Right now it assumes a straight line be it on a road or up and down a mountain.
Right now it assumes a straight line be it on a road or up and down a mountain.
The most commonly used routers for bicycle touring – Brouter and Cycle.travel – certainly take elevation into account and helped me personally out all over the world. Brouter has a hiking mode, though it is still in beta, and perhaps there are hiking-specific elevation-aware routers out there.
Huh? On the OSM.org website you can use Graphhopper or OSRM routing engines. Both are not "tech demos", but proper real routing engines for real world use. They are hosted by volunteers, so you shouldn't rely on them to be free for everyone for ever. If you want to build a business on them, both OSRM & Graphhopper are open source & self hostable
For tracks with steepness up to 30°, the straight line distance will be off by max 15%. If it's steeper then that, the actual terrain is the thing that determines how fast you can move.
https://graphhopper.com/maps/ (click the dots near the bike icon for more profiles)
And the best is: everything is open source and you can easily tweak it according to your needs.