How to figure how much oil for mold.

[pahbi]

How was the .4 calculated?

I apologize in advance for my poor search abilities.

Background:

For several months, I have used the basic formula (H * W * L) * .4 to convert the volume of my mold into the amount of oil to put into a lye calculator.

This method has worked just fine for me.

However, it bothers me that I can't figure out how the .4 was calculated.

I read the stickied thread about calculating oil using the .4 rule of thumb, and it was suggested that the .4 was related to the amount of water that is being mixed with the lye. That sounds reasonable, but to date, I just can't seem to recreate that math.

I have been able to accurately calculate the weight of a oil in grams that will fill a particular mold using the density of the oil to convert from volume to fluid ounces, and then to ounces, and then to grams.

But reverse engineering the .4 is just baffling me.

Does anyone have a link or explanation or just the full formula for how the .4 was derived?

Thanks in advance,
- Paul

 

[Nevada]

I suspect it is anecdotal, someone took notes and "Reversed Engineered" the calculation :idea:
Just my 12 cents (inflation adjusted) ;-)

 

[sososo]

I will try to explain (sorry for my english).
I wil use grams and cubic centimeters, than I will convert in ounce and cubic inch.

First, 3 facts:
1. The density of oils is 0.900 - 0.920 grams / cubic centimeter - for example, the density of OO is 0.918 - see here: [Link no longer functional. Removed by SMF Modmin Team]
2. The density of lye is 2.13 g/cm3. See here:
http://en.wikipedia.org/wiki/Sodium_hydroxide
3. The density of water is 1 gram/cm3 (no link, belive me!)

Let's say that we want to make a 100% olive oil soap using 1000 grams of oil, 0%SF, 33% lye concentration. SoapCalc gives us:

Water - 275.05 g
Lye - 135.472 g

So we have this volumes (I divided the quantities by densities):
Oil - 1000/0.918 = 1089.325
Water - 275.05/1 = 275.05
Lye - 135.472/2.13 = 63.60
--------------
Total volume - 1428 cm3

1000 g (oil) means 35.274 ounces and 1428 cm3 (total volume) means 87.14 cubic inches
Now, the final calculation:
35.274/87.14 = 0.404797 = (aprox) 0.4

Quod erat demonstrandum.

 

[pahbi]

Sososo,

Thank you for taking the time to explain, that does indeed explain the origin of .4

I'm now faced with a new problem. I would like to put this information into a spreadsheet.

Your math skills seem stronger than mine, so let me pose this question:

Based on the information in your example, how would you compute the amount of OO to use, using only the following information:

ps. Please leave all of the calculations in metric.

1) Height, length and width of the soap mold.
2) Density of Olive oil, water and lye.
3) 33% lye concentration.
4) SAP value of Olive Oil.

Thanks,
- Paul

 

[sososo]

Sososo,

Based on the information in your example, how would you compute the amount of OO to use, using only the following information:

ps. Please leave all of the calculations in metric.

1) Height, length and width of the soap mold.
2) Density of Olive oil, water and lye.
3) 33% lye concentration.
4) SAP value of Olive Oil.

Thanks,
- Paul

First, some notations:
height=H
length=L
width=W
oil density=OD
water density=WD
lye density=LD
oil weight=OW
water weight=WW
lye weight=LW
oil volume=OV
water volume=WV
lye volume=LV
SAP=SAP (!)

We calculate total volume (TV) in two ways:
First:

TV=H*L*W

Second, more complicated but not very complicated.

LW=OW*SAP
WW=LW*(100-33)/33=LW*67/33=(aprox) LW*2=OW*SAP*2
OV=OW/OD
LV=LW/LD=OW*SAP/LD
WV=WW/WD=OW*SAP*2/WD
So,
TV=OV+LV+WV=OW/OD+OW*SAP/LD+OW*SAP*2/WD=OW*(1/OD+SAP/LD+SAP*2/WD)

Now we have this equality:
H*L*W=OW*(1/OD+SAP/LD+SAP*2/WD)

And finaly:
OW=(H*L*W)/(1/OD+SAP/LD+SAP*2/WD)

This formula is ok not only for grams and cubic centimeters but also for ounces and cubic inch.

 

[DeeAnna]

Here's an Excel spreadsheet version. I made it more generic, so it can be used with any soap recipe.

The first image is what it looks like when you use the spreadsheet normally. The second image shows the formulas within the spreadsheet cells that do the calculations. The formulas are the parts that start with equals (=) signs.

