Thought experiment about cars and journey times.

[mike_nofx]

I have a bit of a thought experiment and i'm wondering if anyone has any ideas on the outcome.

If 2 cars leave on a 100km journey through a city, leaving from the same point and arriving at the same destination, with car A leading, and car B following from behind after 2 seconds, will they arrive at the destination still only 2 seconds apart from each other?

The rules are that:

- Must always stick to the speed limit

- Driving style between 2 drivers is the same. Same speed take offs, same speed slowing down to stop.

- Must always stick to the left-most lane, with no changing lanes to overtake (If left lane is flowing faster than right lane that is ok).

- Cannot speed through amber lights, stop if you have time.

- Car A cannot wait for car B. If car A gets through a set of lights and car B misses out, car A continues as normal.

- Car B cannot tailgate car A, a normal safe gap must be left (2 second gap) unless stopped.


Things to consider are that due to the fact that the drive is through a city, which includes many sets of traffic lights, its inevitable car A will make it through traffic lights that car B misses out on, and also other cars will almost certainly come between car A and car B, especially if a safe gap is left.

The question again is, will both cars make it to the destination after 100km and still only have a 2 second time difference?

[aussiblue]

100km journey through a city

How many cities do we have with a diameter of 100km or more? I guess you are including their suburbs.

[wodahs]

schrodingers cat come to mind the answer is yes
i mean both are correct but youd never know till you open the box , i mean try it
it is possible but highly un probable to happen

even if car "B" was on a car trailer being towed by car "A" for it to leave the start 2 seconds after car a was to leave car a would probably still be clearing the start area its self unless they were side by side
and the same for the finish even more so if the finish was a drive way as car "B" would be waiting for car "A" to clear the entry for it to be able to enter

[marty351]

..

[Ben73]

Sometimes, but usually no. Too many variables

[snap0964]

Originally Posted by mike_nofx

Things to consider are that due to the fact that the drive is through a city, which includes many sets of traffic lights, its inevitable car A will make it through traffic lights that car B misses out on, and also other cars will almost certainly come between car A and car B, especially if a safe gap is left.

So if Car A is stopped at various traffic lights, Car B has opportunities to catch up at not exceeding the speed limit.

[aussiblue]

Must always stick to the left-most lane,

So what happens if the left most lane is a left turn only; I can see the two car trapped forever running around a block that has left turn only lanes at each corner?

Using queuing theory maths you could develop a computer simulation model provided you make various constraining rules such as no left hand only turning lanes, no car parking in the left hand lane, all road have only two lanes on each side, both cars must use the same route etc.

But it's not a trivial task. I tried to develop a Fortran 77 program as part of a University programming course I did in the early 1980's to try and prove that the Perth Freeway traffic from Canning Bridge to Perth CBD would flow just as fast if all cars kept a safe distance between them (1 car length for every 10km/hr or something like that and a min or 3 meters between each car at all times and factoring in what happened if cars did travel bumper to bumper and there were increased multi-car accidents) and it just became too complex and large a model with all the variables (varying vehicles sizes and braking and acceleration rates etc) even with as I recall virtually a single length of road with traffic lights at each end. I always meant to go back when I had more time and finish it but never did (and I never used Fortran again; it was in its death fros as an in-vogue programming language even then). For my course project I reverted to writing a much simpler simulation about students queuing for access to the University's computer lab (a real problem for most other students - I was the only one with my own computer and dial up access) to show how many lab stations were needed to get various wait time targets over various days and hours.

Now there is software like this you can use https://www.youtube.com/watch?v=6xTLd47SmIs and https://www.youtube.com/watch?v=azmcu1cn2vg And they have graphics that my Fortran program running on a DEC 10 could never have.

[MattSAU2XR8]

The way this is laid out the trip time won't always be the same each time the experiment is conducted since:

- Car A is allowed to get away from car B, if for example car B misses a light that car A got through

- Car B is not allowed to overtake car A?

- So car A MUST get to the destination in front of car B, and only car B is disadvantaged relative to car A by missing lights.

[roKWiz]

Do car A and B have the same amount of fuel in their tanks ?

[yearby]

[QUOTE=mike_nofx;6332961]


- Must always stick to the left-most lane, with no changing lanes to overtake (If left lane is flowing faster than right lane that is ok).



QUOTE]

Is car "B" allowed to overtake car "A" in the left lane?

[mike_nofx]

Originally Posted by aussiblue

How many cities do we have with a diameter of 100km or more? I guess you are including their suburbs.

Could be zig zagging through streets of a city. I used the example of a city because on open roads its easy to stay behind another car.

Originally Posted by snap0964

So if Car A is stopped at various traffic lights, Car B has opportunities to catch up at not exceeding the speed limit.

Yes exactly. And its also a possible scenario car A reaches a stop sign while its busy and has to stop for a while, and when car B reaches that stop sign theres no other cars at the intersection and the stop is very brief. Or the other way around, and car B is even further delayed.

Originally Posted by aussiblue

So what happens if the left most lane is a left turn only; I can see the two car trapped forever running around a block that has left turn only lanes at each corner?

Ok, so left most lane which continues in the intended direction of travel

Originally Posted by MattSAU2XR8

The way this is laid out the trip time won't always be the same each time the experiment is conducted since:

- Car A is allowed to get away from car B, if for example car B misses a light that car A got through

- Car B is not allowed to overtake car A?

- So car A MUST get to the destination in front of car B, and only car B is disadvantaged relative to car A by missing lights.

Yes car A will always get there first. The question really is how far behind will car B be. Will it all even out and still only be a 2 second gap after 100km?

Originally Posted by roKWiz

Do car A and B have the same amount of fuel in their tanks ?

Enough to do the 100km and more.

Originally Posted by yearby

Is car "B" allowed to overtake car "A" in the left lane?

No, because car A is also in the left lane in front.




Personally I am unsure of the outcome. I feel like there will almost always be a longer than 2 second gap at the end of the experiment but I can't say exactly why.

[Mechan1k]

You will find that multi-lane roads under 80km/h does adhere to the keep left unless overtaking rule ... so that's most of suburbia really.

So keeping to the left lane as much as possible shouldn't really be part of the experiment.

But if we talk Sydney traffic ... and the opening statement advises that car A and B don't have to take the same route.

I do understand that it mentions "leaving from the same point and arriving at the same destination, with car A leading, and car B following from behind after 2 seconds"

It doesn't state following 2 seconds for the entire trip .... only after leaving the starting point.

The outcome will be very different on every trip taken.