Recently had the experience of an impatient driver running a red light behind me, then pushing me and angrily waving at me in the rear mirror to speed up. When their was a two lane part he rushed past me. But the next few kms were trafficlight heavy area's all two lane, but no matter what he did, he never got much more than a few 100 meters in front of me. His angry-stressed- and frankly very dangerous driving got him to his destination 5 seconds earlier on a 15 minute trip than me, just patiently flowing with traffic. I tend to believe, these people are in a rush to the end of their lives, but sadly also that of others.
I tell my kids that the reason why some people drive too fast, is that they REALLY have to go potty. We should not be angry at them, only be disappointed that they didn't go potty before they got in the car.
Some of us just shouldnt live in crowded places. If you actually want to get somewhere fast in a city park somewhere and walk more aggressively than most people drive you'll beat out everyone including the vehicles every time
As a cyclists I can second that. Many car drivers are willing to risk potentially lethal maneuvers for 10-20s gain (or none if we meet at the next traffic light).
@@P7777-u7rI recently drove a car in germany with a trailer, so limited to 80km/h (very relaxing, always on the right lane). I noticed that packs of around 5 cars bunched together were going maybe 160km/h (illegal on any public road outside of german I believe), with 2-3 trying to go 180 or so. They were so close that some cars went to the other lane to bleed of speed when the first car had to break due to traffic, construction or whatever. So I would modify your statement slightly: some people aren't made to use machines as dangerous as cars (at least not without more mandatory safety features).
I used to drive public transit buses. Our routes and timetables were poorly designed, seemingly with zero traffic in mind. My stress when driving dropped considerably when I had the realization that the only thing I had control over was the quality and safety of my driving. Everything else was a matter of circumstance, and being stressed or not over would do nothing to affect the situation.
Buses should really have dedicated ROW with separate detection and signal priority, otherwise they're a bit of a waste of time anywhere where there's congestion. Then once they have dedicated row they should probably just be trams. I imagine they'd be much less stressful to drive.
@@skylarius3757 if there's one car lane and one bus lane, and we need a (protected ideally) bike lane, let's get rid of the car lane, keep bus lane. bus + bike moves far more people than car + bike and is better in other ways too
"Gone so far down the urbanist rabbit hole that you found my channel." Ok, I feel a bit attacked. Its not my fault youtube keeps recommending me obscure urbanist related youtube channels. I do really like your channel though. Has a lot of unique insights, and I really appreciate that.
Coast to a stop is great for fuel economy (on non-electric/hybrid cars), but accelerating slowly to save fuel was mostly a thing on old carburetor engine cars (I.E. approx 40+ year old cars) as they weren't as good at having the optimal fuel-air mixture, especially during acceleration. (Technically a "gasoline engine" (really "Otto engine") is the most effictive at the point where you reach max power at a given RPM. I.E. pedal almost to the floor at the highest possible gear. There are a lot of caveats though, like for example cam/valve timing and whatnot, and modern (as in the last 20 years or so) cars have variable valve timing which complicates things). Drivers ed in for example Sweden teach to accelerate swiftly and when accelerating fast enough skip gears. (Drivers ed is almost always done for manual transmissions). The reason is that this is actually more efficient.
@@Thesecret101-te1lm There's a guy from the UK who tested this thoroughly. Accelerating gently increases fuel economy as well. The channel name is Conquer Driving and the video's title is "Can Fast Acceleration Save Fuel?".
@@Thesecret101-te1lm Doubtful. My own fuel economy shows as much when I accelerate gently in my 2019 Nissan Sentra. If I gun the engine to get it to the speed limit, the fuel economy is less than 7 mpg. If I barely touch the accelerator pedal, I can get it to 20 mpg. I don't do it on busy roads.
@@ddrhazy i think the idea is u are in the less efficient acceleration portion. U spend slightly more time at consistent really efficient speed. Idk tho would need testing
It is not high speeds that leads to signals. It is the increase in access points and traffic generators that require changes in assignment of right of way.
@ I agree that number of crossings with streets is main factor, what I meant permission for higher speed limits causes even more hardships for drivers to turn into such stroad, so usually, the most primitive solution to this problem is implemented- traffic lights. The real deal is a proper division of traffic into roads and streets like in the Netherlands
@@paweuutrzrzrz2699 Speed only matters when the road is not at full volume. If the road is at full volume, then it doesn't matter how fast the traffic is going. Perpendicular drivers can't cross or enter. Controlled junctions are added when roads are at full enough volume that this state occurs enough to be disruptive.
I finally found an urban planning/transportation youtube channel that doesn't just make 50 videos on "car bad" with points that everyone else has covered already, and instead provides actual new content
@@davidmendelsohn1583 Considering how dangerous they are 'car bad' for personal transport just seems true - with only a little nuance in that areas that can't be made moderate density kinda have to rely on them.
you will get very few converts here in the US. A lifetime of being told that we are special and individualistic has taught most people that while driving they are an island in competition with everyone else on the road who is just in their way and that the goal is to always get in front of as many drivers as you can no matter where you are. Oh, at it has told us that it is cool to drive super loud cars very fast around other peoples neighborhoods in the middle of the night. Go USA #1!
IMO, the behavior you describe has nothing to do with the cause connect it with. Some of it is quite the opposite. The idiot drivers are acting out because they can do so rather anonymously after being forced in most social situations to conform or be ostracized. There’s not as much respect for individual rights as there used to be. Now it’s all about identity and tribe. The loud mufflers are totally tribal by the way.
@@nunyabidness3075 I dont like the (anti?) "mufflers" that make an engine louder than it would be on just a straightpipe but having a stick up your ass about noise other than during eepy hours is also tribal. For example if you move out to the sticks and complain that the trucks and dirtbikes arent EV quiet youll be laughed out of there by everyone.
@@Descriptor413 Designed so well that bus drivers can snap and change lights? (I'm sure its just transit signal priority, but I thought it was funny how he snapped like that)
It is sensor based, but sometimes even high priority has to slow down for a second. I play this game in the late hours on my bicycle. Pure fun, only one light forces me to a full stop every time. Think I am going to write a big complaint to the municipality...
@@Sullyville It may seem like magic, but it's actually due to the efficient traffic management system. Especially at night, when you approach an empty intersection, the traffic light turns green just before you arrive. That's why I love driving in the Netherlands.
You should repeat the Douglas boulevard scenario but the driver incrementally decreases their max speed for each trial. Make a plot of average speed vs max speed to visualize the non-linearity.
I used to be a pretty aggressive driver when I was younger, weaving between traffic to try and get to my destinations quicker. Over time, as I got more mature (and became less of a self-entitled prick), I came to realize how little difference it made to my travel time, and how much worse it was for my mental health (making myself stressed, frustrated or angry for literally no reason) and fuel economy/wear-and-tear on the car. Thankfully, I'm a better person, and consequently a better driver now.
Ive often wondered about this, figuring that increased speed must improve capacity, but get balanced out by greater following distance. It was really nice to see you sit down and go through the numbers. Subscribed!
Love you point about not being an "urbanist" and the service your channel provides. It wasn't long after I discovered NJB that I thought, "ok, cars are bad, but I want to actually argue with engineers about why things need to change in the US." I wanted to know the actual math. Thanks for providing this side of the narrative. I think you're one of the few TH-camrs doing it.
Putting engineers in charge of decisions that are political decisions not engineering decisions is part of America's problem you shouldn't have to argue with an engineer about this the engineers should be told what to build and their job is to figure out how.
@@supermanifolds You can't order someone to beat physics. So no, engineers need to have a say in things. And by the way...how do we determine what our orders to engineers look like? Mind you, it is not a theoretical question. In Canada, we see exactly that kind of thing being played out right now. A politician, probably with reasonable backing by his voters, orders bike lanes to be removed.
@@supermanifolds Whereas I think these decisions should be made by engineers, not politicians. Maybe politicians can set general goals, but as they usually do not understand how these things work, they should be as far from the actual decisions as possible.
Trust me, there's no point arguing with engineers. The math they work off isn't based in reality, and they make it up to give the result the people holding the purse strings want. Traffic engineering isn't engineering anymore than homoeopathy is medicine.
Filming your daschcam footage from inside of a bus? You are an urbanist, my friend. (Just discovered there is no bus emoji. Work of the "car conspiracy?")
Driving aggressively >might< get you to your destination 'sooner', but the amount of energy expanded is exponentially higher and the recuperation time afterwards will be a net loss relative to any travel time gain. I wonder if there's any scientific studies into this phenomenon.
In the Netherlands because the vast majority of traffic lights are sensor based, aggressive driving in some places can net you a time benefit. Also, because you may be able to squeeze yourself into an earlier traffic light cycle. But this varies a lot depending on the location, traffic volume, and configuration of the lights and such. It's also just plain wasteful.
Hi Celis C, what are trying to do is pure science!, all your need is careful critical oversight of the information you use for your calculations and sensible reliable observations, do your best to exclude subjective assumptions and then allow your brain to think to all through, at some point it will offer the outline of an explanation that correlates with your observations. the next part is to formulate what you come up with into a useable hypothesis which you can then test, the easier it is to test and thus refute the better it is!. All you require for total refutation is just one bit of empirical evidence that confounds the hypothesis which you then abandon and wait for a new one, each time you go through this process you learn another thing that is not true, a properly proven fact, this way you increase your total body of knowledge. In this particular context we can start with a number of scientific principles which we accept as established, these include the given assumptions that the greater the speed of the traffic the more vehicles pass any given point at any given time the greater the total traffic flow, one reason for this is that while the lenght of each vehicle does not vary with speed the distance between them does, in fact with any given number of vehicles of any specific length there is a minimum threshold below which there is no space between them at all at everything stops, it then takes a finite amount of time for them all to start moving again further reduce the flow rate. From all this it follows that fewer shorter vehicles all travelling at a constant speed with the same minimum space between them would be optimal, that however is the 'perfect' state scenario which for very good reason can never happen because reality includes variation and diversity, these factors are much more difficult to enumerate but that is not needed!, allm tht is needed is effective traffic control that reads the flow rate and as it drops reduce the vehiclers allowed on that road, when the flow rate rises again near to the proximate optimal threshold more vehicles can be allowed to join. From that in situations where the backlog at the access ramps become too much other measures must be applied, there is an obvious range of options all the way from reducing the size of vehicles to adding more lanes and building new roads or as a last resort providing adequate public transport using its own part of the road network so that travellers sitting waiting in a car for a space on the road will see bus after bus not full of passengers passing them and they can make their own choices. The manner in which each of us choose to drive has little or no material effect on the whole traffic pattern, it might be 'true' that if all drivers applied exactly the same style we could get more traffic on the same roads but they don't and they won't all do the same as each other. Regardless of political ideology we should be just rational and practical. Cheers, Richard.
@@wewillrockyou1986 I don't think he just means fuel energy. Aggressive driving makes you angry and frustrated, which costs so much more mental and emotional energy for only a minute gain on a 30 minute trip. I always laugh at cars on the high way, push me to the side, speeding up only to be stuck behind the next car they have to push again. In the end they exit the high way only a minute before me, but are a thousand times more frustrated....
In the UK, the Highway Code requires driver to drive within their stopping distance which is a quadratic relationship to speed due to Kinetic Energy being proportional to the square of velocity. In you model you used a linear relationship. If you had used the quadratic relationship you would got the answer that slower speeds always increase capacity. You can see that in action in reverse: when traffic increases speed naturally decreases (congestion) to accommodate the need to increase traffic capacity.
A moving car does not suddenly stop from one moment to another. It is bound by inertia and will slowly come to a stop in a reasonably similar way to the following car. Your distance only needs to account for your own reaction time, so 2s is reasonable. And at least here in Germany it is explicitly coded into law. Probably in the Netherlands as well. Looking at existing traffic out in the world, 2s seems like a gross overestimation. At highway speeds this should turn out to around 60m, but I often find traffic on the left lane too bunched up to even attempt fitting a 5m long car into the gaps ;)
Except in motorway conditions this is tricky. The 2 seconds rule is to account for delays due to reaction speed, but also taking into account that the car in front is not stationary and has its own stopping distance. In reality it would already be great if people kept the 2 second distance on the motorway. For urban traffic the stopping distance is more important, but when adding reaction speed 2 seconds is a good rule of thumb for normal conditions.
Kinetic energy going up by the square of speed is not the reason why stopping distance goes up by the square of your starting speed. That correlation is a myth! Stopping distance can be calculated by multiplying the time it takes to stop, by the average speed. And increasing the starting speed increases both the time _and_ average speed. For example, lets assume we have a car that can brake at a constant rate of 5 m/s/s. If we start at 10 m/s, then it would take 2 seconds to come to a stop, and our average speed would be 5 m/s. So our stopping distance would be 2s * 5m/s = 10 m. If we start at twice that, 20 m/s, then it would take twice the time (4 seconds) and our average speed would also be doubled (10 m/s). So we get 4s * 10m/s = 40 m. If you want a visual, then we can plot this on a graph with speed on the vertical axis, and time on the horizontal. With a constant rate of deceleration like in the examples I gave, then we'd get a straight line with a downwards slope. And the area would be triangle shaped, hence why the average speed is just half the starting speed. (And I'm ignoring drag and the slight lift most cars get from being airfoil shaped. As they roughly cancel out.) And _most_ land vehicles generally have close to constant deceleration when braking. As the resistance from friction (both in the brakes and tires traction) goes up with speed at the same rate as kenetic energy does. And perfectly cancels it out, making the exponential nature of kenetic energy a non-factor in stopping distance.
