Traffic Studies on Flow, Speed & Volume Study Notes

Traffic Engineering

Traffic engineering is that phase of engineering which deals with planning and geometric design of streets, highways, abutting lands, and with traffic operation thereon, as their use is related to the safe, convenient and economical transportation of persons and goods.

Theoretical maximum capacity, (C)

where S = Minimum clear distance between two vehicles (m).

S = 0.2V + 6 where, v = Speed of vehicle in km/hr.

C = Theoretical maximum capacity in vehicle/hour

H_t = Time headway in ‘Sec’.

Where,

C = Traffic capacity or traffic volume in vehicle/hour

δ = Traffic density in vehicle/km

V = Traffic velocity in km/hr

Passenger Car Unit

The PCU may be considered as a measure of the relative space requirement of a vehicle class compared to that of passenger car under a specified set of roadway, traffic and other conditions.

Accident Studies

The problem of accident is very acute in highway transportation due to complex flow patterns of vehicular traffic presence of mixed traffic and pedestrians. Traffic accidents may involve property damages, personal injuries or even casualties.

Where, e = Coefficient of restitution

 Velocity of separation

 Velocity of approach.

V_A = Velocity of vehicle ‘A’ of mass m_A before collision.

V_B = Velocity of vehicle ‘B’ of mass m_B before collision.

 Velocity of vehicle A after collision

 Velocity of vehicle B after collision.

e = 1 for perfectly elastic collision.

e = 0 for perfectly inelastic collision or plastic collapse.

i.e., both vehicle move with same velocity after collision.

Momentum Equation

Types of Collision

Collision of moving vehicle with parked vehicle (assumption: collision is perfectly plastic)

Where, v₁ = Initial velocity of moving vehicle in km/hr.

v₂ = Velocity of moving vehicle after travelling distance ‘s₁’ (in meter)

v₃ = Common velocity of moving & parked vehicle at the time of collision.

s₂ = Distance travelled by both vehicle till both vehicle comes in rest finally.

Two Vehicle Approaching from Right Angle Collide at an Intersection

Where,

 are skid distance just before collision.  are skid distance after collision.

 are speed of vehicle A & B respectively after the collision.

 are speed of vehicle A & B respectively after skidding a distance 

 are speed of vehicle A & B respectively before skidding.

Design Cycle Metho

Trial Cycle Method

Where, X_A = Number of vehicle accumulated in one cycle time on Road A.

X_B = Number of vehicle accumulated in one cycle time on Road B.

T = Total cycle time in ‘sec’ (assumed)

G_A = 2.5 X_A η_A = Traffic count on road A in 15 minutes.

G_B = 2.5 X_B η_B = Traffic count on road B in 15 minutes.

Where, T’ = Total cycle time (Actual)

A_A = Amber time on road A

A_B = Amber time on road B

G_A & G_B are green time on road A & B respectively.

It T’ = T then O.K. otherwise repeat the process.

Approximate Method

Whey, R_A = Red time on road A

R_B = Red time on road B

G_AP = Green time on road A for pedestrians

G_BP = Green time on road B for pedestrians

W_A = Width of road A

W_B = Width of road B

1.2 m/s = Speed of pedestrians G_A = R_B-A_A

G_B = R_A-A_B

Where, G_A = Green time on road A

G_B = Green time on road B

A_A & A_B are Amber time on road A & B respectively.

Websters Method

Where, C_O = Optical cycle time

L = Total lost time

L = 2n+R

Where, n = number of phase

R = All red time

Where, q_A = Normal flow on road A

q_B = Normal flow on road B

S_A = Saturation flow on road A

S_B = Saturation flow on road B

Where, G_A & G_B are green time on road A & B respectively.

Annual Average Daily Traffic (AADT or ADT)

Space Mean Speed (V_s)

Where, V_s = Space mean speed in km/hr.

d = Length of road in meter

n = Number of individual vehicle observations

t_i = Observed travel time (sec) for i^th vehicle of travel distance ‘d’ meter.

Time mean speed (v_t)

Where, V_t = Time mean speed (km/hr)

V_i = Observed instantaneous speed of i^th vehicles (km/hr)

n = number of vehicles observed.

Speed & delay study by floating car method

Average journey time (t) in minute

Where,

q = Flow of vehicles (volume per minutes) in one direction of the stream.

n_a = Average number of vehicles counted in the direction of the stream when the test vehicle travel in the opposite direction.

n_y = The average number of vehicles overtaking the test vehicle minus the number of vehicle overtaken when the test is in the direction of ‘q’.

t_w = Average journey time when the test vehicle is travelling with the stream q.

t_a = Average journey time, in minute when the test vehicle is running against the stream ‘q’.

Relationship between speed, travel time, volume, density & capacity

Travel time per unit length of road, 

Where, V = Speed in km/hr

q=kV_s

Where, q = Average volume of vehicle passing a point during a specified period of time (vehicle per hour).

k = Average density or number of vehicle occupying a unit length of roadway at a give instant (vehicles/km).

V_s = Space-mean speed of vehicles in a unit roadway length (km/hr)

Capacity flow or maximum flow, (q_max)

where, V_SF = Free mean speed i.e., maximum speed at zero density.

K_j = Jam density i.e., maximum density at zero speed

Where, s = Spacing between vehicles.

Rotary intersection

A rotary intersection or traffic rotary is an enlarged road intersection where all converging vehicles are forced to move round a large central island in one direction (clockwise direction) before they can weave out of traffic flow into their respective directions radiating from the central island.

Radius of rotary, (R)

Where, V = Design speed of vehicle (km/hr)

f = Coefficient of friction may be taken as 0.43 & 0.47 for the speed of 40 & 30 km/hr respectively after allowing a factor of safety of 1.5.

(R_min)_{Central Island} = 1.33 (R)_{Entry curve.}

(R_min)_{Central Island} = Minimum radius of central Island.

(R_min)_{Entry curve} = Radius of entry curve.

Where, w = Width of weaving section.

e₁ = Entry width,

e₂ = Width of non-weaving section.

Capacity of Rotary (Q_P)

Where, Q_P = Practical capacity of weaving section of a rotary in PCU per hour.

w = Width of weaving section (6 to 18 m).

e = Average width of entry ‘e₁’ & width of non-weaving section e₂ for the range e/w = 0.4 to 

L = Length of weaving section between the ends of channelizing islands in meter for the range of 

p = Proportion of weaving traffic or weaving ratio.

where, a = Left turning traffic moving along left extreme lane.

d = right turning moving along right extreme lane.

b = Crossing/weaving traffic turning towards right while entering the rotary.

c = Crossing/weaving traffic turning towards left while leaving the rotary.

Parking Facilities

Number of spaces (N)

 for parallel parking with equal spacing facing the same direction.

 for parallel parking when two cars placed closely.

 for 30° angle parking

 for 45° angle parking

 for 60° angle parking

 for 90° angle parking

Out of various angles used in angle parking, 45 degree angle is considered the best from all considerations discussed above.

Highway Lighting

Spacing between lighting units =

Trip Distribution

Where, T_ij = Number of trips from zone I to zone j.

G_i = Trips generated in zone i.

A_i = Trips attracted to zone j.

F_ij = Empirically derived ‘Friction Factor’ calculated on area wise basis.

n = Number of zones in the urban area.

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