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Red Light
Maximum Braking

applies to Red Light Cameras

Page Outline
• Introduction
• Standards
• Variations in Clear Point
• Deceleration
• Yellow Light Duration Formula
  Calculator -- Yellow Light Duration
• Calculate Braking g's
  Calculator -- Maximum Braking
• Examples

Introduction

Some traffic signals require harder braking than others. Braking depends on vehicle speed, yellow light duration, driver reaction time, and stop and clear points. Many communities use the same formula to calculate yellow light duration, however there is a relatively wide range of variables used in the calculation. A way to compare different traffic signals (including controversial red light cameras) is to determine maximum braking. A convenient and practical way to measure braking is to equate (compare) vehicle deceleration to the Gravitional constant (g).

YELLOW DURATION CONCERNS
There are several issues with the way yellow light duration is determined. A commonly used formula does not account for a difference between stop line and clear point. This results in yellow light duration calculating short, on the order of a few tenths of a second to a half a second (unless stop and clear line are the same). Another larger issue is driver reaction times used vary with state from about 1 to 2.5 seconds. The fastest a driver can react has been measured to be about 0.7 seconds, a controlled study measured average time to be 2.3 seconds. Most states use deceleration of between 10 to 11.2 ft/sec² (0.30 to 0.35 g's), reasonable. Some states/places use 14 ft/sec² (0.44 g's), which is close to what many safety experts say is maximum safe braking for the average driver -- 15 ft//sec² (0.47 g's).

RED LIGHT CAMERA CONCERNS

Cameras do not improve safety or fix problematic intersections -- intersections can usually be fixed by increasing yellow light duration, -- longer yellow light duration lowers braking action (safer stops). Cameras have been known to cause collisions -- some drivers aware of a camera brake too soon and get rear-ended. The person the vehicle is registered to gets ticketed -- person vehicle registered to may not have been driving. -- presumption the owner is guilty (no presumption of innocence) -- evidence against vehicle, not driver (no direct evidence against owner). The process is automatic -- a police officer does not have to see alleged violation, -- cannot cross examine electronic circuits (loss of right to confront witness). Camera's real purpose is to collect lots of $money$ -- sometimes the yellow duration is decreased (more tickets and more dangerous). -- up to half of fine can go to a 3rd party (private company that maintains system).

Any measuring device, especially automatic devices (speed and red light cameras), should have established tests (calibrations and/or laboratory test) scheduled on a regular basis. Test records should be maintained and available. Any device not tested and maintained properly has questionable accuracy. Also the chain of control of evidence (photos and data) should have checks and balances with accountability and be well established and followed.

Standards

The Manual on Uniform Traffic Control Devices (MUTCD), established by federal law in 1966, sets national standards for every sign, signal, pavement marking, and traffic control signal device in the USA. The standard (published by the Federal Highway Administration -- FHwA) is intended to insure signs and signals LOOK and are USED in the same manner everywhere in the USA.

The MUTCD only provides guidance for vehicle position when a traffic signal changes to red (no formal standards). Basically each State sets the law regarding yellow light duration and vehicle position, and some of these laws are open to interpretation. Many State laws use language taken directly and/or modified from the Uniform Vehicle Code (UVC). The UVC code is consistent with the MUTCD concerning yellow light duration and vehicle position when light changes red. The MUTCD recommends yellow light duration be 3 to 6 seconds (longer times for greater speeds); and after signal changes to red vehicles cannot enter the intersection.

STOP LINES
Many intersections have a Stop Line, vehicles must stop before crossing the line. If there is no stop line vehicles must stop before the crosswalk, if no crosswalk vehicles must stop before entering the intersection. The intersection is usually defined as the extension of cross traffic curb lines.

Variations in Clear Point

Different states and countries have different standards regarding vehicle location (Clear Point) when a traffic light signal changes to red. Variations for vehicle location when signal changes from yellow to red include but not limited to;

If entire vehicle (not just front bumper) must be clear of some point (intersection, etc.), deceleration will depend on vehicle length -- the longer the vehicle the greater the required deceleration. The distance (d_i) between stop line and clear point is greater for longer vehicles, increasing requried deceleration (braking).

