taking initial gravity reading

[NewBrewerCK]

At what point do I take this reading? What I typically do is pour 2.5 gallons of cold water into my carboy and then pour my hot wort on top of the water. At that point, for no other reason then to have 5 gallons, I pour more water on top of the wort to reach the 5 gallon mark. How do I get an accurate reading of original gravity if I am unable to mix water and wort effectively. I'd like to reach the original gravity intended by the recipe rather than arbitrarily mixing water until there are 5 gallons. Thanks.

[dparsons]

You can take a gravity reading of the concentrated wort and reduce it according to the volume fraction. Using MG for Measured Gravity, and VF for volume fraction of concentrated wort:
OG = (MG - 1.0)*VF + 1.0

Don't forget to cool your sample and account for temperature in the gravity reading.

Alternatively you can take a sample after mixing.

[NewBrewerCK]

Am I to understand that the volume fraction is the fraction of current to final volume? For example - initially I am at 1.5 gallons water. So volume fraction would be 1.5/5 = 0.3? Obviously this isn't exact as water boils off and extract is added to 1.5 gallons. Am I missing something?

[markaberrant]

You could just take a reading once it's all in the fermenter.

[beerking]

Your "total gravity points" will not change.
TG=OG*V
Where OG is gravity minus 1, times 1000
and V is volume in gallons

The equation to figure out your final, mixed gravity is:
OG=CG*(IV/FV), or FV=(CG*IV)/OG, depending on which you are solving for.
Where OG is your target starting gravity for your recipe or starting gravity resulting from the dilution;
CG is the concentrated gravity, that is, the gravity of your post boil wort (gravity of the 1.5 gal in your case)
IV is the initial, concentrated volume in gallons, 1.5 in your case.
FV is the final volume of your wort, usually 5 gallons, although if you are shooting for a particular gravity you may end up with a number more or less than 5 to get your target gravity (OG).

So, if you brew 1.5 gallons, and get a concentrated gravity of 150 (1.150), you get the following formula:

150 * (1.5/5) = 150 * (0.3) = 45 => 1.045.

Looking at total gravity points, we see that:

OG * V = TG => 150 * 1.5 = 45 * 5

Remember, all gravity values are in gravity points. Take the hydrometer density, subtract the one, and drop the decimal.

[NewBrewerCK]

Beerking - I don't know if you experience this when boiling your wort but I must boil off about a half gallon of water give/take including additions of extract. I imagine that these calculations require knowing an accurate initial volume. All I know is that I start out with approximately 1.5 gallons water. How do you account for this?

[JayShaw91]

CK, like Beerking said, your total gravity points does not ever change. To simplfy this, all LME cans have the same gravity. If you added one can of extract to a gallon of water you'd have a certain gravity. Now, add that to 2 gallons of water and your OG is now halved. Your total gravity has not changed since you still have the exact same amount of extract. OG changed because you diluted it further. When you boil, you're losing water, i.e. concentrating your wort, so the OG will go up.

Make sense?

So with this in mind, you want to get your OG *after* the boil. The only time you'd worry about gravity other than after a boil would be if you do all-grain brewing and want to know what your efficiency was.

HTH...

[beerking]

Beerking - I don't know if you experience this when boiling your wort but I must boil off about a half gallon of water give/take including additions of extract. I imagine that these calculations require knowing an accurate initial volume. All I know is that I start out with approximately 1.5 gallons water. How do you account for this?
I am an all grain brewer, so it is a little different, but I think my basic process can work for you. I have a wooden dowel, marked for every half gallon in my pots (except my new "Boilermaker" pot, which has a calibrated sightglass). By using this stick, I can tell how much wort is in the pot at any point in the process. When I am sparging (I do batch sparging for simplicity sake), I measure the amount of my first runnings, and the gravity, and I then know about how much second runnings I want, based on my planned batch size of 6 gallons, and my boil off of about 20%. Once the second running start, I take a reading, and confirm my final pre-boil gravity based on the planned volume of second runnings. If I need to adjust, here is where I run more or less water through the second runnings.
The math for my set up is a little more complicated, but basically the same (I use Pro-Mash, which has a dilution module).
You could measure the amount of your post boil concentrated wort, and do the math to determine how much pre-boiled and cooled water to add to hit your planned gravity.
Then again, you might be more interested in target volume than gravity, and the same math will let you determine your final gravity if you "blindly" top up to 5.5 gallons.
OBTW, my numbers are all above the standard 5 gallons because I tend to lose ~.75+ gallons at various stages of my process, such as lauter deadspace, tubing during transfer, trub in the chilled wort, etc. I suggest 5.5 gal for you because an extract brewer will probably loose less than and all grain brewer, but you still have some loss.
Since I keg my beers, I want a full 5 gal going into the keg to minimize headspace.