One of my sons is the Emergency Manager for the OSU Police Tulsa Division. He recently sent me a design for a patch and/or challenge coin for their agency and ask for my input:
The first thing I noticed is the fine detail in the horse reins, mane, and tail will not reproduce in embroidery, and may not even in a coin. Second, it feels like there is too much white space around the lettering, and all the kerning needs to be adjusted (this is always the case when you wrap text around a circle, and often even when it’s in a straight line.)
Those and some other adjustments led to this:

If they are going to make a challenge coin, they will need a back, so we did this:

Designs should hold up in monochrome, but most things these days have color, so here is the front and back design colorized:

It is sometimes easier to see if something is working if you can see a more photo realistic mockup, so I made this image for the challenge coin:

Finally, the original idea was a patch, so we mocked that up too:

