How Hard to Scoop Will My Gelato Be? (part II)
On why PAC is not the best tool to estimate scoopability or serving temperature, and what to do about it.
Introduction
In the first part of this article we introduced the idea that PAC alone cannot be an indicator of a cream's hardness, because there are other factors involved.
We demonstrated this by showing how different recipes with the same PAC will freeze at different temperatures, so will have different hardness at any given temperature. We introduced the concepts of normalised PAC (PACn) which allows us to determine a recipe's freezing point (FP) and argued that the freezing point of a recipe is a much more reliable indicator since it takes into account the amount of water in the recipe.
In this final part we will extract two new parameters from the freezing point and explain why we think one of them is the best indicator of hardness for practical purposes.
Read on!
Beyond Freezing Point
Now that we have agreed that the freezing point (FP) of a recipe provides much more useful information than its PAC alone, it is time to look beyond it.
As we discussed earlier, the amount of ice in a cream is directly linked with its hardness in the cabinet: as the temperature drops below the freezing point, more water gets frozen so the cream feels harder; conversely, increase the temperature and you will have less ice and more liquid water, so the cream will feel softer.
Another way of putting it is that the play between the frozen and unfrozen water in a cream will determine its hardness: in one extreme, above its freezing point, the cream is liquid (i.e. very soft) because there is no ice in it; on the other, the temperature is too low and there is only ice, so we have a solid (i.e. very very hard) block.
Our sweet spot will be somewhere in between, so we have two tasks at hand in order to find it:
- Find out how much ice a recipe will have formed at a given temperature, based on a set of parameters;
- Find out which balance between frozen and liquid water delivers the hardness we want.
Let's look into it!
Step 1 — Ice Fraction
Luckily, some very clever guys have been hard at work to figure out #1. They created an index to represent this and called it ice fraction. Essentially it expresses the weight of the ice in a solution at a given temperature, based on its freezing point and water content.
Let's have a look at how to calculate it.
We will need to know two parameters, and determine a third:
- The amount of water in the recipe (100-TS)
- The recipe's freezing point (FP)
- The cabinet's serving temperature (Ts)
The first two we already know how to calculate and since the third is our own choice, we are ready to go — all we need is a formula:
Where:
I know it looks terribly complicated, but don't worry, the formula is here for informative purposes only. I promise you won't need to use it unless you really really want, as I have setup a little spreadsheet that does all the calculations (it will be available at the end of the article once we have covered all the topics I want us to).
Anyway, getting back to the ice fraction calculation, you may be asking:
All this is very well, but what do we do with it?
And it is a very good question! I mean, it is clear that a cream with more frozen water in it will feel harder, but how to find how much is hard enough and how much is not?
To answer this, let's have a closer look at what we have found so far.
The ice fraction tells us how much of the recipe's weight is frozen water. (i.e. an ice fraction of 0.5 at a given temperature means that at that temperature, 500gr of every kg of the recipe will be ice). However, the total weight of the recipe includes all its solids, which, as you can imagine, will remain solid irrespective of the serving temperature. So their effect on hardness will not vary, which means that ice fraction will not work as an indicator of hardness at a given temperature.
Which brings us to…
Step 2 — Percentage of Water Frozen
Look at the image above and imagine two scenarios: one where there are very few ice blocks, and another where the surface is completely covered. Which one do you think would be safer (i.e. more solid) for you to walk on?
This is the principle behind how we assess hardness: we will look into how much ice vs. water our recipe will have at the serving temperature.
In order to do this, we correlate the ice and water fractions of the recipe and express them as a ratio, which we call the percentage of water frozen (%WF).
It is calculated as follows:
Both variables were present in the previous calculation, se we now have an easy way to find out how much of the water in a recipe will be frozen at the serving temperature.
Almost there…
Because I can see you thinking that "all this is very well and makes sense, but how do I know what %Wf will yield the consistency I am looking for?!"
And it is another very good question!
Based on experience, that great Gelato consistency we are all fond of is achieved when between 75 — 80% of its water is frozen according to the formula above. Closer to 75% it will have a rather soft (Bologna-style) consistency, while closer to 80% it will be a rather firm bundle.
And that completes our lucubrations. We can now confidently state that:
"In order to have a Gelato at an appropriate serving consistency we shall balance our recipe so that it yields a %Wf value between 75–80 at our chosen serving temperature."
