Help Calculating Maple addition?!

Not sure where i should post this i figured you guys would have the best sense of numbers here...

I brewed up an Irish stout with 004 OG 1.080
Ended up collecting around 4.8gallons into the fermentor

After the 2/3 break i added 16oz of grade b maple syrup to 300ml of boiled and cooled water. I tryed to take a refractometer sample but read over 35 Brix (highest my scale goes)

This sample was now 850ml...not sure how that worked out, possibly more than 16oz of maple in the jar? Flask markings off? anyway....

Can anyone tell me what my new OG gravity should be so i can properly measure ABV after fermentation stops?

THX!!

 

As I have no idea what the requirements for grade B maple syrup are not whether the particular brand you have is right at the minimum requirement what I suggest you do is take the sample which reads over 35 brix and dilute it 1:1 with water, then measure the Brix.

I really wish home brewers would learn to work with Brix and Plato so that they can solve problems like this.

 

That would of been a great idea wish i thought about it then...

The label said 53gms of sugar in 60ml of syrup. Does that help?

 

Yes, it helps a great deal. An invert sugar solution with 53 grams of sugar in 60 mL has density 1.3217 g/cc at 20°C. Sixteen fluid oz is 473.18 cc which weigh 1.3217*473.18 = 625.40 grams of which 53*473.18/60 = 417.98 grams is sugar. Thus the rest, 625.40 - 417.98 = 207.42 grams must be water.

You started with 18.17 L of wort at SG 1.080 so its weight is 18.17*1.080*.998203 = 19.588kg. Apparent SG of 1.080 corresponds to 19.33 °P so the weight of the extract (sugar) is .1933*19.588 = 3.904 kg and the rest, 19.588 - 3.904 = 15.684 kg.water. The net result is 417.98 + 3904 = 4323.0 grams of sugar with 207.42+15684 + 300*0.998203= 16190.9 grams of water for a total mass of 4323 + 16190.9 = 20513.9 grams and an OG of
4323/20513.9 = 21.07 °P corresponding to an SG of 1.0878. Unless I made a math error and I certainly did which is why this has been edited.

 

I'm trying to figure this out for myself and learn to use Plato and Brix, as the gravity/points scale uses very non-intuitive units IMO. Wherever I'm wrong point it out, only way I'm going to learn.

53*473.18/60=417.98, though I suspect this is a typo/misreading as 625.4-417.98=207.42

18L of wort can't possibly only weigh 3.8 kg. I don't know what .998203 is from but I'm guessing a constant of some sort, but either way it is such a small multiplier that I'm ignoring it in my estimate until I actually know. Just volume*density for total weight, right? 18.17 * 1.080 = 19.624 kg

.1933*19624 = 3793g sugar (guessing this is the 3.786 kg you reached above)

19624 - 3793 = 15831 g water

total sugar = 4211
total water = 16038 + 300 ml dissolved syrup into = 16338

4211/(16338+4211)=20.5*P ~1.085 SG

Confirmation with sloppy points scale:
4.8 g of 1.080 wort = 384 points
418 g sucrose ~= .92 lbs ~= 40.5 points
424.5 points

new volume = 4.8 gals + 800 ml (seems really high to me also) = 5.1 gals
424.5/5.1 = 1.083
--EDIT--catching my own math error here, and reading error, should be
new volume = 4.8 gals + 850 ml (seems really high to me also) = 5.02 gals
424.5/5.02 = .846, so 1.0846 SG, much closer than before

The numbers are farther apart than I'd like but in the same basic area, and that .998 multiplier I ignored might bring them closer together.

 

After all the mistakes I made last night I'm not sure I'm the guy to help you but here goes.

There were a couple of simple typos here but the end result was right.

This was, obviously, but not to me in the wee small hours, where I made my biggest goof by multiplying by the Plato fraction and not realizing that I'd done it. This I calculated the extract weight, not the wort weight. 0.998203 is the density of water at 20 °C. To get the density of something else multiply its 20/20 specific gravity by this factor.

Your numbers and mine should now agree to within that factor if you ignored it.

But density is SG*0.998203 so the total weight here is
18.17*1.080*.998203 = 19.588kg

and the sugar weight is indeed 3.786 kg.

I completely overlooked the dilution water!
But this is at the heart of the discrepancy. Originally he had 15.684 kg of water (volume 15684/.998203 = 15712 mL) and he added 207.42 grams of water (volume 207.42/.998203 = 207.8 mL) and then 299.46 grams of water (300 mL) for a total of 16190.9 grams (16220 mL ~ 4.285 gal) but he should have 20.514 kg of wort with density 1.0878*0.998203 = 1.08584 so that the wort would have volume 20.514/1.08584 = 18.90 L (4.99 gal). Thus the sugars have expanded the volume but not uniformly. When he adds 300 mL water (299.46 grams) to the 207.42 grams of water in 473.18 mL of syrup he gets total water 772.64 grams which, with the sugar mass of 417.98 gives a mix of mass 1190.6 grams. The sugar content by weight is 417.98/1190.6 = .351 i.e. the mix is 35.1 °P and has specific gravity of 1.15428 and density of 0.998203 time this or 1.5221 so that the volume of the mix is 1033.32 which is 260 ml more that 300 + 473. Or put another way, that's why we have to work with mass.

 

you guys are awesome!

...and i thought i liked math!