I think a lot of people who insist on drawing these hard lines must be on the spectrum.
I refuse to define myself by such narrow categories as "cyclist", or "car guy" or whatever, primarily because I find people who do so are insufferable closed minded twats, and I don't want to be associated with them.
I'm a guy who likes to ride bikes. Mountain bikes, e-bikes, motor-bikes, etc. More generally, if it's got wheels, I probably like it. Skateboards, cars, trucks, scooters, and boy those one wheel things look like a hoot but I have yet to try one out yet.
Relative to e-MTB's, the most appropriate place for their use is on existing MTB trails, because they're nearly identical in size, speed, weight, appearance, handling, sound, and the skills required to ride them. I've ridden them on motorized trails, and in 90% of the cases, it's just the wrong place for them.
I really don't know anyone who's saying that ebikes are the same as traditional bikes, or should be called the same thing, but I keep hearing that argument. Nobody is saying that. What we are saying is that they should be treated the same. Same trail access, same etiquette, etc. Could we stand to make some tweaks to reduce the chances of a negative interaction? Directional trails where needed, etc? Sure. Access doesn't have to be all or nothing.
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