A 120mph robocar-mostly lane in the off-hours?

I’m here in Newport beach at the Transportation Research Board’s conference on self-driving vehicles. Today in a pre-session there was discussion of pre-robocar technologies and in particular applications of “managed lanes” and what the might mean for these technologies. Managed lanes are things like HOV/carpool lanes, HOT (carpool+toll), reversible lanes etc. Many people imagine these lanes would be used with pre-robocar technologies like convoys, super-cruise, cooperative ACC, Bus Rapid Transit etc.

As I’ve said before the first rule of robocars is “you don’t change the infrastructure.” First you must make the vehicles operate fully on the existing infrastructure. And people are doing that. But we can also investigate what happens next.

Robocars as many envision them do not thus need dedicated lanes, even though some of the simpler technologies might. Earlier we talked about electrification which is a pretty expensive adaptation. Let’s talk about high speed lanes.

Robocars (or any car) would be of much greater interest to people if they could go very fast in them. On one hand, the ability to work, read, watch video and possibly sleep in a robocar will mean to some that trip time is less important than comfort, and they might actually be happy with a slower trip with fewer disturbances. But sometimes a faster trip is very important, particularly on the long haul.

Today people are working hard to make robocars safe. Eventually they should be able to make them safe even at higher speeds, particularly on freeways that were designed for fairly high speeds. Even human drivers routinely see over 100mph on the autobahns of Germany. Problem is if you want to go 120mph outside of Germany , there’s no road you can easily do that on. The other cars, going 65 to 80mph in the fast lane will get in the way, creating an uncomfortable ride and possibly dangerous situations.

Many of today’s “managed lanes” are primarily for use in rush hour, from 5am to 9am and 3pm to 7pm. In other hours, traffic is very light. What if that special lane does not just become an ordinary lane after rush hour, but instead is converted to another special purpose. There are a lot of different technologies that might be able to become viable with such a lane.

The most interesting one to me is high speed. If the carpool lane switched to being the high-speed-car lane at 9:30am, I actually think a lot of people might very well delay their commutes and shift their hours. A one-hour commute at 8am or a 15 minute trip at 9:30am — not a hard choice for many. And lots of people travel mid-day for various purposes.

The high-speed lane would actually mandate a minimum speed, perhaps 100mph when the road is clear. To get in this lane you would need a car that is certified safe at that speed or above. This might be a robocar, but it might also be a human-driven car with sufficient driver-assist technologies to certify it safe at that speed. The lane would probably only be open in good weather, and would probably revert to ordinary status in the event the main road got congested for whatever reason. Vehicles in the lane would have to be connected vehicles, ready to receive signals about changes to the dynamic status of the lane.

There probably would also be a requirement for efficient vehicles. Wind drag at 120mph costs 4 times as much fuel per mile as wind drag at 60mph. These cars would have to be highly aerodynamic designs. They might also be capable of platooning to further reduce drag, though you would want to wait a while to assure safety before platooning at 120mph. You might insist on alternate fuels or even that they be electric vehicles or other low emission vehicles. It doesn’t matter — I think there are a lot of people who would pay a lot of money to be able to go 120mph.

The lanes in general would need to be separated from the main lanes. Most carpool lanes are already like that, though most of the ones in the SF Bay Area are not this style. Ideally they would be the style that even has a special merge lane at the points where entry and egress from the main lanes are possible.

If such a program were a success we could see more. For example, one could imagine adding an extra lane to Interstate 5 in the California central valley and have it be a high speed lane most of the time. The planned California High Speed Rail, which probably will never be finished, is forecast to cost $68 Billion. 2 extra lanes on I-5 in the central valley south of Sacramento would cost well under a billion, and offer fairly high speed travel to those in the valley — faster door to door than the HSR. And my calculations even suggest that aerodynamic electric vehicles would use less energy per passenger-mile than the HSR. (Definitely if they are shared by as few as 2-3 people or when designed for a platoon.) These teardrop-shaped cars would also be much more efficient than today’s cars when they slow down and ply the ordinary highways and streets.

It is not trivial to go 120mph in a robocar though. Your sensors must be long range so you can stop if they see something. If you want to build infrastructure, here is where the road might have sensors which can report on road obstacles and other vehicles to assure safety. If you’re building a whole high speed lane this is not an issue. The first rule of robocars is written to avoid needing new infrastructure to do ordinary driving and get most places — not to prevent you from taking advantage of new spending that justifies itself.

