[Kaiser]

In Reply to: Tom's post in the Sparge Arm thread: http://www.homebrewersassociation.org/forum/index.php?topic=4704.msg55299#msg55299

Get yourself a small graduated cylinder, then dilute the wort with an equal amount of water.  Multiply the refractometer reading by 2, and bob's your uncle.  It will be cheaper than buying a high gravity refractometer, $7.50 from morebeer.

http://morebeer.com/view_product/6540//Graduated_Cylinder_-_10mL

I believe the dilution has to be done by weight. E.g you need to mix 50g of wort with 50g of water. I'm not completely sure for SG. But I'm sure for Plato since that is a weight based extract measure.
 
Kai

[kerneldustjacket]

Get yourself a small graduated cylinder, then dilute the wort with an equal amount of water.  Multiply the refractometer reading by 2, and bob's your uncle.  It will be cheaper than buying a high gravity refractometer, $7.50 from morebeer.

http://morebeer.com/view_product/6540//Graduated_Cylinder_-_10mL

I believe the dilution has to be done by weight. E.g you need to mix 50g of wort with 50g of water. I'm not completely sure for SG. But I'm sure for Plato since that is a weight based extract measure.
 
Kai

I did a quick experiment to see what happened when both methods where used; i.e., one where equal volumes of water and a sugar solution are combined and measured, and the other where equal weights of water and a sugar solution are combined and measured. The refractometer measures in Brix, which is defined as % of sucrose by weight in a solution; where 1 gram of sucrose is in a 100 gram solution, you have 1 Brix. Note however that the actual measurement is made using light refraction, and the reading in brix is extrapolated from the result of that light refraction.

1. a 10 brix solution was made by weighing 10 grams of table sugar on a scale that weighs to a tenth of a gram, and topping it off with water to make 100 grams total weight (Note: prior to the experiment, I made two solutions: one where 10 grams of sugar was combined with 100 grams of water -- making 110 grams total weight, and the other where 10 grams of sugar had enough water added to make a 100 gram total weight solution; the 100 gram total weight solution gave the reading of 10.0, as expected)

2. This sample gave a reading of 10.0 on my refractometer (a "zero" calibration was made to the refractometer just prior); as a cross check, I tested the sample with my hydrometer: 1.040

3. 20 grams of sugar solution was combined with 20 grams of water; this gave a reading of 4.8 brix

4. 15 mL of sugar solution was combined with 15 mL of water; this gave a reading of 5.0 brix

5. I alternated the two samples, taking a total of four readings per sample; the results did not vary. I also carefully cleaned the refractometer between all readings

Now I grant that these results vary by a small amount, likely due to the sample solution being only 10 brix; perhaps a second run with a 20 or even 40 brix sample might better show any variance. But, the equal volumes method seemed to work best for diluting a sample to read half the actual brix of the solution.

I suspect that where refractometers are concerned, dilution of an equal amount of water does approximate the sugar content by half. I think this is because refractometers measure a refraction of light caused by the absolute volume of sucrose present, rather than its weight.
Also note: refractometers ONLY measure sucrose...higher gravity worts MAY read incorrectly, depending on the nature of the wort sugars that are present.

Just my $0.02 worth.

[MDixon]

Ahh, we have error  

They do have hydrometers for the higher gravities, I believe I have a couple. I think I got mine here:
http://www.cynmar.com/home.aspx
Here's one for about 10 beans which came from a quick search
http://www.cynmar.com/item_detail.aspx?ItemCode=09636443

[Kaiser]

John, thanks for taking the time to conduct the experiment. But I don't think that a 10 Brix sugar solution is strong enough to show the difference.

I just did 2 spreadsheet experiments:

starting with a variable SG I calculated the extract content in Plato. I then assumed an arbitrary volume and calculated the weight of the solution and the extract weight. Finally I run the numbers for doing an equal volume and an equal weight dilution. These were the results. The starting extract/gravity is the x-axis and the diluted gravity/extract  is the y-axis:



Interestingly enough, an equal weight dilution gives you the expected 1/2 of the starting extract content when working with Plato, while an equal volume dilution gives you the expected result when working with SG. I was surprised by that but it does seem to make sense.

