Sadly, no. Crimp is not related to fiber diameter.
What we know about fiber has changed over time as our fiber science has improved. People used to think crimp was directly tied to fiber diameter (microns). However, going back to the 1920s and 30s, people knew that the crimp wasn’t necessarily a predictor for fineness in an individual fleece.
Finding open access sources is hard, but here are two older sources that talk about this: https://www.tandfonline.com/…/10.1080/19447024708659308…
Breed standards select for crimp shape and a general range of fiber specifications. However, you can’t pull out one aspect of those specifications and use them to predict the others.
We focus on fiber diameter because it’s an easy, objective measure to compare things. It feels right to think that a 19 micron top of x will have the same softness in a finished yarn as a 19 micron top of something else. Unfortunately, it isn’t the case. Scale height, fiber length variations, fiber condition, and the shape and curves of the fiber strands all come together to determine how fibers feel against the skin.
The really cool thing is that, for softness, your skin will know. If you are at a fleece sale, you can gently feel the wool and find the feel you like. When I look for a fleece, I fingerspin a lock and then see if I like the yarn it makes. You can add and subtract twist, play with the plies, and change up the plying twist.
Crimp is important for more than trying to estimate fiber diameter. Crimp can be broken out into subcategories such as crimp per inch, crimp depth, & crimp dimension (is it a french fry, a corkscrew, a long, lazy wave, or something else altogether).
All of those come together to contribute to luster, elasticity, ability to resist compression, & loft. Those make a big difference to the finished yarn. –More on this in a later post.
From a class handout: http://www.woolwise.com/…/2017/07/WOOL-472-572-12-T-09.pdf
“(Studies) concluded that staple crimp was not a good indicator of fibre fineness, either within or between breeds and strains of sheep. Staple crimp has been shown to have some influence on fabric thickness and possibly fabric handle and bulk”
If you click on the link, there is lots more info and a nice bibliography.
If you have a thing for fiber sci, here is a really cool hand out that is related: Fibre Diameter, Staple Strength, Style, Handle and Curvature.