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Isn’t that exactly how you build a trail up a mountainside? They are usually a series of switchbacks.

Most people on most bikes can only take so much grade before climbing becomes impossible. A maximum grade setting would be very helpful for that exact reason.

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Oh, yeah, I interpreted the parent comment as "minimize the grade" but if it's instead "keep grade below threshold" (for reasonable thresholds) that would make more sense.
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A minimize grade and grade cap would be incredible for folks pushing wheelchairs (or strollers even!).
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I feel like even if the distances are equal, it's faster to walk a bike up a steep grade and bike the rest flat than it is to bike up a moderate grade the whole way. This topic has probably been discussed somewhere else.
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People can generally only output their max power for short durations. The output level they can sustain is generally much lower. I bet you could try to model higher limits for short distances, but what those should be could vary greatly depending on personal fitness.
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I think that too favors walking the bike up the incline. Anyone able-bodied should be able to do it, some faster than others, but biking up an SF incline is more hit or miss, especially when considering different bikes.

My reasoning for the bike-hike being faster is that legs are designed for it. Legs are only inefficient on flatter ground because you have no equivalent of high gear (like extendible legs), so all that torque is going to waste.

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Uhh, excuse me? Legs are inefficient on flatter ground because they don't have wheels.

Legs have to start, go up, go down, stop.

Wheels go brrrrr.

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That's some of it too, but in a way legs aren't all that different from wheels in how they work. Most of it is the gearing. Like there's a gear on every mountain bike that will make your feet go down at the same intervals as walking. That sucks on flat terrain. Legs are also not perfectly designed to push pedals, especially for people who don't bike often.
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I believe the "wheels on the bus go round and round" :-)
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BRouter models this as inertia, I believe.
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But hike a bike is no fun, especially if trying not to sweat
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Unless you are on foot (and even then) the route needs to follow existing roads, you can only zig zag as much as existing roads do it not endlessly.

And almost any practical routing system will have a mechanism for tradeoffs of different aspects. Often there is a distance/time tradeoff which directly relates to speed on corresponding segments. But the tradeoff can also be in the form of "on average x seconds spent waiting green light in each intersection or time to stop before railroad crossing. So there is no reason for a system optimizing grade to completely ignore all other factors, it's just a question of weights and curves of each of them.

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Like the ascent to Mt. Hamilton (southern Bay Area). You can see the peak for like an hour but so much twisting back and forth, going mostly perpendicular to the max gradient. It is an old road and hence graded for mules to carry up telescopes.
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well. That or a nice spiral! :)
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