Traffic Engineering Uninterrupted Flow is defined and regulated by:
- Vehicle-to-Vehicle interactions:
- Speed
- Proximity
- Volume
- Vehicles-to-Roadway interactions:
- Weather conditions
- Surface condition
- Site distance
Examples of Uninterrupted Traffic Flow are:
- Interstate highways
- Expressways
- Rural highways and roads
Concepts and Equations
-
Flow (q)
The rate at which vehicles pass a given point on a roadway in a given time interval. q = n/t (vehicles per hour) and q = Space Mean Speed x Density.
-
Volume (V)
The number of vehicles passing a given point on a roadway in a specified period of time.
-
Time-Mean Speed (vt)
Arithmetic mean of speeds of vehicles passing a point (mph).
The Time-Mean Speed for six vehicles travelling 55 mph, 53 mph, 50 mph, 47 mph, 45 mph, and 44 mph is:
vt = (55 + 53 + 50 + 47 + 45 + 44) ÷ 6 = 49 mph
-
Space-Mean Speed (vs)
The average speeds over a length of roadway (mph).
The Space-Mean Speed for the six vehicles is:
vs = 6 ÷ (1/55 + 1/53 + 1/50 + 1/47 + 1/45 + 1/44) = 48.7 mph
- Free Flow Speed (vf)
The average speed that a motorist would travel if there were no congestion or other adverse conditions (i.e. bad weather).
-
Headway (h)
The time interval or distance between two vehicles traveling in the same direction over the same route. The time elapsed between the arrival of one vehicle and a following vehicle at a designated test point. The inverse of headway is flow (h = 1/q).
-
Time Headway (ht)
Time difference between the front of a vehicle crossing a point on a roadway and the front of the next vehicle crossing the same point (measured in seconds).
-
Space Headway (hs)
Distance between the front of a vehicle and the front of the next vehicle (ft).
-
Density (k)
If n = number of vehicles and ℓ = length in miles, then k = n/ℓ.
-
Critical Density (kc)
The maximum density achievable under free flow.
-
Jam Density (kj)
The maximum density achieved during congestion.
-
Spacing (s)
The center-to-center distance between two vehicles. Spacing is the inverse of density (s = 1/k).
-
Gap (g)
The time elapsed between the rear bumper of the first vehicle passing a point and the front bumper of the second vehicle passing the same point
-
Clearance (c)
The distance between the rear bumper of a vehicle and the front bumper of the second vehicle. Clearance is also equal to the spacing minus the length of the first vehicle.
Greenshield’s Model of Uninterrupted Traffic Flow
Predicts and explains trends observed in real traffic flows:
v = A – B x k, where v = speed (mph)
where A and B are constants determined from field observations, and k = density (vehicles/mile)
Also, vs = vf x (vf/kj)k
Example 1
The Space-Mean Speed for a given freeway is vs = 43.9(1.7 – 0.015k).
Calculate:
- Free-flow speed
- Jam Density
- Maximum flow
- Speed at maximum flow
Solution
Using Greenshield’s Model:
vs = vf – (vf/kj)k = 43.9(1.7 – 0.015k) = 74.63 – 0.6585k
(1) Free-flow speed: (vf) = 74.63 mph
(2) Jam density: vf/kj = 0.6585 or kj = vf/0.6585 = 74.63/0.6585 = 113 veh/mile
(3) Maximum flow: (Definition of Flow)
q = Space Mean Speed x Density = vs x k
q = (43.9(1.7 – 0.015k))k = 74.63k – 0.6585k2
to determine maximum flow: dq/dk = 74.63 – 0.6585(2)k = 0
k = 56.7 vehicles per mile = density at maximum flow
q = 74.63k – 0.6585k2 = 74.63(56.7) – 0.6585(56.7)2
q = 2114.5 veh/hr
(4) Speed at maximum flow:
vmax = 74.63 – 0.6585k = 74.63 – 0.6585(56.7) = 37.3 mph
Related Content:
- Traffic Engineering Highway Capacity Manual
- Basic Design Controls
- Fundamentals of Transportation/Traffic Flow
- Flow, Speed, and Density
- Fundamentals of Traffic Flow and Queuing Theory
- Traffic Stream Characteristics
- Freeway & Highway Level of Service
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