Pyknometers (what hydrometers emulate) revisited!

[PeeBee]

Oh no ... it's Peebee and his flippin' "pyknometers". Are you all screaming yet? No? Don't worry, you will be!

I had to admit using a pyknometer instead of a hydrometer wasn't entirely convenient; there was a bit of arithmetic to do to get the Specific Gravity of your beer sample. But when someone offered me a 100ml pycnometer bottle (I've normally used 25ml bottles) I could appreciate the opportunity to do away with the arithmetic and display the SG directly:

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Okay, there is still some very simple arithmetic to do; shift the decimal place left two digits. So, this is displaying an SG (relative density) of 1.0217.

Note that's four "decimal places", the calibration is for 20°C (and a 20°C water reference). There's a bit of mucking about to get to this point, but it only needs doing once. So, ... (to be continued).

[drjim]

Presume there is some cleverness to offset the weight of the bottle itself???

[drjim]

On thinking about it zero the scale!

[Marshbrewer]

I can see how this works for solutions of alcohol in water, but with beers, how do we know what part of the weight difference is caused by alcohol and what part by suspended yeast?

[IPA]

Silly me. I thought this was a thread about how gypsies calculate the price of scrap metals.

[PeeBee]

Before I got this bottle (from WallyBrew, I'm sure he won't mind me mentioning him, as unlike the "Invert Sugar" supplier I doubt he'll have queues of folk knocking on his door wanting some too!) ... before I got this bottle, I'd use cheap 25ml bottles from China (cost about a fiver each). The quality wasn't great, the 25ml bottle I'm currently using I've calibrated as holding 26.37ml. So, this 100ml bottle by MBL is a bit of a revelation! So much so I thought it was an expensive "calibrated" bottle: I was close ... but it wasn't not calibrated, just probably was originally (it's quite an age) "expensive"!

So, the first obstacle is locating a bottle pretty close to 100ml without parting with a King's Ransom. This bottle I have proved to be just 0.33ml short of 100ml which has made my life very easy indeed! An alternative is find a slightly too large bottle and some glass beads to put in the bottle to get close to 100ml? The second obstacle is getting some half decent weighing scales that weigh reliably to two decimal places of a gram. Not the so-called, postage stamp sized, "drug-dealer" scales; those I've pictured above are not bad and only cost £30-35 (2022 prices)

And you will first need to go through the rigmarole of "calibrating" your bottle (it's not really difficult). Weigh the bottle dry and weigh again full of pure water at 20°C ("full" is easy with a pycnometer bottle 'cos it has a small hole in the stopper that when fitted on the bottle will expel any excess liquid). Subtract the dry bottle weight (the "real" Tare Weight) from the weight full of water at 20°C to get the weight of water in the bottle. However careful you are trying to get the volume close to 100ml, the sample won't weigh 100g (unless you haven't been careful, and the gremlins are playing tricks with you). Divide the sample weight by 0.9982; now it ought to be close to 100 (0.9982 is one of those magic numbers you'll find you will memorise messing with pyknometers: it's the density in grams per millilitre of water at 20°C). Applying the "magic number" means you now have the water pretending to be at its highest density - one gram per millilitre - so the modified weight you have can have its units changed from "grams" to millilitres": Voila, you've got the volume of the bottle!

If your volume isn't within a millilitre of 100ml you probably can't use the rest of this "trick"*, but you still have a calibrated pycnometer that can be used more conventionally. [EDIT: *The volume can be a few milliliters too big. See later.]

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This is my bottle filled with water for calibrating. Actually, it's had the "trick" applied so is weighing 100.00g. Shift the decimal left two digits and you have 1.0000 ... the SG of water, at 20°C and relative to the density of a water at 20°C (itself?). The tea infuser in the shot is temporary apparatus needed to pull off the trick.

... to be continued.

[PeeBee]

Sorry for the delay getting this writeup done. Seems I've unexpectedly found myself in possession of a fine bit of kit (a very nice pyknometer) and I'm trying to translate my trickery into something anyone can have (and I don't mean by using a "hydrometer"!).

Next all the figures to prove it works! So, I had better apologise for that in advance ... sorry! (Might be tomorrow before I post all the numbers).

Silly me. I thought this was a thread about how gypsies calculate the price of scrap metals.

That's a very "not PC" comment these days! But don't be coy, it's only a diddy digression, and few will pick it up.

[IPA]

Sorry for the delay getting this writeup done. Seems I've unexpectedly found myself in possession of a fine bit of kit (a very nice pyknometer) and I'm trying to translate my trickery into something anyone can have (and I don't mean by using a "hydrometer"!).

Next all the figures to prove it works! So, I had better apologise for that in advance ... sorry! (Might be tomorrow before I post all the numbers).

Silly me. I thought this was a thread about how gypsies calculate the price of scrap metals.

That's a very "not PC" comment these days! But don't be coy, it's only a diddy digression, and few will pick it up.

