (10.97 g / 100 ml), or about 11% = 1.044 from the chart
your measurement is 1.051 = 12.61 %, a difference of 1.6 grams per liter between sugar estimate from the label and actual gravity reading. if my math is correct, that is...

as to what those "non-sugar" carbs might be... i don't have much of an idea. pectin is a non-sugar carbohydrate, and maybe someone else knows what sort of amount you can expect to have in solution, but >1 g seems high to me. but the other well known plant carbohydrates, starches and cellulose, are not highly soluble. i think i wouldn't trust the label, and i bet it ferments completely dry.

sorry, my bs calculations were wrong, you have a difference of 1.6 grams / 100 ml not per liter. there goes my B-