Deceleration (-acceleration)

Acceleration (a) is the change in speed over the change in time, and is positive for increasing speed and negative for decreasing speed (deceleration). At a traffic stop light deceleration (when light changes to yellow) is a function of;

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 2.5 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. Some state (such as California) DOT's (Department of Transportation) use a driver reaction time of 2.5 seconds for calculations.

Driver reaction time;
0.7 seconds -- about as fast as it gets,
1.0 seconds -- standard in some states,
1.5 seconds -- standard in some states,
2.3 seconds -- average,
2.5 seconds -- standard for many states (most realistic).

Driver reaction time is the biggest unknown as it varies with person. Many states have adopted, for calculation and comparison pruposes, a standard driver reaction time (responding to a traffic light) of 2.5 seconds (controlled study average rounded up to nearest half second).

ACCELERATION MODEL
The model determines the point a vehicle has just enough time and distance to continue through the traffic signal light based on speed, reaction time, yellow duration, and distance between the stop line and clear point. The model also determines the braking (deceleration) for a vehicle whose driver decides to stop.

Figure 1 --
Deceleration Model

	Proof
GIVEN Vo = Speed tr = dirver reaction time ty = yellow light duration di = distance between stop line and clear point	--	SOLVE FOR dr = distance traveled during react time db = distance traveled during braking time tb = braking time -a = deceleration

Four unknowns (dr, db, tb, a) and 4 equations.
From Layout db = dy - dr - di db = Voty - Votr - di db = Vo(ty - tr) - di | ----->	From Newton's Law of Motion db = Votb + 0.5 a tb2 db = Vo tb + 0.5 (-Vo / tb) tb2 db = Vo tb - 0.5 Vo tb db = 0.5 Vo tb tb = 2 db / Vo	From Layout a = -Vo / tb <-----	By Definition dr = Vo tr dy = Vo ty
tb = 2 (Vo ty - Vo tr - di) / Vo tb = 2 (ty - tr - di/Vo) a = - Vo/tb = -Vo / [ 2 (ty - tr - di/Vo) ]

Solving for Yellow Duration (t_y)
t_y = t_r - (V_o/2a) + d_i/V_o
Applies to flat level surfaces, see below for inclines.
Note, (a) is negative for deceleration (-a).

INCLINES
Someone in a vehicle stopping while on an incline will preceive deceleration differently then when stopping on a flat level surface. Compared to a level surface it is easier to stop going uphill and harder to stop going downhill. To compensate (account) for inclines deceleration (-a) is adjusted (perceived, relative, deceleration) by adding (downhill) or subtracting (uphill) the product of acceleration due to gravity (g) and road grade (G_r = ratio of elevation change to horizontal distance). Adjusting acceleration (deceleration) produces practical results for determining yellow duration and comparing traffic signal lights on inclines and flat surfaces.

The U.S. Interstate system typically uses a maximum grade of 5% (0.05 ratio) in cities, and 6% (0.06 ratio) in mountains.

G_r ratio = 0.01 (G_r % ) Also see Calculate Braking g's below.

Yellow Light Duration Formula

Accounting for incline, if any, the yellow light duration (t_y) formula is;

t_y = Yellow Light Duration
t_r = driver Reaction Time
V_o = initial Speed
a = Deceleration
d_i = Distance from Stop Line to Clear Line
G_r = road Grade ratio (elevation/distance), +G_r uphill, -G_r downhill
g = Gravitional Constant = 9.8 m/s² = 32.2 ft/s²

The Institute of Transportation Engineers (ITE) organization, as well most states, use a common formula for calculating yellow duration. The ITE formula is exactly the same as the above formula (t_y) when d_i = 0. The formula used by most states does not account for a difference between stop line and clear point (point vehicle must be at/past on red). Depending on circumstances yellow duration could be short by a couple of a tenths of a second to a half a second or more.
If d_i = 0, t_y = t_r + V_o / [ 2 (a + g G_r ) ] .