My take on Robo cars and

My take on Robo cars and human culture:

"Connected cAR: Becoming the Cyborg Chauffeur"

http://thesocietypages.org/cyborgology/2012/03/01/connected-car-becoming...

managed lanes

Interesting. I'm dialing in for the webinar feed of the conference today.

I have the sense that folks are struggling with ways to ease into robo-cars; and managed lanes provides one way to control their deployment. This seems to be a little different than your assertion that it's 'what's next'. Anyway, if you have a robo-car that can operate in normal driving environments, and you add in a little connected vehicle vodoo, I don't know why you'd need to modify the infrastructure for a managed-lane approach.

Looking forward to the sessions today. Arghh, they're 35 minutes late!!

Robocars instead of high-speed rail

Robocars are a much better fit for California lifestyle than high-speed rail in so many ways. It lets us keep the "I can drive anywhere, anytime" lifestyle, it is high-tech, individual. Rails were a good fit for densely populated countries with good public transportation infrastructure.

Is there any chance that the high-speed rail initiative might morph into a robocar initiative? I'd vote for an initiative to do this.

120Mph robocar would not be a win for me. It is only 50% faster than 80mph, which is achievable if you are careful, and there is no traffic.

love this

I've fully switched my allegiance from High Speed Rail to Robo cars in the last 12 months. It's obvious that something needs to be done but spending $68B on HSR would not have nearly the impact of investing the same amount of money (or even half) in robo cars. I'd love to see Google (or anyone) do a series of studies that compares robo car technology w/ competing options (current tech, HSR, etc...). If our intuitions and your early calculations are correct, these kinds of full-scale studies would killer HSR even faster and turn the public's attention toward Robo cars.

This just resonates on every level - from high speed lanes and increased energy efficiency to safety gains and low initial infrastructure costs. Start adding in things like decreased insurance rates, more productive commute time, and a dozen other positive externalities and this becomes truly compelling.

Thanks for your work on this! We're on the cusp of something here, can't wait to see it develop over the next decade and have a robo car of my own.

-Chris

High Speed Intersections

I don't think Robocars should have to stop at stop signs or stop lights if there are no mentally controlled autonomous people or animals present.

Robocars can just go through intersections at full speed as long as they leave a few inches for the cross traffic.

But Robocars should stop and wait for humans to make their required stop.

Yes, I agree

I wrote about new ways to do 4 way stops of this sort some years ago, even without robocars. In that a car equipped with a radio could approach a 4-way stop that was computer controlled and had sensors. That car could request the right to blow right through it and would see a green in the car, or a red if they have to stop. If somebody else was there you would have to stop. Cars without the radio would have to stop.

High Speed Intersections

Agree with Carl Pag, but should not forget human presents in traffic, people must travel without being stopped by the robocars.

High speed cars

A recent test of the ``300 mile'' version of the Tesla Model S showed that it went about 238 miles in real world mostly 65 MPH driving. If you want to nearly double that speed, you're probably looking at 60ish miles of range on whatever battery pack Tesla is currently using in its longest range vehicles. A half hour of 120 MPH driving followed by an hour of quick charging may be less time efficient than an hour of 65 MPH driving followed by 15 minutes of quick charging, even ignoring the safety issues and energy efficiency advantages that 65 MPH has over 120 MPH.

A viable 120 MPH electric car for long trips is therefore going to require either significantly better energy density than current batteries, or battery swap technology, or overhead wires, or perhaps faster quick charging.

Absolutely

Electric is not so viable for high speed long distance at present. For that, the green way to do it would be biofuels. However, there is reason to believe that 20 years time will generate better battery chemistry with much more energy density. Get to double the density and planes start becoming viable as well as faster cars with more range.

As noted, there are other options — battery swap etc. Fast charging will not make sense except for ultracapacitors, but they may arrive as well. Not out of the question if this is popular would be refueling while moving like planes do, or battery trailers rather than battery swap.

But I suspect the most viable early option for a green high-speed, long range trip is biofuels, such as algae based diesel. Ditto for aircraft. Batteries make more sense for the intra-urban trips.

I will add, however, that if you are willing to talk not about a tesla, but a single person, lightweight, ultra-low-drag vehicle you can do far better at total drag and make a longer range, high speed electric battery vehicle. Tends to require a too-reclined posture to do it perfectly, and facing backwards is also ideal here (teardrop shape.)

drag vs weight and crashworthiness and battery powered aircraft

The battery pack in the floor of the Model S is not terribly thick. I bet it would be possible to build a car with five of the ``300 mile'' Tesla battery packs stacked one on top of another, with something that otherwise looks a lot like a stock Model S on top of it, with the drag less than doubling in the process vs a stock Model S. Perhaps if you connect each of those packs to its own Tesla Supercharger, you could even get decent quick charging for significantly faster than 65 MPH operation.

