If Newton had an apple and a car...

October 28, 2011 3:20 PM

Please help me solve a traffic equation that I have been throwing around in my head for years...

Here goes... You are sitting at a red light (in a car)...you are one of more than a dozen cars waiting at this light, waiting for the green. When the light turns greens, everyone in the traffic line accelerates at the same speed, and at the same moment. Thus, car number 12 is moving just as car number one is... All things being equal, i.e., every car DOES actually accelerate at the same moment and same speed, is this actually feasible? Is there some law of physics that prevents this from happening. Is it not possible for multiple objects, in a single line, to move, from a stopped position, at the same time?

posted by AlliKat75 to travel & transportation (28 answers total)

No, it's not impossible, and you can prove it to yourself by holding two objects, one above the other, and releasing them at exactly the same time. They'll accelerate all the way to the ground, but maintain the exact same separation!
posted by steveminutillo at 3:24 PM on October 28, 2011 [1 favorite]

Yes, it's physically possible. (Look at the Thunderbirds doing a formation take-off, for instance). I think the problem here is human nature, not physics -- the first driver is watching the light. The second driver is watching the first driver, and maybe the light. The third driver, and drivers n+1 after that are watching the vehicle in front of them. Therefore, it's more of a staggered start, since driver n+1 can't start moving until she 1) sees driver n moving. 2) realizes that it is time to go. 3) uses the accelerator. A friend of mine does transportation analysis for a living and could probably quote me a formula for this, but it'd be about psychology and vision, not physics.
posted by Alterscape at 3:24 PM on October 28, 2011 [1 favorite]

I would guess that the only thing really keeping this from happening are human reaction time (which you've controlled for in your description) and human attention (which you've also controlled for). Further, at several cars back, a driver may not be able to see the light, and must thus rely on the car in front of her moving.

tl;dr The only thing keeping this from happening wouldn't be a law of physics, but, rather, human factors.
posted by cheeken at 3:25 PM on October 28, 2011

At speed these cars would not be maintaining a safe follow distance. Accidents would be unavoidable.
posted by 2bucksplus at 3:26 PM on October 28, 2011 [1 favorite]

Ask this guy. Or just read his book.
posted by webhund at 3:33 PM on October 28, 2011

Isn't this basically what a train does? (not exactly, obviously, because there's some wiggle room in the connectors and whatnot) I mean a train is basically a bunch of separate things that, because of how they're connected, move together.
posted by brainmouse at 3:36 PM on October 28, 2011 [2 favorites]

At speed these cars would not be maintaining a safe follow distance. Accidents would be unavoidable.

That depends on how far away they are when they start out.
posted by goethean at 3:36 PM on October 28, 2011

At speed these cars would not be maintaining a safe follow distance. Accidents would be unavoidable.

But, assuming they were all maintaining a constant acceleration and speed, they would always have the same distance between them as when they started. So, I don't see any accidents happening.

I'm assuming this is more a physics question, and less a traffic question, though.
posted by cheeken at 3:41 PM on October 28, 2011

Essentially we are talking about computer-controlled cars, right? I think that this is physically possible to acheive if we entirely take out the human factor (given some nominal distance between cars to overcome the very very minor differences in clock timing and what have you).

I watched a video once where an unmanned car reasearch group had programmed 6 or 7 cars to travel perfectly in sync (to demonstrate the 'commute of the future') and I THINK they also demonstrated synchronous starts, but I'll have to dig up my old, old, old notes to find the name of the lab. But technically there is no reason why this wouldn't be possible with autonomous cars.
posted by muddgirl at 3:43 PM on October 28, 2011

When the light turns greens, everyone in the traffic line accelerates at the same speed, and at the same moment.
...
Is it not possible for multiple objects, in a single line, to move, from a stopped position, at the same time?

It is possible to do this but not probable. If all the cars were automated and synced to the light I'd say, 'no problem'.

In the real world, the first driver is watching the light. The second driver is watching the first car. And so on. Even if all the drivers watched the light and tried to accelerate at the same time and the same rate I doubt they could do it due to different reaction times and different driving habits.

As always, the problem is human.
posted by mazola at 3:44 PM on October 28, 2011 [1 favorite]

There's nothing impossible about this, but I think the reason it doesn't happen is that car #3 can't rely on car #2 accelerating on time. So #3 has to wait until they can see that #2 is moving before #3 decides to move, else risk rear-ending them; and there's a fair delay between deciding to move and actually moving visibly enough for car #4 to commit. Basically what 2bucksplus said about following distances.

