# Sorbet by the numbers

Since my first taste of bianco vermouth (not to be confused with dry white vermouth), I’ve wanted to make it into a sorbet. I finally managed it, but took an interesting path to get there: I calculated it.

I was first introduced to the idea of formulating frozen desserts mathematically by Michael Laiskonis, and the idea was further driven home in Francisco Migoya’s book Frozen Desserts.

That book suggests that the ideal sugar content for a dessert sorbet is between 25° and 32° Brix – which is relatively easy if you’re building your formula on an unsweetened base, but harder if the base already has significant amounts of sugar, as bianco vermouth does. So how do you figure out how much sugar is in a commercial product like that, especially when a refractometer or hydrometer reading will be thrown off by the alcohol content?

Enter a bartender friend of mine who goes by the handle bostonapothecary on eGullet. In a series of blog posts, he outlines how to calculate the sugar content of various liqueurs, drawing on the fact that alcohol and sugar have a predictable impact on the specific gravity of the product.

I’m not great with solution arithmetic, but I figured since I was working in the kitchen and not the chemistry lab, I could ballpark it and end up with something that works. I started by measuring the specific gravity of the vermouth with a hydrometer borrowed from a home-brewer friend: it read 1.050. Using the table linked to by bostonapothecary, and the 16% alcohol content stipulated on the label, I calculated the specific gravity, corrected for alcohol, as roughly 1.070. According to the other table, this works out to 183 grams/litre of sugar. To get the sorbet base up to 28° Brix (roughly in the middle of the 25°-32° range Migoya suggests), I needed to add 130 grams more sugar.

But wait… I also knew that alcohol suppresses the freezing point, so I decided to dilute the vermouth slightly. I figured 12% was reasonable, so I added enough water to bring the alcohol content to 12%, then enough sugar to bring it up to about 313 grams/litre. I also added some citric acid for flavour, and a touch of xanthan gum for insurance.

When I churned the base, it came out with a very slushy texture, and I was worried that I had done the math wrong. But after leaving it in the freezer for 8 hours, the final texture was pretty close to what I was looking for, only a bit too soft.

Here’s the recipe I used, which I might tweak slightly next time, with a little less sugar and more citric acid, and perhaps a pinch of salt to balance out the inherent bitterness of the vermouth:

### How to make Bianco vermouth sorbet

500 ml Martini bianco vermouth
167 ml water
88 g sugar
1.97 g xanthan gum (optional)
1.3 g (about 1/4 tsp.) citric acid

Dry blend the sugar, xanthan gum (if using) and citric acid. In a bowl, combine the water and vermouth, then add the sugar mixture and stir to dissolve. Chill thoroughly, then process in an ice cream maker according to the manufacturer’s instructions. Pour into a container, then freeze for 8 hours to harden.