A Shinkansen line (arbitrarily chosen because it was the first thing that popped up in my search) can do 13 trains per hour with 1,323 passengers per train, which is equivalent to one 747 every 1.4 minutes.

That would replace one runway, but it still doesn't compare to the number of planes that the sky can handle. Sky which is cheap/free in comparison to building rails. There is definitely a point where trains are more efficient, particularly between a small number of large cities, but moving a large proportion of US air traffic onto trains, imho, is a different problem given the number of routes (1000s) and airports (100s).

I'd have to see the math, but there is also a question as to carbon emissions per-passenger/distance. I believe that on long flights (more time at high altitude) widebody aircraft might be more fuel efficient than high-speed trains stuck on tracks.

How many airports are landing anything like a 747 every 1.4 minutes? Especially given that the Shinkansen runs in both directions, so your airport is going to have to handle exclusively 747s, with high loadings and a headway of around 40 seconds. That's slightly more planes and massively more passengers than London Heathrow.

In terms of carbon emissions you'd need the flights to be long, and the trains to be pretty inefficient and empty (think current Amtrak trains), and even then there is evidence that the high altitude appears to make the emissions significantly more harmful than the equivalent ground-level emissions

> Sky which is cheap/free in comparison to building rails.

Isn't flying the most expensive kind of transportation ? Plus it relies on fossil fuels big-time.

It's hard to compare price because it is very rare for two means to compete directly. It's often apples and oranges. A train that moved as fast as plane isn't going to be very fuel efficient. They can be electric (insert source debate) but planes can also run on biofuel (another debate). And when comparing plane-train, a plane burns much of its fuel taking off and climbing to altitude. Once there (10,000m) it is remarkably fuel efficient in terms of passenger/mile at a given speed. And there are times when rail simply won't ever be an option (over large water). The head of RyanAir gave a great presentation a couple years ago about highspeed rail. His point was that, while great if you live in london and vacation in Paris, most people don't live downtown, that planes can land in places much closer to actual destinations --> reducing total-journey emissions.

I'd love a high-speed rail from Vancouver BC to Calgary Alberta, or Prince George (both places I go every year). But building such a structure is a monumental task (10s of billions) and a fast train would take a vast amount of energy covering that distance. Imho trains just cannot compete in such markets.

As you said, it is two different things.

I take the train everyday. For me, travelling by train for < 4h trips to a city sounds like a good deal.

It is generaly a smoother experience than taking a low-cost flight. But, I realize it really depends on how 'car-first' and large your country is. Definately not an universal solution.

It all depends on the capacity of the train and how frequently it stops. Starting and stopping are the real killers since you need extra spacing (or very long "onramps") to accelerate and decelerate a train.

However, one concept is a train that never needs to start and stop. Passengers move onto a separate car that separates from the main train and can decelerate into the station, and then it reaccelerates and attaches to the next train. Conceptually, this allows you to run much larger trains since you don't need to decelerate it every 10 minutes for a stop.

https://www.youtube.com/watch?v=DIeRrU4_M3Q

This is the original concept. Let's just say I have some doubts about the feasibility of engineering that design in real life, but the concept of detaching cars seems sound to me. Conceptually I do like the idea of the detachable cars being a different type of unit with a higher top speed and better acceleration/deceleration units to assist in the deceleration and overtaking steps.

A simpler implementation would be to have self-propelled carriages that combine motors and passenger space, and have the car accelerate and decelerate on a siding. The main train would have to run at a slower speed than the detached car could achieve in order for it to "catch up" but could then accelerate back to top speed once reattached. This would lead to an "oscillating" pattern of distance between multiple trains on the line.

Also, at the end of the day a runway is still a "one-dimensional" unit of capacity in the same way that a rail line is. You can have multiple multiple runways or rail lines (which I guess is "two-dimensional" in your definition here) but you certainly can't have multiple decks of runways or land multiple airplanes on top of each other. It's actually perfectly feasible to have rail lines running at multiple depths, many subway stations do it.

The runway is one-dimensional, but aircraft still move in 3d. That means planes can be closer (in time) behind each other. Trains must leave room enough to stop. Planes can escape by diverting higher/lower/left/right. So planes stacked up on approach to a runway can safely be far closer together than trains on approach to a station.

Non-stopping trains are interesting, but such a solution would require the multiple parallel lines I mentioned above. And even the non-stopping trains would need some amount of space between them for emergency stopping and speed changes.

Given that it's incredibly important that the planes don't under any circumstances stop they have their own limiting factors. high speed trains using short or ideally variable block signalling and running on segregated high speed lines can achieve spacing which is pretty comparable to airplanes coming in to land.

> the three dimensional world of aircraft.

No, that's not how it works.

En route airways are 3d, but approaches are 2d and landings are 1d. Large US airports are already at capacity, and above capacity in poor visibility conditions (like fog at SFO.)

Also, trains can just add more engines and cars.