The Japanese stiltgrass:
Sorry about the dark pictures, vampire lyf
The issue with the Stiltgrass, aside from spreading everywhere there is open space along a trail, is that it grows tall and eventually lays over on the trail. So even if you wait until it dies / goes dormant, you now have a layer of grass on the trail. In general that isnt a great situation and it will hold moisture on the trail tread. The other annoying thing is the way it lays, you have to get under it to cut it, so you can use a weed wacker, but you can easily "miss" near the roots and you trimmed something, but you didnt clear it. It also rips out pretty easy, however that is very time consuming.
This is at Water Company, there is a trail under there.
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This picture shows a bit better how it almost makes a canopy over the tread.
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I use a hedge trimmer, put the blade under the "canopy" and cut forward or backwards
sweeping away from the tread. I an not a huge fan of the sweeping back and forth over the tread and leaving most of the clippings in the tread. I often do a second sweep in the same area to clear the higher stuff. This is a perfect application for the hedge trimmer blade on the end of the weed wacker. But i typically do a full service trim / high and low at the same time and the hedge trimmer works best for that and I can transport it in my backpack...All that being said, it murders my back bending over with the hedge trimmer.