Static space. In the real world people exist in both space and time. Ten people who complete a journey at 100mph take up the same time-space (ie road) as one person at 10mph. Someone at 1mph takes up as much road as 100 people on the same journey at 100mph.

If the question is how many people can we shove through a pipe/tunnel/travel network, speed is as much a factor as physical size. Bikes and cars both take up massively more time-space than trains or busses. But pro-buslane voices are rare these days.

That's not how the math works out, it isn't linear. The distance it takes to stop anything is dominated by a term quadratic in the velocity. Thus the average safe traffic density decreases with the velocity like v^-2. Since the throughput will just be the velocity times the traffic density, throughput roughly decreases proportional to 1/v. (In the zero velocity limit, physical size terms would dominate, so you don't get infinite throughput.)

https://www.omnicalculator.com/physics/stopping-distance

So if you do the math, bikes take up less time-space, or said better: achieve higher throughput. They are multiple times more dense at their travelling speeds. The only real way out of this would be to travel at unsafe distances.

You assume single passenger vehicles. Do the math again for a 50-person busses. Compared to that, bikes and cars are relatively similar. Even four-person cars, with say 4 seconds between them (one person per second) better single-passenger bikes traveling in pairs. Bikes rarely ever maintian such separations, genrally leaving 7+ seconds between pairs when at speed due to bikes having reduced stopping times from top spèed.

It may be a reasonable assumption; what are typical vehicle occupancy rates?

Also, a bicycle-majority traffic mix wouldn't have to conflict with the presence of high-passenger-capacity buses.

That may be true that cars can have shorter time-distance separation, but I think there's a gap in the modeling there with regard to group travel:

If you have a four-passenger car and compare that to the same group of people traveling together by bicycle, the time-distance separation factor disappears.

In front of a moving vehicle is an amount of that pipe/tunnel/travel network that is basically unusable by people who aren't inside that vehicle. As the speed of the vehicle increases, so does the length of that unusable space.

If I'm a pedestrian who needs to cross a road, or a driver who wants to turn on to that road, it's equally busy if there's a 10mph cyclist half a block away, or a 100mph car 5 blocks away.

The braking distance grows as the square of speed. And the mass that is braking is of course also a factor.

Again, time. The faster vehicle occupies more road but for a shorter time. That fast car down the road and that closer/slower bicycle both occupy relatively similar amounts of roadway in comparison to multi-person vehicles like busses. The fastest way to move people down a given lane is to cram them into trucks army style and then drive slow enough that each truck leaves minimal time between each. A lane can then handle a 50-person truck every 5 seconds, or 10 people per second. That's far more than can be pushed through on individual bikes riding in pairs.

This is assuming a chink of road in isolation. There's also intersections, vehicle separation, signaling, and other needs that take up less space-time on a bike than a car. Perhaps less-so than a bus, but we would probably need simulations to say more.

Of course, but for a discussion of bottlenecks signalling isnt an issue. Putting an intersection at a bottleneck is just stupid. Thats why bridges fan our thier roads on either side.

Please don't forget that those vehicles (except for the public bus) are static all day except for an average of 45~60 minutes. The car does take up far too much space for it's limited usage.

That’s all reasonable analysis if you’re optimizing for shoving people through a space. Most people are trying to go places and do things. The bottleneck isn’t just harming transit completion, it’s harming the whole purpose of being in motion in the first place.

The definition of a bottleneck is a place where we are at a people-shoving capacity, the place where congestion is born. If people-shoving isnt a priority then there isnt really any bottleneck that needs dealing with.

So imagine two hundred people on bikes on a mile of bike lane and twenty people in cars on a mile of freeway. Both are the same freeway width. Just hold the thought of that enormous bike lane for a second. Then go ahead and tell me the same amount of free time-space is available for crossing in both cases.

So let's say that's 10 cars and 200 bikes (being generous, usually cars have only one person in them, and also bikes esp. with children in biking-heavy countries have more than one person carried by them).

If they are evenly spaced, there will be a car every 0.1 miles - and each car is going 100mph according to this thought experiment. This gives 3.6 seconds to cross between 100 mph cars that probably won't swerve to avoid you and may careen out of control if they do.

Meanwhile, there is a bike every 26.4 feet, and you have 1.8 seconds to cross. 10 MPH is speedy for a bike, but they have to only slightly adjust to avoid hitting you if you make a mistake (and are about 1/5th the width if not less).

I'll take the bikes!

you are right to bring up speed as a factor. one interesting study found subway escalators are more efficient when people stand close compared to walking up! Space trumps speed in this case.

In urban environments, cars have a low average speed (e.g. in London UK it's around 14mph) so I think space will dominate here too.

Also remember that as speed increases, so does spacing for safety reasons.

Cycle infrastructure should be built by taking space from cars, not busses.

In terms of bandwidth and latency, bikes can be much closer together (high bandwidth) but have high latency.

In the part of the Netherlands where I live it's not uncommon for a bicycle to be faster than a car at reaching a destination, because it's very dense in the north so your destination is likely in an area where cars can't go faster than 30 and you on a bicycle would go 20 but are far more manoeuvrable and can take shortcuts and don't have to park, additionally you don't get stuck in traffic on the bike lane because you can pass people as people are not allowed to cycle with more than two side by side and due to the quick acceleration people move aside if you ring your bell. That's why in the dense north and the cities it's often faster to go by bicycle and probably why the electric bikes are a popular alternative to cars for people with limited physical ability.

