a6_cee3604_2011_sol - CEE 3604 Introduction to...

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CEE 3604: Introduction to Transportation Engineering Fall 2011 Assignment 6: Mass Transit and Airport Capacity Date Due: October 26, 2009 Instructor: Trani Problem 1 A truck runs out of brakes while traveling at 70 mph on an interstate highway in North Carolina (I-77). An emergency ramp offers the best hope for the driver. The emergency ramp geometry is shown in the figure below. The first 200 feet of the emergency ramp is granule gravel which offers a rolling friction coefficient of 0.32. The inclined section of the ramp is a mixture of sand and gravel with an equivalent rolling friction coefficient of 0.42. The equation of motion for this truck as it enters the first section with gravel can be approximated to be: ma = F f mg sin( θ ) = mg cos( θ ) f roll mg sin( θ ) Assume section one of the ramp has zero slope. The second section has a 7:1 slope. a) Using hand calculations, Matlab or Excel (your choice), find the length of the ramp needed to stop the truck. For the first section the final speed is: V 2 f = V 2 o 2 a 1 d where: V f = final speed (m/s) V o = initial speed (m/s) a 1 = deceleration on section 1 (m/s 2 ) d = distance traveled in section 1 (m) The final speed at the start of the ramp is then 24.4 m/s. The deceleration ( a 2 ) on section 2 (ramp) is given by the equation of motion provided. Simplifying: a 2 = g (cos θ ) f roll sin θ The angle of the ramp is 0.1419 radians a 2 = 5.48 m/s
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