Re: Math for the Traffic Problems

[Iga Nguyen <iga@blue.cft.edu.pl>]

Hi Sonnet and everybody,

On Wed, 27 Oct 1999, Sonnet Nguyen wrote:

> must be larger than : 
>       (Reation Time) * (Your Actual Velocity).  
> .....
> and therefore, the road's passibility does not increase 
> when (almost) each driver on the road increases his/her car's 
> velocity, as at the first sight.    

Wait a minute. I can prove that the typical Driver's Reaction Time 
does not influence on the optimal velocity in the car-fluid model. 
It sounds as new paradox (Isn't it?) but it's true !!
  The second important point I want to denote that the road's 
passibility decreases at high velocity not because there exists
sth you called driver's time reaction but for quite different 
reason, namely : the safe distance (between cars) must increase 
as ... velocity to a power n (where n is bigger than 1).   In 
the reality n equal 2, simply because this distance must be 
bigger than a distance needed to brake the car moving with the 
velocity V ( which is equal  V^2 / ( 4*a ) where a is an avarage 
car's acceleration ).  The necessary distance implied by
the existence of driver's time reaction is linear function of 
the velocity, here, this doesn't play a key.  Here the dominant 
factor as I wrote above, distance needed to stop a moving car, 
is quadratic function of the velocity.     
  
> Hope that some of you can 
> improve the model or develope completely new one.  Use a chance 
> to learn (freely) sth news from others.  It's boring game that 
> I post a simple problems first and later Mrs Iga post a simplest 
> solutions :-)

I do not know wherether my solution is simplest or not, but my 
solution is following:
 
The optimal velocity = 2 Sqrt [ car's acceleration * car's length ]

I suppose that good car's acceleration is appr. equal the 
gravitational acceleration, so 10 m/s^2,  the typical car's
length is equal 4 m, I can go to the conclusion that the
optimal velocity in the road (in the case of high car density 
like in Europe, Cali. or NY) must be app. 12.5 m/s or 45 kmph.

In the town, most typically I drive with the optimal velocity 
near 45 kmph :-))  Hope that you can also apply this quite
interesting result everyday.

The unexpected conclusion to me is that the model could be 
quite complicated with many distributions, parametres, 
variables, etc. but the ending optimal velocity does not depend 
on many factors (like human's attributes), this depends only on 
technical attributes of cars !!  

Iga