The error for using the wrong dilution method only shows up for higher gravities. It is about 4% for a starting wort SG pf 1080 (~20 Plato).

Kai

[kerneldustjacket]

Awesome work, Kai!

Yes, I agree 10 brix was perhaps too small...it would likely not past a statistical test for significance. As I mentioned in my post, testing at 20 or 40 brix would more likely show the variance; I think I'll try that just to see, even though you have expertly used a spreadsheet to conclude there is a difference.

And I agree, it is very interesting that the correct method required is wholly dependent on what measurement system you are using.

So there's something new to put into our brewing box of tools!

Vielen dank!

[tschmidlin]

I believe the dilution has to be done by weight. E.g you need to mix 50g of wort with 50g of water. I'm not completely sure for SG. But I'm sure for Plato since that is a weight based extract measure.
 
Kai

Yes, it is definitely done by weight as you showed with your spreadsheet.  I was ignoring that because I didn't think the error would be as big as you've shown.  Thanks Kai.

So it sounds like the easiest thing for Fred to do would be to dilute a larger sample to something his hydrometer can read and just use that.

[MDixon]

Or to spend 10 bucks...

[denny]

Or to spend 10 bucks...

There you go being pragmatic again!   

[Kaiser]

Yes, it is definitely done by weight as you showed with your spreadsheet.  I was ignoring that because I didn't think the error would be as big as you've shown.  Thanks Kai.

So it sounds like the easiest thing for Fred to do would be to dilute a larger sample to something his hydrometer can read and just use that.

Tom,

Whe measuring sg the equal volume dillution is correct. But when measuring Plato, Balling or Brix (e.g using a refractometer) the equal weight dillution is more accurate. However, I fully Agee that the error you are getting is likely too small to matter.

I find measuring weights easier than volumes. Mostly because I can use my fairly accurate scale for that and I don't have to worry about correcting the volumes for temperature.

Kai 

[tschmidlin]

Or to spend 10 bucks...

Yeah, you could do that   It depends on how you define easy, what your setup is like, when you want to measure it, how you feel about tossing a few ounces of super high gravity wort, and probably a few other things as well. 

Whe measuring sg the equal volume dillution is correct. But when measuring Plato, Balling or Brix (e.g using a refractometer) the equal weight dillution is more accurate. However, I fully Agee that the error you are getting is likely too small to matter.

Right, weights for refractometer and volumes for hydrometer.  I see now I didn't clearly say to do it by volume and use the hydrometer, and since I'd been talking about weights in the previous paragraph it's a natural assumption I still was.  I'd mentally gone back to my original suggestion to measure it by volume and revised it to switch the measuring instrument.  I need to do a better job explaining myself. 

Then again, now that you've generated those charts anyone who is concerned can correct the error any way they choose to dilute and measure the wort 

I find measuring weights easier than volumes. Mostly because I can use my fairly accurate scale for that and I don't have to worry about correcting the volumes for temperature.

Yup I use a triple beam balance to measure out my hops and minerals, it's super easy.  I usually don't think to measure liquids by weight though, I think everything I do is by volume.

[Kaiser]

Yup I use a triple beam balance to measure out my hops and minerals, it's super easy.  I usually don't think to measure liquids by weight though, I think everything I do is by volume.

I actually use one of those 100 g x 0.01g jewlery scales that they sell on Ebay for cheap. I'm impressed how precise they are given their price.

Based on a PM that John sent me I ran an experiment tonight:

A 40 Brix solution was prepared from 8g of sugar and 12 g of water.

Using a graduated pipette I then mixed equal volumes of the 40 Brix solution and distilled water. This solution measured at 21.2 Brix with the refractometer.

Using a scale I then mixes equal weights of the 40 Brix solution and DI water. The resulting solution measured 19.6 Brix.

That seemed odd and I created a 20 Brix solution from 4g of sugar and 16g of water. This solution read 19.6 Brix on the refractometer. Good to know how precise my refractometer actually is. I have the cheap one that most brewing stores and Cynmar sell. The ATC is also not working as advertised and I keep calibrating it with DI water before each use.

