Subway capacities

May 7, 2016

I recall once figuring that the capacity of a single track of subway was substantially higher than a lane of traffic. This is how that is calculated for a real live subway (the MBTA Red Line, also roughly applies to Orange and Blue lines which run similar equipment.)

redline_cars_per_train = 6

Source: Wikipedia red line article

redline_trains_per_hour = 60/4.5 = 13.3

Source: 2014 MBTA Blue Book, page 17.
Headway is 8 or 9 minutes at rush hour on each of the Alewife/Ashmont and Alewife/Braintree lines, or 4.5 minutes on average on the shared portion of the line.

redline_ppl_per_car_policy = 167
redline_ppl_per_car_crush = (267*74+260*58+277*86)/(74+58+86)

Source: 2014 MBTA Blue Book, page 18.
167 is the policy people-per-car. Seated and crush capacities are averages over the red line fleet.

seated_rush_cap = redline_ppl_per_car_seated * redline_cars_per_train
policy_rush_cap = redline_ppl_per_car_policy * redline_cars_per_train
crush_rush_cap = redline_ppl_per_car_crush * redline_cars_per_train

seated_rush_cap * redline_trains_per_hour => 4,671.5596
policy_rush_cap * redline_trains_per_hour => 13,360
crush_rush_cap * redline_trains_per_hour => 21,526.6055

Compare this with a lane of traffic. Rule of thumb is that you get one car every two seconds, or 1800 cars per hour, and an average of 1.2 people per automobile, or 2160 people per lane per hour. Simple seated subway capacity at rush hour is double that, so-called “policy” capacity is 6 times that. Crush capacity, which I’ve seen and not much liked (“nobody takes the subway, it’s too crowded”) is just shy of 10 times the capacity of a lane of traffic.

And understand, this is far from the theoretical capacity of a subway line, it’s just what is actually obtained on a real subway in a real city at rush hour. Run longer trains (requires longer platforms, a completely doable thing) and you can add capacity. Run trains more frequently, and you raise capacity – the London Underground appears to manage 24 trains per hour at rush hour on the Northern Line or not quite double the Red Line’s frequency.

Re-doing the numbers at the London Underground’s rate for scheduling trains:

seated_rush_cap * underground_trains_per_hour => 8,408.8073
policy_rush_cap * underground_trains_per_hour => 24,048
crush_rush_cap * underground_trains_per_hour => 38,747.8899

At the Underground rate, “policy” train packing carries 11% more people than “crush” packing in the current system. And the theoretical “crush” capacity is the equivalent of 18 lanes of traffic.

Earlier this week, I was riding my bike home on a road with a bike lane, and came up to an intersection where the car at the front looked like it was planning to turn right (based on position in lane and angle of wheels) but was not signaling a right turn. The intersection has no advanced stop line for bicycles, just a plain old stop line and crosswalk. And understand, me going first is a completely legal thing, there are two lanes, straight traffic has right-of-way over turning traffic.

This presented several choices. I could stop far enough back that if the driver intended to turn right, they could easily do so (except that they would probably get hung up by pedestrians in the crosswalk and would stop midway, blocking the bike lane and delaying me). If they did manage to turn right quickly, there’s no guarantee that the driver behind might not try to barge on through with their own right turn; that’s happened, I even have video of someone doing this. Or, I could pull up to the stop line, and hope that if they did decide to turn, that they’d notice my presence in time not to hit me, and also not try to just make their turn through intimidation. Or, (and this is what I did) I could stop a little bit in front of the stop line – technically illegal, though I’ve never, ever seen this particular law enforced and drivers violate it constantly – and position myself so that the driver could hardly help seeing me, and even if he didn’t or if he decided to go anyway and there was a collision, I’d land on the hood of the car – relatively safe for me as collisions go, relatively damaging to the hood of the (expensive) car.

I hope it’s clear that this is no way for a normal person to ride a bicycle. I do so because I’ve learned it over the years and it’s no longer difficult, but to think that I would explain this to someone else as “useful tips for riding in traffic” is insane. This is similar to knowing that “it’s okay to ride closer to parked cars in a residential permit parking zone, because people move those cars only about once a day”. Or, “practice riding through potholes no-hands, so you get really good at controlling your bike on our crappy crappy roads”. I’m not making any of this stuff up, I do these crazy things, our roads are messed-up enough that it helps.

