norman w. garrick example of a shock wave at a stop traffic is flowing normal flow, q = 500 veh/hr...
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Norman W. Garrick
Example of a Shock WaveAt a Stop
Traffic is flowing normalFlow, q = 500 veh/hr Conc, k = 10 veh/mi
T = t1 sec
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t2 sec
Flagman stops first vehicle in the queue
Shockwave
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t3 secMore vehicles have joined the queue
The shockwave have moved backwards
Shockwave 1
On either side of the shockwave there are two different state of flow
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Example of a Shock WaveAt a Stop
T = t4 secFlagman releases queue
Shockwave 1
There is now a second shockwave and a third state of flow - the flow state for traffic released from the queue
Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Distance-Time Diagram for Shock Wave
Distance
Time
XShockwave 1
Shockwave 2
Norman W. Garrick
Calculation of Shockwave Travel
The speed of the shockwave can be calculated using the above equation
The sign is important so remember to number the travel states from upstream to downstream
If the sign is +ve it means that the shockwave is moving downstream
usw = (q2-q1) / (k2-k1)
Shockwave 1
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Calculation of Shockwave Travel
Shockwave 1
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
usw1 = (q2-q1) / (k2-k1)(0-500) / (260-10) = - 2 mph
Shockwave 1 is moving downstream at 2 mph
What is the length of the queue after 3 minutesLength = u*t = 2 mph * 3/60 hr = 0.1 mile
How many vehicles are in the queue after 3 minutesno. of vehicles = k * L = 250 *0.1 = 25 vehicles
Norman W. Garrick
Calculation of Shockwave Travel
usw2 = (q3-q2) / (k3-k2)(1000-0) / (110-260) = - 6.67 mph
Shockwave 2 is moving downstream at 6.67 mph
Shockwave 1 Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Calculation of Shockwave Travel
How long will it take to clear the queue if the flagman held the queue for 3 minutes
Length after 3 minutes = u*t = 2 mph * 3/60 hr = 0.1 mile
usw1 = - 2 mph usw2 = - 6.67 mph
Therefore the queue will dissipate at rate of 4.67 mphTime to dissipate a 0.1 mile queue is L/speed0.1 mile / 4.67 mph = 0.021 hr = 12.6 minutes
Shockwave 1 Shockwave 2
State 3q = 1000 veh/hrk = 110 veh/mi
State 1q = 500 veh/hrk = 10 veh/mi
State 2q = 0 veh/hrk = 260 veh/mi
Norman W. Garrick
Norman W. Garrick
Norman W. Garrick
8 vehicles7 spaceGet Distance to find average spacing
Norman W. Garrick
37.7
32.0