Question

A gravitational energy storage system uses a railcar system with a train that has a mass of 200,000 kg. The railroad track is 5 miles long and on a 10% grade (10 ft. elevation gain for every 100 ft. horizontal distance)

a. The electric locomotive uses 1.84 GJ of energy to propel the train up the side of the mountain. What is the efficiency of the system as it is “charging”?

b. The electric locomotive produces 1.44 GJ of electrical energy as it is descending the mountain. What is the efficiency of the system as it is “discharging”?

c. What is the “round-trip efficiency” (including charging and discharging) of the railcar system?

Answer 1

A 10% grade implies an angle of elevation of,  

A track length of 5 miles with 10% grade would result in an elevation of,

Energy required to carry the train of mass, = 200,000 kg, up an elevation is,

a) Ideally the energy required to carry the mass is, E = 1.5709 GJ

Energy actually used by the electric locomotive is 1.84 GJ

Thus, efficiency while charging is,

b) Ideally, the energy generated while the mass descends is, E = 1.5709 GJ

Energy actually generated by the electric locomotive is 1.44 GJ

Thus, efficiency while discharging is,

c) The “round-trip efficiency”,

OR

The “round-trip efficiency”,