I did not use saponification values or lye concentration in this spreadsheet. I assumed the user would start with an existing recipe, so all of the oil, lye, and water weights are already known. It could be used with units of ounces (wt) and inches as well -- I'd just change the units in the table headings and convert the default density from 0.91 g/cm3 to 0.53 oz/in3.

I can't upload a spreadsheet to the forum. If anyone wants a copy, I will be happy to provide it. I can't send spreadsheet files through SMF, so please send me a PM with your direct email address and let me know what units you want to use -- ounces or grams.

Or if you have suggestions for improvement, let me know that too. This is just a quick 'n dirty first try.

 

[pahbi]

Sososo,

Thank you for working on the math for this, I really enjoy seeing how things are calculated.

When I saw your post on my cell phone I was very excited, so I rushed to the computer when I got home from work and tried out the formula.

But I must be doing something wrong, and I'm hoping you can spot my error.

I'm using your final derived formula of:

OW=(H*L*W)/(1/OD+SAP/LD+SAP*2/WD)

The values I'm plugging into the formula are:

L = 55 cm
H = 6 cm
w = 10 cm
OD = .91
SAP = 190
LD = 2.13
WD = 1

The formula gives me 7.016 grams, but I should be getting over 2000 grams. I must be putting a wrong value into the formula somewhere. Could you look over my math and see if you can spot where I goofed?

Thanks,
- Paul

I changed my sap value from 190 to .190 and I am getting an answer that seems more in line with the expected result. Was that my error?

- Paul

 

[bodhi]

DeeAnna, what is the third value for dimensions that self calculates, and why .91 for a default density?

 

[sososo]

I changed my sap value from 190 to .190 and I am getting an answer that seems more in line with the expected result. Was that my error?

- Paul

Yes, this was the error. 0.190 is the correct value to use.
SAP=190 means that you need to use 190 miligrams of lye at each 1 gram of oil. But, because we have to use the same measure unit, the correct value is 0.190 - so, we ned 0.190 grams of lye to saponify 1 gram of oil.

 

[DeeAnna]

"...why .91 for a default density..."

According to Sososo's Post #3, the density of oils ranges from 0.900 to 0.920 g/cm3. I took this info at face value. The average between 0.9 and 0.92 is 0.91 g/cm3. If you have a suggestion for a more accurate default density for typical soaping oils, I'm all ears.

I reverse engineered the "0.4 formula" awhile back, and I'm reasonably certain it assumes a default oil density somewhere around 0.9, give or take a bit. It also assumes the soap recipe is made with "full water" which over estimates the soap volume if a soaper uses a more concentrated lye solution.

"...what is the third value for dimensions that self calculates..."

A rectangular mold has length, height, and width. If you know the volume of the soap recipe and you know any two of the linear dimensions of the mold, you can calculate the third linear dimension. Many people have a mold and want to know how deep a batch of soap will be in the mold. Or they have a specific bar size in mind and want to know how long of a loaf mold to buy. This calculation helps answer those questions.

A similar calculation could be done for round molds too. Given the volume of soap and the diameter of a Pringles can or PVC pipe, how tall does the mold have to be?

 

[sososo]

DeeAnna, if you put on a column in your spreadsheet the SAP values of the oils, you can calculate the lye amount and then, using a certain concentration value (say 33%) you can calculate the water amount. Now these two (lye and water) are manualy entered in your spredsheet.

 

[sososo]

A similar calculation could be done for round molds too. Given the volume of soap and the diameter of a Pringles can or PVC pipe, how tall does the mold have to be?

Pringles can you say? Good idea!!! Thank you!

 

[bodhi]

Aah, i skimmed the posts until i got to the calculations so i missed that. Nope, no suggestions but ill poke around and if i see anything interesting ill let you know. I did find this which you may find useful in your recent experiments. Stearic has a density of .8387 at 180'f. What temps are you norm-ing to on your sheet?

'Many people have a mold and want to know how deep a batch of soap will be...' No kidding! Now that you say it, that is so obvious i should be embarrassed, LOL. It completely baffled me because i couldnt figure out how in the world this would allow me calculate for the depth i wanted-which is how i calculate for volumes-and that's why, its a predetermined recipe, duh, lol. Thank you DeeAnna

 

[pahbi]

Sososo,

I worked the formula into a spreadsheet, and then compared my results to soapcalc, and my values came out close, but the values are far enough off to cause concern.

You've been awesome, and I feel guilty to ask this, but would you be willing to work the math for a soap recipe so I can check myself and make sure I'm doing the formula right.

