Here are the answers to frequently asked questions about traffic signals:
The traffic signal is the cheapest and easiest way to alternate the right-of-way among various traffic streams. Otherwise, a policeman would have to be paid to do this job.
Different signal faces are green at different times, while the other faces are red. In the simplest form, the signal lets one street go, and then stops that street so the other street can go.
That depends on drivers and conditions. Traffic signals reduce the more dangerous right angle collisions, but they can increase the less severe rear-end accidents. Whether a signal reduces accidents depends on whether or not the reduction in right angle accidents is less than the increase in rear-end accidents.
Red-light cameras increase rear-end accidents, especially if the jurisdiction shortens the yellow change interval to increase revenue. This form of decreasing safety to increase revenue should be illegal.
The Manual on Uniform Traffic Control Devices (MUTCD) is a manual prepared by the Federal Highway Administration (FHWA) of the US Department of Transportation (USDOT). It sets requirements on the devices used on all roads and highways in the nation, including some private roads. It sets the rules for the use of traffic signals.
First, an engineering study must be done. They must collect data to see what is actually happening at the location. Different alternatives must be examined. Then the location must be checked against the warrants in the MUTCD for installing a signal. At least one warrant must be met, or no signal may be installed. Finally, funding must be secured.
A signal can cost form a quarter million to half a million dollars to install. Over half of that cost is labor.
A signal controller and cabinet costs about $15000. A mast arm costs almost that much. Signal heads are about $1000 per signal face.
Maintenance is about $8000 per year per signal. This includes parts and labor. Relamping is the primary expense.
No, because it doesn't work. Speeds away from the sign or signal are unaffected. The ideas laymen have about traffic control are often false. This is why layman politicians should not be in charge of traffic control.
Left to himself, a driver will drive the highest perceived safe speed of the road, no matter what speed limits politicians post. Politicians often think they can make a road "safer" by designing the road for 10 mph over the intended speed limit. But then drivers want to drive 10 mph over that limit.
Nothing will ever control the speed of drivers except modifying the perceived safe speed of the road. Often drivers will speed on residential roads that are made too wide because regulations require that all fire equipment must be able to use the road.
The colors come from nautical and railroad practices.
Ships have used red, green, and white lamps for centuries to assign privileged and burdened rights of passage. A green light means the ship whose pilot sees it is privileged, while a pilot seeing the red light knows his ship is burdened, and must turn right or slow down. If both red and green are visible, the ships are approaching each other head-on, and must turn away, usually to the right. The white light indicates the ship was overtaking another ship going the same direction. Multiple white lights indicate the ship is wind powered, and is always privileged over powered craft. Multiple red lights indicate that the ship is so big that it can't change course quickly.
When railroads started using colored signals, the original colors were red for stop, green for caution, and white for go. These colors were fine for signal flags. But white caused a problem at night, when engine drivers saw other lights and mistook them for the signal lights. So the colors were changed to red for stop, yellow for caution, and green for go. But railroad caution signals mean the next signal is red, because the stopping distance of a train is longer than sight distance. The automobile caution signal gives drivers time to stop for the same signal.
These colors were chosen to prevent confusion with vehicle signals.
White was chosen first, as a fourth lens with the word WALK in it, in the 1920s.
Orange was chosen in the 1940s when pedestrian signals were separated from vehicle signals.
Originally pedestrian signals were round. They were then changed to be square for easier identification.
They actually designed standard signal colors so color-blind drivers can tell them apart:
All of the stop indications give some sort of red or yellow stimulus to color-blind people, while all of the go indications give green or blue stimuli. The remaining indistinction is between yellow and red. The signal sequence usually provides the missing information.
The location of the lens in the signal face provides other clues.
These ideal colors had not been fully realized until LED signals appeared, because the incandescent lamps and filters could not produce the correct green bright enough to use in a signal.
For more, see this page.
