Hi I’m trying to estimate how much electricity a new high speed train in the UK would use to go at 400 km/h and how many wind turbines it would require to run it. My physics is a bit rusty so I’d appreciate it if someone would check my calculations. It is difficult to estimate how much energy these trains would draw down from the electric grid. Actual consumption will depend on the weight of the trains, gradients, maximum speeds and stopping patterns. Data produced for the European MEET project illustrates different consumption patterns over several track sections. Results for the consumption by German ICE high-speed trains which have a service speed of 330 km/h fluctuate from around 19–33 kWh per km. Therefore, for estimation purposes I propose to split the difference and say they consume 25kWh per km. 2 questions 1. If a train consumes 25kWh per km and a wind turbine generates 1000kWh on average, how many wind turbines would be required to run at 330 km/hr? Would it be 25 x 330 ÷ 1000 = 8.25 ??? 2. Also, would it be true to say that because energy use rises with the square of speed, trains operating at 400 km/h would use one and a half times more energy than at 330 km/h and require 8.25 x 1.5 = 12.375 wind turbines ??? Please let me know if this is right or wrong.
Yes, that is correct. Check the units: (25 kWh/km)(330 km/h)= 8250 kWh/h= 8250 kW. And, since there are 1000 Watts in a kW, that is 8.25 Watts of power,. Well, 400/330= 1.2121... and its square is about 1.47 so yes, it would take about 1.5 times as much.
You would have to be careful with the extrapolation to 400km/hr the air drag, engine efficiency, rolling resistance etc will vary quite a bit I would imagine.
Power and energy use by trains is strongly affected by the speed profile over its full route. The average power is not necessarily indicative of the incremental power required to boost the speed by some fixed amount. A great deal of the energy used is required to accelerate the train to speed, and typically trains do not get to cruse speed and stay there, as commercial aircraft generally do. They frequently need to change speed for curves, traffic, grades, and station stops. Every time they re-accelerate more energy is used. Then of course most modern train systems also incorporate re-generation of power when they brake, that power either flows to nearby trains that are needing power (e.g. accelerating) or back to the power grid, if they have been setup to regenerate to the power grid (not always feasible). Re-generation of power makes the power/energy estimating messier. Energy use per km is not proportional with max. speed nor with max speed squared. Train resistance (the total of friction, aero-drag, rolling resistance, etc.) typically has terms of a constant, no. of axles, weight, speed and speed^2. For an ideal case, to consider the power increase between cruse speeds 330 km/h and 400 km/h, the train resistance would increase largely as the square of the speed (there would also be a smaller increase proportional with speed). However, as power is Force x Speed, the power would actually increase approximately with the cube of the speed change (400^3 - 330^3) or approximately a 78% increase. The above increase in power is only the difference in power between constant cruse speeds. It does not consider the increase in energy needed to accelerate to the higher cruse speed, which will be significant. Also the distance required to accelerate to the higher cruse speeds (and the distance to brake from it) may be great enough that little advantage may be realized by the higher speed when considering typical inter-city distances.