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## Traffic Flow Characteristics (2)

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**Traffic Flow Characteristics (2)**Traffic Flow Characteristics (2) Traffic Flow Characteristics (2)**Learning Objectives**• To differentiate between interrupted and uninterrupted flow facilities • To define general and linear speed-density relationships • To derive, sketch, and apply Greenshield’s Model of traffic flow**Recap**Spacing**Recap**Clearance**Recap**# vehicles/Distance Density**Recap…**• Speed (v) – ft/sec or mph • Flow (q) – veh/sec or vph • Density (k) – veh/ft or vpm • Spacing (s) – ft/veh • Headway (h) – sec/veh • Clearance (c) – ft/veh • Gap (g) – sec/veh Remember, units are critical!**Fundamental Relationships**• q = k v (veh/hr) = (veh/mi) (mi/hr) • h = 1 /q (sec/veh) = 1 / (veh/hr) (3600) • s = 1 /k (ft/veh) = 1 / (veh/mi) (5280)**Types of Facilities**• Uninterrupted flow • Freeways • Multilane highways • Two-lane highways**Types of Facilities**• Interrupted flow • Signalized streets • Un-signalized streets with stop signs • Transit lanes • Pedestrian walkways**General Speed-Density Relationship**p.130 S V Free normal flow forced flow Traffic Jam Q Capacity K Density at Capacity Jam Density**General Speed-Density Relationship**p.137 K V Traffic Jam Free forced flow normal flow Q Capacity K Density at Capacity Jam Density**General Speed-Density Relationship**p.137 Q V Capacity Free Traffic Jam V K Density at Capacity Jam Density**Greenshield’s Model**• Assume a linear relationship between v and k: Low Density = High Speed vf High Density = Low Speed kj**vf**v0 Greenshield’s Model Q Max flow qmax K Kj K0**Greenshield’s Model**V Vf 1/k0=s0 V0 Q Qmax Max flow**Example**Assuming a linear v-k relationship, the mean free speed is 60 mph near zero density, and the corresponding jam density is 140 vpm. Assume the average length of vehicles is 20 ft. Find: • v(k) and q(k) • Sketch v-k, v-q, and q-k diagrams • Compute v and k at q=1000 vph • Compute the average headway, spacings, clearances, and gaps when the flow is maximum