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I think if we measure the travel time from door to door the benefits of the fast rocket shrink in a relation to where is located.

With airplanes this is solved, by the big infrastructure ( cities sometimes have even 2-3 airports ).

Where I live ( Berlin ) with a flight to NYC would look like :

    1. City center -> TXL  - 20m
    2. Check-in / security - 30m ( no joke, the airport is small )
    3. Flight              - 9h 15m
    4. Check-out / luggage - 50m 
    5. EWR -> City center  - 50m
    ------------- TOTAL ---- 11h 25m
This means that ( ignoring the BFR flight time, since it's just minutes ) the time between you leave the city-center and entering the BFR should take less than 5 hours ( for Berlin ), otherwise you will not arrive faster than a plane.

One thing you're missing:

For a very high profile requirement - say, some kind of huge emergency - you could land the BFR anywhere there's a solid surface the size of a soccer field. Zero infrastructure required.

Getting it out of there again would be difficult, but you could have a team of experts and a whole lot of material resources literally drop down from the sky anywhere on Earth in a matter of hours. Most of that duration would be spent loading the human and material cargo into the rocket.

We have no way of doing that currently.

P.S.: And if the emergency is big enough, you could drop the whole thing into the ocean near the shore and just jettison the passengers and cargo shortly before impact.

Rapid intervention anywhere on Earth. Literally.

Military invasion forces and quick reaction forces would be much easier to insert with tech like that.

I'm not sure about invasion. These things are pretty vulnerable on the descending part of the trajectory.

Total Time is only one portion of the suckage of air travel though. It's that long window of time where you are cramped in a small seat, potentially with large strangers spilling into your space from either side that I dislike the most. If I only have to deal with that bit for 30 minutes, the rest of the trip can take as long as it reasonably wants.

No more deep vein thrombosis. Or screaming kids kicking the back of your chair cause they've got nothing to do for 10 hours. London to Sydney would be a massive improvement because often you have to stop halfway.

Plus you get all the benefits of paying for a Virgin Galactic trip

Auckland to Vilnius is at least 3 flights and 24+ hours of flight time. Door to door is basically 2 days. Elon please save me.

How often do you think you can find a rocket's worth of people who want to go from Auckland to Vilnius?

Hub and spoke model. I can't imagine being more than 5 spaceports per continent. Most popular destination from Auckland would be London. I don't mind taking Ryanair from there.

Hard to know how many would go at one shot. A few hundred? One could move cargo also. Maybe once a day? For a 40 minute trip, maybe a lot more. Depends on the price. The thing is, the infrastructure a rocket needs might be way less than big airplanes. Super chilled CH4 and O2 and a small pad and tower. Along with doing say 20 flights per day, these things can move around the globe easily and go where the demand is.

The Boring Company's tunnels will get you to the spaceport at 200kph with no traffic or stoplights (or 1000kph if you're coming from a distance)

"Without tunnels, we will be in traffic hell forever" -Elon Musk

The reason the video shows a sea launch is that you can use a high-speed ferry to get to an empty area from the city center in less than an hour. Inland cities like Berlin aren't targeted.

Wasn't the commute to and from the terminals also one of the things that killed the Hyperloop?

I believe the rumors of its demise are greatly exaggerated.

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