(When I'm impatient I do often watchthe light or the car 2-3 cars ahead of me to know when to accelerate— and then I have to brake abruptly because another driver has an extra 400 milliseconds of reaction time. Not a good idea, with highly-variable human drivers. I don't see a problem with automatic cars doing this, though.)
posted by hattifattener at 3:49 PM on October 28, 2011 [1 favorite]

No law of physics prevents it, but it would require a level of coordination between the drivers that's unlikely in the real world. Each driver would have to trust that all drivers in front of them would step on their accelerator at exactly the same moment, and that all would accelerate at the same rate.
posted by zombiedance at 3:49 PM on October 28, 2011

As others have said, the issue is of cues: if everyone operated from the green light as the cue to start accelerating, then it might be a seamless movement of items in series moving as one. But it is more like a train, in that each car pulls the next along, so the individual items rely on the object ahead of them as the cue to move.

Furthermore, you need to take into consideration the open space for safety: when stopped, cars can be a foot or two apart and everyone is comfortable. But once you're moving, people have different amounts of space required to feel safe, and that increases as speed increases. Perhaps if everyone was to only drive 5 mph, then drivers could maintain a few feet of distance and feel safe. But once you get up to road speeds, the gaps are sizable, so acceleration must be even more staggered, to provide ample space between cars.
posted by filthy light thief at 3:53 PM on October 28, 2011

i.e., every car DOES actually accelerate at the same moment and same speed

This happens exactly as described at every single standing start in a motor race from Formula 1 down. Just as described. The exact model you suggest.

It just doesn't happen on the road because people are unable to gauge the acceleration of the person in front of them. Inconsistent acceleration means you have to wait not only for them to move but also how fast they move before you can judge how fast you can move away from rest.
posted by Brockles at 3:53 PM on October 28, 2011

'commute of the future'

It's possible for hundreds of people to accelerate at the same speed if they're riding the subway.
posted by justsomebodythatyouusedtoknow at 3:56 PM on October 28, 2011 [2 favorites]

This happens exactly as described at every single standing start in a motor race from Formula 1 down.

YouTube video illustrating Brockles example.
posted by tylerkaraszewski at 4:05 PM on October 28, 2011

It's possible in a purely theoretical framework, but even if the cars are computer controlled and linked and such, you have physical factors to deal with - varying degrees of tire wear, rolling resistance, mechanical tolerances/variation in gearsets or whathaveyou - even if they're 'identical', it's extremely hard to have a complex system like a car match 11 others in every minute detail. All those details can end up affecting the situation. Computer simulation, yeah. Real world? Someone's getting a bumper up the bumper.
posted by pupdog at 4:06 PM on October 28, 2011

pupdog - An autonomous control system has a feedback loop which will account for all that. Essentially it measures it's current position/speed/acceleration, compares it to the desired position/speed/acceleration, and adjusts its controls (the throttle and steering wheel) accordingly. So yes, this is possible (and has been demostrated many times) in the 'real world.'

Now there is some computational delay and error within the control system itself, but given a smart engineer that's not going to make a noticeable difference. (Given a hasty engineer... well, that's a story for another day).
posted by muddgirl at 4:13 PM on October 28, 2011

As others have said, this is feasible in the realm of physics, but not in the realm of actually driving (safely). Example: I was at a light and maybe 8 cars back. We were accelerating fairly like you mention, until I heard a large noise in front of me and stopped abruptly. The car behind me -- watching the light, and not me, crashed into me.
posted by DoubleLune at 5:22 PM on October 28, 2011

The physics says this is just fine, but the second you're talking about traffic, you've entered a world where physics is a very minor player, and human factors is the main limiting force.

Accidents would be unavoidable.

To expand on previous answers, let's assume a dozen totally identical cars, being driven by drivers who have agreed to all leave when the light turns green, and accelerate to the same speed at the same rate. Let's even assume people who are capable of doing this task, despite the vague nature of acceleration rates and the natural variances in reaction times.

Now, a dog runs in front of car #1. The driver stops so it won't hit the dog. You're in car #2. You were driving at speed a fraction of a second behind car #1 (if you have a 5 foot gap when you're stopped, even at the moderate speed of 30 mph, it takes you little more than 0.1 second for your front bumper to pass a point after the rear bumper of car #1).

The only way you can stop in time is to start braking in response to the dog in the same way as car #1. By the time you see brake lights, the driver in car #1 has:
- Seen something enter the clear path of the road
- Determined it was a dog, rather than an empty grocery bag or the Dalai Lama
- Figured out they were likely to hit it given their speed and the dog's trajectory
- Decided that the car needs to slow down at a pretty high rate
- Converted the idea of slowing the car into the need to stop pressing the gas and start pressing the brake
- Moved the foot over to the brake pedal and started pressing on it.

This can be two seconds or more [PDF] and you, in car #2, would have to do this at the same time as the driver in car #1. If you just go off the brake lights (which provide no indication of how fast the car is braking), there may be a little less time in the first three steps, but the pure braking response time is still there. So you, in car #2, need to monitor the situation in front of car #1 as efficiently as the driver of car #1 (and have the same reaction time and response).

