# Measuring ABV or Proof obscured by Sugar using Density and RI

The true ABV or Proof of spirits containing sugar can be determined by measuring the Density and the Refractive Index (RI) of the spirit. The graph below shows how these measurements can overcome the obscuration and reveal the true ABV, and give the sugar content as a bonus.

In this graph the Alcohol Concentration is shown on the horizontal axis and increases from left to right. The Sugar Concentration is shown on the vertical axis and increases from bottom to top. The blue lines show the combinations of alcohol and sugar that result in the same density. Similarly, the red lines show the alcohol and sugar levels that result in constant values of RI.

As an example assume that we have a liqueur for which we have measured the density at 1006 kg/m3 and the refractive index at 1.3496 nD.

It is well known that adding alcohol to water decreases the density of the spirit. If we start at the point marked "1" on the blue 1006 kg/m3 density line and then add more alcohol we would be moving further to the right on the graph. Since we want to maintain the measured density of 1006 kg/m3 and we know that adding alcohol would lower the density it means that we would have to add sugar (which increases the density and "obscures" the alcohol) to maintain the density at the same level. So as we move from point "1" towards point "2" both the alcohol and the sugar levels increase (but the density remains unchanged) and the line slopes upwards towards the right.

From the line 1-2 on this graph we would be able to read off the value of the sugar concentration required to give the measured density of 1006 kg/m3 for any desired concentration of alcohol.

Similarly, it is known that adding either alcohol or sugar to a solution increases the RI. If we start at point "3" on the 1.3496 RI line and move to the right by adding alcohol we have to cut back on the sugar to hold the RI at the same level. As we move from point "3" towards point "4" the alcohol level increases but the sugar level decreases (and the RI remains the same) and the line slopes downwards towards the right.

From the line 3-4 on this graph we would be able to read off the value of the sugar concentration required to give the measured RI of 1.3496 for any desired concentration of alcohol.

Where the 2 lines cross at point "5" we can read the levels of alcohol and sugar that would give both a density of 1006 kg/m3 and an RI of 1.3496. Because the lines are relatively straight, and because the density lines slope upwards while the RI lines slope downwards, any density line will intersect with any particular RI line only once. If we have suitable graphs we can find the unique combination of alcohol and sugar levels that will give rise to any combination of density and RI.

It would be very cumbersome to use graphs to do this analysis on a day to day basis and the obvious answer is to get to the underlying equations so that we can do it analytically in the computer. This technique forms the basis for the calculator included in AlcoDens LQ which enables distillers to simultaneously determine the alcohol and sugar contents of a liqueur or infusion by measuring the density and the refractive index, and therefore overcome the obscuration caused by the sugar. These two measurements of density and refractive index are well within the scope of craft distillers and the equipment needed is very affordable.

## Typical Calculation

This method can be used whenever a spirit contains both alcohol and sugar. Typical use cases would be the determination of ABV during or after fermentation of craft beer, wine or distillers' beer. It is also useful for the determination of ABV in RTD cocktails and liqueurs. Here we will give an example of a spirit that has been used for the maceration of berries and the aim is to determine the ABV and sugar content after filtration.

In order to measure the density of the spirit a hydrometer calibrated for ABV at 20°C is being used, and shows an apparent ABV of 14.6%. The refractive index is measured using a brix-calibrated refractometer, also calibrated at 20°C. The refractometer shows an apparent Brix of 12.3. When this data is entered into the calculator it shows that the true ABV at 20°C is 25.03% and the true sugar content is 3.02 Brix. It is interesting to note that while the sugar obscures some of the alcohol from being measured by the hydrometer, the alcohol causes the sugar that is measured by the refractometer to be over-stated.