The following are the meanings of the traffic signal indications:
|Steady Circular Red (SCR)||Stop*|
|Steady Red Arrow (SRA)||Stop†|
|Flashing Circular Red (FCR)||Stop and proceed when safe|
|Flashing Red Arrow (FRA)||Stop and proceed when safe†|
|Steady Circular Yellow (SCY)||Prepare to stop - right-of-way ending|
|Steady Yellow Arrow (SYA)||Prepare to stop†|
|Flashing Circular Yellow (FCY)||Caution - turns yield to conflicts|
|Flashing Yellow Arrow (FYA)||Yield to conflicting traffic†|
|Steady Circular Green (SCG)||Go - turns yield to conflicts|
|Steady Green Arrow (SGA)||Go - protected turn†|
|Steady White Man (SW)||Start and continue to cross street|
|Flashing Orange Hand (FDW)||Continue to cross, but don't start|
|Steady Orange Hand (SDW)||Do not cross street|
* Some turns may be allowed after stop according to state law.
† Only if turning in the direction of the arrow
There are three indications for general use, two indications for night flashing, and five indications intended for traffic turning in a specific direction. There are also three pedestrian indications. This is the minimum number needed to give all of the meanings needed to safely control traffic.
The flashing orange hand means:
Yes. Here is a partial list:
A HAWK (High-intensity Activated WalK) signal is a three-section signal for a pedestrian crossing (see illustration). It shows the following aspects in this order:
|Dark (go)||Pedestrian signal shows steady orange hand.|
|Flashing yellow (caution)||Pedestrian signal shows steady orange hand.|
|Steady yellow (change interval)||Pedestrian signal shows steady orange hand.|
|Both steady red (absolute stop)||Pedestrian signal shows steady white man.|
|Alternate flashing red (stop and proceed)||Pedestrian signal shows flashing orange hand.|
|Dark (go)||Pedestrian signal shows steady orange hand.|
A Firehouse version of this signal omits the steady red indication.
Neither signal can be placed at an intersection.
The flashing yellow arrow permits the indicated turn after the driver yields to conflicting traffic. Conflicting traffic includes pedestrians and oncoming traffic.
See this page for more on flashing yellow arrows.
The illustration at right is a flashing yellow arrow left-turn signal face.
For the driver turning in the direction of the arrow, both indications mean the same thing.
The difference between the indications is the meaning given to drivers not making the indicated turn.
The circular green causes a danger called yellow trap (see below), because it controls too many movements at once. It can end a permissive left turn at an unsafe time, trapping drivers in the intersection. The flashing yellow arrow prevents yellow trap, if installed properly, by ending the permissive turn at the correct time.
The flashing yellow arrow is useful for allowing permissive turns with the lead-lag signal. This is useful for signal progression. This sequence can be seen here.
Yes. The flashing yellow arrow left turn signal face tells you the color of the oncoming circular indications whenever it permits a movement:
|LEFT TURN INDICATION||MEANING||ONCOMING INDICATIONS|
|Steady Red Arrow||Stop and stay||Any steady circular indication|
|Flashing Red Arrow||Stop, and turn when safe||Steady Circular Green or Flashing Circular Yellow|
|Steady Yellow Arrow||Prepare to stop||Steady Circular Yellow of Steady Circular Red|
|Flashing Yellow Arrow||Yield to conflicting traffic||Steady Circular Green|
|Steady Green Arrow||Go - protected turn||Steady Circular Red|
To avoid yellow trap, the permissive turn must end at or after the time the oncoming circular green ends. Ending it earlier exposes the left-turning driver to yellow trap.
Yellow trap is an unexpected and hard to recognize hazard caused by allowing left turns on a circular green. It occurs when the following happen together:
When this happens, a driver turning left and seeing the yellow light does not know that oncoming traffic still has a green light. He turns in front of live traffic, possibly causing a crash.
See this page for more on yellow trap.
Like the circular green, the circular red controls too many movements at once. It can give a conflicting indication to traffic making another movement, causing drivers to stop suddenly.
The new 2009 MUTCD requires a red arrow for all new separate left-turn signals.
Between 1971 and 2009, a circular red could be substituted for a red arrow, because the red arrow was not very bright. If a circular red was used, a sign reading LEFT TURN SIGNAL was required to be placed next to the left-turn signal. Now that LEDs provide brighter red arrows, the rule allowing a circular red was removed.
The restrictions are:
A doghouse signal is a five-section signal that is shaped like a dog house. See illustration.