Crashworthiness for increasingly fast transportation is still going to be a concern, though. Crash forces are proportional to the square of the impact speed. Tesla did claim, prior to getting their crash safety rating for the Model S, that they thought the frunk instead of an engine made a five star rating easier for them, but I suspect there's still work to be done to improve crashworthiness if we really want 120 MPH automobiles to be accepted by everyone.

Another interesting data point will be the overall public reaction to the 85 MPH toll road in Texas, once it's been in operation for a while. Whether they have nasty crashes will be interesting to see.

Are backwards / reclined single occupancy vehicles any more energy efficient than a conventional 60ish passenger train car (perhaps with the aerodynamics of a modern train) at the same speed?

Traveling reclined and backwards works just fine if you were planning to sleep anyway.

I've been assuming that ~500 MPH travel is going to continue to need something that looks an awful lot like the fuel refined from what we've been pumping out of the ground, and that that may define how much oil we refine once batteries become popular. The Trainer, PA refinery that Delta Airlines bought has been converted to produce as much jet fuel and as little gasoline and diesel as possible, and apparently that works out to 1/3 jet fuel, 2/3 gas/diesel. There are some piston engine airplanes that use gas, but that's tiny compared to the amount of jet fuel consumed. So some automobiles or farm tractors or something are presumably going to have an opportunity to use the cheap waste products of jet fuel refinement if we get to the point where batteries and solar are cheap enough that gas would otherwise seem not worth using, if airplanes still use jet fuel.

But if the total amount of crude oil being refined drops to 1/3 of what is refined today, the price per barrel will likely drop dramatically, too, which reduces incentives to seek alternatives. Aviation is very conservative; aviation gas is the only fuel still using lead. The RoHS standards leave safety-critical avionics exempt.

The Dreamliner is the first airplane that can do non-stop flights between Australia and England with a reasonable passenger load. I think that demonstrates that if you want to completely replace jet fuel with batteries, you're going to need batteries with the same energy density as jet fuel, and I was under the impression that that was far from certain.

Virgin Galactic may eliminate a lot of the jet fuel use on long haul flights if they're successful (along with making the longest flights under two hours); I think they're using rubber as part of their fuel, though, and that probably ends up being oil-derived.

Pipistrel makes some battery powered motor gliders already. The range is probably 40ish miles with the bigger battery pack, given the 40:1 glide ratio and the very rough mile of altitude gain with the big battery pack, if you can't take advantage of updrafts. I think in the NASA competition they demonstrated more than 100 miles on a charge with a one-off design and taking advantage of updrafts along the way. I suspect this sort of motor glider technology is great for local sightseeing flights, in that conventional airplanes are loud, and the motor glider can be pretty quiet, but it's not the right technology for fast, all weather long distance travel.

Five packs

That’s not that practical. That much battery is big, heavy and hugely expensive. You add all that weight and you need more battery to carry the weight.

Alas, for now we need either new battery chemistry or super-fast ultracap style recharge. Otherwise it’s liquid fuel but that’s not that bad if you can move to other fuels for urban because now you only need liquid fuel for intracity, and you need much less of it, and can use more of it with biofuel.

Five packs

I'm pretty sure that at 65 MPH, most of the energy consumed by a Tesla Model S is overcoming wind resistance, and is not directly proportional to the weight of the car.

http://blogs.wsj.com/drivers-seat/2012/07/06/review-tesla-model-s-electr... notes that the battery pack is less than five inches thick, which is a little more than I'd been thinking it might be; adding nearly 20 inches to the height of the vehicle would certainly add some wind drag. On the other hand, I think the Tesla Model X is expected to some somewhat taller than the Model S while only adding 10% to the energy requirements; while there probably won't be a 20" increase in height in the model X, I still suspect that a model S with four extra battery packs added for a total of five is going to require less than double the energy of a stock Model S to move a mile. And these extra battery packs might still leave the modified vehicle not weighing significantly more than half ton (nominal cargo capacity) pickup truck.

That much battery

So much battery is not just heavy and bulky, it’s expensive. You now have a car where the vast bulk of the cost is the battery.

Once you get to that level it becomes more efficient, in spite of the inconvenience, to ride a shorter range vehicle half the distance, and either stop to battery swap or get out and move to another vehicle. The vehicle is cheap, it’s the battery that costs in this case.

