Re: [MLUG - DISCUSSION] Offtopic - speeding now

[Nathan Odle <EMAIL:PROTECTED>]

I was getting ready to throw up my arms in disgust and give my civil 
engineer perspective on the matter, but Jon took care of it for me.  All 
thanks aside, I'm wondering where a cognitive psychologist learned Intro 
to Traffic Engineering :)

-N

Jonathan King wrote:

>On Thu, 4 Dec 2003, Russell Horn wrote:
>
>  
>
>>>Something to think about:  If the average car is traveling at 50
>>>mph, it will spend twice as much time on the road as it would if
>>>it were traveling 100 mph.  Therefore, slower speed limits mean
>>>more cars on the road and more crowded highways.  Crowded roads
>>>may increase accident risk.
>>>      
>>>
>>Actually I've seen a few studies showing the most efficient (in
>>terms of getting traffic to move) speed is just above 50mph. Where
>>traffic is going faster than that, if one car breaks, meets a
>>truck or something and brakes, the effects continue for several
>>miles behind and become exagerated because of the high speeds.
>>    
>>
>
>OK, so there are competing views here that I think seem inconsistent 
>because people are looking at different things.  The traffic geeks 
>generally are interested in maximizing the volume of traffic (flow 
>rate) along a stretch of road; they always call this "q".  Density 
>(concentration) is the number of cars per unit length of roadway, 
>and v is velocity.  So we have:
>
>   q = k v_s
>
>where v_s is the average "space speed" (let's skip the details on
>that).  Intuitvely, and in reality, high traffic densities are
>associated with lower speeds, while at very low densities you can
>drive as fast as you like (the so-called "free speed" v_f).  Even
>more conveniently, this relationship is almost linear in practice,
>so that:
>
>   v = v_f * (1 - k / k_max).
>
>In other words, when density (k) is essentially zero, you move at 
>the free speed, while when k is the maximum density k_max, you don't 
>move at all.  Substituting the second equation into the first, you 
>get:
>
>   q =  v_f k * (1 - k / k_max)
>
>Which again tells you that the maximum flow_rate is achieved at a 
>speed less than the one you would choose if the road were empty.  To 
>get a crude idea about what that speed is, look back at:
>
>   v = v_f * (1 - k / k_max).
>
>k_max is the density of bumper-to-bumper, so you can compute k in 
>terms of how many car lengths there are between you and the other 
>guy.  If you allow 200 feet between cars (for breaking), then 
>that's about 11 car lengths between cars, so k / k_max is like 1/12.
>So you can go very close to your free speed.
>
>The problem from the point of view of speed, of course, is that
>roads tend to be more congested than that.  If you can only give 3
>car lengths between you and the next guy, then k / k_max is 1/4, and
>you are at 75% of the free speed.  That's going to be pretty close
>to 50 mph if you assume that the free speed is the speed limit of 70
>mph.  And, sure enough, the flow rate here is more than twice as
>high.  
>
>Now, the above analysis blows off an explicit analsysis of passing
>and related stuff, but this turns out to be captured decently in the
>trade-off between speed and density: people do drive more slowly
>when densities are high.  And when somebody forces you to change 
>lanes because they are tail-gating, you increase the density of the 
>other lane, and things slow down...
>
>So what really causes problems is *variation* in speed, either in a
>single vehicle or across vehicles.  A moment's thought indicates
>that the only way collisions can happen is when the velocity of the
>hitter and the hittee differ.
>
>So, in the end, though, you are both right.
>
>When Mike is driving his car across a deserted Minnesota highway in
>good conditions, road capacity is maximized and Mike's driving time
>is minimized when he goes as fast as he likes while retaining
>control of his vehicle and keeping his speed variance to a minimum
>by not hitting a bridge pylon or a deer. :-)
>
>When Russell is driving his car on a crowded motorway, road capacity 
>is maximized when the overall speed is chosen to be as fast as is 
>safe, which is going to be rather slower than the free speed, 
>but which could be faster than it currently is if people would not 
>speed up and slow down so much.
>
>And this is why rush hour is such a time and money sink.  If we
>could spread the traffic of one rush hour over two hours, then the
>traffic density at any time would be halved, and average speeds
>would go up a *lot*.  If traffic density at rush hour gives you only 
>one car length in front of you, then doubling that space would allow 
>you go about 50% faster.  This is why congestion pricing is in 
>prcinciple such a good idea.
>
>Now, if you really wanted to improve road safety via ticketing
>people, you would still ticket people who were driving irresponsibly
>fast (80+ on a rain-slicked road), but you would concentrate more on
>the lane-weaving speed-varying maniacs we all know too well.  And,
>alas, also on those people who cannot any longer drive safely at
>highway speeds.  A big hidden problem coming up for us will be how
>we can simultaneously keep the highways safe and manage to keep the
>elderly independently living in an age where there are going to
>many, many more people who "need" to drive but really can't hack it.
>
>jking
>
>
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