A mallethead signal is a four-section signal that is shaped like a mallet (see illustration). It is used for the flashing red arrow signal face, with the flashing red arrow at the upper right.
Those are signals for light rail, streetcars, or special transit vehicles. Meanings for the motorman are as follows:
Other drivers must ignore these signals.
Two red lights are sometimes provided to maintain safety if a lamp burns out.
It also helps color-blind people recognize the red light.
Two sizes are used:
Several technologies have been used:
The following are the advantages:
There are several reasons:
CFLs burn out too fast. A fluorescent lamp's life is not measured in how much time it is lit, but how many times it has been turned on. A fluorescent lamp is good for about 6500 starts. At the normal number of times a day a traffic signal lamp is lit and extinguished (averaging 1440), the CFL would not last even one week before it failed. A flashing beacon would burn out in about two hours.
Those are indications to show a police officer that the signal face is displaying a red light. This is used for enforcement of red-light violations. But these do not show if an arrow is allowing a turn.
Those are indications to emergency vehicles that they have successfully pre-empted the signal. This is necessary, because an emergency vehicle might not have succeeded in taking control. Also, it is possible that two emergency vehicles are approaching the intersection from different directions. Only one of them can have control at a given time.
Various events can pre-empt normal signal operation, bringing into effect special signal operation. The following are special events, listed in decreasing order of priority, which can pre-empt a signal:
One of three things happens when the power fails:
If the power is off long enough, all of the signals will go dark.
When the power comes back on, the signal usually starts up in night flash mode, to warn drivers that operation is resuming. After a few minutes, the signal makes an orderly transition to normal operation.
There are three possibilities:
First, check to see if an officer or flagman is directing traffic.
What you do must take into account all three cases. Treat your approach as a stop sign. If a color appears after some time, the trouble is probably the failure of a single color, and you can figure out which color. Observe the other traffic, to find out if it is obeying a signal, or behaving as if it is obeying a stop sign.
Be especially careful if the only signal out is a complete arrow face. Do not assume that you can go when the circular greens on other faces facing you are lit. Such a failure can cause the yellow trap hazard.
If power is out in the area, treat the intersection as an ALL WAY STOP. But watch for people who are not aware the signal is there, especially at night. This is why signals should not be painted black or dark colors.
For special events (such as football games) where officers are directing traffic, turning off the signals and placing red flares is usually enough. If the signals are not to be used for a long time, the signal heads must be hooded, turned away from traffic, or taken down. Often the lenses are covered with black trash bags taped into place.
A traffic signal controller is the box of electronic equipment that controls the traffic signals for one intersection. Today's controllers are usually operated by microprocessors. It is usually housed in a large metal box on one corner of the intersection.
An electromechanical traffic signal controller is a traffic signal controller that uses synchronous motors, cams, contacts, solenoids, gears, and ratchets to operate the signals. These are obsolete, but some are still in use.
A phase is the part of a traffic signal controller that controls the lamps that control a single traffic movement or set of traffic movements. A phase usually has one circuit for red lights, one for yellow, and one for green. All of the lights on the phase are always the same color at the same time.
Each phase ends with change intervals.
Change intervals are also called clearance intervals, because their purpose is to clear the intersection of traffic before releasing another movement.
The red revert interval is the minimum time a phase must stay red after the yellow and red change intervals before it can turn green again. This is usually not used unless a call for a conflicting phase is asserted, and then cancelled (possibly due to the calling vehicle making a turn on red). In this case, the signal must wait for the red revert period before turning green again.
Two phases are said to be able to overlap if they can be green at the same time. Thus, overlapping phases have movements that do not conflict with each other. They can overlap in time, because they don't overlap in space.
An overlap phase is a phase with no detectors or green timing. It turns green whenever any of the phases designated as its parent phase is green. Overlap phases are usually used for right turns, a straight ahead movement across the top of a T intersection, or double-clearance phasing for offset intersections.
A timing ring is the timing portion of a signal controller. It controls the sequential timing of several mutually conflicting phases.
A single-ring controller has only one timing ring, and so can time only one phase at a time. Overlap phases can add some capabilities, but single-ring controllers can't handle complex intersections. Most of the old electromechanical controllers are single-ring controllers.
