Frequent accelerations and decelerations for rail transit trains adversely affect in the major performance measures of travel time, tractive energy consumption and braking wear between stations. A dipped vertical alignment between rail transit stations provides trains some added advantages from gravity in accelerating as well as in decelerating.

A deterministic simulation model based on basic kinematics and resistance relations has been developed to compute train motions and energy consumption on specified vertical alignments. A baseline case study and the sensitivity of results to parameter changes are analyzed.

Vertical alignments and operating characteristics such as speeds and coasting distances are jointly optimized. Powell’s Method is used for numerically optimizing total costs and other objective functions. Without speed constraints, the optimized total cost savings exceed 6.5%. The optimized alignment depths and total cost savings decrease as speeds are constrained to lower values.

The methods developed here may significantly improve rail transit systems.