I’m not sure how this gets fixed. Safety-in-numbers is some mitigation; with enough people on bicycles, it becomes obvious that there’s bike traffic to the right and bike traffic through intersections and bike traffic past car doors, and the normal distribution of aggression among bicyclists insures that a few of them will help carve out space for the rest. I don’t put much stock in driver education; there’s not that much in it for the drivers, and it’s work to constantly be looking around for bikes. We could pretend to do more enforcement, but in practice the majority has zero appetite for that (evidence: we don’t vote for more enforcement, despite continual infractions and drivers killing thousands of themselves and other people every year). I think I’d like it if we adopted some modern Dutch infrastructure; a lot of that is designed to get rid of these designed-in conflicts and make it easier to see what’s going on. I have some hope that robot cars might be helpful; tedious rules like “always signal a turn at least 10 seconds or 3 car lengths before the turn” are what computers are for, as is “look for bikes in all directions always”.

I both drive cars and ride bikes, and for years I didn’t think much about how much driving a car impairs all your senses, as well as your ability to communicate. To hear how other people talk about traffic and safety, I think I’m not the only person to miss this.

Where this usually comes up is in discussions of rolling stops, and stop-then-go at red lights. The claim from cyclists (and this claim is absolutely true, which is why I’m writing this) is that they generally can see and hear better than people in cars, and thus are in a better position to judge if it is safe to go or not. This is one of the several justifications for the Idaho Stop Law.

So, vision. Someone riding a bike is as tall as they are standing up, if not taller. To stop, most people must hop off the saddle because they sit too high to reach the ground with their feet. Modern sedans tend to be about 4-and-a-half-feet tall (I just measured a Civic and a Camry), so whoever is sitting in them is shorter than that. On a bicycle, seated, your head is about 3 feet back from the front edge of the bicycle, but it’s easy to lean forward to within about a foot of the front. In a car, leaning forward gets you to the windshield, which is five feet back from the front of the car. Add to that whatever fog or dirt happens to be on the windshield and the windows, plus the various pillars and mirrors and fuzzy dice, and I hope it’s clear that the cyclist has a far better view of what’s around.

Next, hearing. Luxury cars are actually marketed for their ability to make you deaf to the world. That ought to be enough right there, but I’ve actually mentioned this to a degreed+prestigious colleague whose snap reaction was “no, I can hear okay in a car”. No, really, you can’t. Even without luxury soundproofing, cars have noisy engines, ventilation fans, tire noise, often a stereo, and quite often their windows are up. All these things act to block exterior sound. On a bicycle, the default is that you hear everything. There’s wind noise when you’re moving, but stopped at an intersection there’s nothing between you and the world and the bike is silent.

And you might like to think that maybe hearing doesn’t matter–after all, we let people who are deaf drive and ride bikes–but it certainly does. When I approach intersections, I can hear cross traffic coming before I can see it; that’s redundant safety information, which is a good thing. I can hear cars approaching from behind, and tell if they’re slowing or swinging out into traffic to pass, and I can judge the size of the car or truck as well (big trucks without sideguards are very dangerous). For pedestrian safety being able to hear matters, because I can carry on a conversation with the people around me. “I see you”, “go ahead, it’s a crosswalk, I’m stopping”, and of course “oops, sorry”. I can communicate with other cyclists, “there’s a blind woman walking ahead of you” (in the dark). All the sound signals that we’re supposed to legally make when approaching pedestrians are useless when approaching cars because drivers are effectively deaf. All the communication that’s easy with people around us is impossible with people in cars.

People on bikes also see more because of their ability to always position themselves near an intersection before stopping. That means we always get to see the light cycles and light timings, and even if we haven’t learned them all yet ourselves, we can see how other cyclists react to them. We don’t need to catch sight of landmarks as we drive through the intersection, because we always have plenty of time to look around at the front. Once you know the usual timing for a light (easily derived from countdown pedestrian timers on the street and cross street – which you can see because you are stopped at the intersection) you can also judge from quite a distance the appropriate speed to make the next light, which allows you to moderate your speed to only what is adequate to catch the green. Lower speeds make for easier pedalling, and are also safer.

