1.) Driver Reaction Times (tr)
Driver reaction time includes recognizing light has changed, deciding to continue or brake, and if stopping engaging the brake (remove foot from gas pedal and apply brake). Reaction times vary greatly with situation and from person to person between about 0.7 to 3 seconds or more. Some accident reconstruction specialists use 1.5 seconds as average driver reaction brake time. However, a controlled study in 2000 (IEA2000_ABS51.pdf) found average driver reaction brake time to be 2.3 seconds. The study included all driver types tested on a controlled track and in a driving simulator.
Driver Reaction Times
0.7 seconds -- about as fast as it gets 1.0 - 2.0 seconds -- used by numerous states 2.3 seconds -- Average (all Driver Types) 2.5 seconds -- standard in few states 3.0 seconds -- NSC and UK Standard
Driver reaction time is the biggest unknown as it varies with person. A few states, including California, have adopted a standard driver reaction time of 2.5 seconds. The United Kingdom's Highway Code and the Association of Chief Police Officers ACPO Code of Practice for Operational Use of Road Policing Enforcement Technology use 3.0 seconds for driver reaction time. The National Safety Council (NSC) recommends 3 seconds minimum spacing (3 second reaction time) between vehicles traveling in the same lane.
2.) Vehicle Length (L)
Vehicle length is a factor because in most cases the vehicle must clear the road sensor to avoid triggering the camera.
3.) Speed (v)
Standard practice is suppose to be speed limits are set to the 85 percentile speed. The 85 percentile speed is the speed 85% of traffic travels at or below, 15% travel faster. A traffic study is suppose to be conducted, over a relatively long period, to determine the 85 percentile speed empirically. Some places set the limit 8 to 12 mph below the 85 percentile speed resulting in more speeders and red light runners.
4.) Yellow Light Duration (ty)
The best way to measure yellow light duration is to video record (film is as good but harder to work with) the signal light changing from green to yellow to red. Several light cycles should be recorded to check for any differences. If possible multiple stoplights should be in the viewing frame.
Once recorded use video editing software to time and/or count the frames the yellow is illuminated. An alternative is to use a playback machine and count the yellow light frames. Time is number of yellow light frames divided by the frame rate. Counting frames will yield results accurate to plus or minus the inverse of the frame rate.
In the U.S. most video cameras record at 15, 30 or 60 frames per second (FPS). Film cameras record at 24 or 30 FPS. In Europe most video and film cameras run at 25 frames/sec. Compressed video can run at 10 or 12 FPS. Most U.S. television broadcast are at 30 frames per second, 25 FPS in Europe.
Frames / Sec
N = frame count
|10||N / 10||± 0.10 sec||Compressed Video|
|12||N / 12||± 0.08 sec||Compressed Video|
|15||N / 15||± 0.07 sec||Video Camera option|
|24||N / 24||± 0.04 sec||Hollywood/Home Film|
|25||N / 25||± 0.04 sec||Video and Film (Europe)|
|30||N / 30||± 0.03 sec||Video and Film|
|60||N / 60||± 0.02 sec||High End Systems|
FRAME COUNTING -- Some frames may appear to have both green and yellow stopping/starting illumination, or both yellow and red stopping/starting illumination (not unusual). The most accurate way to count yellow light frames is to use the first frame the green dims and/or yellow starts to illuminate, the last frame is when the yellow starts to dim and/or the red starts to illumine. If multiple lights captured in frame (picture), whichever light first dims or starts to illumine is used as a frame time mark.
5.) Road Grade (Gr)
To account for inclines braking (g's) is adjusted by adding (downhill) or subtracting (uphill) the road grade ratio. Road grade is the ratio of elevation change to horizontal distance, and is commonly expressed as a percentage (%). Road grade may be posted on the road, if not it can be measured with an inclinometer or other method. The road grade ratio is the tangent of the angle between level and incline, or the ratio of the elevation change distance divided by horizontal distance.
Gr = Road Grade Ratio
ß = road incline angle
y = elevation difference
x = horizontal distance
The U.S. highway systems typically has a maximum grade of 5% city and 6% mountains. The table below list elevation change and incline angle for horizontal distance change of 300 feet (100 yards) for selected road grades.
/ 300 ft
6.) Stop Line to Camera Trigger Line (dt)
The intersection threshold is the camera trigger line, vehicles that cross or are on the intersection threshold line when the stoplight is or changes red, triggers the camera. Distance from the trigger line to the stop line (dt) is positive when the trigger line is after (past) the stop line, and negative when threshold line in front of (before) stop line. The term dt is zero when the camera trigger (intersection threshold) and stop line are the same.
Redflex uses a pole mounted radar located on the far side of the intersection to detect violations. Two radars are required to cover both directions. ATS uses 2 buried magneto resistive sensors spaced about 5 feet apart position in front of (before) the stop line for each lane to detect violations. Each sensor is about 4 inches in diameter and 2 inches deep, and is battery operated and wireless. Other sensors include laser radar, and inductive magnetic loops and piezo ceramic pressure road sensors
7.) Camera Trigger Time Delay (td)
Some red light cameras are programmed to delay the camera trigger. A vehicle has a little extra time, the programmed delay, to get passed the intersection threshold camera trigger line. Typical delay times vary from 0.25 to 1.0 second or more.
di = Distance from Photo Line to Stop Line
Some red light cameras are programmed to delay the camera trigger. A trigger delay greater than or equal to the time it takes a vehicle to cross over the sensor changes trigger detection from vehicle rear to front. The front of the vehicle is the trigger when the sensor time delay is greater than the time it takes the vehicle to cross over the sensor (vehicle length). The equation for vehicle distance from stop line changes because the vehicle front is the trigger instead of the vehicle rear.
Vehicle Rear Triggers Camera
Speed x Delay < Vehicle Length
v td < L
di = dt + L - v td
Vehicle Front Triggers Camera
Speed x Delay >= Vehicle Length
v td >= L
di = dt - v td