My soap recipe is:

60% olive oil
30% coconut oil
10% sunflower oil
33% lye solution

My mold is 22"L x 3.875W x 2.5"H

Thanks,
- Paul

 

[DeeAnna]

Sososo:

"...if you put on a column in your spreadsheet the SAP values of the oils, you can calculate the lye amount and then, using a certain concentration value (say 33%) you can calculate the water amount..."

Yes, I completely agree that could be done on the spreadsheet. By calculating the lye and water from the saponification values and lye concentration, you're basically making a very basic soap recipe calculator. That would be easy to include in the spreadsheet. But...

I was trying to think how most people would use this type of thing, based on what I have read here on SMF. The appeal of the "0.40 rule" is that it distills the calculations into to a single, simple algebra problem. You and I might prefer to do the calculations and make our own assumptions, but many people don't want to do that. I've seen soapers who are having trouble using the 0.40 rule correctly, simple as it is.

I decided the sap values would probably make it harder for an everyday person to use the spreadsheet, since most people would not have the sap values unless they look them up in a soap recipe calculator like SoapCalc. A "real" recipe calculator like SoapCalc is the better place to do the recipe design. Then bring the basic data back to the mold volume calculator and go from there.

I don't use SoapCalc much, because I designed a soap recipe calculator on a spreadsheet that tries to account for all the fine details that you and I like to know. Among other things, the spreadsheet calculates the total batter volume, the number of bars the recipe will make based on the bar weight, the approximate cost per bar, and even the size of the soap pot I need to use. My calculator spreadsheet also includes a database of the properties of fats, including NaOH and KOH sap values, so I don't have to look that information up. It would be easy to add a section to calculate mold volume.

Bodhi: "... Stearic has a density of .8387 at 180'f. What temps are you norm-ing to on your sheet?..."

This thread is about reverse engineering the "0.40 rule" to get a better understanding of the thinking that went into creating the 0.4 rule and to make it more accurate, but I didn't think the goal is to be laboratory precise. Not many people, IMO, add more than a few percent of stearic fatty acid to a typical recipe, if they add any at all, unless they are making shaving soap. I'd say a density estimate of 0.91 or thereabouts is close enough, even for stearic acid, to estimate the volume for most soap recipes most of the time.

But if a mold volume calculator were to include a database of sap values, why not include density values too, hey? It's certainly do-able, but I wonder if the increased accuracy is worth the extra complexity.

And on that note -- if someone is making a soap with a lot of filler material -- say a salt bar with 80% salt, or a whipped soap, or a soap with pureed botanical ingredients like pureed papaya -- then the mold volume calculations in this thread will not be accurate. I suppose the calculator could allow the user to include this information too.

And this is rapidly getting rather complicated, even for me! I feel like a kitten tangled in a large ball of yarn.

 

[bodhi]

I don't use SoapCalc much, because I designed a soap recipe calculator on a spreadsheet that tries to account for all the fine details that you and I like to know. Among other things, the spreadsheet calculates the total batter volume, the number of bars the recipe will make based on the bar weight, the approximate cost per bar, and even the size of the soap pot I need to use. My calculator spreadsheet also includes a database of the properties of fats, including NaOH and KOH sap values, so I don't have to look that information up. It would be easy to add a section to calculate mold volume.

Bodhi: "... Stearic has a density of .8387 at 180'f. What temps are you norm-ing to on your sheet?..."

This thread is about reverse engineering the "0.40 rule" to get a better understanding of the thinking that went into creating the 0.4 rule and to make it more accurate, but I didn't think the goal is to be laboratory precise. Not many people, IMO, add more than a few percent of stearic fatty acid to a typical recipe, if they add any at all, unless they are making shaving soap. I'd say a density estimate of 0.91 or thereabouts is close enough, even for stearic acid, to estimate the volume for most soap recipes most of the time. But if a mold volume calculator were to include a database of sap values, why not include density values too, hey? It's certainly do-able.

Yes, i did digress and that is indeed a topic for another thread. I was just thinking ahead to my calculator-which is similar to yours minus the quick and dirty soap calc for now. (Nice idea including the pot sizes!) And hey why not calculate everything on the same sheet. :crazy: This thread just had me thinking about the totality of it again and if im incorporating concentrations, then why not densities and at the same temps too. I agree .91 is a good enough for the great majority of uses though. I just thought you might like the stearic bit but on second thought you probably already had that.

And this is rapidly getting rather complicated, even for me! I feel like a kitten tangled in a large ball of yarn. :razz:

You can say that again!

