Why don't helicopters have a place in the mobility plan of metropolis?

Helicopters by definition require a power-to-weight ratio >1 and are inefficient compared to fixed wing aircraft, let alone e.g. trains. They're loud, dangerous (comparatively speaking) and inherently expensive. Tall walls can cause them to crash (c.f. vortex ring state) as can the weather.

A subway has none of these disadvantages, with the advantage of serving ~1.5k people at once as opposed to ~15, and the ability to not conflict for surface space.

In addition to other reasons listed, they're hard to fly in calm air and cities are nasty for chaotic air currents: raising the skill barrier for pilots even further.

The toy "indoor" helicopters demonstrate this easily; they don't like to get near "things", or they like it too much.

even in rural areas "air ambulances" run from designated pickup points and win on being able to do straight line flights (debatable, there's arguments to be made they're not a "win" at all). they can't land just anywhere; and there's a surprising volume of space and maintenance need for a viable landing spot.

Helicopters crash. I would not say routinely. But it's far less safe than a fixed-wing aircraft. There are serious safety issues with tens of thousands of VTOL craft zipping around in a city. You'd have one whacking into the side of an office tower or falling out the sky regularly. It already happens from time to time and we really only use them for medical evacuations and the police here. They're also expensive and hard to maintain.

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