13 ms·

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

by jakear 4y ago

> 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)

Retric 4y ago
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.
crygin 4y ago
> 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").
dustimpact 4y ago
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.

by jakear 4y ago

Retric 4y ago

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.

crygin 4y ago

> 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").

dustimpact 4y ago

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.