Recognize a single-ring controller by the fact that it never shows a green light and a yellow light at the same time, except on overlap phases. Left-turn phases are limited to single, simultaneous, and split-phase sequences (see below).
A dual-ring controller has two timing rings, and so can time two phases at a time. Dual-ring controllers can handle complex intersections, such as the eight-phase intersections with left-turn phases in all four directions.
Recognize a dual-ring controller by the fact that it routinely shows green signals and yellow signals at the same time on different phases. Often the dual-ring controller begins and/or ends left-turn phases at different times for traffic from opposite directions.
Barriers are used to divide the phases on a dual-ring controller into groups of phases (concurrency groups) that can be green at the same time. Both timing rings must be timing phases in the same concurrency group at the same time, and both rings must cross the same barrier together.
Usually the phases for one street are separated from phases for the other street by a barrier.
A detector is a device that informs the signal of the presence of a vehicle or a pedestrian. Examples of kinds of detectors:
A television detector (or video detector) is a TV camera used to detect vehicles, bicycles, and pedestrians. It is the only detector that can reliably detect a bicycle. These cameras usually operate in the infrared, so they are not affected by weather. One problem is that they are affected by reflections or shadows from vehicles in other lanes. Another problem is that some vehicle colors match the pavement in infrared light. And finally, the detector is rendered useless if snow packs into the lens opening.
A loop detector is a giant version of the metal detector used to find lost money at the beach. They are often visible as a black square, circle, or octagon in the middle of the traffic lane. The black line is tar, used to seal the saw slot containing the loop wires. But the loops are not visible if they have been paved over. Loop detectors are affected by sudden changes in weather, and can occasionally pick up trucks in adjacent lanes. Most of them are designed to indicate the presence of a vehicle if they fail.
The signal cycle is one repetition of the display of the green lights of all of the phases on the signal. Another way to describe a signal cycle is the sequence of the phases from the display (green) of one particular phase until that same phase is displayed again.
The time it takes to complete one signal cycle is called the cycle length.
A longer cycle length can move more traffic than a shorter cycle length. The cycle length may also depend on the signal progression (see below) plan in use. All signals in a progression plan use the same cycle length. And having more phases requires a longer cycle length.
There are fewer signal changes per hour. Each signal change wastes some time.
Pretimed traffic signals are traffic signals that do not react to the traffic that is actually present. They follow preprogrammed timings for each phase. The timings may be changed by a time clock or a computer for different traffic expected at different times of day.
Traffic-actuated signals are traffic signals that use detectors to change the timings to move the greatest amount of traffic. A traffic-actuated signal can shorten the green of there are few cars present for a traffic movement, or skip the movement entirely if no traffic is waiting to use it.
A fully-actuated signal has detectors for all of its phases. The timing is determined entirely by the traffic present at the intersection.
A semi-actuated signal has some pretimed phases and some traffic-actuated phases. The pretimed phases are often used to impose a fixed background cycle on the signal for coordination purposes. Several types predominate:
A left-turn phase is an added phase intended for moving left turns through the intersection. Oncoming traffic is stopped to leave a cleared right-of-way for the left turns. A left-turn phase uses green and yellow arrows.
Probably not. They are probably moving with the green light of a left-turn phase.
An exclusively protected left-turn phase gives a protected green arrow at some portion of the signal cycle. After the yellow arrow clearance, it shows a red arrow during the rest of the cycle. Left turns are not allowed on the circular green.
A protected/permissive left-turn phase gives a protected green arrow at some portion of the cycle, and also allows left turns to be made through gaps in oncoming traffic on a circular green or a flashing yellow arrow. Left turns are stopped by a red indication while the cross street has a green.
A permissive left turn is allowed to be made through gaps in traffic on a circular green or a flashing yellow arrow. There is no green arrow.
A leading left-turn phase is a left-turn phase which is given its green arrow time just before the oncoming traffic gets its green time.
A lagging left-turn phase is a left-turn phase which is given its green arrow time just after the oncoming traffic gets its green time.
Each signal is designed for the needs of its own intersection. In addition:
See this page for more on leading and lagging left turns.
