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container/site/content/posts/dominos-pizza-sauce/index.md

@@ -9,11 +9,221 @@ title = "🍅 Domino's Pizza Sauce"
 author = "nicholas"
 +++
 
-{{< image
+For a brief moment in time, Domino's website contained the holy trinity of reverse-engineering material: 
-  src="images/dominos-pizza-sauce-nutrition.PNG"
+- ingredient lists
-  caption="Domino's Pizza sauce nutrition" >}}
+- nutrition
+- *total* weights for each food item
+
+This information can normally be found on the site to some degree, but what is unusual this time is the inclusion of the total weight values for each food item. This makes me job especially easy.
+
+## 📋 Ingredient List
+The ingredient list provides the **what**, and the nutrition and total weight info provides **how much**. This gives me an almost complete picture of the sauce.
+
+I begin by looking at the ingredient list for where to start:
 
 {{< image
   src="images/dominos-pizza-sauce-ingredient-list.PNG"
   caption="Domino's pizza sauce ingredient list" >}}
 
+The ingredient list is simple:
+
+- water
+- tomato paste
+- sugar
+- salt
+- spices
+- dehydrated garlic
+- soybean oil
+- citric acid
+
+Right away, I can simplify the list by combining the water, tomato paste, and citric acid. These are the ingredients already exclusively present in **tomato paste** and **tomato puree**. (I have selected tomato puree as the base of my sauce for cost and convenience, the difference is mostly water content). The ingredient list of the tomato puree seems to be in agreement with that of the Domino's sauce:
+
+{{< image
+  src="images/tomato-puree-ingredient-list.png"
+  caption="Contadina Tomato Puree ingredient list" >}}
+
+Now I have:
+- tomato paste/puree
+- sugar
+- salt
+- spices (oregano, marjoram, parsley, basil, tarragon)
+- dehydrated garlic
+- soybean oil
+
+I took some necessary liberties with the spices. It could be anything! I selected my favorites, leaving out any savory herbs like rosemary and thyme. I want this to be a bright, sweet sauce, like Domino's.
+
+## 🧪 Nutrition
+The document published on Domino's website includes pizza sauce nutrition and weight values for each corresponding size of pizza. I look to the *Extra Large* pizza for guidance, since it will contain the greatest weight and nutrition values, which will minimize uncertainty introduced by round numbers to the greatest extent possible.
+
+{{< image
+  src="images/dominos-pizza-sauce-nutrition.PNG"
+  caption="Domino's Pizza sauce nutrition" >}}
+
+Now I can do some simple math to fill in the table.
+
+|Ingredient|weight(g)|
+|-|-|
+|tomato puree|?|
+|sugar|?|
+|salt|?|
+|spices|?|
+|dehydrated garlic|?|
+|soybean oil|?|
+|**TOTAL**|**227**|
+
+### 🗄️ Tomato Product Reference
+From **FoodData Central** database for precise values for tomato puree, tomato paste nutrients, water, calories, etc:
+
+**Tomato Puree**
+|Nutrient|Amount|
+|-|-|
+|Water|89.1 g|
+|Energy|35 kcal|
+|Fiber|2 g|
+|Protein|1.58 g|
+|Carbohydrate|8.04 g|
+|Sugar|4.31 g|
+|**TOTAL**|**100.0 g**|
+
+**Tomato Paste**
+|Nutrient|Amount|
+|-|-|
+|Water|71.9 g|
+|Energy|89 kcal|
+|Fiber|4.7 g|
+|Protein|4.23 g|
+|Carbohydrate|20.2 g|
+|Sugar|11.7 g|
+|**TOTAL**|**100.0 g**|
+
+
+
+
+### 🧂 Salt
+By far the easiest value to derive with simple formula that can convert sodium weight to salt weight:
+
+Let **$x$** be the amount of salt (in grams):  
+
+$$
+x = {\frac{1190 \text{ mg}}{1000 \text{ g/mg}}}\times{2.54}
+$$
+
+$$
+x \approx 3.02 \text{ g}
+$$
+
+### 🍚 Sugar
