Red Light Cameras
Red light cameras exist to exploit math errors traffic engineers make when calculating the duration of the yellow signal light. The errors create redlight runners. Because all traffic engineers more or less follow the same yellow light practice, engineers introduce these math errors into every signalized intersection. The errors are systematic such that anyone who has taken a high school physics class can predict where the most redlight runners are going to be. The redlight camera companies know that bad engineering, not bad driving, is responsbile for the vast majority of redlight runners. But in order to make money, the companies conceal the errors of engineers and shift the blame to drivers. The collective set of drivers have deep pockets.
Dilemma zone. The engineer's calculation for the duration of the yellow light always produces a defect called a dilemma zone. A dilemma zone is a segment of roadway upstream from the intersection where if a driver is in it when the signal light turns yellow, the driver will neither have the distance to comfortably stop nor the time to reach the intersection before the light turns red. The driver must run a red light. Video 4, below, describes dilemma zones.
Where the math errors most oppose the physics of traffic motion, the most redlight running and crashes occur. To learn the math and the physics, watch the first 3 videos.
Video 5 shows what a "redlight violator" usually looks like in the eyes of a redlight camera firm. In their marketting campaigns, redlight camera firms only show camera clips of nasty Tbone collisions in order to scare the city council into buying their product. As you will see in video 5, those clips are falseadvertising. Had the camera companies shown who is their usual redlight violator, the city council would kick the companies out the door.
For those who want to laugh, watch video 6. Video 6 was produced by Blame Societya Wisconsin comedy company. Blame Society's video tells the story of Cary, North Carolina's redlight camera program. It is funny and yet true.
1. Yellow Light History and Math 
2. Errors and Omissions 
3. Legal Problems 
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4. Yellows Explained w/o Math 
5. RedLight Cameras Clips 
6. Funny yet True 
Fearrington, Malmrose vs City of Greenville
North Carolina Appellate Court Decision  March 15, 2022 Greenville loses. Do you still have to pay your tickets? No. You never had to. Paying red light camera tickets has always been voluntary in North Carolina. 

NOTICE: Seeking Plaintiffs for Wilmington and Fayetteville We are starting a lawsuit against Wilmington and Fayetteville. We need plaintiffs who received a red light camera ticket. To be a plaintiff, you must have legal standing. To have legal standing, you must appeal your ticket and lose the appeal: sign up for an administrative hearing. At the hearing, claim 1) that 90% of gross penal fines are not going to the public schools, 2) that in North Carolina, the city cannot enact a local health law. (Redlight cameras affect public safety; therefore, they affect health), 3) that the yellow light is too short, and 4) that the redlight cameras are not allowed to be present because they have been installed by a company not licensed to practice engineering. After the hearing is over, the city must find you guilty. Guilty is good in this case. You must pay $50 (Wilmington) or $100 (Fayetteville). Do these things and you have legal standing. Call 9198150126 for more info. 
ITE Corrects Yellow Change Interval
The Institute of Transportation Engineers (ITE) is a private organization that establishes the practices Departments of Transportation use to set the length of the yellow light. Since 1965, ITE has been publishing a practice that causes every driver in common scenarios to inadvertently run red lights. Over 90% of redlight running is caused by ITE's errors and omissions. About 9.99% of the remaining 10% are caused by traffic engineering errors other than the yellow light.
After 20 years of confrontation, on March 1, 2020, my colleagues and I led ITE to confess that its practice has been wrong. It is a practice that has killed or injured millions of drivers. As the first step, ITE chose to correctly apply the mathematical works of Dr. Alexei Maradudin (19602018), and to newly adopt the mathematical works of Dr. Chiu Liu (2002), Brian Ceccarelli (2010), Jay Beeber (2012) and Mats Järlström (2013).
Jay Beeber, Alexei Maradudin and Mats Järlström
The ITE Journal contains an article by Jay Beeber. Beeber correctly explains Järlström's extended kinematic equation. Beeber's explanation is 100% correct not only about Järlström's equation, but also about the underlying physics principles of what a yellow light is supposed to be. Beeber also includes brief treatises on the requirements for engineering tolerances for law enforcement and the correct application of physics dynamics for the roadgrade adjustment.
You may download the Excel spreadsheet to compute the new official yellow change intervals. I included the yellow change intervals for commercial vehicles so that one can see the range of valid yellow change intervals which accommodate all allowed drivers on the road. ITE now officially acknowledges a valid range of perceptionreaction time and deceleration values, not just the one average value for passenger sedans on dry pavement. ITE does make a strong statement that zerotolerance by redlight camera firms is bad.
The Guidelines document, though it gets the formula right, leaves 4 other errors in tact. (Watch video 2 above.) Also one can read the ITE Guidelines and construe usecases that undermine the physics.
It is important to know that traffic engineers are not legally bound to use the Guidelines. ITE has no legal authority. ITE is a private firm, like Walmart. However there is one exception. The State of Virginia has a statute requiring traffic engineers to use the ITE practice. This exception is actually illegal itself. An attorney can argue that the statute conflicts with the State's Engineering Practice Act. Engineering is supposed to be determined by engineers, not legislators.
Traffic engineers have been using the bad ITE formula since 1965. Even though ITE has corrected its formula, States' traffic engineers will not implement the correction. Implementation means confession. Confession means liability for having killed hundreds of thousands of people, physically injured millions and financially rippedoff hundreds of millions via photoenforcement. The engineers rather harm others than humble themselves. Astonishing as this sounds, as recorded in depositions on this web site, most traffic engineers neither know basic physics nor believe in physics. Those few that understand physics are gaslighted by their ignorant peers. Such ignorance, beliefs and unwillingness to safeguard the public's life, health and property, are all criminal acts for licensed professional engineers according to the engineering practice statutes.
Physics and Math
The Problem of the Amber Signal Light in Traffic Flow; Gazis, Herman, Maradudin 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, Liu 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. The beginning of the paper states explicitly that the turn lane yellows must be longer than the straightthrough. The new ITE guidelines say that Liu's turn lane yellows will be shorter than the straightthrough. 