@@PauldeVrieze The car in front might not instantly stop but another car might pull into your lane or a pedestrian might step out. Either way Rule 126 says "You should leave enough space between you and the vehicle in front so that you can pull up safely if it suddenly slows down or stops. The safe rule is never to get closer than the overall stopping distance (see Typical Stopping Distances diagram)". The stopping distances in the diagram show reaction distances increase linearly with speed but the braking distances increase by the square of speed.
@@vulduv The official braking distances in the UK go up according to a square law and it is those distances together with a linear thinking distance that UK drivers are required to leave between them and the car in front. At 32 km/h the thinking distance is 6m and the braking distance is 6m giving an overall stopping distance of 12m. At 64 km/h the thinking distance is 12m and the braking distance is 24m giving an overall stopping distance of 36m. Whatever you might think, these are the gaps that UK drivers are required to leave.
Im currently following a course on Cooperative Autonomous Driving at my (Dutch) university. A large focus currently is on improving cruisecontrol to decrease space between cars and decrease the chance of traffic jams. Very interesting stuff
The formula F = s*d*t is misleading. The units don't match up (s is in distance/time, d is distance, t is time/time (seconds per hour)) which multiplies to distance^2/time, where you actually want 1/time (rate of cars per unit time). But when you do the formula example, you express following distance as "1 car per 27.8m", which is actually _dividing_ by following distance, not multiplying. So it should be s*t/d. If this is some traffic engineering formula, then maybe this discipline should get better with tracking units. Because it seems like you're treating the quantity "following distance" as an _inverse distance_ (units 1/m) rather than a distance, which is just confusing. Also, having "t" as a unitless quantity (time / time) is also deceptive. Why not just say that the car capacity rate is F = s / d, which gives you units of (time)^-1, and then just adjust the units accordingly. So if you have s in m/s, and d in m, then you get cars/second, and then just multiply by 3600 to get cars/hour.
It is not misleading, it is just wrong. The 2nd parameter is nonsense. "Following distance" is totally inaccurate. The parmeter should be the inverse of headway, or following distance. And the 3rd parameter should simply not be there. The equation is simply flow = speed/headway. With both using compatible dimensions. I.e metre per second and metres.
It’s great to explain these mobility concepts. Would be good to also explain how travel time is only marginally reduced as speed increases (between fixed points). And energy increases exponentially…
A two second following distance is ok at 30 kph, but at highway speeds (90+ kph) the following distance should be 4-5 seconds. So slower traffic might end up giving a higher capacity,
Suggestion for future topic: What are the actual effects of "green wave" traffic lights? I.E. ensuring that a bunch of traffic lights along a major roads are green at each junction for traffic that isn't turning? Also re 1+1 roads (without overtaking abilities) v.s. 2+2 roads: I would say that it's not just about aggressive driving and whatnot. It's also about calm driving. It at least feels way less aggressive to set the cruise control to the legal speed limit (where that is actually reasonable) and overtake everyone who thinks their speedometer is showing actual speed, and thus drives 26km/h on a 30km/h road. Modern cars have automatic distance adaption for their cruise controls, but older cars don't, while at the same time even older cars tend to otherwise have excellent cruise control (kind of thanks to drive-by-wire being the norm for the last 25 years or so). Driving without cruise control also takes away attention from traffic as you every now and then need to check your speedometer. Also re 1+1 vs 2+2 roads: At least in Europe it's fully legal (and I think this is great) for vehicles to be "underpowered", as in a car with say 100-120hp are allowed to haul a total of 3.5t (car + trailer), and those will obviously accelerate slowly, and in that situation 2+2 is great. Sure, a rare case, but not unheard of.
You are assuming people won't just fill both lanes and travel at the same speed. It happens here all the time. I've been on a 3 lane road trapped behind 3 cars all doing about 15 under the limit, all in their own lane.
SOme 30 years ago such a system was installed on a road in Southampton. Whilst on a course in the centre of town I car shared with someone who knew all the short cuts around the traffic queues. We shot right at junctions , sswung left at others, raced down side streets , stopped at traffic lights and got to the destination. I was timeng the drive unknown to the driver. The next day it was my turn, I followed the green wave on the main road, at the moderate speed allowed, with few gear changes needed and little braking. We arrived 5 minutes quicker than the day before.
How good a "green wave" works depends largely on the street network (e.g. grid-style vs. irregular), as well as the prevalent traffic patterns (e.g. is there a dominating route/direction, or are there multiple intersecting streams of traffic). In most cases you can only apply a "green wave" to one direction on one route (or on parallel routes at best, if your city is organized as a grid). If the intersections are not spaced at perfectly regular intervals, everyone else (including drivers on the same route going the opposite direction!) will inevitably get a "red wave". If your city happens to have _one_ dominating route & direction, then a green wave on it could - in theory - work without blocking too many other drivers; but generally you're probably better off distributing the flow of traffic over the whole network. Depending on traffic density even a chaotic pattern of traffic light phases can give better results overall.
@@stephanweinberger Re only being able to apply it in one direction: I vaguely remember systems that had displays stating which speed to drive at. With modern cheaper technology for electronic speed signs, it would be easier to roll out things like that in larger quantities.
→ 3:38 Please use a better multiplication sign - at least one which is centerer. A centered dot (·) works, or even a centered diagonal cross (×). But this six-pointed raised asterisk (maybe a font variant of *?) is definitively not a multiplication signs (at least use the centered one (∗), if you must). - 5:27 Somehow you here managed to arrange the asterisks with the center line here? → Another part to consider is whether the 2 seconds of following distance is actually safe enough with higher speeds. I think you'll actually need more distance to be able to safely stop in case of an accident in front of you.
Maths teacher here: The six-pointed raised asterisk is definitely a multiplication sign. Moreover, it is often preferred to indicate scalar multiplication, where a bullet and cross highlight that vector multiplication is occurring.
@@oliverlamb8892 I've never seen it this way, but maybe things changed in the last decade since I did math. But it should still be aligned with the center line, not put high like here.
@@DrTheRich this is justified by reaction times. If you start decelerating within 2 seconds after the car in front of you started, you'll avoid ramming it with this distance. Assuming that this car actually had enough space to stop normally and did not just crash into something. These are just general safety margins because people are stupid and the'll ignore them anyway.
I'd be interested to see a version of this that covers shorter following distances. There's a lot of interest in self-driving cars especially with Waymo offering rides and Tesla getting close to a general driving solution and when these things take over, there's a lot of potential for these assumptions to be changed. For example, theoretically I can imagine a system where a self-driving fleet's accelerations and decelerations can be synchronised so that very tiny stopping distances can be possible and still safe with the only differences in each individual car's rate of acceleration and deceleration being the factor. In addition, owned cars are partially a status symbol but don't necessarily have to be for hailed autonomous cars so these could be shorter. I know they won't suddenly be on par with buses or trains and I'm not advocating it as a solution to congestion, but it would be cool to see a video on how much of a difference it makes.
I've worked out the math anyway for anyone curious: For cars modelled as points with zero distance, as stopping distance shrinks to zero, flow becomes infinite regardless of velocity so that doesn't really help us. But when you DO account for length, the formula reduces to: flow = 3600 * speed / length So assuming no merging and a hypothetical perfectly standardised and synchronised fleet of bumper to bumper cars of 2m length going 50km/h, flow could increase massively to 20,000 cars/hour. This actually IS in the same league as many forms of public transport. So increasing speed and decreasing the length of cars materially increases traffic flow. How close we end up getting to those values in reality is of course another matter. Working for formula (assumes basically zero math knowledge): flow = speed * (1 car / (distance + length)) * time measured distance = velocity * time, 1 car can be removed from formula since anything * 1 = anything flow = 3600 seconds/hour * speed / (velocity * time) + length In self-driving scenario with perfect synchronisation and standardisation, stopping time shrinks to 0. flow = 3600 * speed / (velocity * 0) + length anything * 0 = 0 flow = 3600 * speed / length
One can imagine many things but is it actually going to be built? Even if you got every car manufacturer to install some standard unit that communicates with every other cal on the road and synchronizes behavior, I think you'd still need to build in slack because yau are dealing with physical objects in an unpredictable environment with life-threatening consequences. So there's no way there'd be bumper to bumper flow. Also, how does the system behave when one cal needs to take a turn or another car needs to enter the road?
I do wish the "distance" was presented as an inverse of distance in the a a beginning. I had to go back to figure out what you were talking about. It's strange that you call the amount of cars per unit distance "distance". Thanks for the otherwise clear and concise video.
@ Those types of roads are almost like highways already. So many drivers exceed the speed limit by 30%. Maybe the sign should read, “What’s The Rush? Traffic Signals Are Waiting For You.”
The use of * instead of either · or × is kinda driving me nuts. * is the symbol for the convolution, after all. Is the assumption of constant following time with speed empirically derived?
I'll try to help...If you spent time writing math equations in one of several programming languages, it would seem natural to use "*". "x" can be confused as a letter (variable), and dots are not ready on the keyboard. 2 seconds is not empirical, but a "goal", commonly taught -- Smith Systems even teaches 3 seconds. Most people (I find) hover at about 1 second, with 1/2 second being fairly common on high speed roads (because everyone I observe is obviously a Formula 1 driver with cat-like reflexes). Also, the reason that the conclusion of equal capacity regardless of speed seems counterintuitive is due to the baked-in assumption that it takes the same time to travel a vehicle's length regardless of speed -- this is slightly inaccurate.
I've tried to "beat the SatNav" - i.e. arrive earlier than the time predicts. After an hour our or so of stressful (and sometimes not entirely legal) driving, I rarely managed to shave more than a minute off the predicted arrival time, at the cost of being stressed and irritable on arrival. Now I focus on the quality of my driving, trying to anticipate and avoid dangerous situations, and keep a relaxed frame of mind. I almost always arrive exactly when the SatNav predicted, but in a much better state of mind. Also was getting much better fuel economy (when I drove a car that used fuel - now I like to think I get further on my battery). I actually think that in some cases, driving slower can actually get you there faster.
I have often checked the average speed record for my car. Over nearly 1000 miles I seem to average 36mph, in spite of most of my journies being at motorway speeds. I once left the Warwick services on the M40 to travel to Portsmouth. My employer left at the same time. He always drive at an indicated 80 mph, I never drove more than indicated 70, on motorways and dual carriageways. When we reached the destination , about 140 miles, my employer was just getting out of his car as I pulled up behind him. He had needed to wait at one set of traffic lights whilst I had not.
I would expect higher speeds reduce capacity at some point because psychologically people would end up keeping longer distances to the preceding vehicle at higher speeds. My basis for this is observing driving on the autobahn, on average people seem to keep better to the 2 second rule at speeds of over 150 or so.
that's why he said 2 seconds and not 2 meters... That way it includes the longer distance at higher speeds. And an average of 2 seconds foor 100+ speeds seem fair too, because too many people sadly (including me admittedly) drive closer than that even, especially at a busy time.
(smart) roundabouts, over/under passes, merging lanes, rerouting traffic in smarter ways, reducing need for cars, lower speeds. If you play any city planner game, you'd realize that hard time-regulated traffic lights are amongst the worst naive solutions to solve a car crossing.
Nice video. You said that the Dutch have two different manuals; one for urban, and one for rural. What are the names of the manuals, if you don't mind?
Knowing the Dutch, probably something like Design Manual for Urban Roads and Design Manual for Rural Roads. But in Dutch. Pretty literal, most of the time. Which is refreshing.
Max Traffic Flow: *Is 1800 cars/hr* Tailgaters in giant pickups: "That won't stop me. I didn't read the driver's manual." Jokes aside, how do traffic engineers compensate for areas where the majority of drivers are aggressive drivers that won't hesitate to break the law? Where I live 5-20 mph over the speed limit is normal (it actually becomes dangerous at times to try to do the speed limit), weaving between lanes is increasingly common, hogging intersections is common, and the general attitude is "the police can't stop us all".
Simple, make the roads more hostile to driving (and reduce hostility in areas where people drive nicely) Just like how you train a dog (cuz that's how these people behave. You drive fast: you loose a bumper You drive slow: one less speedbump for you. (there are lot more things you can do that speed bumps of course, like narrower roads, less smooth paving, more turns, on road obstacles, traffic lights, speed cameras, roundabouts etc.) Road width is the most common thing designed wrong in areas where speeding is too high. The narrower the road the faster you feel you're driving. So if the road feels like a 60mph road but the sign says 40mph, people are going to drive 60 even though those that don't necessarily want to break the law on purpose.
@@DrTheRich Speed bumps don't really encourage slow driving away from the speed bump though. They barely encourage slow driving on the speed bump these days. They kinda worked back when most people drove cars with very little power, but nowdays most cars can do 0-100 kmh in under 8 seconds, and any speed bump that'll break the spine of anyone in a hatchback doing 30 will barely be noticed by someone in an over-sized SUV doing 40. They incentivise buying more dangerous vehicles. Now lane narrowing, chicanes, roadside clutter (tall roadside clutter so SUVs will notice it) are probably better tools. Speaking of SUVs really make everything around you seem further away. I find it much harder to judge my speed in them - though I haven't driven that many. Maybe we should just ban them all together and fix that problem.
Depends where the speeding is. Raise the speed limit by 10k on open highway and enforce "keep right except to pass" and there will be no more weaving and less aggression as people are more spread out. Then you can focus on slowing people down more in town which more people will comply with when they just have to drive slow a short distance of residential area until they hit a well flowing highway that they can go fast on.
@@shraka Speed bumps screw over emergency vehicles who actually need to be speeding like ambulances. When seconds count I dont want my ambulance ride to be stuck doing 20 like everything else.
