Trying to determine OG after adding large starter

[badapplebrewing]

Brewed a foreign extra stout today and ended up with an OG of 1.064. However, when I went to pitch the starter, hardly any of the yeast had flocculated out. I didn't want to waste any of the yeast in solution, so I pitched the whole (WLP001, 1.75 liter, 1.035 OG) starter.

The measurement of 1.064 was taken prior to pitching the starter (which, taking into account the lower OG, would obviously lower the overall beer's OG) and I neglected to take a gravity reading after pitching.

My question is: Is there a formula or maybe even a calculator (i.e. 5.5 gal. at 1.064 + 1.75 liters at 1.035 = 1.0??) that I can use to determine what the actual OG is POST-pitch without physically pulling a sample out of the carboy? I know there are alot of variables, so I'm just looking for some general advice.

Thanks!!

[siwelwerd]

Total volume was 23.75L, so do 1.064*(22/23.75)+1.035*(1.75/23.75)=1.062

[ajdelange]

My question is: Is there a formula or maybe even a calculator (i.e. 5.5 gal. at 1.064 + 1.75 liters at 1.035 = 1.0??) that I can use to determine what the actual OG is POST-pitch without physically pulling a sample out of the carboy? I know there are alot of variables, so I'm just looking for some general advice.

You have 5.5*3.7854 liters of wort at 1.064 SG which weighs 5.5*3.7854*1.064*0.998203 = 22.1124 kg. SG 1.064 is 15.672 °P so the wort contains 0.15672*22.1124 = 3.4654 kg extract and 22.1124 - 3.4654 = 18.647 kg of water. The starter is 1.75L at 1.035 SG so it weighs 1.808 kg and, as 1.035 SG is 8.7811°P so it contains 0.087811*1.75*1.035/.998203 = 0.1593 kg of extract and 1.808 - 0.1593 = 1.6487 kg water. Thus you have a total of 3.4654 + 0.1593 = 3.6247 kg extract in 22.1124 + 1.808 = 23.9204 kg of mixed wort/starter so the mixture is
100*3.6247/23.9024 = 15.1646 °P which is 1.06182 SG.

To do this you must convert 2 SGs to Plato which you can do from Plato = -616.868 + 1111.14*S-630.272*S*S +135.997*S*S*S. To convert from Plato to SG you must put the SG -> P conversion into a spreasheed and use trial SG's until you match the P you are converting. Or, in Excel, let the Solver do it for you automatically.

So yes, there is a procedure. You can compare the "accurate" calculation to the approximate one in the post which precedes this one and see if you think it's worth the trouble.

What you have here is a sort of "effective" OG because you are treating the calculation as if all the sugar went in at once. That seems the only reasonable thing to do. But what about things like evaporation in the fermenter or water you use to sparge hops (don't know if you do that but I'm not leaving any extract behind if I can help it) or extract you lost during a boil over or left in the hops if you don't sparge? Should those be counted in calculation of OG? Because those things are hard to quantify brewers sometimes calculate OG after the beer is finished by analyzing for alcohol content and then sticking that back into the Balling equation to get an OG estimate. That is, to my way of thinking, the ultimate effective OG beacuse it accounts for any losses or gains of water or extract throughout the entire process, including starters. The overall efficiency of the process is the effective OG (in Plato/100) times the mass of the beer you got into kegs divided by the weight of grain/fermentables you used.

[SacoDeToro]

ProMash has a dilution utility that covers this. Yet another reason to throw down a scant $25 for an great brewing tool.

[siwelwerd]

1.06182 SG.

[...]

You can compare the "accurate" calculation to the approximate one in the post which precedes this one and see if you think it's worth the trouble.

The unrounded value is 1.06186316, which gives an error of about 0.004%. I don't know any homebrewer with equipment accurate enough to measure that kind of difference.

[brewinhard]

Did you try crash-cooling your starter after its fermentation was complete? I typically do this if I am making a starter any larger than 1 L so I do not have to pitch all of the oxidized starter into my wort. Anywhere from 24-48 hrs will drop those yeast right out and give you a nice layer on the bottom of your starter container so you can decant and pitch mostly fresh yeast.

[ajdelange]

ProMash has a dilution utility that covers this. Yet another reason to throw down a scant $25 for an great brewing tool.

What I sketched out is exactly what ProMash does except that it uses a root bisector to find SG from Plato.

[quote="siwelwerd" The unrounded value is 1.06186316, which gives an error of about 0.004%. I don't know any homebrewer with equipment accurate enough to measure that kind of difference.[/QUOTE]

No, but we can read to ±0.000005 on density/SG though, of course, we don't do that except when doing researchy sorts of things. The reasons for the algorithm being so precise in ProMash is because pro's use it and it therefore needs to be able to do calculations using the ASBC/EBC/MEBAK calculation methods. I argued that some day some pro was going to do a gedenken experiment in which he added water and sugar and boiled and added sugar etc. in several steps and that calculations had better compare with what he got, to machine precision, when he used the total water and sugar together in one step. ProMash does give the opportunity to turn the precise mode off. The innaccuracies incurred by treating points as if they are linearly proportional to extract mass is insignificant for any homebrewer doing 5 gallon batches using a plastic hydrometer. They are more significant to commercial brewers and the very geeky (that would be me) home brewers.

IOW it's not worth the trouble unless you want to put all that stuff in a spreasheet for giggles (or buy a copy of ProMash)]. Once it's coded it's no more trouble to use than the "points" based calculations (if you stay in Plato for expression of extract - don't have to caculate the final SG in that case).