Comment by sandworm101 | Hacker News Reader

Comment by sandworm101 | Hacker News Reader

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Its all about energy. Accelerating the cars up to speed is one thing, but slowing them down and negotiating corners is another. Whether you use batteries or diesel, speed always takes more energy. As for throughput, we need to know the safe distance between these things at various speeds. Just like on roadways, they need to be able to stop if the car/train ahead of them stops. So slower cars, closer together, probably result in more cars passing per second than at higher speeds with greater stopping distances between cars. Exactly the same as with roads.

Anyone who thinks that because these things are automated that they can safely travel bumper-to-bumper at high speeds hasn't worked with vehicles underground before. Any pileup in a tunnel is a nightmare. Something burning, especially something high-energy like butter or flour, turns the tunnel into a blast furnace. Safety distances will always be required.

https://en.wikipedia.org/wiki/Mont_Blanc_tunnel_fire

>>On the morning of 24 March 1999, 39 people died when a Belgian transport truck carrying flour and margarine, which had entered the French-side portal, caught fire in the tunnel.

> So slower cars, closer together, probably result in more cars passing per second than at higher speeds with greater stopping distances between cars. Exactly the same as with roads.

I hear this from time to time but it doesn’t pass the sniff test. If we assume the vehicles are points, their flow is precisely determined by stopping distance (as measured in seconds). If on the other hand we assume the vehicles are very long, their flow is determined by speed. Thus flow at minimum does not change with respect to speed, but in practice increases with respect to speed, assuming time-constant stopping distances (i.e. you pass X point Y seconds after the vehicle in front of you does)

You can dissipate some amount of energy per second when breaking. The energy is proportional to the velocity squared, so the breaking distance is proportional to the velocity squared. The density is inversely proportional to the spacing (here the breaking distance). The flow is density times velocity, which is ~ 1/V^2 * V ~ 1/V. Therefore, the density decreases linearly with speed.

That means that the slower you go, the more parcels per seconds you will get, because the breaking distance increases more quickly than the velocity!

Of course this is a simplification, Because this assumes the trucks are points. The best case of this model would be an infinite density of non-moving trucks! In reality trucks have some length, which means that they can not be infinitely close, so 30kmph is probably close to the optimum.

First friction limited stopping distance is a function of Velocity squared. Trains running on rails are longer, but the reason they use rails is rails have lower friction.

Which is why real world freight trains have stopping distances at 65MPh of over a mile. This is also one of the reasons they can’t climb seemingly mild inclines.

Limiting the underground freight trains to say 1/10th a mile and maximum throughput is probably close to 30mph.

> I hear this from time to time but it doesn’t pass the sniff test. If we assume the vehicles are points...

Ah yes, the "sniff test", in which things which are untrue are assumed, which make the interlocutor sufficiently confident to pontificate. "Sniff test", as a concept, doesn't pass itself, rhetorically (-- or maybe it's a "code smell").

In fact throughput is sometimes the main constraint on speed. Apparently the high speed train service on some of the busy french lines (like Paris-Lyon) is lower than what these trains would normally operate at so the safety distance can be reduced and the number of trains increased.

Which makes it ironic that planes can get a higher throughput than trains. Despite thier higher speeds, planes can be landed as close as one minute appart. High-speed trains must often stay several minutes appart. Thats the advantage of having access to two/three dimensions of movement over a train's one.

You completely ignored the cargo capacity or number of passengers.

Run the math. 400+ people/minute for a runway is actually much higher than any rail line.

Subway is kind of a rail line and Prague line C subway has sub 2min intervals in peak, with each train having capacity of 1000 passengers. So 500+people/min. EDIT: official number is 448 passengers / minute - https://en.wikipedia.org/wiki/Line_C_(Prague_Metro)

That's an extreme case of rail line, but "much higher than any rail line" is kind of extreme phrasing too :)

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