Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be) - BMW Luxury Touring Community
 
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post #1 of 9 Old Jun 3rd, 2012, 10:17 am Thread Starter
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Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Street lights timed for 35 mph are also timed for 70 mph

I am by no means a mathematician, but this quote above has been bugging me for some time...

I put this into excel and used a 900 foot Manhattan city block and at first blush it looks like using Manhattan as a guide it would not work... I am sure that you can make this work for a specific speed / distance etc. but then the statement would only be true under exact conditions...

I used
Distance Seconds
900 FT took 17.53360608

then I added 10 seconds for the light to be green I came up with this pattern

Block # Distance Seconds Green Red
1 900 17.53360608 12.53360608 22.53360608
2 1800 35.06721216 30.06721216 40.06721216
3 2700 52.60081823 47.60081823 57.60081823
4 3600 70.13442431 65.13442431 75.13442431
5 4500 87.66803039 82.66803039 92.66803039
6 5400 105.2016365 100.2016365 110.2016365


Using this I then took 70 MPH and came up with time to travel 900 feet = 8.766803039 seconds

When I put this I came up with

Block # Distance
1 900 8.766803039
2 1800 17.53360608
3 2700 26.30040912
4 3600 35.06721216
5 4500 43.8340152
6 5400 52.60081823
7 6300 61.36762127
8 7200 70.13442431
9 8100 78.90122735
10 9000 87.66803039
11 9900 96.43483343
12 10800 105.2016365
13 11700 113.9684395
14 12600 122.7352425
15 13500 131.5020456
16 14400 140.2688486
17 15300 149.0356517
18 16200 157.8024547
19 17100 166.5692577
20 18000 175.3360608


So It looks like the 35 MPH driver would be fine, but the 70 MPH driver would hit red at the 2nd or third light depending on when during the green cycle he hit the interesection.

Anyone care to comment?


And I want to thank whoever started the tag line in the first place for taking away 15 minutes of my life I will never get back

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post #2 of 9 Old Jun 3rd, 2012, 11:06 am
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Not flying much these days, Paul?

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post #3 of 9 Old Jun 3rd, 2012, 11:47 am Thread Starter
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Quote:
Originally Posted by deputy5211
Not flying much these days, Paul?

Work has been killing me lately. Fortunatly I have road trips to Miami for the next wee three weeks. so I will be hauling it down 1-95 on the LT...

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post #4 of 9 Old Jun 3rd, 2012, 12:51 pm
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

I love math but not enough to screw my head around this one. At least right now......

This being said I would offer that it would be difficult to prove this empirically. If the signals are set for 35 mph then the speed limit is most likely 35 or 40 mph.

It would seem that going roughly twice the speed limit would most likely draw unwanted attention from law enforcement and the offense might be taken seriously enough (2X speed limit) that you might get to spend some time at the Graybar Spa. From which it would be decidedly difficult to continue the experiment.

Just sayin.......

Loren

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post #5 of 9 Old Jun 4th, 2012, 2:57 am
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Quote:
Originally Posted by pauleknight
Street lights timed for 35 mph are also timed for 70 mph

I am by no means a mathematician, but this quote above has been bugging me for some time...

I put this into excel and used a 900 foot Manhattan city block and at first blush it looks like using Manhattan as a guide it would not work... I am sure that you can make this work for a specific speed / distance etc. but then the statement would only be true under exact conditions...

I used
Distance Seconds
900 FT took 17.53360608

then I added 10 seconds for the light to be green I came up with this pattern

Block # Distance Seconds Green Red
1 900 17.53360608 12.53360608 22.53360608
2 1800 35.06721216 30.06721216 40.06721216
3 2700 52.60081823 47.60081823 57.60081823
4 3600 70.13442431 65.13442431 75.13442431
5 4500 87.66803039 82.66803039 92.66803039
6 5400 105.2016365 100.2016365 110.2016365


Using this I then took 70 MPH and came up with time to travel 900 feet = 8.766803039 seconds

When I put this I came up with

Block # Distance
1 900 8.766803039
2 1800 17.53360608
3 2700 26.30040912
4 3600 35.06721216
5 4500 43.8340152
6 5400 52.60081823
7 6300 61.36762127
8 7200 70.13442431
9 8100 78.90122735
10 9000 87.66803039
11 9900 96.43483343
12 10800 105.2016365
13 11700 113.9684395
14 12600 122.7352425
15 13500 131.5020456
16 14400 140.2688486
17 15300 149.0356517
18 16200 157.8024547
19 17100 166.5692577
20 18000 175.3360608


So It looks like the 35 MPH driver would be fine, but the 70 MPH driver would hit red at the 2nd or third light depending on when during the green cycle he hit the interesection.

Anyone care to comment?


And I want to thank whoever started the tag line in the first place for taking away 15 minutes of my life I will never get back
Wow. Sorry Paul. That line is kinda like "I had a great time, thanks, I will call you". It sure sounds good at the time, but it holds no merit.
I should have just given you an easy question like - "What happens when an irresistible force intersects with an immoveable object?"

"You can tell more about a person by what he says about others than you can by what others say about him."
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Remember folks, street lights timed for 35 mph are also timed for 70 mph. ~Jim Samuels




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post #6 of 9 Old Jun 4th, 2012, 7:57 am Thread Starter
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Quote:
Originally Posted by Cochinosucio
"What happens when an irresistible force intersects with an immoveable object?"
Last time the above happened to me, I got married

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2008 R1200GSA Dec'11 - March '12 (sold)
2009 K1200LT The Черный заяц Nov '10 - Nov '11 (sold )
2000 K1200LT Flying Purple Mile Eater May '10 - Nov '10 (sold)
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post #7 of 9 Old Jun 4th, 2012, 8:26 am
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Wrll, itmight work and it might not, depending upon how the lights are programmed.

Think of it this way. If the lights are programmed so that they do not turn red while you are traveling between the last lifht and this one, that driving twice as fast will not workl. On the other hand if they do turn red in bertween, (then there are two greens while you are traveling,) the going twice as fast might get you to the green that you would normally miss.

In fact if there are an even number of greens (or an odd number of reds) during the programmed trip, then it woild work. Other multiples of the speed limit might also work, depending upon the programming.

In practice however, lights are often not uniform distance appart, there is other traffic to contend with, and in most cities there are through streets (one ways and major thoughrofares) that are programmed for preferential treatment that overrides the timing of the cross streets.

(by the way I am a mathimatician, or at least I used to be before I becaame a software engineer, and now a project manager.

David Tilsen

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post #8 of 9 Old Jun 4th, 2012, 9:00 am
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

I didn't take time to do the math, but didn't really need to. The statement is almost correct. The correct statement is:
Lights timed for 70 mph. are also timed for 35 mph.

From a truth table perspective there are the statement, the inverse, the converse and the contra-positive. If the statement is true then the contra-positive is also true. for the above statement, the CP would be:
Lights not timed for 35 mph are not timed for 70 mph.

Neither the inverse not converse are true:
Lights timed for 35 mph. are also timed for 70 mph.
Lights not time for 70 mph are also not time for 35 mph.

Bottom line is, if you are going exactly 1/2 the speed for which the light is timed (or any multiple of 2 in the denominator), you will hit the light on every other, every 4th, ...etc. cycle. At least until you are going so slow you can't clear the intersection before it turns red again.

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post #9 of 9 Old Jun 4th, 2012, 9:11 am
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Re: Remember folks, street lights timed for 35 mph are also timed for 70 mph (can't be)

Well, yes, maybe.

Is the acceleration time to speed factored in this somewhere?

Anybody know someone who does traffic control?

B D R
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