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mass_transit_capacity_2009

mass_transit_capacity_2009 - Tansportation Engineering...

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Virginia Tech 1 Tansportation Engineering Capacity of Mass Transit Technologies (including Automated People Movers) Dr. Antonio A. Trani Professor of Civil and Environmental Engineering Virginia Polytechnic Institute and State University Blacksburg, Virginia Spring 2009
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Virginia Tech 2 Introductory Remarks • Simplified analysis of mass transit systems using Time- Space diagram analysis • Basic analysis to estimate capacity of mass transit systems including APM applications at airports
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Virginia Tech 3 Review of Equations of Motion
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Virginia Tech 4 Sample Kinematic Models Two models are useful in the analysis of ground transportation systems: a) Constant acceleration/deceleration) b) Variable acceleration/deceleration The use of the model depends on the characteristics of the system studied and the level of accuracy needed. Example 1: in the analysis of deceleration profiles for cars and trains we can use a constant deceleration model Example 2: in the analysis to determine the acceleration of highway and mass transit vehicles the use of a variable acceleration model is recommended
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Virginia Tech 5 Kinematic Models dV/dt dV/dt V V Constant acceleration/deceleration k 1 k 1 /k 2 k 2 k 1 k
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Virginia Tech 6 Constant Acceleration Model The acceleration of the vehicle is equal to a constant ( k ), d V dt ---- k = Integrate once to get speed ( V ) and twice to get distance traveled ( S ) V t V 0 kt + = where: V t is the speed at time t, V 0 is the initial speed of the vehicle and t is the time from start of motion
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Virginia Tech 7 Constant Acceleration Model The distance traveled (S) is, S t V 0 t 1 2 -- kt 2 S 0 + + = where: S 0 is the initial position of the vehicle at time 0 Since k is just the acceleration of the vehicle this equation is equivalent to the well known relationship, S t V 0 t 1 2 -- at 2 S 0 + + = where a is the constant acceleration of the vehicle
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Virginia Tech 8 Constant Acceleration Model The same model can be used to estimate the distance and velocity profile of a vehicle in a deceleration maneuver with constant deceleration. In this case replace the value of a is negative.
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Virginia Tech 9 Variable Acceleration Model Start with, d V dt ---- k 1 k 2 V = Integrate once to get speed ( V ) V t k 1 k 2 --- 1 e k 2 t ( ) V 0 e k 2 t + = where: V t is the speed at time t, V 0 is the initial speed of the vehicle, k 1 and k 2 are constants and t is the time from start of motion
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