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 :)

I know nothing about this project and probably shouldn't comment but from previous logistics projects I've worked on I've learned that maintenance costs from wear and tear all seem to increase non-linearly with mechanical speed. An everyday example is that some buildings choose to run their elevators at slower speeds for this reason, but the speeds of industrial and logistical conveyor belts are carefully chosen with this in mind too. Of course air resistance also goes up non-linearly with speed, and that might be a factor here.

The total throughout (in cars/hour) is given by speed divided by effective length.

Effective length is the length of a carriage plus its share of the distance between trains, which is something like quadratic in speed (since kinetic energy also is)

So the total result is something (caution, probably there are other factors here, such as non-carrying cars like locomotives) like:

          v
 TP = ----------
           Kv^2
       L + ----
            N

Where TP is throughput, v is speed, L is car length, N is cars per train and K is some constant that determines the head between trains.

To maximise throughput, you can't just crank up speed as you start to dominate the line with space between trains (as kV^2 grows). There will be a sweet spot when it is optimum. This applies as long as the braking distance of a train is super-linear, actually, so even if the distance is not quadratic in speed, say it was Kv^1.5, it still holds.

You can make trains longer (increase N) to reduce the number of spaces between trains. But this has its own practical issues.

You can also decrease K with better brakes or sensors that allow to brake earlier. But I imagine there's either a practical limit like forces on the tracks or trains, cost too much, or trains have what they have and can't be upgraded.

You can also make cars hold more per unit length, but that's also difficult in a fixed guage in tunnels.

Finally, if you're running trains as close as you can, there's no point running faster then the slowest train in the system. If a train at any point has to slow to 30kph, say for a corner or climb, that's the speed of the whole line.

Just a guess, but maybe it's just a good starting point. 30kmh is pretty quick for moving goods (if you factor in all the downtime that goods spend in warehouses) and is also not terribly hard to deal with in terms of designing the system and the traction engines. When you combine this with the fact that the density can be higher than with human drivers, 30kmh doesn't seem so bad.

Plus I would think they could gradually increase the speed as the system proves itself more. There are so many other challenges with getting this done, that maybe making the system go as fast as possible took a backburner.

Maybe also packing efficiency. Cargo has to be less rigid and secured, more diverse load types etc.

There will also be significant elevation changes

There will be, but seeing as this is a tunnel system, those elevation changes can be spread out a lot more than they would be if this was overland. I'm sure it's _a_ factor, but not likely to be the biggest factor in the max speed.

Bern is at 550 m (1800 feet) and Basel at 260 m (850 feet). I don't think that elevation changes matter a lot.

They're probably optimizing for consistent throughout rather than latency. Faster vehicles would reduce latency but increases the risk that a breakdown would knock out some of the capacity. (And with an underground network it's not so easy to pull off onto a side street!)

From some googling, average freight speed in the US is under 40km hour. And that includes huge stretches of track without a curve or a mole hill. The capacity limitations end up at the depots anyway so going faster just means hurry up and wait.

Systems are not comparable. US systems are to my knowledge: all above ground; long trains, which require longer stopping distances; require manual loading; coupling of trains is manual; driven by humans; distances traveled are completely different; one-way, single direction, per use; breakdown cannot be routed around; etc.

Is there any benefit to going faster? 30km/hour gets you anywhere in Switzerland in less than 24 hours.

More throughput would be a benefit. Not saying they should; just responding directly to this question.

More throughput means more storage space needed at destination or faster loading / offloading speed and more local delivery rotation which won't be possible in final destination.

Yes and no.

Safe deceleration must be accounted for in these projects. It‘s a lot faster to safely decelerate at 30kph than say 80kph.

Imagine you ordered something from Amazon. It will take about 24 hours till it is at your doorstep. If all that time was spent travelling at 30 km/h, it could have come from 720 km or 450 miles.

In Switzerland, the distance from Geneva to St. Gall is around 360 km.

Container ships travel typically at 16 to 25 knots (between 30 and 36 km/h), and they do this traveling very long distances.

In other words, low speed does not really matter for many goods, especially in small countries.

Also, its the average speed that counts. I doubt the avg speed of a freight truck running between two relatively close swiss cities exceeds 50km/h. Avg speeds drop sharply with any stops or slowdowns.

Given this is goods and not people the more relevant metric is not the average speed of the carts but the volumetric flow rate at each of the nodes in this system.

It seems to be last mile distribution from logistical centers, so targeting rather short distances given the size of the country and distribution of large cities.

First segment is between on of the biggest logistical hub and Zurich (largest city), which are 70km apart.

> Anyone able to comment on why 30km hour was targeted for the high capacity lanes?

Maybe because it's a good start?

And what matters for a project like this is throughput, of which speed is but a single component, uninterrupted flow and volume being others.

I was also suprised they couldn't go faster. Maybe energy efficiency? That is the only reason you would go slower. Maybe they are trying to make this thing hyper-efficient energy wise.

But this project is awesome for two reasons: one, I've always wondered why this sort of thing isn't automated. We could even have humans moving small packages intra-city underground on conveyor belts.

And two, I live in Zurich, so being close to what I believe is the first project of this type ever, is super cool.

First after the Alameda-Weehawken Burrito Tunnel, of course.

https://idlewords.com/2007/04/the_alameda_weehawken_burrito_...

There used to be pneumatic (compressed air) tubes for mail, but it became kind of irrelevant when fax and email obviated the need to send small letters.

They're still popular in hospitals AFAIK, where they are useful for sending e.g. blood samples and medicines around.

Based on my extensive experience on factory building games I would suggest that perhaps also in real world wreight transfer, latency doesn't matter, only throughput.

That is not simple math, that is lying by omission. Trucks only drive 80km/h so talking about 120km/h either makes you sound like an elementary schooler or an Elon Musk fanboy.