Bravissimo!!
Now that we have all the theory and formulas covered, let's have a look at some examples.
The example above displays pretty standard parameters for a classic flavoured Gelato recipe: Total Solids at 40%, PAC 24 and 8.5% MSNF. Two serving temperatures of -10 and -14ºC were chosen as this is the usual recommended range for the serving of traditional Gelato, to give us an idea of how they affect the ice concentration in the cream.
So the example above would probably feel a bit too hard at -14ºC (as it is above 80%Wf) and pretty ok at -10ºC (as it is within 75–80). You also might have noticed that it could be served at an even warmer temperature — in my tests it behaved well up to -9ºC at which it yielded 76%Wf.
Notice something else: how these parameters yield an FP of -2.93ºC.
This is pretty good, as the goldilocks freezing point range is usually considered to be between -2.75 and -3ºC for a serving temperature between -10º and -14ºC.
So we are starting to get somewhere, methinks. We went from a blanket recommendation based on the PAC of a recipe without any regard for other parameters that will have a big impact on hardness (i.e. the proportion between solids and water); to a more holistic approach where we take into account not only PAC, but also Total Solids and serving temperature.
Along the way we uncovered two parameters that will be great guides in determining the hardness of our cream in the cabinet: the Mix's Freezing Point (FP) and Percentage of Water Frozen (%Wf).
Sounds great!!
Before we conclude though, let's have a look at a few other examples to check how the above holds up:
In the example above we are comparing our first Gelato recipe with a Sorbetto. The main differences between them are in Total Solids and PAC. Notice how, as a consequence, virtually all parameters turn out different and yet, the percentage %Wf of both is almost identical.
Notice also how if you calculate PAC ÷ 2 for the first (a Gelato), and PAC ÷ 2.5 for the second (a Sorbetto), you will come to the same RST (Recommended Serving Temperature) of -12ºC.
Now you know how they came out with these magical denominators!! :)
Finally, notice how at this temperature both mixes yield a %Wf of 80.
So, again, %Wf is the indicator we want to focus on to assess the hardness of our Gelato or Sorbetto at a given serving temperature. If you like your Gelato to be served a little firmer you now know what is your ideal %Wf (i.e. 80). If you like it a bit softer, it will be less than that, but not below 75.
And if you are curious, my personal preference is around 77–78…
High five to you — job done!!
Wrapping Up
So there you have it. We went from estimating hardness based on cumbersome PAC rules that don't take into account key factors about our Gelati or Sorbetti, to a consistent system that gives us reliable figures based on simple calculations.
In a nutshell:
- PAC is a very limited tool to assess the hardness of a cream at serving temperature. It doesn't take into account the balance between total solids and the amount of water in a recipe;
- The Freezing Point (FP) is a much more appropriate indicator, because it relates the antifreezing potential of the recipe's PAC with the amount of water available. The usual recommended range for Gelato and Sorbetto is between -2.75º and -3.0ºC, for the serving temperature range between -10º and -14ºC.
- By relating the recipe's freezing point with the serving temperature we can calculate the percentage of water frozen (%Wf), which is the de facto indicator of hardness. The ideal range for Gelato and Sorbetto is between 75 (at the soft end), and 80 (at the harder).
- If you click on the image below it will open a link to a Google Sheets spreadsheet that will calculate the freezing point and the %Wf based on TS, PAC and serving temperature.
And that concludes this two part series.
A presto!!
p.s. — Before we part ways on the topic of Hardness, a little Disclaimer:
Unfortunately, the reality is that there are many more factors that will have an influence on the hardness of a Gelato or Sorbetto in the cabinet. Things like the types of solids present in the ingredients (i.e. chocolate and nuts solids tend to get harder when frozen); the amount of overrun; and more. This means that you may come across a specific recipe or flavour that doesn't yield results 100% in line with the above, particularly if you like to experiment with unorthodox flavours.
The way to avoid this would be to take into account all factors that might influence a cream's Hardness, but this would be very complicated and highly impractical.
That's why I chose to stick with this method in spite of its limitations. It is still a great step forward (actually two!) compared to good old PAC, and yields pretty reliable results in most cases.
I hope you will agree, but let me know your thoughts in a comment if not :)