My calculations expected 21.65 Brix for the equal volume dilution and 20.00 Brix for the equal weight dilution. If I assume an error of 0.4 Brix at the 20 Brix point the experimental results match up with the expectations.

To answer another one of John's questions this happens because the volume that the sugar occupies depends on its concentration. This is the reason why the sg to Brix/Plato conversion is not liner in the first place.

A.J. deLange has written an interesting piece about that: http://ajdel.wetnewf.org:81/Brewing_articles/Sugar_Gravity.pdf.

But for those of you interested you may also do the math using the formula for Brix:

Brix  = m_sugar / (m_sugar + m_water)

You'll notice that when you try to calculate the Brix of a equal weight dilution the resulting solution will have 1/2 of the initial Brix. But when you try an equal volume dilution you'll need to convert Brix to sg to get the volume of the solution to be diluted. And that's where the non-linearity comes into the equation.

Just now I noticed that the equal volume dilution is not truly exact when working with sg. The problem is that the combined volume is not twice the sample volume. This does result from the fact that the volume contribution of the sugar changes when its concentration changes.

Basically we can't write

sg_diluted = (sg_initial * V + V) / 2V

The dividend is the new weight of the solution and is correct. But the divisor is not 2V due to the change in the sugar's volume. I think I also see this in my spreadsheet. The resulting sg for an equal volume dilution of a 1080 solution is 1040.2 and not 1040. But this I really consider too small to matter for our purposes.

This should have deserved its own thread since we are far from the original topic. I also hope I didn't create too much confusion.

Kai

[tschmidlin]

I actually use one of those 100 g x 0.01g jewlery scales that they sell on Ebay for cheap. I'm impressed how precise they are given their price.

Is there one that you recommend?  Because some of those are $1.49 . . . are those the ones that are fairly precise in your experience?

A 40 Brix solution was prepared from 8g of sugar and 16 g of water.
<snip>
Brix  = m_sugar / (m_sugar + m_water)
<snip>
I also hope I didn't create too much confusion.

Just a bit . . . because 8/(8+16)=.33, so that should be 33 brix and not 40 brix, yet it measured ~20 brix when diluted.  To get 40 brix it should be 8g of sugar in 12 g of water.  Just a typo?

[Kaiser]

Is there one that you recommend?  Because some of those are $1.49 . . . are those the ones that are fairly precise in your experience?

This one is very similar to the one I'm using : http://cgi.ebay.com/600-x-0-1-Gram-Digital-Pocket-Scale-Jewelry-jewlery-New-/250731015177?pt=LH_DefaultDomain_0&hash=item3a60bbac09. Except that mine is 200g x 0.01g. I had a different one before which worked well too. With "cheap" I mean something between $10 and $20. Which is cheap compared to real lab scales.

Just a bit . . . because 8/(8+16)=.33, so that should be 33 brix and not 40 brix, yet it measured ~20 brix when diluted.  To get 40 brix it should be 8g of sugar in 12 g of water.  Just a typo?

My bad. I didn't correctly subtract 8 from 20 since I added water to the 8g of sugar until I had a total of 20g. I'll fix the post.

Kai

[kerneldustjacket]

<snip>
To answer another one of John's questions this happens because the volume that the sugar occupies depends on its concentration. This is the reason why the sg to Brix/Plato conversion is not liner in the first place.
<snip>

Ahhh...now that makes sense. Had I know that last night I might not have laid in bed for two hours working this thing out in my head!

Kai, thanks for running an experiment...it's nice to se theory backed up by experimental/empirical evidence.
I think this would be handy information to have typed up as a procedure on how to estimate a high gravity sample given that someone my lack a refractometer or hydrometer that can read high gravities.

Let me apologize as well if this thread was 'hijacked,' what we've covered certainly could have been in it's own thread.

[Kaiser]

I used my powers to split this from the Sparge Arm thread. It was definitely worth its own topic and had little to do with the old thread.

Kai