Calculating Energy Use and Wind Turbine Requirements for High-Speed Trains

  • Context: Undergrad 
  • Thread starter Thread starter Cherwell
  • Start date Start date
  • Tags Tags
    Electricity Trains
Click For Summary

Discussion Overview

The discussion focuses on estimating the electricity consumption of a high-speed train in the UK operating at 400 km/h and determining the number of wind turbines needed to supply that energy. Participants explore the complexities of energy use related to speed, weight, and operational factors, as well as the implications of wind turbine energy generation.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests that a high-speed train consumes approximately 25 kWh per km based on data from the European MEET project and proposes calculations for energy consumption at different speeds.
  • Another participant confirms the calculation for wind turbines required at 330 km/h, stating that 8.25 turbines would be necessary based on the proposed energy consumption.
  • There is a proposal that energy use increases with the square of speed, leading to an estimate of 12.375 turbines for operation at 400 km/h, which is supported by another participant's calculation.
  • One participant cautions that extrapolating energy use to 400 km/h requires careful consideration of factors such as air drag, engine efficiency, and rolling resistance, which may vary significantly.
  • Another participant emphasizes that the average power required for trains is affected by the speed profile over the entire route, noting that energy consumption is not simply proportional to maximum speed or its square.
  • It is noted that the power required increases approximately with the cube of the speed change, and that energy needed for acceleration and braking must also be considered.
  • A participant mentions that wind resistance varies with the square of speed, while power is related to the cube of speed, highlighting the complexity of the relationship between speed and energy use.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between speed and energy consumption, with some supporting the square law and others suggesting a cubic relationship. There is no consensus on the exact calculations or the implications of various factors affecting energy use.

Contextual Notes

Participants acknowledge that actual energy consumption will depend on multiple variables, including train weight, gradients, and operational patterns. The discussion highlights the limitations of simple extrapolations and the need for comprehensive modeling to accurately estimate energy requirements.

Cherwell
Messages
1
Reaction score
0
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.
 
Physics news on Phys.org
Cherwell said:
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 ?
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,.

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 ?
Well, 400/330= 1.2121... and its square is about 1.47 so yes, it would take about 1.5 times as much.

Please let me know if this is right or wrong.
 
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.
 
Wind resistance varies with the square of speed: power by the CUBE of speed.
 

Similar threads

Vertical wind turbine with two concentric rotors
  • · Replies 7 ·
Replies
7
Views
4K
High School How does running in a moving train affect race times?
  • · Replies 27 ·
Replies
27
Views
3K
De-icing the wind turbines in Texas
  • · Replies 22 ·
Replies
22
Views
2K
Undergrad Electricity generation - gear mechanics and speed
  • · Replies 12 ·
Replies
12
Views
3K
Velocity of wind based on the shape of a smoke trail
  • · Replies 16 ·
Replies
16
Views
3K
How exactly does a turbine convert mechanical energy into electrical?
  • · Replies 8 ·
Replies
8
Views
3K
Automotive Wind Turbine on the grill of the car
  • · Replies 26 ·
Replies
26
Views
14K
Electromagnetism and power requirements
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Why is it claimed that Betz's limit is a law?
  • · Replies 30 ·
2
Replies
30
Views
4K
Wind Turbine Hydraulic to Electrical Conversion
  • · Replies 72 ·
3
Replies
72
Views
11K