Some things I wrote a while back:
INS is the saponification value minus the iodine number. Iodine number is a measure of the unsaturated bonds in the fats. In other words, more liquid oils -> more unsaturation -> higher iodine number.
Both iodine number and INS are ways to evaluate a fat mixture for ease of saponification, initial hardness for ease of unmolding, and the shelf life of the soap. They are values originally created for quickly evaluating blends of fats for use in large scale commercial soapmaking, so are not quite so critical for the handcrafted soapmaker. But it's worth understanding the reasoning behind iodine and INS, even if you don't use the guidelines the same way a large-scale soapmaker might use them.
The more unsaturation, the greater potential for a softer soap and greater chance for DOS. A high iodine number is no guarantee of softness or DOS, however; it's just an indicator.
Rather than focus on the iodine or INS numbers, some people keep the sum of linoleic and linolenic acid under 15% to help guard against DOS and softness. Or they have a rule of thumb about limiting the polyunsaturated oils such as canola, corn, soy, sunflower, safflower, etc. to a modestly low % in their recipes. Some watch the iodine number or INS value instead.
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The original meaning of "INS" is lost in the mists of history, but it was developed as a way to figure out what blends of fats would work well for commercial soap making. For handmade soap makers, the INS value is not quite as meaningful, since we are not as focused on making tons of soap for a mass market, but INS can be a reasonable guideline to check when designing a soap recipe.
If a fat has a high INS number, the fat will saponify easily and make a hard soap that cleanses well.
Which fats have high INS values? Coconut is at the top of the list at an INS of about 258, followed by palm kernel, tallow, cocoa butter, palm oil, lard, and shea with INS of 115-230.
Fats with middle INS values of 60-105 are olive, avocado, almond, castor, corn, canola, beeswax, sunflower, and soybean.
At the bottom are fats with INS under 60, such as jojoba, evening primrose, rosehip, and flaxseed (linseed).
Soap calculators like soapcalc recommend a combined INS number somewhere between 135 to 170 which is reasonable for a general purpose type of soap. A single fat such as lard (INS of about 140) would fit the bill. But so would a blend of coconut (INS about 258 ) and olive (INS about 105).
Obviously a lard soap has different qualities than a coconut-olive soap even if the INS happens to be the same, so INS is not the only property that a handcrafted soap maker might want to look at. It's just a useful guideline; definitely not an absolute.
Here is more about the origins of INS and how to calculate INS values:
http://www.jaschesoap.com/homemade-soap/cold-process/soap-ins-values/
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