@@P7777-u7r I found driving in France so much nicer than Australia. People mostly kept left, and slower cars would pull out of your way after they finished overtaking someone. Two lanes flowed way smoother than the three to five we often have here. I don't think you necessarily need higher speed limits, just being able to DO the speed limit when you want to would be a massive improvement. A street / road / highway / freeway hierarchy is really essential for nice urban environments - usually this means routing cars around the slightly longer way, but with fewer traffic lights and freer flowing traffic I'd much prefer that even if it is slightly slower sometimes. It also makes designing for public transport easier.
Very interesting video! One factor beyond traffic flow to keep in mind though is the time saved by individual road users when they get to go faster. Time-efficient travel drives economic growth, which is why humans have always strived to find faster ways to travel: railroads, highways, freeways, airplanes, bullet trains, ... Of course, there is a balance to be found where accidents on ill-adapted infrastructure will also negate these economic gains after a certain point. Furthermore this applies more to long distance travel rather than core-urban travel, but it still matters
Although I'm not a fan of your equation forms, I used a similar approach to demonstrate that a "zipper merge" is an urban myth. The distance between cars is fixed and doubling the traffic density (with a merge) means traffic speed has to be reduced (almost) by half.
How do you think distance affects these calculations? I'd assume higher speeds are more for longer distance trips since higher speeds mean more distance travelled in the same time, but I'm curious how this plays into transportation network design
3:20 to 6 minutes I'm a bit off, as dutch driver, about the calculation for free flow capacity in a lane. Of coarse the theory is correct, I only get some other numbers and the effect of car length increases as the distance between cars decreases. We know that in the Netherlands (rush hour) on the free flow mainroads (highway) the amount of cars exceed that 1800 substantial. (Yes I recognize that this video is also made in the Netherlands). Reason...those 2 seconds distance are only an advise.....however the distance in rushhour is often close to 1 second . (Only when driving closer than 0,5 seconds for prolonged time you risk a penalty in the Netherlands.) The amount of cars on a lane passing suggests that the average distance (including car lenghts) is ca 1,5 seconds. In stop and go traffic we also should take into account how trafficlights influence he average speed...especially in rushhours. This should be connected to reaction times when the light turns green , accelerating speed of cars and the lenght the light is green. In the netherlands often the maximum time the light will be green because that also depends on how much traffic there is. Also drivers behaviour is important. If there are 2 lanes for traffic in one direction before the lane, coversing to one lane, the flow through can increase.... but many drivers are afraid for the merging which means that only one of those 2 lanes is used properly. Oh..an engineer looking to this. The needed speciality could be mechanical engineering, fluid dynamics.... calculations done as they do that for supersonic moving particles. That is closest to traffic behaviour as my child (yes this education including PHD) told me.
Side note: If you don't want to be stuck behind other car users, then you should want investment in public transport. Because even if you don't use it, the other drivers around you will, so that's less cars on the road, and less cars in your way
8:18 You can't just compare the theoretical capacity at low speeds with the practical capacity at high speed and claim that gains from increased speeds are reversed without assuming that traffic inefficiencies are less present at lower speeds. I.e. no gains are wiped away if that car has a 3-second following time at both speeds. But that may be a topic worth discussing: the effect of speed on following time.
Good video. Mythbusters did an episode comparing agressive lane switching to flowing with traffic on a highway if you are looking for more visual examples.
Idea for a next video: ideal distance between bus stops on a straight line for 30, 50 and 70km/h compared to population density. (you may assume an infinite amount of buses and passengers and their destinations are distributed evenly) Walking speed = 1m/s deceleration and acceleration = 3m/s² (or if you can find a more accurate number you can use that)
Regarding the following distance/time given at 3:56, how would self driving cars affect the variable? How much could self driving cars feasibly reduce the distance under 2 seconds?
2 seconds is the best case scenario WITH self driving cars. Self driving cars can reduce things like distracted driving when a car waits a second or 2 longer than it should to drive out of a cue. Or to get a bit closer. But theres still a minimum following distance so a car has time to stop if the car in front of it gets a crash and comes to a full stop. If you want to be more efficient, you might as well get out of the car and onto a bus since thats the only way you can start fitting more people in per square meter/foot.
@@buildthelanes Re having margins to stop if the car in front ends up in a crash - this might be the spiciest take ever, but given that cars have a theoretical capacity of about 4-6 people, while a bus can have 10x as many passengers, and thus it's reasonable for approximately 10 cars to crash into each other if a crash would happen, as it affects about as many people. In practice things like outcome of accidents and whatnot has to be considered. But the thought provocation is that it's more disruptive if a single bus ends up in a crash than if 5 cars crashes. In particular at low enough speeds, i.e. at 30km/h, it might be reasonable to actually have drivers drive close enough that pile-up crashes are unavoidable. (At low enough speeds there aren't even any noticeable damages if cars crash into each other. Can't remember the details but IIRC US regulations require this for 5mph, and it seems like this has been adopted world wide. In other words, at 5mph it would actually be reasonable to require drivers to drive onto the bumper of the car in front, to maximize capacity). Also re self driving cars: A major missing part about self driving is "hive mind". If there were provisions specific for self driving cars in the telecom mobile phone systems, to let them have a "hive mind", it would be super easy to have long stretches of cars slow down if an accident/incident happens. The self driving cars could also have a display turning on stating "slow - accident ahead" warning drivers of non-self driving cars. Another "hive mind" feature would be parking. If every car on a street in a city is self driving with a "hive mind", they could park in each other and just stop in the middle of the street, until a car needs to move, and then those who are in the way would just drive around the block like lemmings. Given that electric cars use very little energy when driving really slow this actually seems like a good way to increase parking space efficiency in cities.
This is a great question, I wasn't thinking it myself but I wish I had been. Thanks for answering, Stephan! Greetings from a fellow Dutch American Stephen.
Nice video, but it would be good to see the analysis using a stopping distance based distance formula - say half of normal stopping distance since we can usually see the vehicle two in front.
In reality, you will not only have to take into account the length of the vehicle but also the safety distance, which quadruples at double speed, that means at lower speeds there can actually be more cars passing a given point on the road
There is an speed that give the highest capacity on a motorway. Studies here in Denmark have the highest capacity at 80-90 kmt on our kind of motorways. Other road layouts has other optimal speeds for higher numbers of cars per hour. The relationship is first seen in USA and the brake distance grows with velocity squared that influences your math, but this relationship is mainly observed in real life.
So what you're saying is we should reduce the following distance to be as close as possible to maximize throughput. Maybe even connect the cars into some sort of long cluster of cars. To improve fuel efficiency we could have a single engine to locomote all these cars.
"Something that everyone in the world has direct experience with, so everything is just assumed to be known." It's so much fun when my professional field (public school education) and my TH-cam diversions overlap. Seriously, having once been a student doesn't make one any more knowledgeable about education than having driven a car makes one an authority on traffic policy.
Another factor: in an urban environment you shouldn't just drive with a fixed 2-seconds gap, but you should adapt your distance according to the _stopping_ distance, to account for all the possible disturbances/hazards/obstacles that can pop up at any time in such an environment. Then the formula for vehicle flow basically becomes a slanted parabola (since there is a quadratic term in the formula for braking distance, and that is overlaid on the constant factor of car length), with its maximum at around.... drumroll... _30_ _km/h_ (for typical car lengths and braking deceleration values). So in a city you get the best throughput around 30 km/h even without taking intersections into account! Consequently it's not a big surprise that the actual average speed ends up somewhere in that region as well (traffic is basically "solving" that mathematical optimization in real life). The nice thing about such a low speed limit is that in many cases traffic lights become obsolete altogether (as the slow speed gives drivers more time to take in and react to their surroundings and other traffic), which in turn makes traffic flow even better (as long as the road networks isn't overloaded, but then traffic lights also wont help). This in turn also reduces noise, fuel consumption and pollution (due more gentle cruising and less stop&go, which is the main contributor to fuel burn). Oh, and if course also reduces cost for electricity and maintenance... Also, since for low speeds the stopping distance is _shorter_ than the 2-second spacing, the capacity is actually _higher_ than in the free-flow case for the same speeds, without compromising safety! (Up to ~1670 vehicles/h for 5 meter cars @30 km/h, and still almost 1600 vehicles @50 - in fact it's only at ~55 km/h where 2-second-distance starts to take the lead, but even at 80 it does not surpass the optimum!). So lower speeds limits (around 30 km/h) really are a win-win-win situation for everyone (residents, pedestrians, taxpayers, _and_ drivers).
Addendum: I have put the formula into a spreadsheet on google docs. Unfortunately YT doesn't like external links (and is very good at detecting obfuscations by now), so you'll have to piece it together (+ dot, # slash): docs + google + com # spreadsheets # d # 10d3wQApBxluszhclXlrOpGETT7flAD0-eHJ8sFR0ll4 (English version is on the second sheet) Btw. this table also shows why slower speeds are so much safer: the whole stopping distance from 30 km/h (
Since youtube is intent on removing everything that even vaguely resembles an external link (to a spreadsheet where I did the math with nice graphs), here's the old-fashioned way: let a = braking deceleration (about 7.5m/s² on dry asphalt), r = reaction time (usually about 1s), l = vehicle length (average about 5m), v = speed in m/s then the space a single car occupies on the road is: s(v) = r·v + v²/(2·a) + l hence the occupation time of a section of road by a vehicle is: t(v) = s(v)/v = r + v/(2·a) + l/v find the minimum: dt/dv = 1/(2·a) - l/v² = 0 → v = sqrt(2·a·l) = 8.66 m/s = 31.2 km/h = 19.4 mph Throughput at this speed is 3600/t(8.66) = 1670 vehicles per hour.
We need to change the formula again because holding "seconds" constant assumes that we don't care about the social and economic costs of traffic accidents. 1st accidents are going to happen because people's reaction times are variable based on cell phone usage or other impairments. So if we have 1% of the population With 1.7s reaction times and a 1% chance something odd happens that requires an emergency stop, (the accuracy of the numbers don't matter just acknowledge that accidents hapen) then we can see that increasing speeds will give disproportionately more damaging accidents. So, in order to keep social costs constant we must increase following distance at higher speeds to ensure distracted driving collisions cause equal damage regardless of speed. Since people have proven that they will not consistently modulate their following distance when checking their phone. This is of course only applicable to limited use highways where violence is limited to car on car/motorcycle/truck
Retail bicycle outlets need to do more to encourage young people and older adults to ride bicycles. Sponsoring bike trains to escort children on their rides to school would be a great start. Organizing volunteers, teachers and other to ride along would be a great start. Getting children out of minivans and onto bicycles would be healthy exercise, build independence and make society healthier. Fun ride should also be organized. Getting a local bike club or school to sponsor an annual event to a local park or trail would encourage both adults and children to ride bicycles. Getting local elected officials to help with sponsored activities would help to educate them about the need for safe, protected bike lanes and trails in their community. Offering space and coffee for local riders to meet up would also improve store traffic.
I would not let my kid ride a bike in the city, or most american towns. Its simply too dangerous. Pedestrians and Bicycles are among the fast growing fatality rates in the entire transportation system. Rides are great, but the city has to make actual efforts to develop cyclist protection before people would feel safe doing so.
@@cadenorris4009 That is why safe, separated bike lanes and trails are needed. It is so older adults and children can ride bicycles safely separated from cars.
I worked for a construction company in The Netherlands and they bought a plot of land in France to build a holiday bungalow park, outside town. The entrance of the park is at a departmental road where you can drive about 90km an hour, not an ideal road for cycling. And certainly not one I wanna risk my life cycling on. In order to sell the bungalows to Dutch people they asked the municipality to provide a separate cycle path from the park to town. It took almost 2 years to get the cycle path, because it isn’t (or wasn’t) common practice to provide separate roads for cyclists in France. But they wanted to accommodate the bungalow owners because they could revive a dismal local economy. It is great to be able to cycle 20min to the local bakery to get fresh bread every morning instead of getting it by car. A great daily exercise. It’s sad that there no other cycling paths in the area. It would be great to cycle around the area instead of sightseeing by car.
A question related to the video (and not to the point you’re making): Why were you driving a bus on the 455 (and 32(?)) bus lines? Did Haarlem not trust you to drive a bus closer to home/work/in own province 😋?
About overtaking everyone: IT IS FASTER, maybe you will get stopped by the next intersection, but you will have these one or two rubber banding while starting and stopping cars less. Which in with my anecdotal evidence can be the difference between being stopped for another intersection cycle couple intersections down the road. This doesn't mean it's good for ecodriving, it's clearly a tradeoff that is more akin to gambling that the saved carlengths will help you catch green somewhere.
I would be very curious to compare what empirical studies show are the maximum car throughputs of different speeds - has any freeway ever got close to 1500 vehicles per lane across an hour?
It's pretty difficult to have a real life scenario with 1500 vehicles per lane for an hour long. It's also very easy to get a (phantom) traffic jam in 1500-1800 vehicles per hour range. With the use of AI controlled cars, you can reduce the following distance to a minimum and get a much higher throughput then the 1800.
Wait. For the freeflow thing, the time between cars (even if we asume them to be dots) its not the same for every speed. Higher speeds typically mean less time between cars (it doesnt increase lineraly with speed)
That's the distance drivers _should_ keep though. The 2 seconds are basically a buffer for reaction time + full application of the brakes, so that you don't rear-end the car in front of you in case its driver suddenly has to brake. And of course that rule only applies to roads without hazards from other directions (i.e. basically highways without intersections, pedestrians, etc.).