But I think for now better to have biofuel or even natural gas (which is what is making most of the electricity in California anyway.) NG is bulky by volume but its energy density by weight is quite good, way better than batteries.

Natural gas

The MBTA in the Boston area has a bunch of compressed natural gas buses. They are the loudest buses in the fleet, which makes them not especially well loved, and at the rate things are going, with New Flyer claiming they will sell battery powered buses that make good economic sense within a few years, I suspect the MBTA is going to end up replacing them with battery powered buses when they reach end of life.

Natural gas might still be a good choice for 120 MPH vehicles, maybe, but it's not clear that we're going to end up with roads where they're legal in the US.

I suspect even a stock 85 kwH Tesla Model S has the battery pack as the majority of the cost of the vehicle. There's the theory that the battery cost will come down with time, but it may turn out that that process will also have the side effect of improving the energy density.

Drag vs Speed

Unless you are traveling in a vacuum, traveling at a high speed is always a loser no matter the method of propulsion you use, because drag increases as the cube of the velocity.

http://www.inference.phy.cam.ac.uk/withouthotair/cA/page_255.shtml

The square

Overall drag does increase like that but total energy per mile only goes up with the square. That’s not trivial of course, which is why the most efficient high speed travel has involved various tradeoffs.

  • Trains can be long and thin, which is good. They travel in dense air, which is bad
  • Planes have broad profiles due to their wings, but they travel up in thin air, which is good.
  • Cars tend to do worst, though they are easier to design into the most aerodynamic shapes. If they can form trains it can help.

So the high speed car is not the winner in overall efficiency, and will not likely ever be efficient at really high speeds. They are, however, the most convenient and that actually has something to do with efficiency, especially in robocars. Trains and planes run on schedules, so they often run less than full. Their efficiency win is highly reduced if their load factor is not high. It’s possible for robocars and robovans which always run full because they are sized to the load to do pretty well in efficiency. Ie. if only one person is going, use a very small and thin teardrop car. If 10 people are going, put them in a 10 person van. If nobody is going, nothing goes at all. (Though some vehicles may have to move empty at low speed for balancing.)

Fully loaded trains are the winner at present, though if the electric plane becomes a reality (due to a breakthrough in energy storage) there is the potential to fly at super-high altitudes because you don’t need oxygen to burn the fuel, and the potential for smaller wings since you can land VTOL with high torque electric motors.

The problem is to get fully loaded trains, you must both plan well and not make the trains too frequent. (You must also not make them too infrequent.)

Similar Technology

Trains and cars are always less energy efficient when they travel at higher speeds given similar technology. This is where robocars come it. What is a more efficient use of your time? Driving manually at 60 or riding in a robocar at 30? Driving at 60 time is mostly wasted. Riding as a passenger at 30 can be used for work or recreation.

Efficient batteries would be great, but given a cheap source of electricity, you can convert the electricity and air and water into Ammonia for fuel and you only have Nitrogen and water as an exhaust. Ultimately rapid travel will be ballistic where the vehicle only has to expend energy at each end. I don't know if it is true, but I read one time that a jumbo jet flying to Australia actually expends more energy per kilo of cargo than it would take to put a kilo in orbit.

Of course the ultimate system would be maglev trains in evacuated tunnels built in catenary curves, but that is more 22nd century technology.

Slower but productive

This is somewhat true but not entirely.

If the question is taking HSR at 300km/h (where you can also sit and relax or work) vs. a car at 160 km/h (where you also sit and relax or work) then the car wins over short and medium distances because it goes door to door, without schedules or stations. Which is to say it wins on total time, not just convenience. However, on the long haul, the train starts to win.

If the car is only going to go 80 kph to save energy, it now loses on time for medium trips, and must entirely win on convenience.

Yes, suborbital will be cool when we can do it.

I want to do an analysis though of various systems of transportation with different vehicle sizes. Large size vehicles (train, bus) are efficient when full but often not full. Cars are less efficient when used solo but also efficient when full, but because they have other advantages and can leave on demand, they may be able to send always full with minimal delays, resulting in greater efficiency from the less efficient vehicle.

nearly empty transit trips

http://www.humantransit.org/02box.html claims that if you have to pay developed world wages for a driver, the total cost of operating transit is mostly proportional to the driver's time, and that seems to be why transit agencies tend to run relatively large vehicles for off-peak trips (and for that matter, for peak trips, instead of operating smaller vehicles at greater frequencies). (PATCO seems to be an exception, in that they apparently do run shortened off-peak trains to save energy.)