If all of the signals had to have the same sequence, the following problems would occur:
The following factors usually require exclusive protected phasing:
The following measures can prevent yellow trap:
Note that when there is only one left-turn phase on a street, yellow trap becomes a hazard for the left turn on the opposite leg on the same street.
There are nine possible left-turn phasings. The Yellow Trap column shows the result without flashing yellow arrows:
|Single Lead||One direction has a left-turn phase that leads oncoming traffic.||P/P phase skip|
|Single Lag||One direction has a left-turn phase that lags oncoming traffic.||E/P & P/P|
|Dual Simultaneous Lead||Both lefts have one turn phase that leads before straight ahead traffic.||Never|
|Dual Simultaneous Lag||Both lefts have one turn phase that lags after straight ahead traffic.||Never|
|Dual Split Lead||Both left phases lead, can be skipped, and can end separately.||P/P phase skip|
|Dual Split Lag||Both left phases lag, can be skipped, and can begin separately.||P/P|
|No-Split Lead-Lag||Each approach on the street has its own phase. Also called Split-Phase.||Never|
|Single-Split Lead-Lag||One left leads, the other lags. The lead ends before the lag begins.||P/P|
|Double-Split Lead-Lag||One left leads, the other lags. The lag can begin before or after the lead ends.||P/P|
See this page for more on leading and lagging left turns.
See this page for more on left-turn phases.
Yes. The following sequences are not confined to one street. The Yellow Trap column shows the result without flashing yellow arrows:
|Clockwise||Each leg has its own green. The green advances clockwise (seen from above).||Never|
|Anticlockwise||Each leg has its own green. The green advances anticlockwise||Never|
|Merged Phases||A left-turn phase has a channelized merge with a thru phase from leg on the right.||Always*|
|Continuous Flow||Left turns cross oncoming traffic before the intersection. No extra phase needed.||Never|
|Parallel Flow||Left turns cross oncoming traffic during cross street phase.||Never|
|Contraflow Left||Left-turn lane placed to left of left-turn lane in opposite direction.||Never|
|Diverging Lefts||Simultaneous green for one left turn from each street.||Never|
|English Left||Left turns cross before intersection. All four lefts use the same phase.||Never|
* The use of merge phases and channelization requires prohibiting turns on circular green or flashing yellow arrow. Even with flashing yellow arrows, yellow trap occurs in the change to a merge phase.
See this page for more on left-turn phases.
A dual left-turn signal has two left-turn phases. Both of the left-turn signals are on the same street. A dual ring controller is usually required. This setup usually needs five phases.
A quad left-turn signal has left-turn phases on all four approaches. A dual ring controller is usually required. This setup usually needs eight phases.
Yes. They have been improved over the years to make them safer and easier to understand. Here is a rough chronology:
A half signal stops only one direction of traffic on the main street. It is used at T intersections where the thru movement on the side of the main street away from the side street need not be stopped. This signal can always provide perfect progression.
A dual half signal stops each direction of traffic on the main street independently of the other direction. It is used at Superstreet intersections. The advantage is that each half signal can be progressed independently of the other.
Coordination is used to cause many traffic signals to act with the same pattern, relative to each other, for each signal cycle. It is used to make signals able to handle more traffic by keeping one signal from blocking traffic released by another signal.
Signal coordination and signal synchronization are the same thing.
Progression is coordination of signals in a way to time signals for traffic moving along one street in such a way that the signals turn green as the platoons of cars come to them. Thus drivers traveling along that street do not have to stop at most of the lights.
See this page for more on progression.
Progression is actually very hard to achieve. The following factors enter into the decision:
That works for an isolated one-way street. For two-way streets and street grids, it gets much more difficult:
The time-space diagram is a tool used to design signal progression. One is shown here.
The through band is the part of the cycle length where cars can follow the wave of green lights without stopping. It is usually given as a fraction of the cycle.
See this page for more on progression.
A platoon is a group of cars being progressed through coordinated signals. It is formed by the first signal, and ideally it stays together throughout the entire progression system.
The single-alternate system is the most commonly use progression system. As you look down the street, the lights alternate colors for adjacent blocks, e.g. red green red green....
