# The Hydrometer method

I've received a few questions about the method I use to determine the sugar content in Rum (what we assume to be sugar), so I thought that I would write a detailed description on the method and also give some background info.

The Hydrometer.
When measuring the Alcohol content in a Liquid (in this case Rum), there are a few ways to do it. The most simple way is to use a Hydrometer which has a scale showing the alcohol by volume in % (also called %ABV). This type of Hydrometer is also refferred to as an Alcoholmeter. A Hydrometer works according to Archimedes law, which states:

Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

So when the Hydrometer is put into the rum, it start to sink towards the bottom due to the weight of the Hydrometer. The "Glass bubble" on the Hydrometer, displaces the rum as it sinks, and the weight of the rum it displaces, is the amount of upward force that occurs on the Hydrometer (Pushing the Hydrometer upwards). When the Hydrometer sinks to the level where the upward force (due to displaced rum), and the downward force (due to the weight of the Hydrometer), are identical, the Hydrometer will level out and stay at that level. When this level is reached and the Hydrometer is not moving, the %ABV level is read on the scale at the top of the beaker (the surface of the Rum). If you take two rums with different %ABV (eg. 40% and 60%), the 40% rum has a higher density (more heavy, due to less Alcohol) compared to the 60% rum which has a lower density. So in the 60% rum, the Hydrometer will sink further into the rum, compared to the 40% rum, before it levels out and stop sinking.
Why this long description of how a Hydrometer works? Well its all about getting an understanding about density. In a Water/Alcohol solution, the density depends on the amount of Water (Higher density then alcohol) compared to Alcohol (Lower density then Water). What happens to a Rum when sugar (or something else) is added. In case of sugar, the density of the Rum increases, causing the weight of the rum to increase. So if you take a 40%ABV rum, and add sugar to it, the %ABV is still 40%ABV but due to the higher density, when measurements are done with a Hydrometer, you get an incorrect reading. The upward force applied to the Hydrometer is higher because the density of the rum increase when sugar is added. As a result, the Hydrometer does not sink to the correct level before it stops, and the reading on the Hydrometer shows an incorrect %ABV.

How does this correlate into sugar added then?
If we have a table that list the density of a liquid when sugar is added, and another table that lists the density of alcohol at different %ABV, we can use that information to create a conversion table.A description of the conversion table and the math behind it, will follow further down in this article.

All I need to get an estimated sugar added i g/L is the following:

1. Read the %ABV listed on the Rum bottle label (According to EU law, this listed value must be within 0,3% accurracy of the real %ABV of the Rum).
2. Measure the %ABV of the Rum using a Hydrometer (Understanding that if something is added to the Rum, the measurement will give a wrong value as described above). This must be done at 20°C since the Hydrometer is calibrated to that temperature. In case the temperature differs, I have a correction table to adjust the measurement.
3. Lookup in the table I created, using the values obtained in step 1 and 2 above.

The following assumptions is important to understand:

1. I assume that those rums, that results in a different %ABV (What's written on the label compared with the Hydrometer measurement), has something added. Something has caused the density of the rum to change. If we look at EU document 110 from 2008 which holds the definition of Rum, it is allowed to "Sweeten", Add caramel for colouring, but Flavouring is not allowed. So given those facts, I can only assume, that it's the "Sweeten" that impact the density. Aging in oak barrels, also add "something" to the rum (wood extracts), but according to information I have received from Richard Seale at Foursquare Distillery (Barbados), this will only have very little impact (resulting in a maximum of 3g/L miscalculation). (Update: Measurements has shown up to 5g/L for a specific rum from Lost Spirits Distillery).

2. The table I use to in my calculation, which lists density change in a liquid when sugar is added, is based on a solution between water and sugar. In rum we have a Water and Alcohol solution. The density of the two solutions (Water/Sugar and Water/Alcohol/Sugar) are different, but my calculations is about change in density, and not the fixed values at different solutions. So I assume that the density change is identical (checking my measurements with measurements done by Swedish state controlled Systembolaget and Finnish Alko, shows almost identical measurements).

3. The values for density change in a liquid when sugar is added, is not 100% linear, but very close to (in the range I use for my calculations). I assume that the density increase is linear in my calculations.

These 3 assumptions are the reason why I lists my results with the word "Estimated" sugar added.

Creating the conversion table.

The first table I use for the conversion table, is the document that describes the density change in a water/sugar solution as sugar level increases. This is described in Circular of the National Bureau of standards C440, Polarimetry, Saccharimetry and the sugars by Frederick J.Bates and Associates (issued May 1, 1942). From the document, I’ve used the first column (% of sucrose by weight (brix)) and the 3rd column (Apparent specific gravity at 20C/20C)
The values is used to calculate the average increase in gravity pr. Brix degree change. 1 degree brix is approx. 10g sugar/L. Since the rum we want to measure most likely has below 100g/L, I have chosen to do the average density change for the brix range 0-10 brix (approx. 0-100g/L sugar added). Within that range, the average density increase/Brix change is 4,00331 (Value used in formula later on).

The second table used for the conversion table is the document that describes the density of a water/alcohol solution. This is described in the document called Tables Alcoométriques internationales (International Alcoholmetric Tables). From the document, I’ve used table IVa  on page 51-53 to get a listing of the density of the rum at different % levels.

Input to the formula (with example):

40%ABV rum that with a Hydrometer has a "wrong" value of 35%ABV.

At 40%ABV the density of the Rum is: 948,05 kg/m3
At 35%ABV the density of the Rum is: 955,59 kg/m3
The average density increase pr brix: 4,00331
Calculation is 100mL solution, so multiply with factor 10 to get value in g/L

The result is:
(("Density Hydrometer %ABV" - "Density label %ABV") / "Average density increase pr. brix" ) * 10 = Sugar added in g/L

((955,59 - 948,05) / 4,00331) * 10 = 18,8 g/L

The conversion table I've produced, are listed in the picture below.

Validating the method.
The Swedish state controlled "Systembolaget" and the Finnish "Alko" have published values about the amount of sugar in some rums (listed in g/L). Not knowing the method used for these measurements, I can only assume that these measurements has been done in a lab with highend equipment, giving accurate results. With my simple Hydrometer measurements and the conversion table, I've measured some of the same rums, and these are the results:

 Brand Lab My measurement Angostura 1824 Aged 12 years 17 18 Angostura 1919 14 13 Botran Solera 1893 Gran Reserva Anejo 9 9 Diplomatico Reserva 8 anos 7 9 Diplomatico Reserva Exclusiva 12 anos 41 30 El Dorado 12 year old 45 36 El Dorado 15 year old 31 37 Plantation Jamaica Old Reserve 2000 17 16 Ron Zacapa Centenario 23 45/20 38

Another way to validate the method, is by adding a specific amount of cane sugar to a white rum which have no sugar added to start with. In the example below, a cheap white supermarket rum which has an %ABV of 37,5%, was used. 200mL of the rum was poured into a beaker, and a picture was taken, showing that the Hydrometer sink to the bottom. 8 gram of cane sugar (8g/200mL = 40g/L) was added to the white rum and dissolved by stirring the rum for a few minutes. After the sugar had dissolved into the rum, the Hydrometer was placed back into the rum and a second picture was taken. On the second picture, the Hydrometer does not sink to the bottom, but stays at the surface. In both cases the rum is 37,5% ABV, but the density change due to added sugar, causes the Hydrometer to measure a wrong value. The "wrong" value measured are 26,4% ABV and this was measured at 24°C so we have to temperature correct the measurement using a correction table. 26,4%@24°C = 25%@20°C , looking up in the Sugar g/L conversion table I've created, 37,5% on the label and 25% incorrect Hydrometer measurement gives an exact match to the expected 40g/L sugar added.

References to EU documents:

Accuracy of %ABV listed on the label:
http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:32011R1169
Annex XII ALCOHOLIC STRENGTH
4.Any other beverages containing more than 1,2 % by volume of alcohol  0,3 % vol.

Sugar is allowed in rum:
http://eur-lex.europa.eu/legal-content/EN/TXT/?uri=CELEX:02008R0110-20140207
Article 5 General rules
1 (e) solely be sweetened to round off the final taste of the product, according to Annex I(3). The maximum level for the products used for rounding off listed under Annex I(3)(a) to (f) shall be decided upon in accordance with the regulatory procedure with scrutiny referred to in Article 25(3). The particular legislation of the Member States shall be taken into account.

Definition of rum:
ANNEX II SPIRIT DRINKS 1(a-f)
Categories of spirit drinks
1.    Rum
(a) Rum is:
(i) a spirit drink produced exclusively by alcoholic fermentation and distillation, either from molasses or syrup produced in the manufacture of cane sugar or from sugar-cane juice itself and distilled at less than 96 % vol. so that the distillate has the discernible specific organoleptic characteristics of rum, or
(ii) a spirit drink produced exclusively by alcoholic fermentation and distillation of sugar-cane juice which has the aromatic characteristics specific to rum and a volatile substances content equal to or exceeding 225 grams per hectolitre of 100 % vol. alcohol. This spirit may be placed on the market with the word ‘agricultural’ qualifying the sales denomination ‘rum’ accompanied by any of the geographical indications of the French Overseas Departments and the Autonomous Region of Madeira as registered in Annex III.

(b) The minimum alcoholic strength by volume of rum shall be 37,5 %.

(c) No addition of alcohol as defined in Annex I(5), diluted or not, shall take place.

(d) Rum shall not be flavoured.

(e) Rum may only contain added caramel as a means to adapt colour.

(f) The word ‘traditionnel’ may supplement any of the geographical indications mentioned in category 1 of Annex III where the rum is produced by distillation at less than 90 % vol., after alcoholic fermentation of alcohol-producing materials originating exclusively in the place of production considered. This rum must have a volatile substances content equal to or exceeding 225 grams per hectolitre of 100 % vol. alcohol and must not be sweetened. The use of the word ‘traditionnel’ does not prevent the use of the terms ‘from sugar production’ or ‘agricultural’ which may be added to the sales denomination ‘rum’ and to geographical indications.

This provision shall not affect the use of the word ‘traditionnel’ for all products not covered by this provision, according to their own specific criteria.