Cutting carpet in a way it won't fray
 

I have a wear spot in my carpet where my heel hits (actually it's a hole at this point :)

I want to cut a square opening in the carpet and insert a piece of hard rubber to provide a harder wearing surface than the carpet.

I'm wondering the best way to cut the carpet to ensure it won't fray after cutting. I was planning to use a hot knife to sear the edges while it's cutting, but I'm wondering if there are better ways. Any ideas?

Having you thought about just laying the rubber over the carpet? How are you planning to attach this said bit of rubber?

I have watched upholstery guys make up carpet sets. Edges are bound. But, as noted above, drivers heel pads are usually stitched right on top of the carpet. The real advantage of that is when the heel pad wears out, the stitches can be cut and a new one sewn in.

Use Oster hair clippers and a #40 blade to shear the carpet from the backing in the shape you want. Rubber cement the rubber mat to the carpet backing.

I use a heat gun to melt off the edges, it works well. Rub off the dingles, no fray.

Use a new blade to start, then latex adesive to seal the edges after you cut them, although its white when wet, it will dry almost clear, you wont notice it, and the carpet wont fray afterwards, its not going to be affected by the heater either once its dry.
As a 16 year old, i was trained as a carpet fitter!
Hope this helps.
A...

I cut some carpet on my car and ended up taking the piece to a local automotive upholsterer and he sewed on the edge beading for $10.

There is always the option of dropping in a Rennline track mat.

I think my carpet is a little too far gone at this point to just lay the rubber on top. There's a sizeable divot and there's a hole. I had planned to use pressure sensitive carpet seaming tape on the underside once I got the rubber piece properly inset. The rubber I found is pretty much exactly the same thickness as the carpet.