I had meant to make a much longer rant about “windshield vision”, but I think this is good enough for a start. You might ask yourself, if you could drive and fool yourself into thinking that you weren’t half-blind and mostly-deaf, and not realize what you were missing stuck back in a line of traffic, if you might not be self-fooled about some other things. If your reaction to the facts stated here is that they’re the crazy opinions of one of “those cyclists” – don’t forget, I am a licensed driver, I drive often enough, I own a car, and this is true of most adults riding bicycles (knowing this stuff makes driving a lot less fun. Don’t expect any auto advertising to mention this ever).

Bonus sensory deprivation video, in case you still don’t believe me: watch the second driver in this video roll right over a bicycle and a bicyclist’s foot, and not be able to believe she did it. Said bicyclist has right of way, in clear daylight, riding straight on a straight road, wearing a dayglo-yellow jacket, with a front flashing light. The second driver did not see, did not hear the crash, did not hear the crunch of the bike as she drove over it, did not hear the guy she was running over yelling at her.

It occurred to me a few days after posting this that “people on bikes behave unpredictably” is consistent with “people on bikes make decisions based on information I don’t have”. Probably not the only explanation, but worth thinking about before jumping to pejorative conclusions.

Most times you see discussions on the internet of global warming, traffic congestion, and road safety, the advocates of the status quo are quick to claim that “we cannot ban cars, because [reasons]”. I’ve got no respect for this style of arguing the point because #1, even pseudo-serious calls to actually “ban all cars” are quite rare ( this recent article is the strongest statement I’ve seen, and that’s just one writer at Gizmodo ), #2 the reasons all assume that we’d do nothing to adapt and when possible remedies are proposed, new reasons are concocted (we can play this game all day), and #3, there’s real live reasons to reduce car use by quite a lot, and those cheerfully get ignored.

Just to motivate this, here are some very good reasons to drive a whole lot less. It’s also helpful to keep this in mind when considering alternatives; if they’ve got the same problems, then maybe they’re not good alternatives.

  • Cars kill thousands of people in crashes, including over 4000 pedestrians per year.
  • Cars kill their drivers through lack of exercise, enough to raise their annual mortality risk by about 25-30% 

    (summed over the population of car commuters, this is probably more early death than results from cigarette smoking ).  As long as exercise is its own separate activity, you’re unlikely to get enough of it.

  • Ignoring the less-death part of the equation, the regular exercise that you get from not-driving to work and results in just plain better health; you get more wind, more stamina, more flexible joints. It tends to help you keep weight off, tends to help blood pressure, tends to help blood levels of cholesterol and triglycerides, tends to ward off type 2 diabetes.  None of this is guaranteed for any one person, but it’s a really good bet.
  • Cars are a source of both particulate and noise pollution, which both contribute to poor health. Noise pollution from cars makes public spaces more annoying and less useful; you can’t hear as well.
  • Cars use roads very inefficiently. In urban areas the resulting congestion is so serious that one additional car added to Manhattan traffic is calculated to have an aggregate cost of $160 through delays to others on the roads.
  • Cars are a major source of CO2 emissions which contribute to global warming and climate change.
  • Paying for fuel for cars puts money into the pockets of nations and groups that do not share our values. Al Qaeda was mostly funded from oil money. Daesh is funded from oil money. Iraq would have been a non-issue without oil money (murderous dictators of poor nations don’t get much attention from us). Iran, officially an enemy of the US and ally of our enemy in Syria, runs on oil money.
  • From an economic-theory point-of-view, cars are a poster child for market failure. Their use is not independent of other people’s choices; if I want to take the bus, traffic from cars makes my bus ride slower and more expensive. If I want to ride my bike, cars can make the ride so much more unpleasant that many people won’t ride a bike. Even if I want to compromise and just drive a smaller car, the mass of larger cars makes me less safe in any collision; even for cars, it is a safety arms race. These externalities (pollution, noise, risk) are not accounted for in gas taxes. Even the direct costs of driving itself–repair and expansion of the roads–is not fully paid by the gas tax. The one reason that economic theory says ought to motivate people not to drive–that driving is very bad for your health–falls victim to human over-optimism about their good intentions and future luck; we won’t invest rationally in our (near-) future health, because we think we’re “healthy” and don’t need to do more. All this means that you can’t use hand-waving appeals to popularity and market outcomes to prove that profligate driving is what happens in the best of all possible worlds.