Capacity constraints not typically faced by bicyclists. Here’s a consideration. Optimal conditions for maximum throughput. I’m talking professionals racing on a closed course. A 33-car Indycar pack at The Brickyard can probably fly by, all bunched together on the opening lap in… I dunno, 10 seconds? Meanwhile, the 176 members of a Tour de France day 1 peloton during the leadup to a sprint finish can go by in a similar amount of time. That’s more than 5x the amount of cyclists, and at the Tour, this is usually on public roads maybe half the width of the Indianapolis Motor Speedway. Obviously real world conditions do not reflect race conditions. Nevertheless, the difference is striking.
Your asymptotic graph looks plausible, but there are models that find a different relation. Can you comment on the Lighthill-Whitham-Richards model? Do the Dutch manuals give an explicit mathematical model?
My burning curiosity is this: can "smart", "networked", or "AI" intersections improve throughput significantly? My second burning curiosity is do lane jumpers increase decrease or not affect traffic throughput. Thanks for your answer, kkbye.
Exactly. In an urban environment we cannot apply the 2-second rule, but have to use the real stopping distance. If you do the math (i.e. calculate the occupation time of a vehicle + its stopping distance at speed v, then find the minimum) you find that the optimal speed is about 30 km/h. let a=braking deceleration (about 7.5m/s² on dry asphalt), r=reaction time (usually about 1s), l=vehicle length (average about 5m), v=speed in m/s then the occupation time of a section of road by a vehicle is t(v) = (rv + v²/(2a) + l)/v find the minimum: dt/dv = 1/(2a) - l/v² = 0 -> v = sqrt(2al) = 8.66 m/s = 31.2 km/h Throughput at this speed is 3600/t(8.66) = 1670 vehicles per hour.
the 2 second rule is to always be able to stop when the car in front makes an emergency stop, based on 1 second reaction time and 1 second to move your foot to the other pedal and apply braking. And you can't move to a different lane when there more cars in those lanes.
@@kempo_95 OK, buta preceding car won't stop in place. It also have it's braking distance. You will not reach that car in 2 seconds like to a static object. Your relative speeds will be much lower.
Takeaways: Bigger cars are worse for traffic. Speeding does not make a difference. Follow distance is a key factor but safety is also important. The best traffic is no traffic. Build train tracks
Is it just me or does it seem like about 15% of the audio is missing? I notice this on other channels/videos too and for me at least, it's difficult to focus on the content.
Great video that gives useful tools to urbanists and safety advocates. Unfortunately in the US the problem is political. Ignorance itself is political, theres a reason we all grow up assuming gridlocked roads should just be expanded, while no one ever corrects us. Facts just do not matter to the voting public and politicians who rely on our ignorance to support their schemes.
1:47 As a software engineer I have to disagree, the stuff I see in my field is way more stupid than anything I have seen described when it comes to transportation. Then againm both are very abstract fields about flow that at first glance look very practical.
All these numbers go down the drain the moment when driving aggressively makes you feel that you actually done more to get there on time. And that alone will always be enough for most people to keep pushing through traffic regardless of end result.
Holding 2 seconds distance while going 70 - 90 km/h is nuts. And when all cars in a long row hold 2 seconds distance, it is a catastrophy waiting to happen. The formula for kinetic energy EK=0.5mvv is the key, here. Speed has the squared impact on it.
It's not nuts, is a common thought practice in driving schools across the world for highway driving. The thing you are forgetting in your thinking here, is that you are not driving to seconds behind a still standing concrete wall. The car in front of you has more or less the same breaking distance as you, so as long as you start breaking within those 2 seconds, you won't hit the car in front of you. The 2 seconds has nothing to do with kinetic energy formula, but with reaction time. That reaction time stays the same if you drive 10 kmph or 100 kmph Technically, if humans were robots with no reaction time, in a perfect world, cars could be driving bumper to bumper at 100 kmph, and if they all instantly brake at the same time, they would all stop perfectly fine. (mixed of significantly different mass to traction ratio like cars vs trucks should keep longer distance, and then E=½mv² is relevant.
The 2 second rule assumes the car in front of you isn't going to defy physics and come to an immediate stop. The 2 seconds is to account for reaction time to both determine the car in front is braking, apply the brakes, then realise how much the car in front is braking - then it assumes you'll both come to a stop at roughly the same rate. This is why trucks usually leave a bigger gap and why people who cut trucks off deserve their cars to be crushed into cubes with them still inside.
@ I learned three seconds distance. One for reaction time and two for stopping distance. And what you say about a concrete wall may not be so true. What often happens is that a car suddenly brakes hard for something. For every car behind it, they start braking later and later, untill they hit a massive lump of cars without even starting braking. Then we have very highly chances of fatalities in the cars in the middle of that lump of cars. And braking distance increases with the square of the speed increase. So when going faster, we should all increase the time distance to the cars in front of us. This is the reason higher speed gives or should give lower road capasity.
@@th5841 The physics doesn't change along the line. If every car figures out how hard they need to brake within those 2 seconds nobody should hit anyone else unless the car in front hits a solid immovable object.
@@shraka You shouldn't assume that everybody will figure out their optimal action. That is naive. You should assume the oposite. Let's do a physics class, shall we? When you are driving 80 km/h, you are doing 22 m/s. In two seconds that is 44 meters. Let's say there is a chain collision in progress in front of you, but you haven't noticed, yet. The car in front of you didn't either, so it crashes straight into it without braking. Now you have 44 meters to act before you are a part of this mess. You spend 1 second (average reaction time) to cope with what just happened and to react. You then have 22 meters left. Braking distance increases with the square of the speed increase. A car need 2 meters to stop from a speed of 20 km/h. This is what I learned on the teory lessons when taking my driver's license. This number may be 1.7 or 1.8 or sometimes much more, but 2 is a good number and for your safety it is better to round up than down. 80 is 4 times more than 20. The braking distance is 4 squared times the distance of 20; 16 * 2 m=32 m. That is 10 meters too much, so you crash. Your speed in the moment of the crash can also be calcualated, using the same logic as abow. So your crashing speed is calculated to be 45 km/h. And then you can embrace for the next car to hit you. Hopefully it doesn't go more than 45 km/h in that moment. Remember that when you brake, the driver in back of you doesn't instantly know if you are braking hard or just adjusting your speed a little. 2 seconds is ok when doing lower speeds. But not for higher speeds.
Road capacity is higher cause ain't fucking NOBODY in The Netherlands actually keeping 2 sec distance. Especially not on the highway. That kinda gap can and WILL fit 2 cars. Cause 2 cars will definitely slide in there.
When you said an average following distance of 2 seconds, i laughed out loud. And when the distance is shorter, speed varies a lot more (phantom traffic jams). I hope people don't get the impression far if everyone followed 0.1 seconds behind the car in front that it would improve traffic flow. Because, as you said, the real world is messy. It doesn't work that way.
Since the typical reaction time of average drivers is about 1 second, and it also takes some time for the brakes to fully apply, everything less than 2 seconds is just a pile-up waiting to happen.
@stephanweinberger 100%. And yet when driving here in Brisbane, Australia, a 2 second gap is very rarely seen...and people wonder why multi vehicle nose to tail crashes are extremely common and cause many delays, as well as damage and injuries.
*FEEDBACK* Yes, the video does help. It's not an interest of mine, but it does help me a bit to become more knowledgeable. I don't think that it's too useful, though. *TOPIC REQUEST* I recall a guy sharing his discovery that slow driving in the right lane unplugs traffic jams much more quickly, as opposed to fast driving in either lane. It was so counter intuitive, but he somehow explained it. If you know that this is true, then would you explain it, please? Perhaps it incentivizes fast people to stay on the left.
@@eugenetswong No, I haven't watched it. But that's what I imagine he was talking about. The most common thing to create a traffic jam is people braking abruptly.
3600/2 = 1800 in simple terms. Basically for an observer a vehicle passes every 2s therefore speed is immaterial. *the 2s rule was what I learned in 1979 at student driving education.
This only works on the assumption that the only possible obstacle is the car in front of you, and your car brakes at least as good. Then the 2s are basically just a buffer for your reaction time + the response time of the brakes, so that you don't rear-end the vehicle before you even have a chance to apply the brakes. But in a city, obstacles/hazards can basically pop up at any time, so driving by this rule isn't really applicable in this environment. (Fortunately it is on the safe side up to speeds of about 50 km/h, because then the actual stopping distance is typically shorter than the distance driven in 2s.)
@stephanweinberger I was being slightly facetious, and the video goes into details which include car length. My point was that for most people on the open road the 2s rule means that within the range of typical speeds, say 40 to 80mph doubling the speed doesn't double the number of cars per hour.
i already understood this concept but frankly the way you explained it here made it more confusing. You should talk more clearly about stop and go vs continuous flow at a higher level (a graphic would help). I was having trouble following the central message you were trying to push in part because it didn’t feel like you established your “thesis” well at the beginning of the video
Shouldn't the distance between cars (in seconds) be increased for higher speeds? The kinetic energy of the car and thus the breaking distance increase as a square function of speed. Yet this model uses a linear relationship between speed and distance between cars.
sure, but most traffic models assume just a 2 second spacing. The highway capacity manual uses the 1800 veh/hr based on the point particle assumption. Just to give you an idea of how unscientific the whole thing is! But, in reality all of these maximums are theoretical because were just never going to get close to these with imperfect traffic conditions. So trying to calculate everything perfectly is nice but not very helpful in the long run.
@@buildthelanes, yes that point was very clear in your video and I have no qualms about that. I wanted to consider this aspect primarily for love of mathing things out - even if practically useless. A secondary reason was that in public debate there are people confidently arguing for both "higher speed = higher capacity" and "lower speed = higher capacity". Practical application is unfortunately a secondary factor in public debate, and political decision making is a contingent on public sentiment. As an experiment I ran the numbers with different following distance and even half a second difference favours slower speeds (30 km/h, 1,5 s distance, 5 m car -> 1714 cars/h). This is absolutely not applicable to real life, 30 km/h speeds logically would be applied only in situations where there is a lot of interplay between cars, bikes, pedestrians, transit etc and as to your point, that makes the calculation irrelevant. It's just fun to calculate and good to have a case if the argument "higher speed = higher capacity" just won't die.
Recently had the experience of an impatient driver running a red light behind me, then pushing me and angrily waving at me in the rear mirror to speed up. When their was a two lane part he rushed past me. But the next few kms were trafficlight heavy area's all two lane, but no matter what he did, he never got much more than a few 100 meters in front of me. His angry-stressed- and frankly very dangerous driving got him to his destination 5 seconds earlier on a 15 minute trip than me, just patiently flowing with traffic.
I tend to believe, these people are in a rush to the end of their lives, but sadly also that of others.
I tell my kids that the reason why some people drive too fast, is that they REALLY have to go potty. We should not be angry at them, only be disappointed that they didn't go potty before they got in the car.
Some of us just shouldnt live in crowded places. If you actually want to get somewhere fast in a city park somewhere and walk more aggressively than most people drive you'll beat out everyone including the vehicles every time
As a cyclists I can second that. Many car drivers are willing to risk potentially lethal maneuvers for 10-20s gain (or none if we meet at the next traffic light).
@@P7777-u7rI recently drove a car in germany with a trailer, so limited to 80km/h (very relaxing, always on the right lane). I noticed that packs of around 5 cars bunched together were going maybe 160km/h (illegal on any public road outside of german I believe), with 2-3 trying to go 180 or so. They were so close that some cars went to the other lane to bleed of speed when the first car had to break due to traffic, construction or whatever. So I would modify your statement slightly: some people aren't made to use machines as dangerous as cars (at least not without more mandatory safety features).
I used to drive public transit buses. Our routes and timetables were poorly designed, seemingly with zero traffic in mind. My stress when driving dropped considerably when I had the realization that the only thing I had control over was the quality and safety of my driving. Everything else was a matter of circumstance, and being stressed or not over would do nothing to affect the situation.
Buses should really have dedicated ROW with separate detection and signal priority, otherwise they're a bit of a waste of time anywhere where there's congestion. Then once they have dedicated row they should probably just be trams. I imagine they'd be much less stressful to drive.
@@shraka we have bus lanes for that in the UK. Although some are being removed (in London) to make way for cycle lanes.
My favorite bus drivers drive slowly. Like they are practicing to be limousine drivers
@@skylarius3757 They should just get rid of the car lanes... And replace the bus lanes with trams.
@@skylarius3757 if there's one car lane and one bus lane, and we need a (protected ideally) bike lane, let's get rid of the car lane, keep bus lane. bus + bike moves far more people than car + bike and is better in other ways too
"Gone so far down the urbanist rabbit hole that you found my channel."
Ok, I feel a bit attacked. Its not my fault youtube keeps recommending me obscure urbanist related youtube channels. I do really like your channel though. Has a lot of unique insights, and I really appreciate that.
I coast to a stop and gently accelerate. My fuel economy is great but all the suburban motorists hate me. Which is okay because I hate them even more.
Coast to a stop is great for fuel economy (on non-electric/hybrid cars), but accelerating slowly to save fuel was mostly a thing on old carburetor engine cars (I.E. approx 40+ year old cars) as they weren't as good at having the optimal fuel-air mixture, especially during acceleration.
(Technically a "gasoline engine" (really "Otto engine") is the most effictive at the point where you reach max power at a given RPM. I.E. pedal almost to the floor at the highest possible gear. There are a lot of caveats though, like for example cam/valve timing and whatnot, and modern (as in the last 20 years or so) cars have variable valve timing which complicates things).