The signals are spaced and the cycle length is set so that, as you approach each cross street, the signal turns green, while the next signal beyond that one and the signal behind you turn red. The time-space diagram shown above is a single-alternate diagram.
The double-alternate system is used when the cross streets are too close together to use the single-alternate system. It has a smaller through band than the single-alternate system. The signals alternate in pairs, e.g. green green red red....
This is the case where the lead-lag signal sequence becomes useful for progression. It can make up for the normally smaller through band. The time-space diagram shown to the right is a double-alternate diagram.
The simultaneous system has all of the signals on the street green at the same time. It can be used for streets with very long, but equal, distances between signals.
It is also used for coordination without progression where distances between signals are too short. This is often called the "rabbit system," because the traffic moves forward in jumps.
The single-direction system is used on a one-way street, and when progression is impossible to achieve in both directions. It has a larger through band than other systems. But on a two-way street, it causes drivers going the other way have to stop more often, wasting gasoline.
The best location depends on the type of signal:
Doubled signal strips are needed for locations marked C, since the signal is green in one direction when it is red in the other direction.
Yes. Engineers develop different timing plans for different traffic conditions. These are activated by time clocks, traffic adjusted control, or digital computers.
The principal problem is changing the signals from one plan to another. Progression is often disrupted during the actual changeover from one coordination plan to another. This means that the coordination plan for a heavy traffic period must be put in place before the heavy traffic actually begins, and it must stay in place until after the heavy traffic has ended.
The cycle length, split (division of signal time among phases), and offset (timing of the beginning of the green in the coordination plan) of each signal are usually different in each coordination plan. The problem is getting the signal to the new settings without seriously disrupting traffic. There are three methods:
One or more detectors are connected to each actuated phase. The detectors have two effects on the phase:
In other words, the signal doesn't really look for cars, but the absence of cars. When cars are absent on one phase, the signal changes to a different phase with cars present.
There are several different methods:
It's busy. The signal controller must do everything else that must be done before you get a green light. This includes all of the following:
If the signal does change to green the moment your car is detected, the controller was resting.
When a traffic-actuated signal is not serving any traffic, it is resting. This means it is not timing any intervals. The last interval has already timed out, and no cars have arrived to start any new intervals. A setting on the controller selects how the controller rests. There are four kinds of resting:
No. Detectors usually note only the presence or absence of vehicles, not their number or motion. And the signal must finish what it is doing before it changes to your phase.
This misconception probably arose from erratic behavior of earlier detectors. They failed to detect vehicles that stopped in certain places. Moving the vehicle moved it into an active location.
You can fool the signal into thinking you are not there by creeping up beyond the stop line. Then the detector can no longer detect you, and the signal forgets you were there.
There are several possible reasons:
There are several reasons:
Traffic adjusted control uses detectors to measure traffic volumes at various locations. The results are then used to select one of several coordination plans, rather than to change individual signals.
A right-turn overlap is an overlap phase controlling a right turn that is a green arrow when either the straight-ahead phase from the same leg is green, or the left turn from the leg to the right is green.
Second yellow trap occurs when a permissive left turn is trapped on a yellow light by a green arrow shown to the opposing right turn as a right-turn overlap. This causes yellow trap even if the left turn uses a flashing yellow arrow. The traffic turning on the green right-turn arrow prevents the opposing left turn from clearing properly.
The following can prevent second yellow trap:
Third yellow trap is caused by a pedestrian phase that delays or inhibits a flashing yellow arrow phase when it is called by a pedestrian. Everything is safe unless the oncoming circular green phase is reserviced while green, to restart the pedestrian phase. If the flashing yellow arrow turns steady yellow, then red, for the reservice, while the parent phase stays green, third yellow trap occurs.
The following can prevent third yellow trap:
Use the following formula:
V = 3600 * S * (L / H) - C - P, in vehicles per hour
V = Vehicles per hour
S = Split = Portion of the signal cycle the phase is green (entered as a fraction)
L = Number of lanes
H = headway in seconds per vehicle (2 for cars under 45 mph, 3 for cars over 45 mph, larger for heavy trucks).
P = 500 if parking is allowed along the right side of the right lane, 0 if not.
