Calculations for Superfatting

[megaptera]

I think, due to differing SAP values of oils, calculating superfat in order to leave a specific fat unsaponified (which only makes sense in HP I know), can be calculated by:

Superfat = 1 - x/y

where x is the amount of lye needed to saponify the base recipe (without the SF oils) at 0% SF, and y is the amount of lye needed to saponify all the oils (again, calculated at 0% SF on the calculators).

Example (not my recipe, just an example):
palm oil 135 g
coconut oil 135 g
olive oil 317 g
shea butter 65 g (10% of total oils)

In the example, let's say I want a 10% SF, and leave all the shea butter unsaponified.

According to SoapCalc, x = 86.8 g lye and y = 95.1 g lye.

SF = 1 - (86.8/95.1) = 8.7% SF

Is all of this correct?

If so, can I redo the equation to calculate how much lye I need if I want a 10% SF of shea butter? Like this:

0.10 = 1 - (x/95.1)
x = 85.6 g lye

It seems to me that I would use 85.6 g of lye to saponify the palm, coconut, and olive oils in an HP cook, then add the 65 g of shea butter, giving me a 10% SF leaving all the shea butter unsaponified.

Is my math crazy?

 

[Primrose]

I'm not very good at maths, so it makes sense to me to use a lye calculator which will do the calculation for you. Soapee.com has an option to tick a box "add SF after cook"

 

[Dawni]

I suck at math too... I'd just like to point out that there's no guarantee that it's all of your superfat that's not going to be saponified. Higher chances in HP than CP, but not a definite 100%.

It's one reason I HP.. That maybe.

It's interesting though

 

[megaptera]

I'm not very good at maths, so it makes sense to me to use a lye calculator which will do the calculation for you. Soapee.com has an option to tick a box "add SF after cook"

I will check out Soapee, thanks!

I suck at math too... I'd just like to point out that there's no guarantee that it's all of your superfat that's not going to be saponified. Higher chances in HP than CP, but not a definite 100%.

It's one reason I HP.. That maybe.

It's interesting though

Good point. I only HP, but have never tried SF-ing by adding it after the cook.
Thank you for your reply!

 

[Dawni]

Good point. I only HP, but have never tried SF-ing by adding it after the cook.
Thank you for your reply!

Oh. I always have. I heat it up too, the SF. Helps keep things fluid while I'm working on the other additives (hot too, if they're liquid)

 

[DeeAnna]

Example (not my recipe, just an example):
palm oil 135 g
coconut oil 135 g
olive oil 317 g
shea butter 65 g (10% of total oils)

In the example, let's say I want a 10% SF, and leave all the shea butter unsaponified.
According to SoapCalc, x = 86.8 g lye and y = 95.1 g lye.
SF = 1 - (86.8/95.1) = 8.7% SF

Your math is okay about the 8.7%, but your understanding of the "why" is faulty.

Soapcalc (and most soap recipe calcs) use the term "superfat" because that's the word commonly used, but the calculation is actually a "lye discount" calculation. They reduce (discount) the NaOH weight by the percentage you enter --

If you want a 10% lye discount, then the NaOH weight is reduced by 10%. For your example, Soapcalc says the NaOH = 95.1 grams at 0% lye discount, and it says the NaOH = 85.6 grams at 10% lye discount. Here's how that calculation is done --

Lye discount = 10/100 X 95.1 = 9.5 grams
NaOH weight at 10% lye discount = 95.1 - 9.5 = 85.6 g​

***

If you want to reduce the NaOH weight for this recipe to remove just the NaOH needed to saponify the shea, then here is how you would do that calculation.

First figure out how much NaOH is required to saponify ONLY the shea --

Shea wt = 65 g
Shea NaOH sap value = 0.128
NaOH needed to saponify Shea = 65 X 0.128 = 8.3 g​

You already know the NaOH to saponify all fats at 0% lye discount = 95.1 g.
So what is the NaOH weight to saponify the fats without the shea?

NaOH without shea = 95.1 - 8.3 = 86.8 g​

What is this lye discount?

Lye discount % = (NaOH to saponify shea) / (NaOH to saponify all at 0% superfat) X 100

= 8.3 / 95.1 X 100 = 8.7%​

***

Yes, 8.7% is smaller than 10%, but this is the correct answer.

The reason why the lye discount is 8.7% for the shea is because the sap value for shea is lower than the sap values for the other fats in the recipe. Saponification values -- coconut: 0.182, palm: 0.142, olive: 0.138, shea: 0.128.

The saponification value represents the number of molecules of NaOH needed to saponify 1 gram of a particular fat. The NaOH molecules get distributed to each fat in proportion to the sap value. Big sap value for a particular fat => more NaOH per gram of that fat. Lower sap value => less NaOH per gram of fat.

Even though the 65 grams of shea is 10% of the total weight of fats in your example, it doesn't deserve a full 10% of the NaOH molecules. It only needs 8.7% of the NaOH molecules to fully saponify.

