The Problem is the Yellow Light
For 100 years traffic engineers have been setting the duration of the yellow light in conflict with the laws of physics that govern the motion of traffic approaching an intersection. The yellow light is too short. According to international practice as established by the Institute of Transportation Engineers (ITE), the yellow light is half the time it takes a driver to stop his car. In addition to that problem, the practice accommodates only the average person driving an average passenger car on dry pavement. When the driver sees the light turn yellow and no longer has the distance to stop comfortably, the practice mandates the driver to proceed toward and enter the intersection at the speed limit or faster. The practice requires that the driver knows the exact location upstream from the intersection where stop turns into go.
Any driver who falls on the wrong side of average, who is a commercial truck driver, who drives in the rain or snow, who is slowing down to turn or avoid a pedestrian, or who cannot determine the location of the invisible stopgo point to within a foot, is systematically entrapped to run red lights.
Engineers introduce the defect into every signalized intersection. It is called a systematic malfunction. The result is entire city populations running red lights. With a dozen red light cameras flashing for 10 years, a city and red light camera will issue about 150,000 tickets.
Traffic engineers create the problem. The government and its red light camera vendor profit from the problem. This is called "racketeering." Racketeering is a federal crime.
The Yellow Change Interval: Four Major Engineering Errors and Omissions This paper explains the four major ways traffic engineers as a profession misapply the physical and mathematical sciences thus putting in harm’s way the life, health and welfare of the public.
 
Yellow Time: Contrast between Practice and What is Required How much yellow time do reasonablyperceptive drivers need? Do commercial vehicle drivers need more time? This chart reveals how traffic engineers systematically short the yellow for reasonablyperceptive drivers and for various of types of vehicles. 

Does the MultibillionDollar Red Light Camera Sector Owe Its Existence  and Profits  to Traffic Engineers' Misapplication of the Yellow Change Interval Formula? Traffic Technology International, a Londonbased journal, published this cover story about red light cameras exploiting the faulty ITE equation in its October/November 2013 issue. This story summarizes much of the literature on this web site.
 
Animations Illustrating the Problem by Johnnie Hennings, P.E., Accident Reconstruction Analysis, Inc., Raleigh. The animations are to scale and true to the laws of physics. In the animations you will see the "critical distance". The critical distance line marks the closest point to the intersection where the driver can still stop safely and comfortably. The line is the point of no return. By federal guideline the amount of time the light is yellow equals the time it takes the driver to traverse the critical distance on the precondition that he travels at the speed limit. You see this fact play out watching the straightthrough unimpeded drivers in the following videos. But notice how the yellow will be too short for turning and impeded drivers.
Most States implement a shorter turn lane yellows than throughmovement lanes. This demonstrates that traffic engineers do not understand the kinematics of the ITE yellow change interval formula. A new federal guideline called NCHRP 731, formalizes the implementation of the error. One of the 731's authors is Richard Retting, the father of the red light camera industry in America. 

ITeam: Are Yellow Lights Too Short When Making Turns? ABC WTVD, Channel 11, Raleigh, NC: May 5, 2014. This newscast includes an interview with Dr. Alexei Maradudin, the inventor of the yellow change interval formula. Maradudin rebukes DOTs all over America for their misapplication of physics. Kevin Lacy, a spokesman for the NCDOT, responded to ABC. Lacy claims that there is no deterministic equation which models all traffic. Lacy is wrong. The deterministic equation not only models all traffic, but all objects in the universe. It is a = v/t, eq. 41 here, of Newton's second law of motion. The equation for turning traffic is eq. 13 here. The red light camera empirical data proves that the deterministic equation is the solution. That should be expected. Everyone (other than traffic engineers) have known about this equation since 1687 when Isaac Newton discovered it. Johnnie Hennings, P.E., an accident reconstructionist, wrote a rebuttal to Kevin Lacy's/NCDOT's letter. 

Derivation of the ITE Yellow Change Interval Formula This paper shows the mathematical steps it takes to derive the yellow change interval formula from scratch; that is from F= maNewton's second law of motion. The paper describes the physics and the assumptions. 

Misapplied Physics in the International Standards that Set Yellow Light Durations Forces Drivers to Run Red Lights This paper describes the formula, what it does and how today's traffic engineers misapply it. This paper also presents red light camera citation data showing how minor changes in yellow light durations dramatically and permanently affect red light running counts. 

