Ice Cream Series: Part 3
As with pizza, music, politics, deities, and whiskey, opinions on ice cream styles range wide. There are aficionados of rich, French custard-based ice creams, with up to eight egg yolks per quart; of the lean, eggless Philadelphia-style that disappears on your tongue and has to be eaten straight from the machine; of the dense, bright, intense, eggless and creamless gelatos of southern Italy, of the chewy, gooey, almost cake-like ice creams of New England, or the even chewier, gooeyer versions from Turkey and Japan that blur the lines between dairy and taffy …
We’re not going to get into the details of every style here, but my hope is to highlight the various textural qualities that define any ice cream, so you’ll be able to see all these versions as existing on a continuum. From that point, with a little ice cream science and technique and experimentation, you should be able to replicate—or invent—just about anything.
The Master Template
Water: 55%–65% (58–63% typical) (generally water = everything that’s not total solids)
It gets a bit tricky with eggs, which come pre-packaged. Whites keep nicely in the freezer, but not yolks. So I generally design recipes with a discreet numbers of yolks. The yolk of a “large” sized egg weighs about 18 grams. So I’ll make sure the recipes use 18, 36, 54 grams, etc..]
|Dr. Traci Mann, at University of Minnesota’s Health and Eating Lab (Her usual research is not maraschino cherry-centric)|
You’ll see that a lot of these values are interdependent. If you reduce the fat, you’re also reducing the total solids. So you’ll have to compensate by increasing the nonfat solids.
These are just a few examples.
- 87.3% water (range of 85.5% – 88.7%)
- 3.6 % milkfat (range of 2.4% – 5.5%)
- 8.8% solids-not-fat (range of 7.9 – 10.0%):
- protein 3.25% (75% of this is casein)
- lactose 4.6%
- minerals 0.65% – Ca, P, citrate, Mg, K, Na, Zn, Cl, Fe, Cu, sulfate, bicarbonate, many others
- acids 0.18% – citrate, formate, acetate, lactate, oxalate
- enzymes – peroxidase, catalase, phosphatase, lipase
- gases – oxygen, nitrogen
- vitamins – A, C, D, thiamine, riboflavin, others
- 58% water (range of 45.5% – 88.7%)
- 36 % milkfat (range of 25% – 68%)
- 5.6% solids-not-fat (range of 4.5% – 6.8%):
- protein 1.69 – 2.54%
- lactose 4.6%
- ash 0.37% – 0.56%
Egg Yolk Composition:
- 50% water (9g per 18g yolk)
- 23% fat (4g)
- 27% solids-not-fat (5g)
- protein 16%
- 8% Lecithin (1.44g)
- cholesterol 1%
- carbohydrates 1%
- minerals and trace elements 1g
In the next post, we’ll look at this template in action, by taking a typical simple recipe and creating a couple of variations.
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Great question. I should have addressed this. Most invert syrup is about 80% solids. The rest is water.
Corn syrup and other glucose syrups are all over the place. I'd generally estimate about 70% solids
What is interesting is when you make invert sugars using different grades of cane sugar…not just white. The sweetness profile and the PAC is different.
Are invert sugars ie, corn syrup considered solids?
And if so, what percentage of them is solids?
The sugars in the invert syrup are solids. The exact percentage can vary, but it’s typically around 70% solids (the remainder is water).
Honestly folks, I enjoy reading your blog. Particularly appreciate your text on stabilizers. But you have to reckon that while the whole you have here is very informative. It is not very actionable.
Anyways, I’ve coded a spreadsheet. Better than anything I’ve found for “free” on the web. Would very much appreciate any kind of feedback or suggestion on it.
Just noticed I at-mentioned your account at Reddit when I posted it there…
Hi Francisco, I understand your criticism; it’s something that we’ve been working on. We’ve built our own spreadsheets and models (screen shots are on the Consulting page). These have been in progress for a couple of years, with input from a number of dairy PhDs around the world. I’d like to be able to offer a simplified version as a download, but would want to work on the user interface, and find a way to design it so it’s useful without giving away our entire consulting platform.