Given this motivation, let’s suppose we did ban cars. The question I’d like to see thought about and answered is not “why is this impossible?” but rather “what changes do we need to get by in a hypothetical car-less future? What changes would a lack of cars allow us to make?” My hope is that we would make some of those changes now, so that more of us won’t feel like driving a car is our only option. If the assumption is “cars are banned”, that removes the option of not thinking about a problem by assuming “well of course, for that we would use a car”.

One problem with using the thought experiment for this purpose is that there’s a difference between cars-banned and cars-reduced. If we actually banned cars, we wouldn’t need “bike lanes” because we’ve already got bike lanes. They’re called “roads”, but right now they’re full of cars. But if there’s still many cars on the road, we don’t get those “bike lanes” for free.. So keep that caveat in mind; if we’re planning to use tools from the hypothetical world in the real world, because some might not survive translation.

Another problem is: “what about the car-like things?” This might mean delivery trucks, golf carts, buses, trikes. What about self-driving cars? What about really big “bicycles”? Are those cars? Do we ban them too? I think what makes sense is to look at the costs of each and how they interact with what’s around them. Anything heavy tends to impose unusual wear-and-tear on the roads; this includes city buses. Anything human-guided has the potential for inept or careless use, so there should be some combination of small size, low speed, and/or safeguards to mitigate that risk. Inefficient transportation will produce excess CO2 until our energy supply is properly carbon-free. Even if a motorized robot-guided chair is carbon-free, safe for others, and kind to roads, it is still a motorized chair and will have the same detrimental health effects for its passenger.


So, to consider some of the problems:

There are people who cannot ride a walk long distances or ride a bike.

Anything that assumes bike riding or increased use of transit by default assumes some basic fitness, and some people lack that. How should they get around? In practice I think quite a few of them would use mobility scooters of some sort; modern electric wheelchairs travel as fast as 5mph (according to a wheelchair user I asked) but if they could be made stable we’d want more than that. I think they could be made stable. A larger, faster real-world example is a golf cart, though this is cheating slightly on the “ban cars” assumption. For people who lose their balance a tricycle sometimes works.

There are people with very long commutes.

Back before cars were so popular we tended to use a lot more rail; people would take the train in to urban areas to work. Would we restore our train networks? If the rail line doesn’t pass close by home and work, how are those endpoints connected? My default answer is “bicycles”. Another answer is to modify the zoning regulations that prevent people from living close to transit and work; artificially restricting that supply drives up prices and forces longer commutes. I expect this is one of the harder changes to make because it involves change near where people live; allowing greater density near transit would financially benefit anyone owning that property, and it would also provide an advantage to those somewhat near transit who wanted to use it (higher density allows transit to function efficiently allows better service). However, widespread density increases closer to urban centers might have the effect of reducing property values sufficiently far out as a simple consequence of increased near-urban supply reducing far-suburban demand.

For an all-bicycle commute, from personal experience I’d say 6-7 urban miles is fine, but 10 miles is pushing it, though that depends on conditions. The median commute is nearly 9 miles, which means that half might be done on bikes, but half also almost certainly will not. It’s possible to make biking somewhat faster — current bike routes often contain many gratuitous stops or are far from direct, and bikes with aerodynamic fairing or modest electric assist can cruise at 20mph (a human doing this without “cheating” is likely to get very sweaty) which reduces the time for a 10-mile ride to 30 minutes, which is about what my 6-mile commute-with-stops-and-old-legs takes.

There’s weather.

Sometimes it rains, sometimes it snows, sometimes it’s hot. As a general rule the only truly difficult weather is hot weather; we can add rain coats, umbrellas, gloves, boots, and hats for the wet and cold. Some cities have building codes that allow for pedestrian awnings, and those help with sun, snow, and rain. We’d probably do more of that in a car-less world. One useful thing about banning cars is that you no longer need to deal with your car and the weather; no need for car washes, no need for digging cars out of the snow. A pedestrian or a bicycle can fit down a narrow lane, or if in a hurry, can simply push through/over a snow pile rather than shovel out a wide path.

