## TRAFFIC CHARACTERISTICS: Speed, Volume, Density (Definitions and Formulas)

**traffic speed, volume, and density,**are used to describe the quality and quantity of traffic in a stream.

###
**Speed:**

####
*Journey Speed:*

*Journey Speed:*

[mathop mu limits^ – = frac{{Total;Distan ce;Travelled;}}{{Total;Journey;Time}}]

###
**Uses of Journey Speed:**

####
*Running Speed:*

*Running Speed:*

$Running{rm{ speed = }}frac{{Total{rm{ distance}}}}{{{rm{Running time}}}}$

###
**Uses of Running Speed:**

####
*Time Mean Speed (Spot Speed):*

*Time Mean Speed (Spot Speed):*

[{mathop mu limits^ – _t} = mathop {{mu _{spot}}}limits^ – = frac{1}{N}sumlimits_{i = 1}^N {{mu _i}} ]

###
**Uses of Time Mean Speed**

Used for determining the enforceable speed limits, which is the 85

^{th}percentile

^{th}percentile is employed

^{th}percentile of observations, is useful for research purposes

###
**Methods of Measuring Time Mean Speed (Spot Speed)**

*Stop watch (and enoscope)*: This is a manual method of measuring the time mean speed. It involves establishing two separate points along the lane, with enumerators observing time and identifying vehicles as they pass the observation points, then spot speeds are estimated using time lapse and distance apart.

*Pneumatic Tube or Pressure Contact Strip Method:*In this method, two pneumatic tubes separated by 1000mm are fixed on the pavement surface, and counting box is attached to the tubes for counting vehicle speeds (and classification). The pneumatic tube or pressure contact strip, estimates speed of vehicles by making use of the lapse in time between bursts which it receives, due to compression pressure caused by passing vehicles over the tubes. It also classifies vehicles based on the distance between axles with respect to time.

*Radar Speed meter or Speed gun:*Radar speed meter, requires the use of speed gun device by a traffic enumerator assisted by another person for recording collected data. Both enumerators stand by the road side for as long as it behooves them to collect the data.

*Time Lapse Photography:*This is a computerized process that requires capturing or videoing vehicle images as they travel along sections of the road on the field. The video is thereafter played in the laboratory for analysis, in order to generate data using on screen marks or pavement markings.

*Induction Loops:*This is a loop of turned wire imbedded into the pavement. It is made up of an oscillator and a cable which sends signals to a traffic counting device when vehicles pass over a set of two loops imbedded on the pavement in series, such that vehicle lengths and speeds are estimated on the basis of time lapse whenever there are changes in the magnetic field due to the passing of vehicles over the magnetic field.

####
*Space Mean Speed (Harmonic Mean Speed)*

*Space Mean Speed (Harmonic Mean Speed)*

[bar t = frac{1}{N}sumnolimits_{i = 1}^N {frac{D}{{{u_i}}}} ]

[{bar mu _s} = frac{D}{{bar t}} = frac{D}{{frac{1}{N}sumlimits_{i = 1}^N {frac{D}{{{mu _i}}}} }} = frac{1}{{frac{1}{N}sumlimits_{i = 1}^N {frac{1}{{{mu _i}}}} }}]

${{bar mu }_t} = {{bar mu }_s} + frac{{{sigma ^2}_s}}{{{{bar mu }_s}}}$

${{sigma ^2}_s}$= Variance about the space mean speed.

**travel pace**, are entirely different.

**Travel pace**could be defined as the 10 mph increment in speed in which the highest percentage of drivers are observed. It is used for predicting traffic crash.

###
**Traffic Density:**

**Traffic density (k),**or

**concentration**could be defined as the average number of vehicles occupying a unit length of roadway at a given time. Its unit of measurement is vehicles per kilometer (veh/km).

*Mathematically,*

${rm{Density, k = }}frac{{Average{rm{ number of vehicles travelling over D}}}}{D}$

${rm{Density, k = }}frac{q}{{{{bar mu }_s}}}$

Where:

$q$ = flow rate (veh/h), and

${{{bar mu }_s}}$ = space mean speed (km/h)

**Critical Density:**Critical density could be defined as the maximum density attainable under free flow condition.

**Jam Density:**Jam density could be defined, as the minimum density achieved under congestion.

[mu = {mu _f} = (1 – frac{k}{{{k_j}}})]

The inverse of

**density**is known as

**spacing**, (s), which is the distance between two successive vehicles measured from bumper to bumper.

###
**Volume:**

**Traffic volume (v)**could be defined as the number of vehicles which pass through a reference point on a highway, or through a given lane or direction of a highway, within a specified unit of time, usually one hour.

**flow rate.**

**Headway**is defined as the time lapse between two successive vehicles (ith and I + ith) passing a reference point in space.

Originally posted on January 25, 2020 @ 11:48 pm