I have read that you can calculate specific gravity by dividing the weight of a known volume of liquid in the weight of a known volume of water. After reading that I thought about filing my fermenter with 20L(5 gallons) of water and putting them on a scale, then putting my next batch on the same scale, that way I could measure SG as much as I wanted without wasting liquid or risk in contaminating my beer. My next thought was "if It's that simple, Why doesn't everyone do it?" Why isn't this a common practice? What's the down side?
Yes the math is possible with accurate readings.
Basically for every molecule of cO2 produced 1 molecule of ethanol is produced.
By calculating the reduction of weight and factoring cO2 absorption in solution you can calculate ABV.
Here's the problem. You need a scale that will be accurate within 1 gram. This may be viable for a 1 gallon batch using a postage scale or something similar. But for a 5 gallon and greater volumes these scales are very expensive. For example using a digital bathroom scale can easily be +/- 1lb when weighing 50lb, and swing 2-4 lb around 200lb just from temperature changes in the sensor.
A calibrated hydrometer is £5, a refractometer is £30, and my set of calibrated 100Kg scales are ~£150. I can use the same hydrometer on my on anything from 5 litres to 500,000 litres whereas a set of scales would be very size specific to have the degree of accuracy required, and freaking expensive.
I have a sample tap on my vessels and draw about 300ml a time for gravity, pH, colour and clarity checks. Also, 300ml gives me enough to be able to run all my tests and still have enough left for us all to have a swig or 2 and taste/smell for any discrepancies. A set of scales does not allow me to check clarity, pH taste and smell, I would still have to draw a sample for these.
Even if I had scales for calculating the mass of the vessel and sugar I could work out the OG with this, but changes in SG over time and FG would be difficult as the mass would not change much but the density proportionally changes more than the mass. Allowing for a more accurate reading off very simple equipment.
Even though I have a hygienic stainless sample tap I still disinfect it with PAA before and after every sample is taken. If in doubt, sanitize, sanitize then sanitize some more.
Because it is not practical.
What is easier? Manipulating a fermenter of 20 kg, or 100 ml of wort?
With a scale, you probably mean a balance. If you have one, good for you. But how much do you pay for a balance which must be able to carry 20 kg or more? Trying to find one only gave me spring balances.
And scaling up is not really an option. Big balances are expensive. For a measuring glass and a hydrometer you will pay approximately 15 EUR/$. For that price you will not have a scale that can weigh 20 kg.
With regards to your objections.
I brew smaller batches than you, but if I brewed 20 litre, I would not object wasting 100 mL of fermented beer.
Second, it is not as if beer gets contaminated when you lift the lid and have a sniff of it, or expose it for a minute to the ambient air. The first time that I did a gravity measurement, I had to use a racking tube, which takes some time, and I even put the measured liquid back into my fermenter. My beer was fine.
Work clean, disinfect your measuring tools and be acutely aware of what you are doing, then you will surely not have any contaminated beer.