Traffic Wisam Abdulla Najim ALHalfi

CHAPTER THREE
SPEED AND DENSITY
Speed :

Rate of motion, which is expressed by the distance to the unit time.

generally as (mi/h) or (Km/hr).

In characterizing the speed of a traffic stream, a representative value must be

used, because a broad distribution of individual speeds is observable in the
traffic stream, average travel speed is used as the speed measure because it is
easily computed from observation of individual vehicles within the traffic
stream and is the most statistically relevant measure in relationships with
other variables.
Average travel speed is computed by dividing the length of the highway,
street section, or segment under consideration by the average travel time of
the vehicles traversing it.
If travel times t1, t2, t3,..., tn (in hours) are measured for n vehicles
traversing a segment of length L, the average travel speed is computed using
Equation
nL L L
S n
 
1 n ta
i  ti
n i 1
i 1

where
S = average travel speed (mi/h),
L = length of the highway segment (mi or Km),
ti = travel time of the ith vehicle to traverse the section (h),
n = number of travel times observed, and
1 n
ta =  ti = average travel time over L (h).
n i 1

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The travel times in this computation include stopped delays due to fixed
interruptions or traffic congestion. They are total travel times to traverse the
defined roadway length.
Several different speed parameters can be applied to a traffic stream. These
include the following:

Average running speed: A traffic stream measure based on the observation

of vehicle travel times traversing a section of highway of known length. It is
the length of the segment divided by the average running time of vehicles to
traverse the segment. Running time includes only time that vehicles are in
motion.

Average travel speed: A traffic stream measure based on travel time

observed on a known length of highway. It is the length of the segment
divided by the average travel time of vehicles traversing the segment,
including all stopped delay times.

Space mean speed: A statistical term denoting an average speed based on the
average travel time of vehicles to traverse a segment of roadway. It is called a
space mean speed because the average travel time weights the average to the
time each vehicle spends in the defined roadway segment or space.

Time mean speed: The arithmetic average of speeds of vehicles observed

passing a point on a highway; also referred to as the average spot speed. The
individual speeds of vehicles passing a point are recorded and averaged
arithmetically.

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Free-flow speed :The average speed of vehicles on a given facility, measured

under Free-flow speed, low-volume conditions, when drivers tend to drive at
their desired speed and are not constrained by control delay.
For example, three vehicles are recorded with speeds of 30, 40, and 50 Km/h.
The time to traverse1 Km is 2 min, 1.5 min, and 1.2 min, respectively.
The average spot speed is 40 Km/h, calculated as (30 + 40 + 50)/3.
The space mean speed is 38.3 Km/h, calculated as (60)[3 ÷ (2.0 + 1.5 +
1.2)].

Design speed:
Is defined as the maximum safe speed that can be maintained over a
specified section of highway when conditions are so favorable that the design
features of the highway govern.
Operating speed – maximum safe speed a vehicle can be driven without
exceeding design speed.

Speed limit (posted speed)

This is the maximum speed permitted by law on a section of road. It is the

speed which decision-makers (and not necessarily the design engineers) say is
the maximum permitted speed at which any vehicle may travel along the
section of road concerned. For any section of existing road there may or may
not be a direct relationship between speed limit and design speed.

—
Design Speed Considerations
1. Functional classification of the highway.
2. Character of the terrain.
3. Density and character of adjacent land uses.
4. Traffic volumes expected to use the highway.
5. Economic and environmental considerations.
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Spot speed study:

Spot speed studies are used to determine the speed distribution of a traffic
stream at a specific location. The data gathered in spot speed studies are used
to determine vehicle speed percentiles, which are useful in making many
speed-related decisions. Spot speed data have a number of safety applications,
including the following :
1. Determining existing traffic operations and evaluation of traffic control
devices
a. Evaluating and determining proper speed limits
b. Determining the 50th and 85th speed percentiles
c. Evaluating and determining proper advisory speeds
d. Establishing the limits of no-passing zones.
e. Determining the proper placements of traffic control signs and markings.
f. Setting appropriate traffic signal timing.
2. Establishing roadway design elements.
a. Evaluating and determining proper intersection sight distance.
b. Evaluating and determining proper passing sight distance .
c. Evaluating and determining proper stopping sight distance .
3. Assessing roadway safety questions
a. Evaluating and verifying speeding problems
b. Assessing speed as a contributor to vehicle crashes
c. Investigating input from the public or other officials
4. Monitoring traffic speed trends by systematic ongoing speed studies
5. Measuring effectiveness of traffic control devices or traffic programs,
including signs and markings, traffic operational changes, and speed
enforcement programs

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Speed Percentiles :

