The Problem is the International Standards
Does the Multibillion-Dollar 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. An engineer making an intersection safe never means he made the intersection such that it allows traffic to move legally.
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 limit--a fact you can see by watching the straight-through driver.
In these animations the left turn yellow is shorter than the straight-through yellow. This additional flaw exists in States like North Carolina, California and Virginia. While the straight-through 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 straight-through. In these animations the left turn driver enters the intersection at 20 mph but the yellow duration should be 5.4 seconds.
I-Team: 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, and for the case of turning traffic, 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 left 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 instructs the engineer to short the yellow by about 3 to 4 seconds as stated in the newscast. We also know that your 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).
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= ma--Newton'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) co-authored 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 Left-Turn 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 follow-up 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 peer-reviewed.
The beginning of the paper states explicitly that the turn lane yellows must be longer than the straight-through.
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 I stop? Do I go? There is obviously a slop in my decision. Can the slop be expressed mathematically? Yes. This paper computes the slop in the yellow change interval. Should not law enforcement be aware of this uncertainty? Should it not grant the driver the tolerance required by the engineering?
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 rear-end 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 life-and-death 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 NCHRP-731 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 Left-Turn Yellow Change and All-Red 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 side-stepped 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 well-respected 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 real-life 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.