Järlström's Extended Kinematic Equation Explanation, Beeber, ITE Journal Mats Järlström's equation is for both right and left turning. This article appears in the March 2020 issue of the ITE Journal. It is a perfect explanation of both Järlström's equation, the purpose of the yellow light, and the general principles of tolerances and when it is correct to use the grade adjustment.  
Extended Kinematic Equation, Järlström This is Mats Järlström's technical paper describing his turning equation. The GPS/RaceLogic data Järlström uses profiles a rightturning vehicle's approach to the intersection. It is beautiful. One can visually compare reality with his equation of physics. Järlström's equation models a different type of vehicle approach than Liu's equation. Yet both equations are correct. The equations yield similar values. Using either equation is good practice. Järlström's equation has the added benefit of capping the yellow change interval to the stopping timewhich would be the time it takes a driver to make a U turn.  
Yellow Change and AllRed Clearance Equations of Physics, Ceccarelli This paper lists the physics equations which allow different types of traffic movements to legally enter an intersection. Equation 14 differs from Liu and Järlström. Equation 14 models the velocity/distance profile for the fastest turning approach into the intersection. Liu's and Järlström's equation models the profile for the slowest turning approach.  
Derivation of the ITE Yellow Change Interval Formula, Ceccarelli This paper shows the mathematical steps to derive the yellow change interval formula, both the ITE throughmovement and Liu's equation from F= maNewton's second law of motion. The paper describes the physics and the assumptions. 

Uncertainty in the Yellow Change Interval, Ceccarelli In the presence of the misapplication of stochastic methods, like using the average perception/reaction time or 50th percentile deceleration, one must compute tolerances for the yellow change intervals so that law enforcement does not punish drivers entering the intersection on red within the uncertainty of engineering calculation. The method to do this is called error propagation. This paper describes the mathematical technique of propagating errors. Typical tolerances range from about +/ 2.0 to 3.5 seconds. It is the responsibility of the traffic engineers, not the redlight camera industry, to compute the tolerance. The redlight camera grace period must be at least the tolerance. 

The Yellow Change Interval: Five Major Engineering Errors and Omissions, Ceccarelli This paper explains the five major ways traffic engineers as a profession misapply the physical and mathematical sciences thus putting in harmâ€™s way the life, health and property of the public.
 
Yellow Time: Contrast between Practice and What is Required, Ceccarelli 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. 

Misapplied Physics in the International Standards that Set Yellow Light Durations Forces Drivers to Run Red Lights, Ceccarelli 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. 

Letter Condemning ITE for Misapplying His Formula, Maradudin 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, Maradudin 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. 

Does the MultibillionDollar Red Light Camera Sector Owe Its Existence  and Profits  to Traffic Engineers' Misapplication of the Yellow Change Interval Formula?, Ceccarelli, Shovlin 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. 
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