13 - Network Planning - Speed, Time and Energy Flashcards
Overview of network planning
Timetable - planned in advance
Line speeds - fixed in advance
Aim - drive to meet the timetable using the least energy
How are energy and power calculated?
Force isn’t constant with speed and acceleration is not uniform
Equations of motion for uniform acceleration do not apply, Newton’s 2nd Law does apply
What equation is used for propulsive resistance and what does it show?
The Davies equation
General equation showing dependence of train resistance to motion on velocity
Disadvantage of the Davies equation
Other resistances exist not captured by this equation (e.g. more energy consumed in curves than in straight motion is ignored)
Tractive force vs speed
‘Pull’ available from the engine/motors of a train varies with speed
Real engine or traction control systems can be tuned depending on requirements - high loads, high speeds etc.
Common properties: constant force at slow speeds and constant power at higher speeds
Real world complications to models
Braking hard to stop is not usual driving - drivers retain a safety margin
Other features of network cause slow-downs (e.g. junctions)
Braking rate is limited to around 0.5-0.9m/s^2 by the maximum deceleration that passengers/luggage can take without falling
Low friction coefficient (0.09) can be achieved with very low rail-wheel friction (i.e. lots of extra force available under most conditions)
Assumptions for models
Tractive force: simplified form
Resistance to motion: simplified form; still capture dependence of forces on speed and therefore non-uniform acceleration
Braking: simple friction coefficient and constant force
Gradients: ignored; simple to do but no additional insight
Curves: ignored; adds to train resistance; simple to do but no additional insight
Four modes of operation
Accelerating
Cruising (maintaining constant speed, zero net force)
Coasting (no power applied, brakes off)
Braking (no power applied, brakes on)
Difference between braking and acceleration distances
Typically braking distances are shorter as distance/time taken to reach higher speeds are very long
When is energy used by a train?
Most in acceleration
Also in maintaining constant speed
Nothing in braking
Opportunity to save energy in train operation?
Take power off earlier and coast towards destination using no engine power
Steel wheel on steel rail means can coast a long way without power applied
What is energy in relation to power and time?
The integral of power over time
How to know when to coast
Train driver’s experience
Driver Advisory Systems (DAS) - GPS software
Fuel saving algorithms advise where to slow down
Either: timetable advice - ‘EARLY’ or specific instruction - ‘COAST’
C-DAS (connected DAS) - next generation system aware of real-time position of other trains (e.g. ensuring trains arrive in the best order to minimise delay and stop/start energy at junctions
Eco-systems case study
Class 185 diesel units
560kW under floor engine per coach
More power available than is needed in most cases
More efficient to run fewer engines at high power than all engines at low power output (also maintenance reduction)
Normal operation - 2/3 of engines running, avoidance of max power output even from these, gentle accelerations
Empty train movements, in depot - 1/3 of engines running
Very steep hill starts - all engines must run, GPS enabled software will kill 1/3 of engines as gradient becomes less steep
Use of higher power allowed if train is late
Estimated to save over 7% (1.8 million litres) of fuel per year
Questions to answer to aid network planning
Does high speed rail make sense in a small country with lots of places to stop?
Should we fix a speed restriction?
How much energy or time could we save by reducing train weight?
How much energy could we save using energy storage (flywheels, batteries), or regeneration?