Now think of the driver of car #12. For the same reasons, they can't be looking at the brake lights of the cars ahead of them, they would need to watch the road in front of car #1. But at this point, they are 200 feet farther back than car #1, and they have 11 cars between them and the dog, so they actually need much better perception (well beyond the practical) than the driver of car #1. Of course, there's no reason a dog couldn't run out in between car #11 and car #12, so the driver of car #12 is also monitoring 10 gaps between cars at the same time.

Certainly, autonomous computer-controlled cars remove a lot of the uncertainties; car #1 can nearly instantaneously send the message "stop accelerating and brake at level 8.21 now" to the following cars, and the delays in signal processing mean that the cars can remain quite close together. (If you leave the recommended two seconds of space between your car and the one in front, at highway speeds, that's 175 feet.)

There's a reason we don't have these "highways of the future" past physics (which says that there's no problem for two objects to accelerate in parallel) and engineering (which says that you need very tight control systems, but not beyond the range of our computing power - or that of a generation ago).

Right now, there are a huge number of collisions on the highways. If someone, (say, Google) set up a system that enabled cars to automatically drive themselves in tight platoons, the roads would be more efficient and there would be fewer collisions. But the few collisions that still happened would now all be Google's fault.
posted by Homeboy Trouble at 5:34 PM on October 28, 2011

There's no debate of any sort here.

You've described your constraints and aren't asking about human factors issues. Nothing in those constraints precludes coordinated motion.

It makes about as much sense as asking if the front and rear of the same car are moving at the same speed. They are. There aren't any 'equations' involved.

Now, if you want to ask a question about human factors, response times, vehicle-to-vehicle variation, you can include most of the above explanations. Most, however, don't address your simple, basic, self-answered question.

(If you are interested in the concept of exact simultaneity of course, there are spacetime issues involved, but you are asking about a car, not the Enterprise.)
posted by FauxScot at 6:49 PM on October 28, 2011 [1 favorite]

If someone, (say, Google) set up a system that enabled cars to automatically drive themselves in tight platoons

This has been a dream of traffic engineers since at least the Futurama exhibition. I think you would love the heck out of some Intelligent Transportation System videos -- e.g. and espcially this automated highway system demo.
posted by dhartung at 9:51 PM on October 28, 2011

When the light turns greens, everyone in the traffic line accelerates at the same speed, and at the same moment.

Imperceptibly close to the same moment and close to the same speed is possible.

Exactly the same moment is not possible, because of relativity. It takes time for the signal to go (the green wavelength light) to make it down the line. So even if all reaction time a computational time is removed, the last car will still be starting a little bit later than the first car. This is true no matter where the signal begins. It takes time for information to propagate, so unless the cars are arranged along a perfect circle, the signal to "go" can't reach the different cars in different locations at exactly the same time.
posted by yeolcoatl at 12:09 AM on October 29, 2011

You have all given me EVEN MORE to think about. I believe we should all get together at red light nearby and see what happens. Thank you, all, for all these ideas.

P.S. Homeboy...Determined it was a dog, rather than an empty grocery bag or the Dalai Lama...that's just plain funny.
posted by AlliKat75 at 2:08 AM on October 29, 2011

Is it not possible for multiple objects, in a single line, to move, from a stopped position, at the same time?

A thought experiment:

Mentally switch out all your cars for train carriages, since it's perfectly clear that a train starting from rest does behave essentially the same way your proposed line of cars should.

Now put an engine in each carriage, and run controls over a wireless network so that instead of each carriage being accelerated by a balance of tension forces from front and rear couplings, that exact same pattern of net force vs. time is applied via the wheels. Clearly, the overall behavior of the train will be the same as before.

Now, since all the forces on the carriages arrive via the wheels, there's never any force on any of the couplings, which means they're not actually doing anything and you can just remove them all. Still works.

Now make the carriages car-shaped. You have your original scenario back, and it still works.

But you do need the magical wireless-network controls fitted to all the cars. Doing it by human guesswork would be bumpy.
posted by flabdablet at 8:36 AM on October 29, 2011

When stopped assume the cars are 2 feet apart. At 30 MPH they need to be three car-lengths apart as typically recommended for safety. It is impossible to get from condition 1 to condition 2 without the cars accelerating at different times and/or rates.

Your scenario would be more likely if cars always stopped at a light at least three car-lengths apart. Then they could maintain the same distance apart as they accelerated. But of course people don't stop three car-lengths apart.
posted by JackFlash at 10:43 AM on October 29, 2011

Put more succinctly:

State 1: Cars are stopped at a light and are 2 feet apart.

State 2: Cars are traveling steadily at 30 MPH and are 40 feet apart (about 3 car lengths).

It is physically impossible to get from state 1 to state 2 unless the cars accelerate at different times and/or different rates.
posted by JackFlash at 3:05 PM on October 29, 2011

At 30 MPH they need to be three car-lengths apart as typically recommended for safety

30 MPH is 13 metres/second. A typical family car is a little under 5m long. So three car-lengths at 30MPH is about 1 second apart, which isn't enough.
posted by flabdablet at 3:08 AM on October 30, 2011