I'm not sure I would recognize rancid fat if I encountered it. When I make bone broth, after reheating the bones and the broth several times, depending on the source of the bones and the litte bits of meat in the pot, the broth can smell strong and "gamey." But, I don't think the fat is rancid, just strong smelling.
What's the easiest way to make some paleo fat go rancid so I can train my nose to detect it? And, what is it that makes bone broth smell very gamey at times?
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It smells like paint if you're really old like me. ;-) The kind of paint I'm talking about is based on linseed, or flax oil. It's nothing like modern petroleum based house paints, or of course, latex paints. But this is a really strong smell. The comment above about art-supply smell is correct, as most artists oils are linseed oil based.
If you have an old popcorn popper around (not an air popper), just open it up and smell it. Most people just wipe them clean, leaving a nice layer of oxidized oil on the surface. If you have a used deep fry daddy/baby around, smell the plastic lid. It's likely tacky with rancid oil. These too are strongly rancid smells. You're unlikely to encounter something this rancid in a bottle.
If anyone in your house is a ramen eater, just look through the packages, and pick the one that shows canola or cottonseed oil as part of the wheat noodles (they're usually deep fried in it) and smell the noodles. They're covered in rancid oil. The older they are, the stronger the smell, of course.
All the brown rice I've encountered recent memory has smelled rancid, too. So if you have a bag of that hanging around that's been open awhile, smell it as an example. It's most likely rancid. It's a far more subtle smell than the above items,but it's there.
It's hard to describe, and I've only explained it to my husband by showing him examples.
You can smell it often in the oils left out in restaurants for oil and vinegar on salads. Those bottles sit out forever, so they have plenty of time to get rancid.
You could make rancid oils yourself at home. Leave olive oil, flaxseed oil, and any other natural, unrefined, seed oils out on your counter for a while. I'd recommend putting a layer of each in a dish so it can access oxygen and light to speed up the process. Smell them every few weeks.
Rancid oils (themselves) smell neither like crayons nor like paint to me. Haha, the best I can describe is that they smell like "OMG, DON'T EAT THAT".
Some people say it smells like crayons. Rancid nut butters taste/smell like paint. I haven't experienced it personally either.
Rancid animal fats smell to me like rotting meat. The odor is due mostly to butyric acid formation due to fat oxidation. http://www.cip.ukcentre.com/Rancidity.htm
rancid fat which destroys certain vitamins and may lower the nutritive value of the protein; a fish meal diet might precipitate vitamin deficiency in poorly nourished people. Moreover the flavour of the rancid fat is unacceptable in many societies, though not in all.