Drivers ed in for example Sweden teach to accelerate swiftly and when accelerating fast enough skip gears. (Drivers ed is almost always done for manual transmissions). The reason is that this is actually more efficient.
@@Thesecret101-te1lm There's a guy from the UK who tested this thoroughly. Accelerating gently increases fuel economy as well.
The channel name is Conquer Driving and the video's title is "Can Fast Acceleration Save Fuel?".
@@ddrhazy Maybe it differs for different engines/vehicles?
@@Thesecret101-te1lm Doubtful. My own fuel economy shows as much when I accelerate gently in my 2019 Nissan Sentra. If I gun the engine to get it to the speed limit, the fuel economy is less than 7 mpg. If I barely touch the accelerator pedal, I can get it to 20 mpg. I don't do it on busy roads.
@@ddrhazy i think the idea is u are in the less efficient acceleration portion. U spend slightly more time at consistent really efficient speed. Idk tho would need testing
What is more, higher speed on muliti-lane stroads causes more traffic lights to be installed and average speed drops further
It is not high speeds that leads to signals. It is the increase in access points and traffic generators that require changes in assignment of right of way.
@ I agree that number of crossings with streets is main factor, what I meant permission for higher speed limits causes even more hardships for drivers to turn into such stroad, so usually, the most primitive solution to this problem is implemented- traffic lights. The real deal is a proper division of traffic into roads and streets like in the Netherlands
@@paweuutrzrzrz2699 Speed only matters when the road is not at full volume. If the road is at full volume, then it doesn't matter how fast the traffic is going. Perpendicular drivers can't cross or enter. Controlled junctions are added when roads are at full enough volume that this state occurs enough to be disruptive.
@traffic.engineer
That's why high-speed roads don't belong in urban areas. They should go around cities, not through.
@@traffic.engineer It's both... if you made a formula, both in combination would be variables leading to a higher number in traffic lights.
I finally found an urban planning/transportation youtube channel that doesn't just make 50 videos on "car bad" with points that everyone else has covered already, and instead provides actual new content
Damn, never heard of CityNerd? You’re missing out. That said, I agree with the sentiment, the analysis is nice.
@@Co1010z I'll give them a go, looks like they're also covering new topics
I'm liking this content, too. In fairness, "car bad" is correct quite a lot of the time. "Car dependency bad" is correct almost all of the time.
@@davidmendelsohn1583 Considering how dangerous they are 'car bad' for personal transport just seems true - with only a little nuance in that areas that can't be made moderate density kinda have to rely on them.
@@shraka Agreed, the more urbanized an area is, the more 'car bad' is true.
you will get very few converts here in the US. A lifetime of being told that we are special and individualistic has taught most people that while driving they are an island in competition with everyone else on the road who is just in their way and that the goal is to always get in front of as many drivers as you can no matter where you are. Oh, at it has told us that it is cool to drive super loud cars very fast around other peoples neighborhoods in the middle of the night. Go USA #1!
America's driving style of "sit at the same speed in every lane" seems counterintuitive to getting in front and going fast.
Such loud assholes are not just found in the U S.
IMO, the behavior you describe has nothing to do with the cause connect it with. Some of it is quite the opposite. The idiot drivers are acting out because they can do so rather anonymously after being forced in most social situations to conform or be ostracized. There’s not as much respect for individual rights as there used to be. Now it’s all about identity and tribe.
The loud mufflers are totally tribal by the way.
@@nunyabidness3075 I dont like the (anti?) "mufflers" that make an engine louder than it would be on just a straightpipe but having a stick up your ass about noise other than during eepy hours is also tribal. For example if you move out to the sticks and complain that the trucks and dirtbikes arent EV quiet youll be laughed out of there by everyone.
@9:54 did that bus driver just cast a spell to make the light turn green?
Nah, the Netherlands is just really well designed
@@Descriptor413 Designed so well that bus drivers can snap and change lights?
(I'm sure its just transit signal priority, but I thought it was funny how he snapped like that)
I do it all the time. It works! Sometimes 🤣
It is sensor based, but sometimes even high priority has to slow down for a second.
I play this game in the late hours on my bicycle. Pure fun, only one light forces me to a full stop every time.
Think I am going to write a big complaint to the municipality...
@@Sullyville It may seem like magic, but it's actually due to the efficient traffic management system. Especially at night, when you approach an empty intersection, the traffic light turns green just before you arrive. That's why I love driving in the Netherlands.
You should repeat the Douglas boulevard scenario but the driver incrementally decreases their max speed for each trial. Make a plot of average speed vs max speed to visualize the non-linearity.
I was surprised this morning to learn that my TH-cam algorithm had not brought me to Not Just Bikes
I used to be a pretty aggressive driver when I was younger, weaving between traffic to try and get to my destinations quicker. Over time, as I got more mature (and became less of a self-entitled prick), I came to realize how little difference it made to my travel time, and how much worse it was for my mental health (making myself stressed, frustrated or angry for literally no reason) and fuel economy/wear-and-tear on the car. Thankfully, I'm a better person, and consequently a better driver now.
Ive often wondered about this, figuring that increased speed must improve capacity, but get balanced out by greater following distance. It was really nice to see you sit down and go through the numbers. Subscribed!
When you say "following distance" most US drivers scratch their heads and say "what is that?".
@@stink1701 😮💨yeah
This was honestly an enlightening video for me, thank you
Love you point about not being an "urbanist" and the service your channel provides.
It wasn't long after I discovered NJB that I thought, "ok, cars are bad, but I want to actually argue with engineers about why things need to change in the US." I wanted to know the actual math.
Thanks for providing this side of the narrative. I think you're one of the few TH-camrs doing it.
Putting engineers in charge of decisions that are political decisions not engineering decisions is part of America's problem you shouldn't have to argue with an engineer about this the engineers should be told what to build and their job is to figure out how.
@@supermanifolds You can't order someone to beat physics. So no, engineers need to have a say in things. And by the way...how do we determine what our orders to engineers look like?
Mind you, it is not a theoretical question. In Canada, we see exactly that kind of thing being played out right now. A politician, probably with reasonable backing by his voters, orders bike lanes to be removed.
@@supermanifolds Whereas I think these decisions should be made by engineers, not politicians. Maybe politicians can set general goals, but as they usually do not understand how these things work, they should be as far from the actual decisions as possible.
NJB does not say "cars are bad". The point he makes is that car centric infrastructure development is bad.
Trust me, there's no point arguing with engineers. The math they work off isn't based in reality, and they make it up to give the result the people holding the purse strings want.
Traffic engineering isn't engineering anymore than homoeopathy is medicine.
Filming your daschcam footage from inside of a bus?
You are an urbanist, my friend.
(Just discovered there is no bus emoji. Work of the "car conspiracy?")
🚌🚎
These are busses no?
And trams?
I think it's worth noting that in your second model for free flow traffic, road capacity would decrease if average vehicle size were to increase.
Driving aggressively >might< get you to your destination 'sooner', but the amount of energy expanded is exponentially higher and the recuperation time afterwards will be a net loss relative to any travel time gain.
I wonder if there's any scientific studies into this phenomenon.
In the Netherlands because the vast majority of traffic lights are sensor based, aggressive driving in some places can net you a time benefit. Also, because you may be able to squeeze yourself into an earlier traffic light cycle. But this varies a lot depending on the location, traffic volume, and configuration of the lights and such. It's also just plain wasteful.
Hi Celis C, what are trying to do is pure science!, all your need is careful critical oversight of the information you use for your calculations and sensible reliable observations, do your best to exclude subjective assumptions and then allow your brain to think to all through, at some point it will offer the outline of an explanation that correlates with your observations.
the next part is to formulate what you come up with into a useable hypothesis which you can then test, the easier it is to test and thus refute the better it is!. All you require for total refutation is just one bit of empirical evidence that confounds the hypothesis which you then abandon and wait for a new one, each time you go through this process you learn another thing that is not true, a properly proven fact, this way you increase your total body of knowledge.
In this particular context we can start with a number of scientific principles which we accept as established, these include the given assumptions that the greater the speed of the traffic the more vehicles pass any given point at any given time the greater the total traffic flow, one reason for this is that while the lenght of each vehicle does not vary with speed the distance between them does, in fact with any given number of vehicles of any specific length there is a minimum threshold below which there is no space between them at all at everything stops, it then takes a finite amount of time for them all to start moving again further reduce the flow rate.
From all this it follows that fewer shorter vehicles all travelling at a constant speed with the same minimum space between them would be optimal, that however is the 'perfect' state scenario which for very good reason can never happen because reality includes variation and diversity, these factors are much more difficult to enumerate but that is not needed!, allm tht is needed is effective traffic control that reads the flow rate and as it drops reduce the vehiclers allowed on that road, when the flow rate rises again near to the proximate optimal threshold more vehicles can be allowed to join.
From that in situations where the backlog at the access ramps become too much other measures must be applied, there is an obvious range of options all the way from reducing the size of vehicles to adding more lanes and building new roads or as a last resort providing adequate public transport using its own part of the road network so that travellers sitting waiting in a car for a space on the road will see bus after bus not full of passengers passing them and they can make their own choices.
The manner in which each of us choose to drive has little or no material effect on the whole traffic pattern, it might be 'true' that if all drivers applied exactly the same style we could get more traffic on the same roads but they don't and they won't all do the same as each other. Regardless of political ideology we should be just rational and practical.
Cheers, Richard.
@@wewillrockyou1986 I don't think he just means fuel energy. Aggressive driving makes you angry and frustrated, which costs so much more mental and emotional energy for only a minute gain on a 30 minute trip.
I always laugh at cars on the high way, push me to the side, speeding up only to be stuck behind the next car they have to push again. In the end they exit the high way only a minute before me, but are a thousand times more frustrated....
I just came here to enjoy about ten minutes of uninterrupted prime condition infrastructure footage.
In the UK, the Highway Code requires driver to drive within their stopping distance which is a quadratic relationship to speed due to Kinetic Energy being proportional to the square of velocity. In you model you used a linear relationship. If you had used the quadratic relationship you would got the answer that slower speeds always increase capacity. You can see that in action in reverse: when traffic increases speed naturally decreases (congestion) to accommodate the need to increase traffic capacity.
A moving car does not suddenly stop from one moment to another. It is bound by inertia and will slowly come to a stop in a reasonably similar way to the following car. Your distance only needs to account for your own reaction time, so 2s is reasonable. And at least here in Germany it is explicitly coded into law. Probably in the Netherlands as well.
Looking at existing traffic out in the world, 2s seems like a gross overestimation. At highway speeds this should turn out to around 60m, but I often find traffic on the left lane too bunched up to even attempt fitting a 5m long car into the gaps ;)
Except in motorway conditions this is tricky. The 2 seconds rule is to account for delays due to reaction speed, but also taking into account that the car in front is not stationary and has its own stopping distance. In reality it would already be great if people kept the 2 second distance on the motorway. For urban traffic the stopping distance is more important, but when adding reaction speed 2 seconds is a good rule of thumb for normal conditions.
Kinetic energy going up by the square of speed is not the reason why stopping distance goes up by the square of your starting speed. That correlation is a myth!
Stopping distance can be calculated by multiplying the time it takes to stop, by the average speed. And increasing the starting speed increases both the time _and_ average speed.
For example, lets assume we have a car that can brake at a constant rate of 5 m/s/s.
If we start at 10 m/s, then it would take 2 seconds to come to a stop, and our average speed would be 5 m/s. So our stopping distance would be 2s * 5m/s = 10 m.
If we start at twice that, 20 m/s, then it would take twice the time (4 seconds) and our average speed would also be doubled (10 m/s). So we get 4s * 10m/s = 40 m.
If you want a visual, then we can plot this on a graph with speed on the vertical axis, and time on the horizontal. With a constant rate of deceleration like in the examples I gave, then we'd get a straight line with a downwards slope. And the area would be triangle shaped, hence why the average speed is just half the starting speed. (And I'm ignoring drag and the slight lift most cars get from being airfoil shaped. As they roughly cancel out.)
And _most_ land vehicles generally have close to constant deceleration when braking. As the resistance from friction (both in the brakes and tires traction) goes up with speed at the same rate as kenetic energy does. And perfectly cancels it out, making the exponential nature of kenetic energy a non-factor in stopping distance.
@@PauldeVrieze The car in front might not instantly stop but another car might pull into your lane or a pedestrian might step out.
Either way Rule 126 says "You should leave enough space between you and the vehicle in front so that you can pull up safely if it suddenly slows down or stops. The safe rule is never to get closer than the overall stopping distance (see Typical Stopping Distances diagram)".
The stopping distances in the diagram show reaction distances increase linearly with speed but the braking distances increase by the square of speed.
@@vulduv The official braking distances in the UK go up according to a square law and it is those distances together with a linear thinking distance that UK drivers are required to leave between them and the car in front.
At 32 km/h the thinking distance is 6m and the braking distance is 6m giving an overall stopping distance of 12m.
At 64 km/h the thinking distance is 12m and the braking distance is 24m giving an overall stopping distance of 36m.
Whatever you might think, these are the gaps that UK drivers are required to leave.
Im currently following a course on Cooperative Autonomous Driving at my (Dutch) university. A large focus currently is on improving cruisecontrol to decrease space between cars and decrease the chance of traffic jams. Very interesting stuff
Recommending the book "killed by a traffic engineer" by Wes Marshal
Holly shit man!! Killing it with this videos! Happy holidays from an old friend!
Cool to hear from you man!