So back to the .4, I hadn't incorporated the volumes into my spreadsheet yet because the .4 was hit or miss -i rarely use full water. These posts are sorting out the math which i find boggling so I may now be able to account for the various concentrations. Im very grateful this was brought up again and for the fabulous breakdowns in calculations.

 

[pahbi]

For me, this thread has been extremely helpful, and I'm thankful for everyone, who has taken the time to participate.

This thread is a good canidate for stickying imo.

- Paul

 

[DeeAnna]

"...the .4 was hit or miss -i rarely use full water..."

Yep, same here. I am wary of swallowing "common wisdom" without first chewing it well. When I read about the 0.4 rule, I took the time to figure it out for myself. I realized it would overestimate the size of my molds, so I just did the math from scratch to figure the mold sizes I wanted.

On a slab mold, oversizing the depth of the mold is not a big deal. But for a loaf mold, the bar size and shape can get really messed up if the volume calculation is not reasonably accurate.

 

[sososo]

Sososo,

I worked the formula into a spreadsheet, and then compared my results to soapcalc, and my values came out close, but the values are far enough off to cause concern.

Don't foget to put in soapcalc: 0%SF and "Lye concentration"=33% - because these are the values I used in my formula. And pay atention to SAP value to be the same as in soapcalc.

You've been awesome, and I feel guilty to ask this, but would you be willing to work the math for a soap recipe so I can check myself and make sure I'm doing the formula right.

My soap recipe is:

60% olive oil
30% coconut oil
10% sunflower oil
33% lye solution

My mold is 22"L x 3.875W x 2.5"H

Thanks,
- Paul

Ok, let's see. So now you have 3 oils, not just one. In general, I will use the same demonstration I used for one oil but now we have three oil density - OD1, OD2, OD3, three SAP values - SAP1, SAP2, SAP3, three oil weights - OW1, OW2, OW3, three oil volumes - OV1, OV2, OV3 and thre oil percentages - P1, P2, P3.

LW=OW1*SAP1+OW2*SAP2+OW3*SAP3
WW=LW*(100-33)/33=LW*67/33=(aprox) LW*2=(OW1*SAP1+OW2*SAP2+OW3*SAP3)*2
OV=OW1/OD1+OW2/OD2+OW3/OD3
LV=LW/LD=(OW1*SAP1+OW2*SAP2+OW3*SAP3)/LD
WV=WW/WD=(OW1*SAP1+OW2*SAP2+OW3*SAP3)*2/WD
So,
TV=OV+LV+WV=OW1/OD1+OW2/OD2+OW3/OD3+(OW1*SAP1+OW2*SAP2+OW3*SAP3)/LD+(OW1*SAP1+OW2*SAP2+OW3*SAP3)*2/WD

Now we will write OW2 and OW3 using OW1:
OW2=(OW1*P2)/P1
OW3=(OW1*P3)/P1

So, TV using only OW1 is:
TV=OW1/OD1+(OW1*P2)/P1/OD2+(OW1*P3)/P1/OD3+(OW1*SAP1+(OW1*P2)/P1*SAP2+(OW1*P3)/P1*SAP3)/LD+(OW1*SAP1+(OW1*P2)/P1*SAP2+(OW1*P3)/P1*SAP3)*2/WD

or:
TV=OW1*(1/OD1+P2/P1/OD2+P3/P1/OD3+(SAP1+P2/P1*SAP2+P3/P1*SAP3)/LD+(SAP1+P2/P1*SAP2+P3/P1*SAP3)*2/WD)


so:
OW1=TV/(1/OD1+P2/P1/OD2+P3/P1/OD3+(SAP1+P2/P1*SAP2+P3/P1*SAP3)/LD+(SAP1+P2/P1*SAP2+P3/P1*SAP3)*2/WD)

...and now, that you know OW1, for calculate OW2 and OW3 you have these two:
OW2=(OW1*P2)/P1
OW3=(OW1*P3)/P1

 

[pahbi]

Thank you Sososo, I achieved success with my spreadsheet.

I created a mold with small blocks that can be adjusted based on the size of the soap loaf to create.

I can now input the measurements of the mold into my spread sheet, and be confident I have accurate calculations. My values compare almost exactly with Soapcalc, with the only differences due to me rounding to the nearest gram.

The next step will be to upload the spread sheet to Google Docs, so that I can access the spreadsheet on my android tablet.

I will need some time to really digest and understand all of the calculations.

Thanks again,
- Paul