Obviously, robocars have the potential to change that, and will likely lead to on-demand carpools replacing a lot of the lower density fixed route bus service. An interesting question here is whether a Google Carpool service that worked a bit like calling a taxi, except that you use a smartphone app to request the service, and you get a robocar instead of a human driver, and you might share the car with other riders, could charge unsubsidized fares that would be competitive with existing subsidized bus fares. If yes, then Google can trivially put the transit agencies out of the coverage-focused part of their business, and governments will be happy to stop subsidizing the empty buses; otherwise, for routes where Google Carpool is still cheaper than bus fare plus government subsidy, there may be challenges in trying to get the government to subsidize Google Carpool but only in the areas that have traditionally had bus service.

robobuses and robovans

I think the future will be robobuses and vans. There won't be any fixed routes. The routes will be adjusted dynamically based on the demand. People will put in their destinations and arrival times and they will get and get a SMS message with their pickup time. They will have smaller vehicles to handle the off-peak demand.

The problem with trains is that they are using a 19th century model for a 21st century problem. Robotrains should have a motor for each passenger car, so that each car can leave as soon as they have a full load. That reduces the problem with empty cars and people can travel any time they want. You can tweak the algorithm to allow cars to leave with less than a full load if they have been sitting long enough. We would continue to use conventional trains for cargo.

I notice the Elon Musk has proposed a system of supersonic tunnels. The biggest problem I see is that the tunnel cost seems to be a couple of orders of magnitude lower than what I would consider feasible. After what he has done with SpaceX, I willing to listen to what he has to say.

http://www.businessweek.com/articles/2012-09-13/elon-musk-the-21st-centu...

Group transit

Yes, trains should leave on demand, but most train systems are not built with offline stations unfortunately so trains can’t bypass stations or go around other cars. Trains are designed to use very long (multi-minute) headways, so tiny short trains are not popular with the safety engineers, as they need shorter headways. Trains can’t avoid collision by steering. Trains also like to be long because there is less drag per passenger if you have less frequent, longer trains, for better energy use.

The budgeting of transit is complex. Most transit agencies can’t afford to have a fleet of different sized buses, though they can have different length trains if not for the reasons cited above. They can’t run lots of small vehicles at rush hour as they don’t have the staff and can’t hire staff just for rush hour with no work in the middle of the day. (Robocars fix this one.)

Also, often the vehicles and infrastructure come from federal grants, while the drivers and energy come from local money.

On-demand vans and small buses are indeed efficient, but on-demand single person vehicles are also surprisingly efficient, and at the same time offer door-to-door without stops for other passengers, privacy, customization to the individual and many other seductive things. I think people will go for private vehicles unless the roads don’t have capacity to handle all the private vehicles. Yes, it seems “so easy” to notice that two people are going on the same route, but you would be surprised at how even the little things like tiny diversions etc. will cause lower customer satisfaction. The one big thing that larger vans have is the ability to stand up and stretch because you can afford the drag of a taller vehicle if you have 10 people in it. You can start to afford things like toilets etc. too.

transit geometry

I'm pretty sure there are some transit agencies that manage to pay part time hourly workers to work only during the morning and afternoon rush hours, so I don't think that's such an issue. It's not a great jobs program success, but people sometimes consider that an improvement over being unemployed.

http://www.humantransit.org/2009/11/minneapolis-unlocking-downtown-with-... claims that a single lane busway with no passing capability can handle 60 buses per hour, and when you have two lanes (one for buses to stop, the other for passing), 180 buses per hour works. 180 vehicles per hour is still not going to support single occupancy vehicles. That does seem to lack data on how many vehicles you're likely to get achieving good speeds through the passing lane if they never stop, in addition to the 180 vehicles per hour that do stop.

Trains of different lengths cause their own headaches. One of the MBTA's excuses for only being able to have two trains per hour arrive and depart at each dead end platform track at South Station is that the trains of different lengths become non-interchangable. When combined with single track segments that can force long layovers at South Station, that can become challenging. (They acknowledge that other agencies have been known to operate three trains per hour on dead end platforms; and other sources suggest that four trains per hour is achievable.) Additionally, typical US commuter equipment has power cables and brake lines that have to be manually disconnected before cars can be uncoupled, and for safety reasons blue flags need to be placed at the end of the trains before someone can disconnect the cables. This contributes to labor costs that may make train length adjustments less worthwhile.