Equation inputs vary with state. Driver reaction times (t_r) vary from 1 to 2.5 seconds. Deceleration (a) varies from about 10 to 11.2 ft/sec² (3 to 3.4 m/sec²). Speed (V_o), for calculating yellow duration, is typically the 85 percentile speed (speed that 85% of traffic travels at or below). In many places the speed limit is set 8 to 12 mph below the 85 percentile speed.

Also see;
-- Variations in Clear Point above.
-- Standards below.
-- Acceleration Parameters (In-work).

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Calculator -- Yellow Light Durtation
Calculates yellow light durtation (t_y) based on speed (V_o), driver reaction time (t_r), deceleration (a), road grade (G_r), and distance between stop and clear lines (d_i).

Calculate Braking g's

Deceleration (-a) can be equated (compared) to the Gravitional Constant (g), acceleration due to gravity. By International definition 1 g is a change in speed of exactly 9.80665 meters per second every second (32.17405 ft/s²). Also see Acceleration Parameters -- In-Work.

g_v = Perceived Vehicle Acceleration
V_o = initial speed
t_y = yellow light durtion
t_r = driver reaction time
d_i = distance between stop line and clear point
G_r = Road Grade ratio (elevation/distance), +G_r uphill, -G_r downhill
g = Gravitional Constant = 9.8 m/s² = 32.2 ft/s²

The longer the yellow light duration (t_y), the lower the braking g's. The greater vehicle speed (v_o) and/or the greater driver reaction time (t_r) and/or the greater the distance between stop line and clear point (d_i), the greater the braking g's.

Standards (really parameters) used to determine and/or analyze traffic signal lights vary. Driver reaction times vary from as little as 1 up to 2.5 seconds (2.5 seconds is the most realistic). Maximum deceleration (to determine yellow duration) generally varies from 10 to 11.2 ft/sec².

Many safety experts use 15 ft/sec² (0.47 g's) as the maximum deceleration that is safe for the average driver to maintain control (good to excellent tires, dry surface). A reasonably skilled driver can stop at 20 ft/sec² (0.62 g's) safely. Most production street vehicles have a maximum braking around 0.8 g's.

Note below approximations;
0.0 - 0.3 g's -- light braking,
0.3 - 0.4 g's -- Moderate braking,
0.4 - 0.5 g's -- Heavy braking,
0.5 - 0.6 g's -- HARD braking,
0.6 - 0.8 g's -- DANGEROUS braking,
> 0.8 g's -- EXTREME BRAKING.

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Calculator -- Red Light Maximum Braking
Calculates braking g's, distance (d_b), and time (t_b), distance traveled during react time (t_r), and distance traveled during yellow duration (t_y) to clear point. Calculations based on speed (V_o), driver reaction time (t_r), yellow light duration (t_y), road grade (G_r), and distance between stop line and clear point (d_i).

The following two graphs plot braking g's versus yellow light duration (t_y) for speeds (v_o) between 20 and 65 mph. Both graphs are for stop line and clear point the same (d_i = 0). The first graph uses a reaction time of 1.5 seconds, the second graph uses a reaction time of 2.3 seconds.

Using the above graph (t_r = 1.5 sec, and d_i = 0), and yellow light duration of 3.5 sec for a speed of 35 mph indicates maximum braking of 0.4 g's (Moderate braking).

Using the above graph (t_r = 2.3 sec, and d_i = 0), and yellow light duration of 3.5 sec for a speed of 35 mph indicates maximum braking of 0.67 g's (HARD braking).

The following table shows braking g's for driver reaction time (t_r) of 2.5 seconds and stop line and clear point the same (d_i = 0) given yellow light duration (half second increments) and speed (5 mph increments).

Using the above table (t_r = 2.5 sec, and d_i = 0), and yellow light duration of 3.5 sec for a speed of 35 mph indicates maximum braking of 0.80 g's (border line Extreme braking).

© Copyright 2005, 2010 Donald S. Sawicki, All Rights Reserved.