Week 7: Design: Vertical Curves, Grades, Controlling Grade, Velocity Profiles

To be able to design a vertical curve for a railroad, considering AREA recomended limits
To be able to understand the implications of grade on train performance, including the concept of ruling or controlling grade
To be able to understand railroad energy concepts, and demonstrate their use through the development of a velocity profile
To be able to understand the applications and utility of the velocity profile

Use parabolic curves (same as highway design), see Lab 2, problem 3 for equations and example
less friction on drive wheels
max. grade usu. 1% (2.5 % in mountains)
length of vertical curves is limited by forces that tend to break apart trains (more severe in sags - why?)
minimum length of sag curve (high speed main track) = 20(change of gradient), e.g., if 1%, 2000' curve
minimum length of crest curve (high speed main track) = 10(change of gradient), e.g., if 1%, 1000' curve
for secondary track, you may use curves half as long
for classification yard "hump" must use a very short curve, but cars must not "bottom out"

potential energy = elevation head
kinetic energy = velocity head = .035 V² in feet
recall from physics that kinetic plus potential is constant (less heat input or lost)
Click here for graphical explanation of velocity profile concept
Click here for development of example profile
velocity profiles give you the same information that you get from acceleration and deceleration curves you are using in your lab
velocity profiles allow you to read directly speed at any point and distance to accelerate
time between points may be estimated by dividing the distance between 2 points by the average speed between the two points
fuel use can be estimated by calculating time and the level of effort of the locomotives (they consume about 10% of max. fuel rate at idle)
computers can give this information today (but someone has to program the computers!)