The formula F = s*d*t is misleading. The units don't match up (s is in distance/time, d is distance, t is time/time (seconds per hour)) which multiplies to distance^2/time, where you actually want 1/time (rate of cars per unit time). But when you do the formula example, you express following distance as "1 car per 27.8m", which is actually _dividing_ by following distance, not multiplying. So it should be s*t/d. If this is some traffic engineering formula, then maybe this discipline should get better with tracking units. Because it seems like you're treating the quantity "following distance" as an _inverse distance_ (units 1/m) rather than a distance, which is just confusing.
Also, having "t" as a unitless quantity (time / time) is also deceptive. Why not just say that the car capacity rate is F = s / d, which gives you units of (time)^-1, and then just adjust the units accordingly. So if you have s in m/s, and d in m, then you get cars/second, and then just multiply by 3600 to get cars/hour.
It is not misleading, it is just wrong. The 2nd parameter is nonsense. "Following distance" is totally inaccurate. The parmeter should be the inverse of headway, or following distance. And the 3rd parameter should simply not be there. The equation is simply flow = speed/headway. With both using compatible dimensions. I.e metre per second and metres.
It’s great to explain these mobility concepts. Would be good to also explain how travel time is only marginally reduced as speed increases (between fixed points). And energy increases exponentially…
A two second following distance is ok at 30 kph, but at highway speeds (90+ kph) the following distance should be 4-5 seconds. So slower traffic might end up giving a higher capacity,
Suggestion for future topic:
What are the actual effects of "green wave" traffic lights? I.E. ensuring that a bunch of traffic lights along a major roads are green at each junction for traffic that isn't turning?
Also re 1+1 roads (without overtaking abilities) v.s. 2+2 roads:
I would say that it's not just about aggressive driving and whatnot. It's also about calm driving. It at least feels way less aggressive to set the cruise control to the legal speed limit (where that is actually reasonable) and overtake everyone who thinks their speedometer is showing actual speed, and thus drives 26km/h on a 30km/h road.
Modern cars have automatic distance adaption for their cruise controls, but older cars don't, while at the same time even older cars tend to otherwise have excellent cruise control (kind of thanks to drive-by-wire being the norm for the last 25 years or so). Driving without cruise control also takes away attention from traffic as you every now and then need to check your speedometer.
Also re 1+1 vs 2+2 roads: At least in Europe it's fully legal (and I think this is great) for vehicles to be "underpowered", as in a car with say 100-120hp are allowed to haul a total of 3.5t (car + trailer), and those will obviously accelerate slowly, and in that situation 2+2 is great. Sure, a rare case, but not unheard of.
That's one reason junctions have more lanes that merge back into one
You are assuming people won't just fill both lanes and travel at the same speed. It happens here all the time. I've been on a 3 lane road trapped behind 3 cars all doing about 15 under the limit, all in their own lane.
SOme 30 years ago such a system was installed on a road in Southampton. Whilst on a course in the centre of town I car shared with someone who knew all the short cuts around the traffic queues. We shot right at junctions , sswung left at others, raced down side streets , stopped at traffic lights and got to the destination. I was timeng the drive unknown to the driver.
The next day it was my turn, I followed the green wave on the main road, at the moderate speed allowed, with few gear changes needed and little braking. We arrived 5 minutes quicker than the day before.
How good a "green wave" works depends largely on the street network (e.g. grid-style vs. irregular), as well as the prevalent traffic patterns (e.g. is there a dominating route/direction, or are there multiple intersecting streams of traffic).
In most cases you can only apply a "green wave" to one direction on one route (or on parallel routes at best, if your city is organized as a grid). If the intersections are not spaced at perfectly regular intervals, everyone else (including drivers on the same route going the opposite direction!) will inevitably get a "red wave".
If your city happens to have _one_ dominating route & direction, then a green wave on it could - in theory - work without blocking too many other drivers; but generally you're probably better off distributing the flow of traffic over the whole network. Depending on traffic density even a chaotic pattern of traffic light phases can give better results overall.
@@stephanweinberger Re only being able to apply it in one direction:
I vaguely remember systems that had displays stating which speed to drive at.
With modern cheaper technology for electronic speed signs, it would be easier to roll out things like that in larger quantities.
Great content! Love the explanation of the math behind this stuff. Subscribed!
→ 3:38 Please use a better multiplication sign - at least one which is centerer. A centered dot (·) works, or even a centered diagonal cross (×). But this six-pointed raised asterisk (maybe a font variant of *?) is definitively not a multiplication signs (at least use the centered one (∗), if you must). - 5:27 Somehow you here managed to arrange the asterisks with the center line here?
→ Another part to consider is whether the 2 seconds of following distance is actually safe enough with higher speeds. I think you'll actually need more distance to be able to safely stop in case of an accident in front of you.
2 seconds is the distance they teach you at drivers lessons here in the netherlands (where the youtuber is from)
Maths teacher here: The six-pointed raised asterisk is definitely a multiplication sign. Moreover, it is often preferred to indicate scalar multiplication, where a bullet and cross highlight that vector multiplication is occurring.
@@oliverlamb8892 I've never seen it this way, but maybe things changed in the last decade since I did math. But it should still be aligned with the center line, not put high like here.
@@oliverlamb8892 eh, the asterisk is an awkward replacement for the centered dot. If the dot is available, it should be used.
@@DrTheRich this is justified by reaction times. If you start decelerating within 2 seconds after the car in front of you started, you'll avoid ramming it with this distance. Assuming that this car actually had enough space to stop normally and did not just crash into something. These are just general safety margins because people are stupid and the'll ignore them anyway.
I'd be interested to see a version of this that covers shorter following distances. There's a lot of interest in self-driving cars especially with Waymo offering rides and Tesla getting close to a general driving solution and when these things take over, there's a lot of potential for these assumptions to be changed. For example, theoretically I can imagine a system where a self-driving fleet's accelerations and decelerations can be synchronised so that very tiny stopping distances can be possible and still safe with the only differences in each individual car's rate of acceleration and deceleration being the factor. In addition, owned cars are partially a status symbol but don't necessarily have to be for hailed autonomous cars so these could be shorter. I know they won't suddenly be on par with buses or trains and I'm not advocating it as a solution to congestion, but it would be cool to see a video on how much of a difference it makes.
I've worked out the math anyway for anyone curious:
For cars modelled as points with zero distance, as stopping distance shrinks to zero, flow becomes infinite regardless of velocity so that doesn't really help us. But when you DO account for length, the formula reduces to:
flow = 3600 * speed / length
So assuming no merging and a hypothetical perfectly standardised and synchronised fleet of bumper to bumper cars of 2m length going 50km/h, flow could increase massively to 20,000 cars/hour. This actually IS in the same league as many forms of public transport. So increasing speed and decreasing the length of cars materially increases traffic flow. How close we end up getting to those values in reality is of course another matter.
Working for formula (assumes basically zero math knowledge):
flow = speed * (1 car / (distance + length)) * time measured
distance = velocity * time, 1 car can be removed from formula since anything * 1 = anything
flow = 3600 seconds/hour * speed / (velocity * time) + length
In self-driving scenario with perfect synchronisation and standardisation, stopping time shrinks to 0.
flow = 3600 * speed / (velocity * 0) + length
anything * 0 = 0
flow = 3600 * speed / length
One can imagine many things but is it actually going to be built? Even if you got every car manufacturer to install some standard unit that communicates with every other cal on the road and synchronizes behavior, I think you'd still need to build in slack because yau are dealing with physical objects in an unpredictable environment with life-threatening consequences. So there's no way there'd be bumper to bumper flow.
Also, how does the system behave when one cal needs to take a turn or another car needs to enter the road?
I do wish the "distance" was presented as an inverse of distance in the a a beginning. I had to go back to figure out what you were talking about. It's strange that you call the amount of cars per unit distance "distance". Thanks for the otherwise clear and concise video.
Great video !
10:12 Douglas Boulevard needs additional signs saying “You Are Averaging ONLY 30 mph”.
I can just imagine the number of complaints to the city that signs like that would generate, each one demanding that the speed limit be increased.
@ Those types of roads are almost like highways already. So many drivers exceed the speed limit by 30%. Maybe the sign should read, “What’s The Rush? Traffic Signals Are Waiting For You.”
The use of * instead of either · or × is kinda driving me nuts. * is the symbol for the convolution, after all.
Is the assumption of constant following time with speed empirically derived?
I'll try to help...If you spent time writing math equations in one of several programming languages, it would seem natural to use "*". "x" can be confused as a letter (variable), and dots are not ready on the keyboard. 2 seconds is not empirical, but a "goal", commonly taught -- Smith Systems even teaches 3 seconds. Most people (I find) hover at about 1 second, with 1/2 second being fairly common on high speed roads (because everyone I observe is obviously a Formula 1 driver with cat-like reflexes). Also, the reason that the conclusion of equal capacity regardless of speed seems counterintuitive is due to the baked-in assumption that it takes the same time to travel a vehicle's length regardless of speed -- this is slightly inaccurate.
I've tried to "beat the SatNav" - i.e. arrive earlier than the time predicts. After an hour our or so of stressful (and sometimes not entirely legal) driving, I rarely managed to shave more than a minute off the predicted arrival time, at the cost of being stressed and irritable on arrival.
Now I focus on the quality of my driving, trying to anticipate and avoid dangerous situations, and keep a relaxed frame of mind. I almost always arrive exactly when the SatNav predicted, but in a much better state of mind. Also was getting much better fuel economy (when I drove a car that used fuel - now I like to think I get further on my battery).
I actually think that in some cases, driving slower can actually get you there faster.
At 10:52 where is that street? A Bus Lane that allows cars to crosso to go right on signals. Amazing infrastructure and effectiveness with only paint!
It can be a bit dangerous though. Cars don't expect to be overtaken on the right side. It requires a bit of anticipation from the bus driver.
It seems to be the Afrikaweg in Zoetermeer, the Netherlands, near the intersection with the van Leeuwenhoeklaan.
@@crytocc thanks!!
I have often checked the average speed record for my car. Over nearly 1000 miles I seem to average 36mph, in spite of most of my journies being at motorway speeds.
I once left the Warwick services on the M40 to travel to Portsmouth. My employer left at the same time. He always drive at an indicated 80 mph, I never drove more than indicated 70, on motorways and dual carriageways. When we reached the destination , about 140 miles, my employer was just getting out of his car as I pulled up behind him. He had needed to wait at one set of traffic lights whilst I had not.
Love the video!
I would expect higher speeds reduce capacity at some point because psychologically people would end up keeping longer distances to the preceding vehicle at higher speeds. My basis for this is observing driving on the autobahn, on average people seem to keep better to the 2 second rule at speeds of over 150 or so.
that's why he said 2 seconds and not 2 meters...
That way it includes the longer distance at higher speeds. And an average of 2 seconds foor 100+ speeds seem fair too, because too many people sadly (including me admittedly) drive closer than that even, especially at a busy time.
So how do you fix these terrible intersections? It's brutal sitting at a red light when no one is coming the other way.
Install roundabouts. No stop required, just yield.
Use smart traffic lights that have sensors to detect traffic and react accordingly, or install roundabouts if feasible.
(smart) roundabouts, over/under passes, merging lanes, rerouting traffic in smarter ways, reducing need for cars, lower speeds. If you play any city planner game, you'd realize that hard time-regulated traffic lights are amongst the worst naive solutions to solve a car crossing.
If the speed is low enough you don’t need lights or signs at all
Well done! Thanks!
Hope you get a lot of, same level, engineers to get useful discussions going!
Best wishes for 2025!
As a Civil Engineer for transportation system I confirm that everything you say is right. :)
Nice video. You said that the Dutch have two different manuals; one for urban, and one for rural. What are the names of the manuals, if you don't mind?
The CROW manuals. There is a whole bunch of them, so have a look on their website(s), which are available in english.
Knowing the Dutch, probably something like Design Manual for Urban Roads and Design Manual for Rural Roads. But in Dutch. Pretty literal, most of the time. Which is refreshing.
Nice opening, the first 12 seconds of the video is Delfgauw, next to my hometown of Delft
Delftsestraatweg, from the perspective of lijn 55, I presume :)
You should really look into manim for the math equations.
Max Traffic Flow: *Is 1800 cars/hr*
Tailgaters in giant pickups: "That won't stop me. I didn't read the driver's manual."
Jokes aside, how do traffic engineers compensate for areas where the majority of drivers are aggressive drivers that won't hesitate to break the law? Where I live 5-20 mph over the speed limit is normal (it actually becomes dangerous at times to try to do the speed limit), weaving between lanes is increasingly common, hogging intersections is common, and the general attitude is "the police can't stop us all".
Simple, make the roads more hostile to driving (and reduce hostility in areas where people drive nicely)
Just like how you train a dog (cuz that's how these people behave.
You drive fast: you loose a bumper
You drive slow: one less speedbump for you.
(there are lot more things you can do that speed bumps of course, like narrower roads, less smooth paving, more turns, on road obstacles, traffic lights, speed cameras, roundabouts etc.)
Road width is the most common thing designed wrong in areas where speeding is too high. The narrower the road the faster you feel you're driving. So if the road feels like a 60mph road but the sign says 40mph, people are going to drive 60 even though those that don't necessarily want to break the law on purpose.
@@DrTheRich Speed bumps don't really encourage slow driving away from the speed bump though. They barely encourage slow driving on the speed bump these days. They kinda worked back when most people drove cars with very little power, but nowdays most cars can do 0-100 kmh in under 8 seconds, and any speed bump that'll break the spine of anyone in a hatchback doing 30 will barely be noticed by someone in an over-sized SUV doing 40. They incentivise buying more dangerous vehicles. Now lane narrowing, chicanes, roadside clutter (tall roadside clutter so SUVs will notice it) are probably better tools.