Speed percentiles are tools used to determine effective and adequate speed
limits. The two speed percentiles most important to understand are the 50th
and the 85th percentiles.
The 50th percentile is the median speed of the observed data set. This
percentile represents the speed at which half of the observed vehicles are
below and half of the observed vehicles are above. The 50th percentile of
speed represents the average speed of the traffic stream.
The 85th percentile is the speed at which 85% of the observed vehicles are
traveling at or below. This percentile is used in evaluating/recommending
posted speed limits based on the assumption that 85% of the drivers are
traveling at a speed they perceive to be safe .In other words, the 85 th
percentile of speed is normally assumed to be the highest safe speed for a
roadway section.
Weather conditions may affect speed percentiles. For example, observed
speeds may be slower in rainy or snowy conditions.
A frequency distribution table is a convenient way to determine speed
percentiles. An example is given in Table 1. The frequency of vehicles is the
number of vehicles recorded at each speed. The cumulative frequency is the
total of each of the numbers (frequencies) added together row by row from
lower to higher speed. The fourth column is a running percentage of the
cumulative frequency.
The 50th and 85th speed percentiles are determined from the cumulative
percent column. For the example data in Table 1, the 50th percentile falls
between 27 and 30 mph and the 85 th percentile falls between 33 and 36 mph.
The calculation of speed percentiles is easier if a sample size of 100 vehicles
is collected. When the sample size equals 100 vehicles, the cumulative
frequency and cumulative percent are the same. As can be observed from
Table 1, the exact 50% and 85% (50th and 85th percentiles) are not found in
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the cumulative percent column. To reach these exact percentages, a

calculation is completed using percentages and speeds from the distribution
table.

Table1. Example Frequency Distribution Table

Speed Frequency Percentage of Cumulative

( km / hr) Frequency
15 1 1 1
18 2 2 3
21 6 6 9
24 12 12 21
27 13 13 34
30 20 20 54
33 18 18 72
36 14 14 86
39 6 6 92
42 6 6 98
45 1 1 99
48 1 1 100
Sum. 100

The 50th percentile of speed = 29.4 km / hr.

The 85th percentile of speed = 35.8 km / hr.

Calculate Vehicle Speeds:

To calculate vehicle speed, use the predetermined study length and the
elapsed time it took the vehicle to move through the course (as recorded on
the stopwatch data form) in the following formula
D
V = 3.6
T
where V = spot speed (Km/h), D = length (meter), and T = elapsed time
(seconds). In the equation, 3.6 is a constant that converts units of meter per

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second into Km/hr per hour. For example, if the spot speed study length is
30and the motorist’s elapsed time is 2.5 seconds, the motorist is traveling at
V = 3.6 ( 30 / 2.5 ) = 43.2 Km/ hr.

Density:
Is the number of vehicles (or pedestrians) occupying a given length of a lane
or roadway at a particular instant. For the computations, density is averaged
over time and is usually expressed as vehicles per mile (veh/mi) or passenger
cars per mile (pc/mi) or ( veh/Km).
Direct measurement of density in the field is difficult, requiring a vantage
point for photographing, videotaping, or observing significant lengths of
highway. Density can be computed, however, from the average travel speed
and flow rate, which are measured more easily. Equation below is used for
under saturated traffic conditions.
q flowrate
K= 
v averagetravelspeed
where
q= flow rate (veh/hr),
v= average travel speed (mi/hr), and
K = density (veh/mi).
Example :
Calculate the density of vehicles with flow rate ( 1350 veh/hr) and average
travel speed ( 80 km/hr)?
Sol.
K = ( 1350 / 80 ) = 17 veh/Km.
Density is a critical parameter for uninterrupted-flow facilities because it
characterizes the quality of traffic operations. It describes the proximity of
vehicles to one another and reflects the freedom to maneuver within the

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traffic stream. Roadway occupancy is frequently used as a surrogate for

density in control systems because it is easier to measure.
Occupancy in space is the proportion of roadway length covered by vehicles,
and occupancy in time identifies the proportion of time a roadway cross
section is occupied by vehicles.

Lengths of vehicles(  L I )
Lane occupancy (LO)% = * 100%
length of roadway section Lr 
Average density (k),veh/km = Lane occupancy(LO)
1000

Average vehicles lengths
Example :
For vehicles ( 5.5,6,6.4,6.7) m long are distributed over length of free way
lane 100m. Find LO & K?
Sol.
∑ L I = 5.5 + 6+ 6.6 + 6.7 = 24.6
LO = ( 24.6 / 100) * 100% = 24.6%
Average vehicle length = (5.5 + 6+ 6.6 + 6.7 ) /4 = 6.15 m.
K = 0.246 x 1000 / 6.15 = 40 veh/Km.

Jam density : The density at which congestion stops all movement of persons
or vehicles, usually expressed as vehicles per kilometer per lane or
pedestrians per square meter.

Note :
The example and the important notes will be given in the class.

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