In the MBTA's case, layover facility space is also limited, and that hurts energy efficiency. It appears that many commuter rail lines may have crossed state lines up until the point when the railroads went bankrupt, and then when Massachusetts started subsidizing commuter rail and the adjacent states didn't, routes were abruptly truncated, without new layover facilities magically appearing in the logical places. NIMBYism plays a role here; the current Haverhill Line layover facility, somewhat near Haverhill but somewhat to the south, doesn't have space for one of the trains that ought to spend the night there, and the neighbors don't want that expanded. There may end up being a layover facility built in Plaistow, NH (which would extend commuter rail from Boston into New Hampshire for the the first time in decades) to address this, but that may end up with its own NIMBYism (along with the challenges of working out the funding).

In the Washington, DC area, where the commuter rail agencies don't own the mainlines they use, there is much less off-peak and reverse-peak service, and more willingness to build adequate layover capacity, especially on the lines owned by freight railroads. (Amtrak owns the track for one of the MARC lines; the others are owned by freight railroads.)

Bus throughput

There is a difference of course in what you can do with old trains and rolling stock and what might be done in the future. While a bus might not be able to do the 2 second headway of cars (around 2000 vehicles per hour) they can do a lot better than 180 per hour depending on how and when they are stopping.

Though if we note that wide-gap convoys can do about 7,000 cars per hour, at 4 persons per car that would be 28,000 people down a lane it you somehow filled all the cars. At 60 buses with 40 people per hour that’s only 2,400 people per hour. At rush hour this is done but sadly the average bus in the USA holds 9 people.

There’s no question you could build a very interesting transit system with robotic vans and buses. I suspect that will happen in some of the most dense cities, and older cities with limited streets in their older districts. The challenge is that there will be no desire for that system outside of rush hour because the streets will have the capacity to give everybody private vehicles, and I think those private vehicles can be very cheap to operate, and they will be highly desired.

So to get the fancy robot bus system (combined with legacy trains) you need to work out how to finance it only at rush hour. You may be able to do this just by charging appropriately so that it’s very expensive to travel at rush hour and sharing is the only economical thing to do for most. And you can make the robotic bus system almost as good as private car so it will not be hard to get people to use it.

I imagine a combination of private and shared vehicles. A private vehicle comes to your door and takes you a modest distance to a parking lot somewhere. In that lot is a waiting van or bus. A dozen other people, all going roughly the same direction as you are also arriving simultaneously — it’s well timed. You wait no more than a minute or two, and get into the bus, and off it goes to somewhere not far from the various destinations of the people on it. The bus itself goes to another small parking lot where a dozen single person vehicles are waiting. You transfer and off they go to the direct destination. Door to door, with short transfers — about as appealing as transit can get.

robocarpools, and merging across high density lanes

The smartphone app to order a robocarpool can also give you options to pay more to avoid changing vehicles, or to get a discount if you do change vehicles. Thus, people with lots of luggage going to the airport can pay a bit more to avoid moving that luggage unnecessarily, and those who just want get to their destinations cheaply can fill in the extra space in those vehicles for part of the trip. Likewise, discounts can be offered for being willing to wait longer at a connecting point, or for walking a bit at one or both ends of the trip. Some people may care about 60 second transfers, but transit advocates have been known to claim that 15 minute headways are good enough, which implies that less affluent commuters may willingly tolerate an average of 7-8 minutes of waiting. Budget travelers with a lot of luggage may be willing to let their trip take an extra 15-30 minutes if that will save them money, but may not want to have to transfer.

How much flexibility is there for merging across a 7000 car per hour lane? Does that really scale to highway trips that might only be 5-20 miles long to the point where the middle lane can have 7000 vehicles per hour and cars in the left lane can still merge over to the right for exits?

Price and convenience

The question is whether the price difference is that much of a savings.

I predict that small single-person vehicles will be quite inexpensive in the future. The electricity to run them will be trivial — sub-penny per mile — so the real cost of hiring one will relate to the depreciation and time value of the vehicle, but that will also be just a few cents per mile.

As such, if your trip is going to cost $2, would you wait 5 minutes to save a buck? Not in the affluent world. If it would save you that much.

Yes, 7,000 vehicles per hour (or a headway of half a second) requires a heavy density of cars able to do that, though you can still merge if the system is prepared for it. We would never do this except at rush hour in more planned traffic. Of course with 1.5 meter wide single person cars, you can have 14,000 vehicles/people per hour in a lane. In the extreme. Though if you do combine, and start having 4 person vehicles that are filled with that headway, it’s a lot of people.

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