Speaking of SUVs really make everything around you seem further away. I find it much harder to judge my speed in them - though I haven't driven that many. Maybe we should just ban them all together and fix that problem.
Depends where the speeding is. Raise the speed limit by 10k on open highway and enforce "keep right except to pass" and there will be no more weaving and less aggression as people are more spread out. Then you can focus on slowing people down more in town which more people will comply with when they just have to drive slow a short distance of residential area until they hit a well flowing highway that they can go fast on.
@@shraka
Speed bumps screw over emergency vehicles who actually need to be speeding like ambulances. When seconds count I dont want my ambulance ride to be stuck doing 20 like everything else.
@@P7777-u7r I found driving in France so much nicer than Australia. People mostly kept left, and slower cars would pull out of your way after they finished overtaking someone. Two lanes flowed way smoother than the three to five we often have here. I don't think you necessarily need higher speed limits, just being able to DO the speed limit when you want to would be a massive improvement. A street / road / highway / freeway hierarchy is really essential for nice urban environments - usually this means routing cars around the slightly longer way, but with fewer traffic lights and freer flowing traffic I'd much prefer that even if it is slightly slower sometimes. It also makes designing for public transport easier.
Very interesting video! One factor beyond traffic flow to keep in mind though is the time saved by individual road users when they get to go faster. Time-efficient travel drives economic growth, which is why humans have always strived to find faster ways to travel: railroads, highways, freeways, airplanes, bullet trains, ...
Of course, there is a balance to be found where accidents on ill-adapted infrastructure will also negate these economic gains after a certain point. Furthermore this applies more to long distance travel rather than core-urban travel, but it still matters
Although I'm not a fan of your equation forms, I used a similar approach to demonstrate that a "zipper merge" is an urban myth. The distance between cars is fixed and doubling the traffic density (with a merge) means traffic speed has to be reduced (almost) by half.
How do you think distance affects these calculations? I'd assume higher speeds are more for longer distance trips since higher speeds mean more distance travelled in the same time, but I'm curious how this plays into transportation network design
this is the youtube channel the National Capital Authority doesn't want us to know about.
3:20 to 6 minutes I'm a bit off, as dutch driver, about the calculation for free flow capacity in a lane. Of coarse the theory is correct, I only get some other numbers and the effect of car length increases as the distance between cars decreases.
We know that in the Netherlands (rush hour) on the free flow mainroads (highway) the amount of cars exceed that 1800 substantial. (Yes I recognize that this video is also made in the Netherlands).
Reason...those 2 seconds distance are only an advise.....however the distance in rushhour is often close to 1 second . (Only when driving closer than 0,5 seconds for prolonged time you risk a penalty in the Netherlands.) The amount of cars on a lane passing suggests that the average distance (including car lenghts) is ca 1,5 seconds.
In stop and go traffic we also should take into account how trafficlights influence he average speed...especially in rushhours. This should be connected to reaction times when the light turns green , accelerating speed of cars and the lenght the light is green. In the netherlands often the maximum time the light will be green because that also depends on how much traffic there is.
Also drivers behaviour is important. If there are 2 lanes for traffic in one direction before the lane, coversing to one lane, the flow through can increase.... but many drivers are afraid for the merging which means that only one of those 2 lanes is used properly.
Oh..an engineer looking to this. The needed speciality could be mechanical engineering, fluid dynamics....
calculations done as they do that for supersonic moving particles. That is closest to traffic behaviour as my child (yes this education including PHD) told me.
Side note: If you don't want to be stuck behind other car users, then you should want investment in public transport.
Because even if you don't use it, the other drivers around you will, so that's less cars on the road, and less cars in your way
8:18 You can't just compare the theoretical capacity at low speeds with the practical capacity at high speed and claim that gains from increased speeds are reversed without assuming that traffic inefficiencies are less present at lower speeds. I.e. no gains are wiped away if that car has a 3-second following time at both speeds. But that may be a topic worth discussing: the effect of speed on following time.
Good video. Mythbusters did an episode comparing agressive lane switching to flowing with traffic on a highway if you are looking for more visual examples.
Idea for a next video: ideal distance between bus stops on a straight line for 30, 50 and 70km/h compared to population density. (you may assume an infinite amount of buses and passengers and their destinations are distributed evenly)
Walking speed = 1m/s
deceleration and acceleration = 3m/s² (or if you can find a more accurate number you can use that)
Regarding the following distance/time given at 3:56, how would self driving cars affect the variable? How much could self driving cars feasibly reduce the distance under 2 seconds?
2 seconds is the best case scenario WITH self driving cars. Self driving cars can reduce things like distracted driving when a car waits a second or 2 longer than it should to drive out of a cue. Or to get a bit closer. But theres still a minimum following distance so a car has time to stop if the car in front of it gets a crash and comes to a full stop.
If you want to be more efficient, you might as well get out of the car and onto a bus since thats the only way you can start fitting more people in per square meter/foot.
@ Thanks for the response!
So I presume that 2 seconds is what you get if you assume instantaneous reaction when the car in front stops?
pretty much
@@buildthelanes Re having margins to stop if the car in front ends up in a crash - this might be the spiciest take ever, but given that cars have a theoretical capacity of about 4-6 people, while a bus can have 10x as many passengers, and thus it's reasonable for approximately 10 cars to crash into each other if a crash would happen, as it affects about as many people. In practice things like outcome of accidents and whatnot has to be considered. But the thought provocation is that it's more disruptive if a single bus ends up in a crash than if 5 cars crashes. In particular at low enough speeds, i.e. at 30km/h, it might be reasonable to actually have drivers drive close enough that pile-up crashes are unavoidable.
(At low enough speeds there aren't even any noticeable damages if cars crash into each other. Can't remember the details but IIRC US regulations require this for 5mph, and it seems like this has been adopted world wide. In other words, at 5mph it would actually be reasonable to require drivers to drive onto the bumper of the car in front, to maximize capacity).
Also re self driving cars:
A major missing part about self driving is "hive mind". If there were provisions specific for self driving cars in the telecom mobile phone systems, to let them have a "hive mind", it would be super easy to have long stretches of cars slow down if an accident/incident happens. The self driving cars could also have a display turning on stating "slow - accident ahead" warning drivers of non-self driving cars.
Another "hive mind" feature would be parking. If every car on a street in a city is self driving with a "hive mind", they could park in each other and just stop in the middle of the street, until a car needs to move, and then those who are in the way would just drive around the block like lemmings. Given that electric cars use very little energy when driving really slow this actually seems like a good way to increase parking space efficiency in cities.
This is a great question, I wasn't thinking it myself but I wish I had been. Thanks for answering, Stephan! Greetings from a fellow Dutch American Stephen.
Nice video, but it would be good to see the analysis using a stopping distance based distance formula - say half of normal stopping distance since we can usually see the vehicle two in front.
In reality, you will not only have to take into account the length of the vehicle but also the safety distance, which quadruples at double speed, that means at lower speeds there can actually be more cars passing a given point on the road
There is an speed that give the highest capacity on a motorway. Studies here in Denmark have the highest capacity at 80-90 kmt on our kind of motorways. Other road layouts has other optimal speeds for higher numbers of cars per hour.
The relationship is first seen in USA and the brake distance grows with velocity squared that influences your math, but this relationship is mainly observed in real life.
So what you're saying is we should reduce the following distance to be as close as possible to maximize throughput. Maybe even connect the cars into some sort of long cluster of cars. To improve fuel efficiency we could have a single engine to locomote all these cars.
before you reinvent the train, remember this only applies in a free flow environment
"Something that everyone in the world has direct experience with, so everything is just assumed to be known." It's so much fun when my professional field (public school education) and my TH-cam diversions overlap.
Seriously, having once been a student doesn't make one any more knowledgeable about education than having driven a car makes one an authority on traffic policy.
Is 2 seconds really safe? I'm asking because the time to stop when decelarating increases at higher speeds.
Another factor: in an urban environment you shouldn't just drive with a fixed 2-seconds gap, but you should adapt your distance according to the _stopping_ distance, to account for all the possible disturbances/hazards/obstacles that can pop up at any time in such an environment.
Then the formula for vehicle flow basically becomes a slanted parabola (since there is a quadratic term in the formula for braking distance, and that is overlaid on the constant factor of car length), with its maximum at around.... drumroll... _30_ _km/h_ (for typical car lengths and braking deceleration values).
So in a city you get the best throughput around 30 km/h even without taking intersections into account! Consequently it's not a big surprise that the actual average speed ends up somewhere in that region as well (traffic is basically "solving" that mathematical optimization in real life).
The nice thing about such a low speed limit is that in many cases traffic lights become obsolete altogether (as the slow speed gives drivers more time to take in and react to their surroundings and other traffic), which in turn makes traffic flow even better (as long as the road networks isn't overloaded, but then traffic lights also wont help). This in turn also reduces noise, fuel consumption and pollution (due more gentle cruising and less stop&go, which is the main contributor to fuel burn). Oh, and if course also reduces cost for electricity and maintenance...
Also, since for low speeds the stopping distance is _shorter_ than the 2-second spacing, the capacity is actually _higher_ than in the free-flow case for the same speeds, without compromising safety! (Up to ~1670 vehicles/h for 5 meter cars @30 km/h, and still almost 1600 vehicles @50 - in fact it's only at ~55 km/h where 2-second-distance starts to take the lead, but even at 80 it does not surpass the optimum!).
So lower speeds limits (around 30 km/h) really are a win-win-win situation for everyone (residents, pedestrians, taxpayers, _and_ drivers).
Addendum: I have put the formula into a spreadsheet on google docs. Unfortunately YT doesn't like external links (and is very good at detecting obfuscations by now), so you'll have to piece it together (+ dot, # slash):
docs + google + com # spreadsheets # d # 10d3wQApBxluszhclXlrOpGETT7flAD0-eHJ8sFR0ll4 (English version is on the second sheet)
Btw. this table also shows why slower speeds are so much safer: the whole stopping distance from 30 km/h (
Since youtube is intent on removing everything that even vaguely resembles an external link (to a spreadsheet where I did the math with nice graphs), here's the old-fashioned way:
let a = braking deceleration (about 7.5m/s² on dry asphalt), r = reaction time (usually about 1s), l = vehicle length (average about 5m), v = speed in m/s
then the space a single car occupies on the road is: s(v) = r·v + v²/(2·a) + l
hence the occupation time of a section of road by a vehicle is: t(v) = s(v)/v = r + v/(2·a) + l/v
find the minimum:
dt/dv = 1/(2·a) - l/v² = 0 → v = sqrt(2·a·l) = 8.66 m/s = 31.2 km/h = 19.4 mph
Throughput at this speed is 3600/t(8.66) = 1670 vehicles per hour.
We need to change the formula again because holding "seconds" constant assumes that we don't care about the social and economic costs of traffic accidents. 1st accidents are going to happen because people's reaction times are variable based on cell phone usage or other impairments. So if we have 1% of the population With 1.7s reaction times and a 1% chance something odd happens that requires an emergency stop, (the accuracy of the numbers don't matter just acknowledge that accidents hapen) then we can see that increasing speeds will give disproportionately more damaging accidents. So, in order to keep social costs constant we must increase following distance at higher speeds to ensure distracted driving collisions cause equal damage regardless of speed. Since people have proven that they will not consistently modulate their following distance when checking their phone. This is of course only applicable to limited use highways where violence is limited to car on car/motorcycle/truck
Based on your road capacity video, could you redesign certain streets, such as Manhattan's 3rd avenue, based on those principles
Retail bicycle outlets need to do more to encourage young people and older adults to ride bicycles.
Sponsoring bike trains to escort children on their rides to school would be a great start. Organizing volunteers, teachers and other to ride along would be a great start. Getting children out of minivans and onto bicycles would be healthy exercise, build independence and make society healthier.
Fun ride should also be organized. Getting a local bike club or school to sponsor an annual event to a local park or trail would encourage both adults and children to ride bicycles. Getting local elected officials to help with sponsored activities would help to educate them about the need for safe, protected bike lanes and trails in their community. Offering space and coffee for local riders to meet up would also improve store traffic.
I would not let my kid ride a bike in the city, or most american towns. Its simply too dangerous. Pedestrians and Bicycles are among the fast growing fatality rates in the entire transportation system. Rides are great, but the city has to make actual efforts to develop cyclist protection before people would feel safe doing so.
@@cadenorris4009 That is why safe, separated bike lanes and trails are needed. It is so older adults and children can ride bicycles safely separated from cars.
I worked for a construction company in The Netherlands and they bought a plot of land in France to build a holiday bungalow park, outside town. The entrance of the park is at a departmental road where you can drive about 90km an hour, not an ideal road for cycling. And certainly not one I wanna risk my life cycling on. In order to sell the bungalows to Dutch people they asked the municipality to provide a separate cycle path from the park to town. It took almost 2 years to get the cycle path, because it isn’t (or wasn’t) common practice to provide separate roads for cyclists in France. But they wanted to accommodate the bungalow owners because they could revive a dismal local economy. It is great to be able to cycle 20min to the local bakery to get fresh bread every morning instead of getting it by car. A great daily exercise. It’s sad that there no other cycling paths in the area. It would be great to cycle around the area instead of sightseeing by car.
It has little to do with people not wanting to cycle. It has everything to do with road design.
A question related to the video (and not to the point you’re making): Why were you driving a bus on the 455 (and 32(?)) bus lines? Did Haarlem not trust you to drive a bus closer to home/work/in own province 😋?