There’s kids.

It turns out bikes work pretty well for hauling tiny kids, and once they’re too large to haul, they can ride their own bikes.  With cars banned it’s vastly safer for little kids to ride bikes (turns out a ban isn’t even necessary if you design your infrastructure right).

Grocery shopping.

Not much need to adapt here. People who walk already use folding carts. My old retired now-deceased neighbor just carried his bags. People riding bicycles have many options, everything from backpacks to huge messenger bags to front racks to baskets and panniers mounted on racks. Even on a “normal” bike proper equipment allows six bags of groceries (2 front panniers, 2 rear panniers, 2 in basket). Actual intended-for-cargo bikes carry more.

There are heavy things that require heavy machinery to deliver.

True, but this is far from the common case. Delivery vans nowadays are large to amortize the cost of the driver who guides them, and then they drive as fast as allowed to also amortize the cost of that driver. The van is large, but the delivery generally is not. Consider the potential capabilities of self-driving delivery vehicles that need not to be large and fast. We can estimate this somewhat by looking at what humans on bicycles and tricycles are able to deliver. The point is not “this is what humans should be doing” or “look at those crazy people”, but rather, with a small vehicle and a small motor, it is possible to deliver this much stuff if you aren’t in a terrific hurry. Examples: Haley Trike and 400 lbs of sand (video); a chicken coop; a trailer full of Citibikes; a ludicrously large pile of stuff; a mattress, table, chair, and box. Robots could deliver loads of this size, and if it becomes economical for self-driving cars to ferry people around, then it will also be economical for self-driving carts to ferry cargo around in smaller batches.

Emergency vehicles

Well of course, for that we would use a car.  With all the other cars and trucks banned, they should be able to move really quickly through the traffic that’s not there.  (Bikes don’t take up much space and you can haul them completely off the road if you need to clear a path for an ambulance.)

Steep Hills

There is already (one) cable-lift assist for bicycles.  E-assist also helps, if a hill must be crossed regularly.  For one-shot annoying hills, walking works.

Rural Areas

No good answers here yet.  Horses?  Even electric vehicles are dicey, for sufficiently cold and remote values of rural.

I did a round of noodling in a spreadsheet to try to get a feel for how different ways of carrying people or cargo damage roads. The formula for damage is the sum of the cubes of the wheel loads; crudely, the gross weight of a vehicle cubed, divided by the square of the number of wheels. This can lead to some pretty non-intuitive results — city buses in particular are non-intuitively bad for roads .  Overall the most surprising thing is that even when results are calculated either per-passenger or per-pound, you end up needing a log scale to display them meaningfully; heavy vehicles are that bad for roads.

I’m not quite sure what to do with this information; there are other things to optimize for besides road damage.  For example, it would not surprise me in the least if a semi-trailer were more fuel-efficient per-pound than a human on a bike; bikes are efficient, but we do have to eat to run them and food is quite often energetically costly.  Similarly, though bicycles are far safer for pedestrians than cars and trucks, per pound of cargo they will lose most of their advantage against delivery vehicles (the comparison is quite tricky; a cargo bike can easily carry 100 lbs in addition to its rider, and 250 is not out of the question, and such large bicycles are even less likely than “normal” bicycles to travel at pedestrian endangering speeds.  Contra that, a human pedaling a loaded cargo bike has an incentive to not stop because it takes quite a lot more energy to bring that larger weight back up to speed).

Note that a single-occupancy vehicle still fails badly on efficiency and safety metrics, but trucks of various sizes need not.


I’m a little reluctant to post this because it’s got a bit of a gloating feel to it (“look at my massive calves and thighs!”) but people should understand that if they don’t have the opportunity to bike to work, they’re missing out and they’re being cheated. That means they have to know the sort of thing that they’re missing.

This doesn’t necessarily work for everyone, but it’s clear that most people are suspicious of doing things because it’s supposed to be good for the planet. Instead, I’d like to suggest reasons for biking to work because it might be good for you. I’ll try to be concrete.