I haven’t taken a good look at your spreadsheet yet. From experience I can say that these projects are more difficult than they appear … if you’re hoping for accurate analysis. Estimating freezing point depression is hell of an applied math puzzle, and most of the solutions that are available on the web are wildly inaccurate. Accounting for other factors that influence the hardness of ice cream gets into the realm of some very young and incomplete science. We’re working with some original research on this topic, to account for the hardening potential of cocoa butter and other similar ingredients.
I`m currently working on a web-tool that aims to provide a more comfortable UX than the different spreadsheets that are circulating the web. FDP approximation is done accordingly to the well-known Goff paper (https://www.uoguelph.ca/foodscience/sites/default/files/FreezingCurveCalculation.pdf) that seems to be the most common starting point for this task and is not overly complicated to implement. The additional hardening of cocoa or nut pastes is in fact another issue and it seems there is no common approach on this that is generally aggreed on throughout the literature on this topic. E.g. Angelo Corvitto recommends to account negative PAC values as counter measurement, while other gelatieri just seem to ignore this effects in their calculations. So if anyone has some advice on this it would be quite helpful for me.
The current beta status of the tool can be found at:
I would be very grateful for any comments or feedback.
Hi, thanks for writing. I’d love to see a useful online tool, so I’d be happy to check this out. Give me a few days.
On freezing curve calculation: that equation from the Goff paper will be of limited use. I tried it out in some of my early forays, and found it inaccurate. When I corresponded with Dr. Goff, he affirmed that it’s accurate up to 50–55% ice fraction, and then starts to overestimate. The problem is that we mostly care about ice fraction in the 70–75% range.
There are two approaches that work well in my experience. One is to plot the known sucrose calculation / ice fraction data (from Experimental Data from Pickering (1891) and Leighton (1927), adjusted by Smith and Bradley (1983), and further augmented by Goff & Hartel (2013)). You can hunt this down pretty easily. the catch is that it only goes to 180% sucrose concentration, which again isn’t high enough. I extrapolated data by continuing the line to 250%—probably not dead accurate, but it gives useful data. Use software like Excel to trace this curve with a 4th order polynomial equation.
You then have to use this equation in regression to find the temperature at each concentration. This result needs to be summed with the freezing point depression of salts, alcohol, and other small molecules. These can be calculated with the standard linear FPD equation that Goff and everyone else uses.
The second approach is a shortcut that I found. There’s a standard freezing curve equation for generic foods called the Miles (1974) equation. This requires a starting FPD, for which I use the folowing polynomial equation, fitted to the freezing curve by Dr. Michael Mullan:
[S=g equivalent sucrose / 100g water]
(R² = 0.9999)
The Miles equation requires a “bound protein” number. I use milk and egg proteins times 0.3. Finally, I found it needed to be adjusted with a correction factor of 0.957. This gives a quick formula that lets you plug in a temperature and get an ice fraction. I find it pretty close to the regression method between -10 and -16°C, 10% and 14% MSNF.
TLDR: this gets complicated as fuck, and all you can really hope for is an estimate that accurate enough and flexible enough to be useful. If you create a formula and can consistently get ice cream that’s nicely scoopable at the right temperature, you’ve done well. Don’t worry about absolute accuracy, or if your numbers exactly match mine or Dr. Goff’s.
Hardening fats: there’s even less science here! Negative PAC is an inelegant solution, but I found Corvitto’s actual numbers useful. I leave the PAC values alone, but create a hardening fats figure that’s based on similar thinking. Pretending it’s not a factor (as you’ve noticed most people doing) is a terrible solution. You’ll never be able to calculate a chocolate or hazelnut ice cream without accounting for the saturated fats. My methods are a more complicated but somewhat more flexible and elegant version of what Corvitto does … the general approach we both use is probably not accurate but has proven useful, at least within normal concentrations and temperature ranges.
The basic idea is to take that negative PAC information and build a separate value. Create a an effective hardness by adding this value to the ice fraction
Questions remain: how different are various saturated fats? What does the temperature / hardness curve for these fats look like? Are they similar to each other (as we assume)? Are they similar to the water freezing curve (as we assume)? Has anyone done real research here that we can poach?