Diddy digression ? When I was young they were called Diddy Coy

[PeeBee]

I've always been bemused as to why "Specific Gravity" ("Relative Density") was "relative" to anything. Why Hydrometers have two calibration temperatures (one of the two is barely known about to most people). Why don't we just use "density" and do away with this "relative" business?

Until this recent bout of playing with pyknometers that is!

You still need to know the weight (Tare) of the dry bottle. Stash samples of wort and water near each other for a while so they are the same temperature. With each liquid, fill the pyknometer and weigh it, deleting the "Tare" so you only have the weight of each sample. Divide the weight of wort by the weight of water. You have the "Relative Density" (SG) of the wort. No "is it 20°C", no "what volume is the bottle (it could be a barrel!). And Hydrometers inherited this silliness!

Amazing the things you can learn!

And I was always puzzled why the labrats still had their 60°F calibrated hydrometers? It's because they've got much better tools to tell them density, why bother to replace the old 60°F/60°F hydrometers gathering dust in some cupboard with the 20°C/4°C calibrated "Standard" ones.


And why does this Microsoft editor keep changing my correct spelling of "pyknometer" to the mis-spelled "pycnometer"? Grr!

[PeeBee]

... When I was young they were called ...

Okay. We don't need to know how long ago that may have been.

[PeeBee]

Numbers? Right ... I'm going to break this up into three parts so as to ...1: Make it easier on some of you (think "BBC Bitesize"!) ...2: Make it easier on me; if you're struggling with the numbers, I'm trying to juggle them with a Severe TBI (eh? Clue: I don't pay council tax 'cos the local council deem me "S.M.I.", a particularly nasty non-PC term I'd like to see "adjusted"), and ...3: Give cleverer folk opportunity to scan what I'm doing and if necessary, point out corrections!

Starting with the bottle as it is. This is a normal way of dealing with pyknometers, i.e. No trickery (yet! This is just some preliminary work and "revision", the "trickery" comes later!). I'll use my bottle as an example:

Weigh the bottle (with stopper) dry. This is the "real" TARE weight. Two decimal places with half-decent scales ... at least, e.g. 35.72 grams.

Fill bottle with pure water (distilled if you must) at 20°C, replace stopper, dab off any excess water on the bottle, and weigh again. e.g. 135,21 grams.. This is the GROSS weight containing pure water at 20°C.

Subtract the TARE weight from the GROSS weight too get the NETT weight of the 20°C water sample. e.g. 99.49 grams.

Remember that "magic number? Divide the NETT weight by the "magic number" to get the bottle's VOLUME. e.g. 99.49 / 0.9982 = 99.67 millilitres.


You need to do this once for every pyknometer bottle. But only once, so make sure the numbers are recorded for that bottle (with paired stopper) somewhere safe. Now, to use this information, conventionally that is:

Fill the bottle with beer wort at 20°C, replace stopper, dab off any excess from outside the bottle, and weigh.

Delete the TARE weight to get the sample's weight.

Divide the samples weight by the bottle's VOLUME. This gives the sample's density in grams per millilitre (g/ml).

Divide this "density" by the "magic number" (which is the density of water at 20°C) to arrive at the "Relative Density" (SG) of the wort.


What a phaff! Hence, I'm going to dive into some "trickery". ... to be continued



NOTE: Don't show this to anyone knowledgeable. Especially the "trickery" to come. They will probably start screaming! The electronic scales I'm using are two decimal digits; the Labrats would probably use highly sensitive balances that weigh to four decimal places of a gram (0.1 milligrams), and the "trickery" to come will induce errors. But I'm only trying to make beer, and if I can show accuracy to be better than half a "gravity unit" (i.e. 0.0005 SG) that'll be massively better than the hydrometers in use by homebrewers (and a shedload easier to read). Err ... but if anyone starts suggesting the use of those cheap (£10-20) "drug-dealer" 0.01g scales, I'll start screaming!

Anyway, most of these naff "drug-dealer" scales can't weigh more than 100g. Full 100ml pyknometers weigh more than 100g.

[PeeBee]

Okay ... First "trick". Let's get rid of that "magic number". Actually, I could have done this for the 25ml pyknometer I was using; it just hadn't occurred to me at the time. So, this trick might be applied to any size of pyknometer, but it won't get the SG displayed on the weighing scales: That'll come next!

For this trick to work it really needs the correction to be a "simple" addition or subtraction constant. But this "magic number" is used in division so it's not a constant in the same way. Now "0.9982" (the "magic number") is so close to "one" and the range to be applied to so short, I can ignore any tiny (and it is really tiny!) error a simple solution might induce.

So, a sample that shows the density to be 0.9982g/ml using the pyknometer at 20°C, will have an SG of 0.9982 / 0.9982, or 1.0000 (the sample seems to be water!). Now brewing a really strong beer: The density of the unfermented proves to be 1.1479 ... or an OG of 1.1479 / 0.9982, or 1.1500! (Rounded up from 1.1499699...etc.). Now, if the pyknometer holds 100ml the first sample (water) weighed 99.82 grams, the second sample 114.79 grams (at 20°C). So, if the first sample weighed 0.18g more at 20°C then (99.82 + 0.18) / 100 will equal ... 1.0000! The weight of the sample will reflect the relative density (SG) not the actual density (at 20°C).

