Ben and Jerry’s Butter Pecan
- 2 cups heavy cream
- 1 cup whole milk
- ¾ cup sugar
- 2 eggs
- ½ cup butter
- 1 cup chopped pecans
- ½ tsp salt
This lists all of the liquid and soluble ingredients. The pecans aren’t listed since they play no part in calculating the freezing point depression (FPD) of the mix. It also doesn’t list liquid sucralose since those drops are of insignificant volume and do not provide any meaningful contribution to FPD. All of the relative volume or weights are embedded in the calculations of the column values. Adjusting the value in the “Amount” column will update all of the other values in the row. All of the FPD calculations are automatic. Obviously, new rows can be added for additional ingredients and new tabs can be created for new recipes. The last tab on the spreadsheet contains the data table to calculate the sucrose equivalent FPD. The FPD for Ben and Jerry’s Butter Pecan is 2.23 (i.e., -2.23 ⁰C). This gives us an idea what our target FPD should be.
Let’s try modifying the original recipe to make it low carb:
- 2 cups heavy cream
- 1½ tbsp Truvia
- 21 drops of EZ-Sweetz (liquid sucralose equivalent to ¾ cup of sugar)
- 2 eggs
- ½ cup butter
- 1 cup chopped pecans
- ½ tsp salt
- 1 tbsp vegetable glycerin
- ¼ tsp xanthan gum
UPDATE 2014-02-14: I made a batch of butter pecan using no glycerin and 4 tablespoons of Truvia. The taste is... different to say the least. It wasn’t very scoopable. I had to warm the container in the microwave. I hereby declare vegetable glycerin the magic ingredient for low carb ice cream. One tablespoon is all that’s needed.
UPDATE 2014-04-10: I want to add that part of the reason I believe the freezing point depression experiment I ran in February failed was that the erythritol from the Truvia was probably insoluble. Most ice creams have a much higher water content and involve heating that dissolves granular sweeteners. My mix recipes are extremely high in butterfat and aren’t heated. I suspect most of the Truvia is suspended in the mix and may not lower the freezing point appreciably.
* The original recipe calls for pecan halves. Use them and you’ll jam up the ice cream maker. Raw chopped pecans is what you want or chop the raw pecan halves yourself. Do not buy “pieces” or “chips” because they are too small. Do not by “roasted” or “toasted” pecans. The pecans should be raw since they will be cooked in the butter and salt.
Completely useless, but fun math stuff
You might have noticed the additional columns in the FPD table sheet. I was mucking around with polynomial curve fitting in an attempt to replace the table with a formula. Spreadsheets can do advanced stuff like interpolation rather easily, but if I needed to port this calculator to a different platform that didn’t easily provide that kind of math library, a formula-based approximation could suffice. There’s a 15 order and 24 order polynomial equation examples and their deviation from the actual values. Both formulas would be sufficient in my humble option since this whole FPD business seems pretty loosey-goosey.
I used the following free website to get the factors for the polynomial expressions based to the data in the table: http://www.arachnoid.com/polysolve/. If there are any math geeks out there, please feel free to tell me how badly I screwed up and suggest a better method.
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