Elsewhere less dense it's probably a different story if you have to travel a few kilometres over a 60 km/h road to reach your destination.

It’s the same here in Washington DC: bikes are faster for most trips, especially e-bikes, unless you’re going all the way across the city (10mi square) on a handful of routes and have parking available next to your destination.

That last part is something which drivers usually leave out in their travel time estimates: off-peak, a car can often go faster to the general area but the time needed to find parking, pay, and walk back usually cancels any savings several times over.

Not only the Netherlands; even without dedicated cycling infrastructure, cycling will be faster for distances under a couple miles for pretty much any walkable town or city. Deliveroo uses bicycles extensively.

That’s assuming your traffic is free flowing. In city traffic it’s not at all unusual for bike to match or exceed cars’ speed. For example the average speed of traffic in inner London is less than 12mph (in the centre its more like 7).

Yeah, I got an electric scooter a few months ago. It’s always fun going along the separated bikeway alongside one of the big six to eight lane freeways coming in and out of the middle of the city I live in, and at some times even at 25 km/h still going faster than the car traffic!

This is why congestion is so exacerbated with cars. All it takes is a slowdown in one section of the road to ripple out the effects of the reduced throughput further back.

Yeah it goes both ways. Not only does a fast car consume less space, a slow car consumes more space. So once you have stop and go traffic the amount of space a car consumes for the sake of safety is just absurdly large.

Good points, but we should also account for reductions in throughout due to parked vehicles, which I think offsets this somewhat.

Parking is a whole other problem but in cities where everyone has to commute in/out of an area the bottleneck is more often the roads than lack of parking spots. (Parking can be built up/down while roads are built in 2d.) Underground parking structures (3d) also use space that is generally unusable otherwise. Few offices are permitted deep underground due to fire codes.

Not so, huge numbers of cars in NYC are just driving around looking for a park! If you raise the cost of parking fewer will drive, so the two are closely interconnected.

Because NY has chosen to not have spots, to build other things. There is plenty of physical space if every building dug out an underground car park during construction.

This is a ludicrously expensive suggestion. Also imagine the queues as each car waits to turn into its destination building.

I think there's room for both. The advantage of walking or taking a personal vehicle (car, motorcycle, or bike) is flexibility: you can depart at any time without waiting for a transit vehicle to come along.

I'm not a fan of that example - the cars photo is more zoomed in than the others.

I mean... whatever: https://i.imgur.com/TVeeDBa.jpg

Those pictures are supposed to bring a point across, not be used for an accurate scientific measurement.

Either way people will be aware not even three out of those 60 cars could drive in the space of that bus.

Here are the originals. What's interesting is that the car picture isn't among them in that form. I don't know whether it has been digitally edited, or they've taken another picture as well. However, the car picture looks like four rows with more than 15 cars each, but it's hard to tell as it gets fuzzy.

https://www.stadtwerke-muenster.de/blog/verkehr/das-wohl-bek...

It also assumes the cars have one occupant. I rarely drive alone these days

Most average occupancy rates for private automobiles is less than 2, in the US I believe it’s about 1.3.

Still not enough compared to how much space and how many resources they consume, let alone the externalities.

... Buses on the other hand are used about 60-80% of the day whereas a privately owned car is used 3-5% of the day.

Cars do not just take up space driving. They also take up a huge amount of space when not in use.

That's context dependent. Where I live it's not a problem that a car takes up space (my car is parked in my home's basement).

Where I typically go to it's a relatively minor problem - most places I go to only need 4 to 5 places to park cars.

Work is in the middle of nowhere, again not an issue except that the government employees have reserved the lot by the building for themselves despite it being large enough to house the contractors as well (the govt. employees want to ensure they get the spots nearest the building).

Should the city of Rome have cars? No. But we don't (nor can we!) all live in a small European city

It also doesn’t illustrate the real scale of space required to operate each vehicle. A car needs several car-lengths of space between them. Bikes can be operated more closely together. At speed all of these vehicles scale up to more space differently.

"A car needs several car-lengths of space between them."

The distance between bumpers actually cancels out (actually it comes out in the car's favor). First notice that in the picture the cars are almost touching, so clearly you mean in fast moving traffic.

In fast moving traffic the carrying capacity of a lane is equal of the inverse reaction time (typically engineers use a large margin of safety and 2 seconds is used -> 1800 cars/(lane hour)).

For bikes, since they travel more slowly, you have to add the time it takes to travel their own length. So the carrying capacity of a lane is 1/(reaction time + length of bike / speed of bike).

The "several car lengths between them" is literally space that exists only because cars have generated themselves by virtue of going very fast (since fast moving vehicles get to where they want to be quicker and therefore get off the road to make space for someone else).

This doesn't mean that cars make sense in dense cities. They don't.

This doesn't means cars don't take more space by virtue of being longer in slow traffic. They do

But it does mean that, if there are "several car lengths between them", they are in fact operating in a more space efficient regime.

In the US road engineers go to strategy for safety is to just make the roads wider. When drivers feel safe they start driving faster than the speed limit. Those roads were designed to be "safe", not fast, meaning high speeds are more likely to lead to worse accidents.

To paraphrase Sartre: "Traffic is other people."