But how can the sample be made to weigh 0.18g more? ... Easy, alter the "real" TARE to an imaginary TARE of (TARE - 0.18). And what will this do to the "really strong beer wort" readings? ... After the "imaginary" TARE is deleted from the GROSS sample weight (100ml sample) it will weigh: (114.79 + 0.18), or 114.97, or an SG of 1.1497, instead of 1.1500, or an error of +0.0003, or too small to give a second thought too!

How do you alter the TARE? ...I'm sure there are scales that will do this, but what I did is create a Tare weight. Temporarily I'm using a tea infuser containing a measured amount of beans and rice, but this will need changing for something more permanent (that won't dry out or suck moisture from the air. Zero the scales with this Tare weight, NOT the empty pyknometer bottle (which will be very difficult to dry each time it is used too).

This doesn't include any errors induced by the weighing, which is why I suggest some half decent weighing scales (and be careful to keep them in good nick). And there's a lot of assumption of the bottle holding 100 millilitres. I'll deal with that next ... to be continued ZZZzzzzz

[PeeBee]

Presume there is some cleverness to offset the weight of the bottle itself???

I suppose you'd guessed right? I like the "cleverness" bit! I'm all in favour of compliments.

[PeeBee]

Last throw of the dice (for now anyway). Blimey, this has been hard work! Knowingly inducing errors and then proving the errors are irrelavant; it's not how I'm (or anyone here is?) used to working. Still, others always have the option of approaching the task more simply but with unknown random errors (buy a hydrometer from your local homebrew store!). All this long written drivel is so I can be very open about what I'm doing, but it's mainly so I can keep track of what I'm doing!

Now where was I? Bottle (pyknometer) volume. I want it as near 100ml as possible, maybe within 1ml, or even 0.5ml.

If the bottle if less than 100ml, you can't do much about it, so you hope it's within the required tolerance (within 0.5ml, 1.0ml at a pinch, of 100ml). But if the bottle has more capacity than 100ml, and all the "cheap" (Chinese) bottles I've had so far are on the larger side, you may get the volume within tolerance by filling with suitable "packing". I earlier suggested glass beads, but they'd be a pain rolling out of the bottle and getting lost! You'd probably need something you can easily sanitise as at 100ml you may want to return the sample to the vessel it came from? Rods? Length of flexible cord? As long as you can get it out, but it doesn't easily find its own way out. You don't want heavy item that might break the bottle if shaken.

Dreaming up ways of padding out cheap bottles has absorbed a lot of my time since figuring out my WallyBrew supplied bottle was far from the "cheap" variety (well, what else could I have expected from WallyBrew!). It seems the bottles supplied by "reputable" lab equipment retailers may be roughly useable at the printed capacity, but at a price! (£60, £80 ... or more!). The "cheap" bottles (direct from China say) can only be used after calibrating (the printed volume is decidedly "nominal").

Any small deviation (either as-is or after a bit of packing) can be absorbed by the "trick" I used with the Tare weight. The bottle's volume (at 20°C) is as found earlier (e.g., 99.67ml), so you want the difference compared to the intended volume (e.g., -0.33ml). Adjust this difference with the "magic number", but the adjustment will be minuscule small, so just change the units to grams (e.g., -0.33g).

Add the difference to the Tare weight, which is currently at [TARE - 0.18g] (e.g., Tare-weight + (-0.33)). In my case it was TARE (35.72g) less 0.18g (to dispense with the "magic number") plus the difference in volume of my bottle and 100ml, as grams (35.72 - 0.18 + -0.33 = 35.21g).



What I'm thinking of next is having a collection of "Tare weights" (3 should do) to cover different temperatures (say 60°F, 70°F, 80°F, or 15.6°C, 21.1°C, 26.7°C; I have my reasons for switching to Fahrenheit) and to cover higher gravity (above 1.070) where the "errors" are perhaps accumulating to noticeable size (still within one "gravity point ... moving the "zero error" point, currently at 1.0000, may be enough).

That'll keep me amused/silent for a few days.

[PeeBee]

After all this waffle, you may need a reminder of what it's all about. So, linking back to the OP:



Displaying SG or "relative density" (1.0217) at 20°C (water reference also at 20°C). Imagine the Decimal Place is two units left! Easier to see and more accurate (4DP, not three) than a, probably dodgy, hydrometer.

[EDIT: I should have included ... The wort was also checked with the "100ml" bottle using the long-hand method (no tricks, just calculated from the "raw" data). I.e. The scales do not show the SG, the actual density is calculated by taking the actual weight at 20°C and dividing by the actual volume, and then dividing by the density of the reference (pure water at 20°C, or 0.9982g/ml) and it came out as 1.0218. That's 0.1 of a gravity point difference (SG 0.0001) ... close enough for me!]