I am 55. I weigh between 220 and 225lbs, and I’m 6 feet tall. That makes me officially quite overweight. I hate dieting and so I don’t really do much more than try to keep sweets out of reach. Beer is a regular part of my diet, and food is free at my new job. I weighed more before I started biking to work 9 years ago, but in the last year I started biking even more.

My commute to work, since March, is 6.1 miles by the fast, direct, and less-fun route, and I reliably do that in 30 minutes on a bike without running red lights. At rush hour biking is faster than driving. If I am in a hurry I can do it in 26 minutes, though I may end up sweaty (all I need to go faster is to breathe more; the legs just go as fast as oxygen debt allows). Traffic jams are not a problem; I ride through the gaps and go almost as fast. Parking is not usually a problem (we do almost fill the bike cage at work, but less so now that the weather is cooler, and there is other parking). If I instead take the less-annoying route, biking takes about as long as driving, but not longer. Oh yeah, my bike weighs about 65lbs.

Since March, I have gained over a centimeter in circumference in my thighs, a centimeter in my calves, and I’m regularly pulling my belt a notch tighter. Even before the new commute when I was biking somewhat less per week, I still had enough wind and stamina to shovel snow like a machine; I expect it’s rather better now because the new commute includes more sprints that punch my heart rate up a bit.

So. Would you like a faster commute to work, no parking hassles (and it’s FREE), a little weight loss, a slightly smaller waist, more muscles, and enough wind to shovel snow without fear of heart attack? If your commute is like mine, perhaps you should ride a bike. If your commute is about as long as mine but too unpleasant for you to tolerate, have you considered pestering your local government for some combination of better enforcement of traffic rules (if it’s speeding cars that make it unpleasant) or a reasonably sized lane in which to ride your bike (or perish the thought, a segregated path or lane)? Failure to provide you an adequate place to commute by bicycle is depriving you of a faster commute and measurable improvements in your health and fitness.

And do understand, if you want this and your roads don’t allow it, you should be angry. If I had to give up biking to work I’d be very unhappy. Statistics say this would increase my annual risk of death by about 30%. Do you think it is reasonable to live with that kind of extra risk? Do you have any idea how much larger that risk is than all the risks that usually get people all wound up and excited? That’s not an acceptable status quo.

One warning; if you’re out of shape, your first commutes will not be as fast or as fun. It’ll take about a month and a half to get over that, and then there will be gradual improvement for a few years — not necessarily faster, but one day you may find yourself regarding hills as merely annoying, instead of as an obstacle to go around. Eventually you’ll learn to run up an oxygen debt charging up hills and then rest on the downhill, because that is fastest, and because one day, you can.

Anyone who takes this seriously, if you’re looking for a bike, you could do a lot worse than a 3-speed with fenders, chain guard, dynamo hub, and fat tires. The fatter the tires, the better; you’ll be more comfortable, at less risk from potholes and road cracks, and you’ll spend less time pumping up your tires because they’ll hold their air longer. If you’re gung-ho, get a cargo bike, either an EdgeRunner , Yuba, Big Dummy, or a Gr8, or maybe a Kr8 or one of the several other USproduced cargo bikes.

Parcel delivery robots

December 12, 2015

I was thinking about how we would deliver goods in a hypothetical ban-cars world, and realized that people on bicycles carrying stuff are not a bad model for what robots might also deliver on vehicles of modest size. Because we don’t normally see huge deliveries on small vehicles we tend not to think that it’s possible, or even when we do see it shuffle it into the ignorable category of “crazy”. But it is possible and it happens, whether we believe it’s “crazy” or not, and if you want to think about what a small robot vehicle might be capable of, it helps to remember that a human is a somewhat idiosyncratic 250 watt motor, and that a robot running a 250 watt motor and carrying 100lbs of batteries has similar capabilities.

So, what can humans carry on bicycles?

Haley Trike and 400 lbs of sand (video)

a chicken coop

a trailer full of Citibikes

a ludicrously large pile of stuff

a mattress, table, chair, and box

People carrying that much stuff don’t move very fast, but they move, and there’s no particular reason for a robot to travel quickly either; there’s no driver being paid by the hour, and it reduces the risk and severity of any possible crashes.