This is a brief explanation, but I hope it sheds a glimmer of light on things.

 

[megaptera]

Your math is okay about the 8.7%, but your understanding of the "why" is faulty.

Soapcalc (and most soap recipe calcs) use the term "superfat" because that's the word commonly used, but the calculation is actually a "lye discount" calculation. They reduce (discount) the NaOH weight by the percentage you enter --

If you want a 10% lye discount, then the NaOH weight is reduced by 10%. For your example, Soapcalc says the NaOH = 95.1 grams at 0% lye discount, and it says the NaOH = 85.6 grams at 10% lye discount. Here's how that calculation is done --

Lye discount = 10/100 X 95.1 = 9.5 grams
NaOH weight at 10% lye discount = 95.1 - 9.5 = 85.6 g​

***

If you want to reduce the NaOH weight for this recipe to remove just the NaOH needed to saponify the shea, then here is how you would do that calculation.

First figure out how much NaOH is required to saponify ONLY the shea --

Shea wt = 65 g
Shea NaOH sap value = 0.128
NaOH needed to saponify Shea = 65 X 0.128 = 8.3 g​

You already know the NaOH to saponify all fats at 0% lye discount = 95.1 g.
So what is the NaOH weight to saponify the fats without the shea?

NaOH without shea = 95.1 - 8.3 = 86.8 g​

What is this lye discount?

Lye discount % = (NaOH to saponify shea) / (NaOH to saponify all at 0% superfat) X 100

= 8.3 / 95.1 X 100 = 8.7%​

***

Yes, 8.7% is smaller than 10%, but this is the correct answer.

The reason why the lye discount is 8.7% for the shea is because the sap value for shea is lower than the sap values for the other fats in the recipe. Saponification values -- coconut: 0.182, palm: 0.142, olive: 0.138, shea: 0.128.

The saponification value represents the number of molecules of NaOH needed to saponify 1 gram of a particular fat. The NaOH molecules get distributed to each fat in proportion to the sap value. Big sap value for a particular fat => more NaOH per gram of that fat. Lower sap value => less NaOH per gram of fat.

Even though the 65 grams of shea is 10% of the total weight of fats in your example, it doesn't deserve a full 10% of the NaOH molecules. It only needs 8.7% of the NaOH molecules to fully saponify.

This is a brief explanation, but I hope it sheds a glimmer of light on things.

This makes so much sense, thank you!

So, I guess if the calculators calculate lye discount, that number (if using a combo of oils) is most likely NOT equal to the SF number? Since I've never tried SF-ing with a specific oil, I've never really though about it.

Again, thank you for the detailed explanation.

 

[DeeAnna]

"...if the calculators calculate lye discount, that number (if using a combo of oils) is most likely NOT equal to the SF number?..."

Um, not exactly sure what you're thinking when you say this. The lye discount always creates a superfat, meaning there is more fat in the finished soap than is needed to exactly react with the NaOH. But most people aren't too concerned about what fat is the superfat. It sounds like you are.

You are wanting to use the superfat concept in a more specific way. Because of this, your calculations for superfat are going to be a bit more complicated than simply entering in a percentage in the "superfat" box and leaving it at that. But the method I've outlined will work for what you want to do.

edit: Oh, okay, I think I know what you mean. If the sap values for all of the fats in your recipe are the same or almost the same, the superfat % will be roughly equal to the lye discount %. An example would be a recipe with, say, olive oil, avocado oil, and tallow, all of whom have sap values of 0.135 to 0.137. If the sap values are greatly different, as in your example, then the superfat % (the % of excess fat based on the total fat weight) will very likely not be the same as the lye discount % (the % reduction of NaOH based on the total NaOH weight).

Some caveats for others reading this thread --

If you make cold process soap, you cannot control what fat remains as the superfat. The lye will react with any and all of the fats without you having any control over what it does. This is true even if you add the "superfat" at trace. Despite what you read in many soap making books or on the internet, NaOH is still active at the time of trace, so this isn't a useful technique.

If you make hot process soap, you can add the superfat after the soap is completely cooked and have some assurance that this particular fat will be the superfat at least for awhile. There is no guarantee this fat will remain intact indefinitely, due to the way soap behaves chemically.

 

[megaptera]

edit: Oh, okay, I think I know what you mean. If the sap values for all of the fats in your recipe are the same or almost the same, the superfat % will be roughly equal to the lye discount %. An example would be a recipe with, say, olive oil, avocado oil, and tallow, all of whom have sap values of 0.135 to 0.137. If the sap values are greatly different, as in your example, then the superfat % (the % of excess fat based on the total fat weight) will very likely not be the same as the lye discount % (the % reduction of NaOH based on the total NaOH weight).

Yes, that's what I meant; I didn't explain it well. Thank you for all the great info.