_"Although the following distance changes according to the speed, the length of the car stays the same."_ Einstein:
Light speed traffic congestion....
Just another reason why cars approach a point mass as speed increases
More speed means less time for people to merge on a road , right? So the higher speed traffic goes the less merging, do less capacity
great channel
what about highways on which cars can actually overtake each other, and assuming everyone stays right except to pass
But every one is tailgating like mad, if the follow distance is a static 50 ft, now the capacity does go up as speeds increase.
Nope thats a what you just described is a traffic jam
and then everyone wonders about the pile-ups that eventually (inevitably) happen...
About overtaking everyone: IT IS FASTER, maybe you will get stopped by the next intersection, but you will have these one or two rubber banding while starting and stopping cars less.
Which in with my anecdotal evidence can be the difference between being stopped for another intersection cycle couple intersections down the road.
This doesn't mean it's good for ecodriving, it's clearly a tradeoff that is more akin to gambling that the saved carlengths will help you catch green somewhere.
I would be very curious to compare what empirical studies show are the maximum car throughputs of different speeds - has any freeway ever got close to 1500 vehicles per lane across an hour?
It's pretty difficult to have a real life scenario with 1500 vehicles per lane for an hour long. It's also very easy to get a (phantom) traffic jam in 1500-1800 vehicles per hour range.
With the use of AI controlled cars, you can reduce the following distance to a minimum and get a much higher throughput then the 1800.
Wait.
For the freeflow thing, the time between cars (even if we asume them to be dots) its not the same for every speed. Higher speeds typically mean less time between cars (it doesnt increase lineraly with speed)
That's the distance drivers _should_ keep though. The 2 seconds are basically a buffer for reaction time + full application of the brakes, so that you don't rear-end the car in front of you in case its driver suddenly has to brake.
And of course that rule only applies to roads without hazards from other directions (i.e. basically highways without intersections, pedestrians, etc.).
@stephanweinberger maybe.. however I feel like for 50km/h or so, distance between cars is more constant than time
Doug Ford needs to see this!
My source is….
Capacity constraints not typically faced by bicyclists.
Here’s a consideration. Optimal conditions for maximum throughput. I’m talking professionals racing on a closed course. A 33-car Indycar pack at The Brickyard can probably fly by, all bunched together on the opening lap in… I dunno, 10 seconds? Meanwhile, the 176 members of a Tour de France day 1 peloton during the leadup to a sprint finish can go by in a similar amount of time. That’s more than 5x the amount of cyclists, and at the Tour, this is usually on public roads maybe half the width of the Indianapolis Motor Speedway.
Obviously real world conditions do not reflect race conditions. Nevertheless, the difference is striking.
@Build the Lanes, best video yet. Can you do the same for an intersection capacity/hr in relation to lanes, through and turn?
Thank you!
Your asymptotic graph looks plausible, but there are models that find a different relation. Can you comment on the Lighthill-Whitham-Richards model? Do the Dutch manuals give an explicit mathematical model?
My burning curiosity is this: can "smart", "networked", or "AI" intersections improve throughput significantly? My second burning curiosity is do lane jumpers increase decrease or not affect traffic throughput. Thanks for your answer, kkbye.
Lane jumpers decreases traffic throughput because it forces other people to slow down and that can even create traffic jams.
2s rule assumes that a car in front of me stops immediately and on spot. Average driver needs
Exactly. In an urban environment we cannot apply the 2-second rule, but have to use the real stopping distance.
If you do the math (i.e. calculate the occupation time of a vehicle + its stopping distance at speed v, then find the minimum) you find that the optimal speed is about 30 km/h.
let a=braking deceleration (about 7.5m/s² on dry asphalt), r=reaction time (usually about 1s), l=vehicle length (average about 5m), v=speed in m/s
then the occupation time of a section of road by a vehicle is t(v) = (rv + v²/(2a) + l)/v
find the minimum:
dt/dv = 1/(2a) - l/v² = 0 -> v = sqrt(2al) = 8.66 m/s = 31.2 km/h
Throughput at this speed is 3600/t(8.66) = 1670 vehicles per hour.
the 2 second rule is to always be able to stop when the car in front makes an emergency stop, based on 1 second reaction time and 1 second to move your foot to the other pedal and apply braking. And you can't move to a different lane when there more cars in those lanes.
@@kempo_95 OK, buta preceding car won't stop in place. It also have it's braking distance. You will not reach that car in 2 seconds like to a static object. Your relative speeds will be much lower.
The increased speed is perfectly offset by the car crashes
Takeaways:
Bigger cars are worse for traffic.
Speeding does not make a difference.
Follow distance is a key factor but safety is also important.
The best traffic is no traffic. Build train tracks
Is it just me or does it seem like about 15% of the audio is missing? I notice this on other channels/videos too and for me at least, it's difficult to focus on the content.
Nice food for thought
Great video that gives useful tools to urbanists and safety advocates. Unfortunately in the US the problem is political. Ignorance itself is political, theres a reason we all grow up assuming gridlocked roads should just be expanded, while no one ever corrects us. Facts just do not matter to the voting public and politicians who rely on our ignorance to support their schemes.
short answer
higher speed = more distance between cars = cars per hour doesnt change much
where can one study transport engineering/science?
the only program for transportation engineering in the US is Morgan State University in Baltimore. Otherwise you need to go out of country.
1:47 As a software engineer I have to disagree, the stuff I see in my field is way more stupid than anything I have seen described when it comes to transportation.
Then againm both are very abstract fields about flow that at first glance look very practical.
All these numbers go down the drain the moment when driving aggressively makes you feel that you actually done more to get there on time. And that alone will always be enough for most people to keep pushing through traffic regardless of end result.
Holding 2 seconds distance while going 70 - 90 km/h is nuts. And when all cars in a long row hold 2 seconds distance, it is a catastrophy waiting to happen.
The formula for kinetic energy EK=0.5mvv is the key, here. Speed has the squared impact on it.
It's not nuts, is a common thought practice in driving schools across the world for highway driving.
The thing you are forgetting in your thinking here, is that you are not driving to seconds behind a still standing concrete wall. The car in front of you has more or less the same breaking distance as you, so as long as you start breaking within those 2 seconds, you won't hit the car in front of you.
The 2 seconds has nothing to do with kinetic energy formula, but with reaction time. That reaction time stays the same if you drive 10 kmph or 100 kmph
Technically, if humans were robots with no reaction time, in a perfect world, cars could be driving bumper to bumper at 100 kmph, and if they all instantly brake at the same time, they would all stop perfectly fine.
(mixed of significantly different mass to traction ratio like cars vs trucks should keep longer distance, and then E=½mv² is relevant.
The 2 second rule assumes the car in front of you isn't going to defy physics and come to an immediate stop. The 2 seconds is to account for reaction time to both determine the car in front is braking, apply the brakes, then realise how much the car in front is braking - then it assumes you'll both come to a stop at roughly the same rate. This is why trucks usually leave a bigger gap and why people who cut trucks off deserve their cars to be crushed into cubes with them still inside.
@ I learned three seconds distance. One for reaction time and two for stopping distance.
And what you say about a concrete wall may not be so true. What often happens is that a car suddenly brakes hard for something. For every car behind it, they start braking later and later, untill they hit a massive lump of cars without even starting braking. Then we have very highly chances of fatalities in the cars in the middle of that lump of cars.
And braking distance increases with the square of the speed increase. So when going faster, we should all increase the time distance to the cars in front of us.
This is the reason higher speed gives or should give lower road capasity.
@@th5841 The physics doesn't change along the line. If every car figures out how hard they need to brake within those 2 seconds nobody should hit anyone else unless the car in front hits a solid immovable object.
@@shraka You shouldn't assume that everybody will figure out their optimal action. That is naive. You should assume the oposite.
Let's do a physics class, shall we?
When you are driving 80 km/h, you are doing 22 m/s. In two seconds that is 44 meters.
Let's say there is a chain collision in progress in front of you, but you haven't noticed, yet. The car in front of you didn't either, so it crashes straight into it without braking. Now you have 44 meters to act before you are a part of this mess. You spend 1 second (average reaction time) to cope with what just happened and to react. You then have 22 meters left.
Braking distance increases with the square of the speed increase. A car need 2 meters to stop from a speed of 20 km/h. This is what I learned on the teory lessons when taking my driver's license. This number may be 1.7 or 1.8 or sometimes much more, but 2 is a good number and for your safety it is better to round up than down.
80 is 4 times more than 20. The braking distance is 4 squared times the distance of 20; 16 * 2 m=32 m. That is 10 meters too much, so you crash.
Your speed in the moment of the crash can also be calcualated, using the same logic as abow. So your crashing speed is calculated to be 45 km/h.
And then you can embrace for the next car to hit you. Hopefully it doesn't go more than 45 km/h in that moment.
Remember that when you brake, the driver in back of you doesn't instantly know if you are braking hard or just adjusting your speed a little.
2 seconds is ok when doing lower speeds. But not for higher speeds.
Road capacity is higher cause ain't fucking NOBODY in The Netherlands actually keeping 2 sec distance. Especially not on the highway.
That kinda gap can and WILL fit 2 cars. Cause 2 cars will definitely slide in there.
When you said an average following distance of 2 seconds, i laughed out loud. And when the distance is shorter, speed varies a lot more (phantom traffic jams). I hope people don't get the impression far if everyone followed 0.1 seconds behind the car in front that it would improve traffic flow. Because, as you said, the real world is messy. It doesn't work that way.
Since the typical reaction time of average drivers is about 1 second, and it also takes some time for the brakes to fully apply, everything less than 2 seconds is just a pile-up waiting to happen.
@stephanweinberger 100%. And yet when driving here in Brisbane, Australia, a 2 second gap is very rarely seen...and people wonder why multi vehicle nose to tail crashes are extremely common and cause many delays, as well as damage and injuries.
*FEEDBACK*
Yes, the video does help. It's not an interest of mine, but it does help me a bit to become more knowledgeable. I don't think that it's too useful, though.
*TOPIC REQUEST*
I recall a guy sharing his discovery that slow driving in the right lane unplugs traffic jams much more quickly, as opposed to fast driving in either lane. It was so counter intuitive, but he somehow explained it.
If you know that this is true, then would you explain it, please? Perhaps it incentivizes fast people to stay on the left.
Slowly decreasing and increasing speed unplugs traffic jams more then doing it abruptly. I think that was what he was talking about.
@@kempo_95 Oh, okay.
Did you see the same video/article?
@@eugenetswong No, I haven't watched it. But that's what I imagine he was talking about. The most common thing to create a traffic jam is people braking abruptly.
No, manually driven vehicles are supposed to maintain distance in time, not a set number of feet/meters
3600/2 = 1800 in simple terms.
Basically for an observer a vehicle passes every 2s therefore speed is immaterial.
*the 2s rule was what I learned in 1979 at student driving education.
This only works on the assumption that the only possible obstacle is the car in front of you, and your car brakes at least as good. Then the 2s are basically just a buffer for your reaction time + the response time of the brakes, so that you don't rear-end the vehicle before you even have a chance to apply the brakes.
But in a city, obstacles/hazards can basically pop up at any time, so driving by this rule isn't really applicable in this environment.
(Fortunately it is on the safe side up to speeds of about 50 km/h, because then the actual stopping distance is typically shorter than the distance driven in 2s.)
@stephanweinberger I was being slightly facetious, and the video goes into details which include car length. My point was that for most people on the open road the 2s rule means that within the range of typical speeds, say 40 to 80mph doubling the speed doesn't double the number of cars per hour.
i already understood this concept but frankly the way you explained it here made it more confusing. You should talk more clearly about stop and go vs continuous flow at a higher level (a graphic would help). I was having trouble following the central message you were trying to push in part because it didn’t feel like you established your “thesis” well at the beginning of the video
I dunno, saying that urban roadways should be designed differently than rural ones sounds pretty urbanist to me
Or its just good engineering 🤷
@ well whatever you want to call it, I’m on board 😊
Shouldn't the distance between cars (in seconds) be increased for higher speeds? The kinetic energy of the car and thus the breaking distance increase as a square function of speed. Yet this model uses a linear relationship between speed and distance between cars.
sure, but most traffic models assume just a 2 second spacing. The highway capacity manual uses the 1800 veh/hr based on the point particle assumption. Just to give you an idea of how unscientific the whole thing is!
But, in reality all of these maximums are theoretical because were just never going to get close to these with imperfect traffic conditions. So trying to calculate everything perfectly is nice but not very helpful in the long run.
@@buildthelanes, yes that point was very clear in your video and I have no qualms about that. I wanted to consider this aspect primarily for love of mathing things out - even if practically useless. A secondary reason was that in public debate there are people confidently arguing for both "higher speed = higher capacity" and "lower speed = higher capacity". Practical application is unfortunately a secondary factor in public debate, and political decision making is a contingent on public sentiment. As an experiment I ran the numbers with different following distance and even half a second difference favours slower speeds (30 km/h, 1,5 s distance, 5 m car -> 1714 cars/h). This is absolutely not applicable to real life, 30 km/h speeds logically would be applied only in situations where there is a lot of interplay between cars, bikes, pedestrians, transit etc and as to your point, that makes the calculation irrelevant. It's just fun to calculate and good to have a case if the argument "higher speed = higher capacity" just won't die.
It is hard focusing on what your saying when you keep showing places I frequently see. Lol
Lost oppurtunity to mention that (unnesecarily) long vehicles will also reduce capactiy, regardless of all other factors.