Gas or Break!?

How do you time that annoying yellow light right without breaking any laws?  Well, right now we are going to find out!

Well, lets take your average badly timed intersection:

This is the intersection of Burnet and North Loop.  I don't go that way much but Jack Houtz says it's bad so I'll take his word for it.  

Just to give you a reference, going West to East the intersection was measured to be 25 meters (82 ft)

The intersection's speed limit is 30 miles per hour.  Converting this to meters per second will make this problem a lot easier.

30mph * 5280ft / 3600 sec / 3.28 ft  = 13.4 meters per second

We also know that the yellow light at this intersection is a duration of 4 seconds.

Lets say a vehicle approaching the intersection at Burnet and North Loop.  That vehicle is going the speed limit, 30 mph or 13.4 mps, and will continue to go the speed limit throughout the event.  

This vehicle, at 13.4 mps , will travel 53.6 meters in 4 seconds.

The City of Austin Connection states that a red light violation will occur when a vehicle enters an intersection after a light changes from yellow to red.  So the vehicle can be a maximum of 53.6 meters at the exact time the light turns from green to yellow to legally make the light.

So if a vehicle, going the speed limit, can legally make the light if it crosses the point at 53.6 meters at the same time or before the light changes from yellow to red.


Now lets say that vehicle driven by someone that is not in a hurry to get somewhere, and they decide to stop.


We found that a standard vehicle traveling at 13.4 mps is able to stop safely and effectively in a minimum of 11.5 meters.


Thus a vehicle traveling at 13.4 mps and approaching the intersection would have to begin stopping 11.5 meters away from the front of the intersection in order to break safely.

With these two points, the farthest point a vehicle needs to reach to make the light and the closest point a vehicle can reach to stop effectively.  We can see an area between these two points is 42.1 meters.

This area represents the distance a vehicle driver has to decide whether to legally make the light or safely stop.  At the speed limit, this distance takes 3.1 seconds to traverse. 

 Say we give the vehicle driver a 1 second reaction time.  This means that the driver takes 1 second between perceiving the change in light color, and beginning to decide what to do.  Thus the driver has 2.1 of that 3.1 seconds to decide whether to go or stop.

Thus we have discovered the maximum distance from the intersection a vehicle can be to make this red light, the minimum distance the vehicle can be to comfortably stop, and the time a driver actually has to make a final decision.


Sources:


"City of Austin - Red Light Cameras - FAQ." City of Austin - Austin City Connection: Home Page.    Web. 25 Oct. 2011. <http://www.ci.austin.tx.us/redlights/faq.htm>.


Calculators, Converters, Apps and Source Code. Web. 25 Oct. 2011.        <http://www.csgnetwork.com/stopdistinfo.html>.