Let me know if this is helpful: [email protected]
Thank you very much for your exhaustive response.
My current implementation pretty much follows the approach you described in the first part.
As an approximation for the Pickering et al. table I extracted the 2nd-order polynomial
FDP(SE) = 0.7592693269656435 * SE² + 6.5366647596977 * SE – 0.1876732904734074
out of the data and found it being sufficient. Be aware that the input value is the normalized sucrose equivalent, so it needs to be in the interval [0, 1.8]. The average absolute error is 0.1 °C which should be acceptable I think. I now did the calculation again also for 4th order and I´m getting slightly different coefficents than Mullan:
[a=-7.413037763056872*10^-9, b=1.605707495080694*10^-6, c=5.894876813534917*10^-5, d=0.05623763887800826, e=0.03774741866354958]
probably because he used some different input data. Maybe I´m going to do a comparision of the three equations and coming back with the results at some time.
The values for salt, alcohol, etc. are just converted to SE and then included straight forward in the calculation, with the one exception of the salt content of the MSNF. Here I´m following the Goff paper and account this as a separate factor it´s own calculation, even if I still wonder why this is required.
The Miles equation is something I have not heard about yet. It sounds very interesting and could be a neat addition to the current state of the tool. Do you have any pointers to the original paper?
Also I would be very curious to learn more on your approach on determining the additional hardening of the saturated fats and it´s exact differences to Corvittos method. So in case you are willing to share your findings I could imaginge this would make up a great topic for a blog post.
I agree with your assumption that the hardening of fats probably is not a simple linear dependency but affected by some parameters, like the type of fat or the amount of emulsifiers in the mixture. And it seems odd in fact that there seems to be so little verified knowledge on this topic. Goff just states:
“Fat, proteins, large molecular weight carbohydrates such as the starch fragments found in CSS, stabilizers, and emulsifiers do not contribute to freezing point depression because fat is immiscible with the aqueous phase, and proteins and polysaccharides are very large molecules. However, as these substances are increased in concentration, there is less water in which solutes can dissolve, so the presence of these materials will result indirectly in depression of the freezing point.” So one could think it would be sufficient to maintain the right ratio of total liquid and solid phase and no additional accounting of the saturated fats would be required.
But beside this considerations I also see the need to keep the required input managable. Having to deal with PAC and POD values is from my observation already a bit of a hurdle for some folks. So e.g. observing that relative sweetness is also not linear but dependent on the concentration of the solution and thus replacing POD with some coefficients would make a software tool completely inaccessible for the vast majority of users. So I think the goal has to be to find an approximation model that is good enough to predict most real world scenarios and simple enough to be used without the need to get a diploma in applied physics first.
I wouldn’t worry about your equations looking different from someone else’s. Any small change in input, and any small difference between curve tracing algorithms is going to give different equations. The real-world differences will probably be minor, as long as everyone’s using good data and sound methodology. Half a degree here or there just won’t matter for our purposes.
“So one could think it would be sufficient to maintain the right ratio of total liquid and solid phase and no additional accounting of the saturated fats would be required.” It’s a nice thought, but it just doesn’t work that way. Ingredients like cocoa butter get rock-hard in the freezer. It’s better to compensate for this, even with an imperfect model, than to try to wish it away.
I agree with the need to keep things simple. But there are different simplicity needs for the end user and for the propellerhead who’s building the model. In my case it’s the same person! If you’re making a product, then you have some UX work to do—you want the customer to be able to use it intuitively.
For the person building the model, the limit is just how much complexity you can handle. I’m actually terrible at math. I studied humanities in college, and most people know me as a writer and an artist. I learned to build models like this just by beating my head against them—and by studying lots of scientific papers, and by asking lots of smart people for help. This has its limits, but I’ve so far got a better model than any others I’ve found.
An old adage is that all models are wrong—but some are useful. Mine crossed over into being useful when it was just a couple of months old. But it’s still wrong, and always will be. The ongoing goal is to come closer to nailing a formula on the 1st try. Right now I mostly get it on the 2nd or 3rd.