Maradudin's Letter Condemning ITE for Misapplying His Formula This is a letter (July 2015) from Professor Alexei Maradudin, the last surviving inventor of the yellow change interval formula. In an upcoming yellow light guideline which ITE is about to publish (called the RP), ITE misquotes Maradudin. Maradudin does not take kindly to that. Maradudin does not like ITE misapplying his formula to turning motions and to any motions impeded within the critical distance. Maradudin does not like that ITE intentionally and knowingly forces drivers to run red lights by establishing a standard which sets the speed used in the formula to values less than the posted speed limit.  
Dos and Don'ts of the Yellow Change Interval Formula This is a letter (July 2013) from Professor Alexei Maradudin, the last surviving inventor of the ITE yellow change interval formula. Every Department of Transportation in the world does the don'ts which cause drivers to inadvertently run red lights. 

The Problem of the Amber Signal Light in Traffic Flow Gazis, Herman and Maradudin (GHM) coauthored this paper in 1959. In 1965 ITE miscopied this paper's equation 9 into its Traffic Engineering Handbook. By omitting GHM's "Analytical Considerations", ITE has been instructing traffic engineers to abuse this formula for over 50 years. 

Determination of LeftTurn Yellow Change and Red Clearance Interval The American Society of Civil Engineers (ASCE) Journal of Transportation Engineering published Dr. Chiu Liu's paper in 2002. This paper is the followup work to Gazis, Herman and Maradudin. Dr. Chiu Liu's formula computes the minimum yellow duration which allows all traffic to move legally. Chiu's formula is equation 13 on page 454. This paper is peerreviewed. The beginning of the paper states explicitly that the turn lane yellows must be longer than the straightthrough. 

Uncertainty in the Yellow Change Interval When seeing the light turn yellow, do you stop or do you go? Many times the decision is not clear. Can the indecision be expressed mathematically? Yes. This paper computes the uncertainty in the yellow change interval. Should not law enforcement be aware of this uncertainty? Should not law enforcement grant the driver the tolerance required by the engineering? 
Television Newscasts
Preexisting Condition  Yellows Too Short
Many people assume that cities have a nefarious agenda which calls for the shortening of yellow lights once the cameras go in. That assumption is false. Cities need not shorten yellow lights in order for a handful of cameras to flash tens of thousands of innocent motorists annually. The "federal guidelines" already makes yellows too short. When you hear a city or a DOT justify its yellow times saying, "We are just following federal guidelines", they are truly saying, "We are ripping you off and causing many of you to crash."
The federal guidelines consist of two things. 1) A math formula called the ITE yellow change interval formula, and 2) The MUTCD which sets the minimum and maximum lengths of a yellow light.
Both guidelines are wrong. Adherence to these guidelines force hundreds of millions of drivers who are doing nothing wrong to unintentionally run red lights daily.
It gets much worse than this. There are cities like Winnipeg, Chicago and New York City who pride themselves with not complying to the ITE formula. They set their yellows even shorter than the formula's calculation. But the ITE formula does apply physics. The ITE formula satisfies one type of traffic movement which represents the shortest possible yellow time. Any shorter than the ITE calculation grows a steady stream of unintentional red light runners to a fastflowing river.
The Red Light Cameras of Cary, North Carolina
by Chad Vader
This is a true story. This is an account of the red light camera program that existed in the Town of Cary, North Carolina. Dr. Moley represents the reallife person Brad Hudson. Hudson came to work once a month and without looking at the videos, accused and convicted everyone of running a red light. Baby Cookieflex plays the part of Maria, an employee of Redflex. She worked at the Safelight office in Cary. If you had a problem with the ticket, the Cary police sent you to Maria or to Frank Rubino. Maria indeed said, "Aren't you happy that your $50 goes to public schools? Don't you care about children?" Until the very end of the Safelight program, Cary had spread Redflex's propaganda line to the local TV stations and the newspapers. Cary never said what percentage goes to schools. By contract, the Town of Cary paid Redflex $49.50 of every $50 for approaches which had less than 120 violations per month. That is 99%. That leaves 50 cents to the schools. The contract contained a tiered compensation clause. When the Town of Cary and the NCDOT engineers caused more than 120 drivers to run red lights per months for an approach, Cary had to pay Redflex 60%. Once Cary took out its own administrative costs, about $5.00 out of $50.00 went to the schools.