C = vehicles in conflict (veh/hr)
So a 2-lane approach with a 60% split, passenger cars at 30 mph, no conflicts, and no parking gives this result:
V = 3600 * 6/10 * (2 / 2) - 0 - 0 = 2160 veh/hr (vehicles per hour)
The dilemma zone is a dangerous section of roadway upstream from a traffic light that develops at higher speed. Within the dilemma zone, the driver seeing a yellow light has a problem:
Note these items:
The following can be used to remove the danger of the dilemma zone:
The distance between the stop line and the edge closest to the stop line is equal to the distance covered during the change intervals at the speed limit. Use this formula to find it:
d1 = 5280/3600 * s * (y + r) - w, in feet
d1 = Distance from stop line to the nearest edge of the dilemma zone.
s = Speed limit in miles per hour
y = Yellow change interval, in seconds
r = Red change interval, in seconds
w = Width of the intersection in the direction the car is traveling, in feet
The distance between the stop line and the edge farthest from the stop line is equal to the normal stopping distance at the speed limit. Use this formula to find it:
d2 = 5280/3600 * s * 3/4 + s2 / 30 / (f + g), in feet
d2 = Distance from stop line to the farthest edge of the dilemma zone
s = Speed limit in miles per hour
f = Coefficient of friction between tires and road
g = Grade as the tangent of the slope angle, where positive is a slope uphill
If d2 < d1, there is no dilemma zone.
So a level approach to a 40-foot intersection at 50 mph, with a 4-second yellow and no red change, and a coefficient of friction of 0.3, has a dilemma zone of:
d1 = 5280/3600 * 50 * (4 + 0) - 40 = 293.33 feet (near end)
d2 = 5280/3600 * 50 * 3/4 + 502 / 30 / (3.3 + 0) = 332.77 feet (far end)
The dilemma zone is 39.44 feet long.
Use the following formula to calculate the basic change interval:
c = 3/4 + 1/2 * v / 15 + (w + l) / v, in seconds.
c = Change interval in seconds
s = Speed limit in feet per second (multiply miles per hour by 5280/3600)
a = Deceleration, in feet per second per second
w = width if the intersection in feet
l = length of vehicle in feet
On a 30 mph street with a 40 foot intersection, a 25 foot car, the basic change interval is:
3/4 + 1/2 * 30 / 15 + (40 + 15) / 30 = 3.583 seconds
Normally the basic change interval is used for the yellow change, and a 1-second red change interval is added. But there are exceptions:
Use the following formula to find optimum signal spacing for a given speed and cycle length:
d = 5280/3600 * s * C / k, in feet
d = Distance between signals in feet
s = Speed in miles per hour
C = Cycle length in seconds
k = Progression type: 1 = simultaneous, 2 = single alternate, 4 = double alternate
On a 30 mph street with a 60 second cycle length, the spacings should be:
5280/3600 * 30 * 60 / 1 = 2640 feet, for simultaneous signals
5280/3600 * 30 * 60 / 2 = 1320 feet, for single alternate
5280/3600 * 30 * 60 / 4 = 660 feet, for double alternate
Use the following formula to find the optimum speed for a given signal spacing and cycle length:
s = 3600/5280 * d * k / C, in mph Use the definitions above.
On a street with a 60 second cycle length, and spacings of 1320 feet, the speed should be:
3600/5280 * 1320 * 1 / 60 = 15 mph, for simultaneous
3600/5280 * 1320 * 2 / 60 = 30 mph, for single alternate
3600/5280 * 1320 * 4 / 60 = 60 mph, for double alternate
Use the following formula to find the optimum cycle length for a given signal spacing and speed:
C = 3600/5280 * d * k / s, in seconds Use the definitions above.
On a 30 mph street with spacings of 1320 feet, the cycle length should be:
3600/5280 * 1320 * 1 / 30 = 30 seconds, for simultaneous
3600/5280 * 1320 * 2 / 30 = 60 seconds, for double alternate
3600/5280 * 1320 * 4 / 30 = 120 seconds, for double alternate
The following are methods used to reduce the number of signal phases needed, usually by the removal of left-turn phases:
There are several reasons: