The Problem is the International Standards
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 published this cover story in its October/November 2013 issue. This story summarizes much of the literature on this web site. By federal standard, the length of the yellow light is half the time it takes one to stop his vehicle. This unusual characteristic of the yellow creates dilemma zones. These are stretches of roadway upstream from the intersection where if the driver is in one when the light turns yellow, either the physics will literally force the driver to run a red light, or the driver does not have the clairvoyance to know exactly whether to stop or go. Red light camera data for the Town of Cary, North Carolina shows that 92% of 140,000 tickets issued were issued because of dilemma zones. Dilemma zone is the official term for this problem. Engineers acknowledge that dilemma zones have been a problem for 50 years and that dilemma zones exist at every intersection. However engineers do not understand that it is the federal guideline that creates dilemma zones. That being so, engineers blame innocent drivers. When confronted with the physics of the federal guideline, engineers offer no defense. They only say they have been using the formula for 50 years.  
Yellow Time: Contrast between Practice and What is Required What engineers do in practice is incompatible with what is required by driver behavior, vehicle characteristics and the physics of traffic movement. The incompatibility causes crashes and it is a boon for the red light camera industry. Engineers treat commercial vehicles as if they are passenger cars. Engineers treat all passenger cars as if they are driven by alert 25 year olds. Engineers treat all drivers as if they are approaching the simplest of intersections. Engineers treat all drivers as if they are going straight and going the speed limit to and through the intersection. Engineers treat all drivers as if hazards will never appear at the intersection. 

Laura passed away on September 23, 2014 from a crash a week earlier. The circumstances surrounding the crash impute dilemma zone failures created by the yellow light formula. 

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. The problem demonstrated in these animations is the sole reason why the red light industry exists. The industry exploits a systematic physics error in the federal standard which determines the duration of a yellow light. Watch the animations. The critical distance line marks the closest point to the intersection where the driver can still stop safely and comfortably. By federal standard the amount of time the light is yellow is the time it takes the driver to traverse the critical distance at the speed limita fact you can see by watching the straightthrough driver.
In these animations the left turn yellow is shorter than the straightthrough yellow. While the straightthrough yellow is 4.5 seconds for the 45 mph road, these States set the left turn yellows typically to 3 seconds. By the laws of physics the turn yellow must be longer than the straightthrough. In these animations the left turn driver enters the intersection at 20 mph but the yellow duration should be 5.4 seconds. This shorter turnlane yellow flaw exists in States like North Carolina, California, Virginia and States that implement a new federal standard called NCHRP 731. One of the 731's authors is the father of the red light camera industry. 

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. Kevin Lacy of the NCDOT responded to ABC. In turn we reply to Kevin Lacy: The deterministic equation which models all traffic is eq. 41 here. The case for turning traffic is eq. 13 here. The red light camera data proves that eq. 41 is the overall solution. The "Notes" section of your NCDOT spec misapplies Maradudin's formula to turns, and then that same section instructs the engineer to compound the error by plugging into it the wrong speed (20 mph). Physics and Maradudin require the speed to be at least the speed limit. NCDOT's 20 mph even violates federal guidelines. The result is that the NCDOT shorts the yellow by about 3 to 4 seconds as stated in the newscast. We also know that the engineer's assumption "If you make the yellow too long, people will treat the yellow as a green." is a rumor. This rumor has never been shown to be true, not even once in a hundred years. Maradudin himself dismissed the exact same rumor in his day: (page 131). Johnnie Hennings, P.E., an accident reconstructionist, wrote a full 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. 

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. No DOT makes the turn lane yellows longer because traffic engineers do not understand the physics of the ITE formula. Traffic engineers think drivers go slower in the turn lane and thus deduce that the yellow can be shorter. But traffic engineers do not know that the yellow light duration is about how long it takes to traverse a fixed distance. That fixed distance is the distance it takes to comfortably stop your car from the maximum allowable speed. The slower a driver goes, the longer the yellow must be. That misunderstanding is enough to convict every traffic engineer in the United States and Canada for violating the legal mandates for professional engineers. Every State and Province requires that a professional engineer must possess and apply the knowledge of the mathematical and physical sciences necessary for his job. 

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
ITeam: Are Yellow Lights Too Short When Making Turns? ABC WTVD, Channel 11, Raleigh, NC: May 5, 2014. 

ITeam: Raleigh Fraudulently Issuing Red Light Camera Tickets ABC WTVD, Channel 11, Raleigh, NC: Feb 5, 2014. 

Red light Camera Traps: Does Science Prove Our Yellow Lights are too Short? "The Institute of Traffic Engineers miscopied the yellow change interval formula into its 1965 engineering handbook. Traffic engineers, the socalled experts, do not know the math and science behind their own formulas." CBS WTKR, Channel 3, Hampton Roads, VA: February 5, 2014. 

Newport News Reevaluating Yellow Light Times after NewsChannel 3 Investigation CBS WTKR, Channel 3, Hampton Roads, VA: February 7, 2014. 

Redflex Tells Local Cities Where to Put Cameras Based on ‘Violation Calculator’ CBS WTKR, Channel 3, Hampton Roads, VA: February 19, 2014. WTKR proves what we suspected. Redflex knows physics too. Given the predictable failings of the ITE yellow change interval formula, Redflex wrote a violation calculator to compute exactly where the engineering failures produce the most revenue. 

Red Light Cameras Take Advantage of Flawed Physics Formula, Physicist Says NBC WNCN, Channel 17, Raleigh NC: February 16, 2015. In the WNCN broadcast, the public gets a flavor of traffic engineers' confidence in their methods. The confidence is a reaction to my challenge. However the confidence is a facade for the desperate face of denial, a denial in order to hide ignorance. My concern is over the misuse of a physics formula that computes yellow light durations. I know that traffic engineers do not understand this formula. In the broadcast Rusty Thompson states, "Brian's concerns have been disproved." Thompson is a liar. WNCN told me that Thompson's statement originates from an IIHS article. I know the IIHS article. The article addresses a paper I wrote in 2010. What IIHS wrote in its article does not address my concerns, let alone disprove them. Thompson never read my Derivation paper to find out if IIHS got it right. This was my response to IIHS. You can read IIHS article and compare it to my paper and know for yourself that IIHS, ITE, Rusty Thompson, Jed Niffeneggar, the entire community of traffic engineers do not understand their own formula. Their misunderstanding is obvious even to a high school physics student. The opposite of Thompson's disapproval statement is true. Every physicist and professional engineer who has considered my work confirmed it. My work is simple Newtonian mechanics. My work is nothing unusual. My work is nothing new either. Both Dr. Chiu Liu of CalTrans, and Dr. Alexei Maradudin, the inventor of the formula itself, long ago published in peerreviewed journals what I repeat again. Last May, ABC interviewed Dr. Maradudin. On air, Maradudin condemned every DOT in the country for misusing his formula, and wrote in a letter to CalTrans that traffic engineeers misunderstand his formula. Both interview and letter are at this website. Niffeneggar's statement, "Red light cameras reduced tbone collisions by 54% and so the program is definitely worth it." For the same report also says that the "red light cameras increased rearend collisions by 32%." Ask a victim of newly induced rearend collision if he thinks that red light cameras are worth it. You will get a resounding, "No!" There any many science problems with the Niffeneggar's report which I enumerate here. The WNCN broadcast mentioned that I lost my lawsuit against Cary. It is important to know what that means. It is not what people assume. First of all, Cary shut down its red light camera program immediately after the judge classcertified our complaint. Prior to that Cary shut down all its leftturn lane camerasthe ones we called out in the lawsuit. One look at the graph of yellow light duration versus red light running counts and it was obvious even to a child that the NCDOT calculated its left turn yellow durations incorrectly. Secondly, the judge did not award legal fees to the Town of Cary. Thirdly, I did not lose because the NCDOT proved that its traffic engineers were applying physics correctly. Even though the misapplication of physics was my complaint, the judge never ruled on that. Instead the judge ruled that Cary was abiding by the statutes. Very different. The statutes allow the NCDOT to make errors. The judge ruled that the NCDOT was following its engineering practices, even though the NCDOT's practices include using obsolete signal plans with wrong speed limits and subsequence miscomputed yellow light durations. My problem is that the practices are wrong. The judge ruled according to the statutes, not according to whether NCDOT uses current plans and devised its specifications conforming to science. The judges ruling, unfortunately, indirectly overruled the laws of physics. Though the red light cameras are gone in Cary and Knightdale, the physics problem with the NCDOT yellow persists. It is still out there causing crashes and fatalities.

Press Release  Laura Yost, Victim of Yellow Light
Press Release  Brief 
Brief with North Carolina 
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 guarantees a steady stream of unintentional red light runners for every type of traffic movement.
The Problem is with the Yellow Light
Everyday when confronted with a yellow light we ask, "Should I stop? Should I go? Should I beat the light? Should I slam on the brakes? Do I have time to make the turn? Am I going to run this light by a fraction of a second?" To us these questions are part of everyday driving. We do not give them a second thought until we get a red light camera ticket. We must understand that it is the nature of the yellow light which gives birth to our questions. The yellow light poses predicaments which though we are familiar, we cannot solve correctly 100% of the time. Our failure to solve sometimes ends up by us unintentionally running a red light. Sometimes the yellow light even poses a unsolvable situation which forces us to run a red light. All the predicaments, situations and even the questions themselves rise from mathematical formula traffic engineers use to set the length of yellow lights.
Traffic engineers use the the ITE formula to set yellow lights. The formula sets the yellow time to 50% of the time it takes a driver to stop his vehicle. We want to change the formula so that it gives the driver 100% of the time. Because some drivers think that yellow light means stop, they will stop aggressively causing a rearend collision. Some will skid into the intersection on a red. For some drivers who go instead of stop, yellow light means "go really fast." While we poke fun at that definition in movies like "Starman", that definition is actually the truth. You will find that definition in the 1982 ITE publication Transportation and Traffic Engineering Handbook.
It is necessary to have faith in traffic engineers, but we learned in the last four years that that expectation is not warranted. In spite of the lifeanddeath responsibility they have with setting yellow durations, traffic engineers (as a profession) do not know how to set a yellow light. They misunderstand the formula. The ITE formula is like a picture and a picture is worth a thousand words. Those words are in the language of physics, a language which traffic engineers apparently do not understand. At this web site's North Carolina Exhibits section, you can read the depositions and affidavits of 4 NCDOT traffic engineers. 4 of 4 did not know where "v" is supposed to measured. 4 of 4 do not know that the formula cannot be applied to turning movements. 4 of 4 did not know that this formula creates dilemma and indecision zones. 4 of 4 did not recognize that this formula is not an equation of motion, a physics term meaning that one cannot apply this formula to objects in the universe and expect drivers to conform to it. 3 of 4 did not know that the ITE formula embeds the safe stopping distance formula. 1 of 4 could not name a single one of Newton's Laws of Motion and believes that "physics only applies to a partially vacuumed Earth."
The misunderstanding of the ITE Formula extends beyond the borders of North Carolina. It extends to the National Transportation Board. The November 2012 report NCHRP731 explicitly exhibits this misunderstanding. Written by Hugh McGee, Sr., Keven Moriarty, Kim Eccles, Mindy Liu, Timothy Gates and Richard Retting, these authors represent the typical beliefs of traffic engineers. These authors make the same mistake. They misapply the ITE formula to turning movements. Read their treatment for left turning drivers. Then compare it with our paper The Derivation of the Yellow Change Interval Formula, Dr. Chiu Liu's paper Determination of LeftTurn Yellow Change and AllRed Clearance Interval and the original paper on the amber signal, The Problem with the Amber Signal Light in Traffic Flow and recent letter by the inventor of the yellow change interval formula himself, Dr. Alexei Maradudin.
We found that the Courts are not the venue to resolve problems of physics. We had sued the Town of Cary over these issues. The case began in 2009 and the trial ended January 17, 2013 with the Court ruling in favor of Cary. The judge, Paul Ridgeway, signed the Order and Judgment on March 4, 2013. Ridgeway used a local ordinance to trump the laws of physics. From the bench he ruled that "Mr. Ceccarelli and Ms. Millette violated the traffic ordinance of running a red light." But the lawsuit had doing to do with that. The complaint was that yellow light durations violating the laws of physics, NCGS 89C and the MUTCD. Ridgeway did not address the complaint! He sidestepped the issue and in so doing, ruled that the Town of Cary can financially exploit the errors of the NCDOT, that legitimate engineering practices can contain errors both typographical, mathematical and scientific, and that physics is irrelevant to the motion of cars. The NCDOT abided by its own practices, correct or not, and so Cary was not responsible for the NCDOT's ineptitude. That judgment came in the light that Cary's own traffic engineers had confessed to some of the mistakes. Cary could take all the money it wants from hundreds of thousands of innocent motorists and not be liable for it.
We decided not to appeal. Because Ridgeway is a wellrespected judge, we felt that we could only expect the same ruling from appellate judges.
Source of Red Light Camera Revenue
Cary, North Carolina told by Chad Vader
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.