+*Added* sugar can be estimated by comparing the $sugar:carbohydrate$ ratios of tomato product and the final sauce. This is not an exact science. All of the values included in these calculations are either averages, estimates, or rounded numbers, so they will result in values with very limited precision.
+
+**Tomato Puree**
+$$
+\text{sugar} : \text{carbohydrate} = 4.31 : 8.04
+$$
+
+$$
+\quad \text{or} \quad
+$$
+
+$$
+\frac{4.31}{8.04} \approx 0.536
+$$
+
+**Tomato Paste**
+$$
+\text{sugar} : \text{carbohydrate} = 11.7 : 20.2
+$$
+
+$$
+\quad \text{or} \quad
+$$
+
+$$
+\frac{11.7}{20.2} \approx 0.579
+$$
+
+
+**Domino's Pizza Sauce**
+$$
+\text{sugar} : \text{carbohydrate} = 16 : 25
+$$
+
+$$
+\quad \text{or} \quad
+$$
+
+$$
+\frac{16.0}{25.0} = 0.64
+$$
+
+Domino's definitely has a higher sugar:carbohydrate ratio, which makes sense because of the added sugar. I can use the values above to calculate how much sugar I need to add to match Domino's sauce ratios. This works because little else besides the sugar and tomato puree contributes to the carbs. There is maybe a gram of carbohydrates in the spices, but I do not care if I am off since this is all guesswork anyway.
+
+**Tomato puree**
+$$
+\frac{0.64}{0.536} - 1 \approx {0.194} \text{ (19.4\\%)}
+$$
+**Tomato paste**
+$$
+\frac{0.64}{0.579} - 1 \approx {0.105} \text{ (10.5\\%)}
+$$
+
+However much tomato puree/tomato paste I need, I will need to add between $10.5$ and $19.4\\%$ additional sugar. For example, if I need 100 g tomato paste, which contains 11.7 g sugar, I will need $11.7 \times 0.105 \approx 1.23$ g more sugar.
+
+
+### 🥫 Tomato Puree / Paste
+
+I will use **tomato paste** values to do the rest of my calculations, since I can "add" water (on paper) to achieve similar makeup to Domino's Pizza Sauce.
+
+The strategy here will be to find an amount of tomato paste that will account for all of the fiber present in the Domino's sauce. No other ingredient will meaningfully contribute to fiber. For now I will mostly ignore the weight of water, since I can either boil it off later or add it if I need to thicken or thin the sauce. It is not known yet exactly how much water is in Domino's sauce, but it will reveal itself as I solve for other values.
+
+First I find percent fiber in tomato paste:
+$$
+x = \frac{4.7 \text{ g fiber}}{100 \text{ g tomato paste}} = 0.047
+$$
+
+Then calculate how much tomato paste is needed to account for 6 grams of fiber:
+
+$$
+x = \frac{6 \text{ g fiber}}{0.047} \approx 128 \text{ g tomato paste}
+$$
+
+Let me see if this value looks approximately correct for the rest of the nutrition:
+
+- **Protein**
+$$
+x = \frac{5 \text{ g protein}}{0.0423} \approx 118 \text{ g tomato paste}
+$$
+Close enough
+
+- **Carbohydrates**
+(This does NOT account for added sugar)
+$$
+x = \frac{25 \text{ g carbs}}{0.202} \approx 124 \text{ g tomato paste}
+$$
+
+✅ This all looks pretty consistent. There is likely $\approx 120$ grams of **tomato paste** present in the sauce.
+
+
+### 🧄 Garlic Powder, Spices
+I do not trouble myself with discovering the exact blend of spices. Instead, I have come up with a blend of spices that I like. The table includes the spice and its ratio in volume.
+
+|Herb|Volume ratio|
+|-|-|
+|Oregano|4|
+|Marjoram|2|
+|Parsley|1|
+|Basil|4|
+|Tarragon|2|
+
+
+
+### 🧴 Oil
+The amount of calories from fat is given (5), which implies an absolutely tiny amount of total fat, and an even tinier amount of *added* fat in the form of "soybean oil".
+
+ $\frac{5}{9} \approx 0.56$ grams fat.
+
+ I do not bother adding any fat at all.
+
+### 💧 Water
+The amount of water in the sauce ends up being around 50%. I simply subtract the ingredient weights (tomato paste, salt, sugar, spices) from the total (227 grams). 
+
+e.g. $w = 120 - 3 - 1.5 - 1.5$