MAIT Mechanics Project: Long distance travel

Comparison of energy losses for various modes of transport

Introduction

The object of this study is to establish the basic energy losses of various modes of transport and to show the limits to reducing losses that could conceivably be achieved existing technology.

The motive for this study is to establish what savings might be made in travelling longer distances in MAIT Cabins. Each Cabin could carry:

• 6 seated passengers with hand luggage with leg room better than a bus or economy airline.
• 4 seated passengers with normal holiday luggage and leg room better than first class rail.
• 2 passengers sleeping fully horizontally and normal luggage.

In order to make a comparison with other modes of transport, we will use the Cabin as the unit of accommodation where 1 Cabin is equivalent to:

• 6 economy airline seats
• 4 rail seats
• 3 first class rail seats
• 1 road car

The following factors are not included because there is an uncertain scope for improvement that is applicable to all the different modes to some degree:

• Energy required for heating and lighting. This will vary with climate and time of day and depend on the thermal insulation of the Cabin in-situ. For higher speeds it is probably insignificant.
• Energy loss due to motor efficiencies less than 100%. This depends on the drive technology which is constantly developing. Linear motors have been demonstrated with more than 90% efficiency.
• Usage efficiency, ie proportion of seats filled. Our proposed new style of transport using Cabins is expected to allow more efficient use of capacity with greater convenience to passengers, but at this stage we can only guess by how much.
• Losses other than rolling friction and aerodynamic drag, such as the velocity dependent component of rolling friction. This is assumed to be relatively insignificant and can be added to the rolling friction without too much error.
• Energy supply efficiencies. The scope for improving supply efficiency is not clear but broadly applicable to all the different modes.
• Energy consumed in the manufacture of the vehicles and infrastructure.

Comparison of energy losses

Fig 1 compares the energy losses of the various modes of transport as a function of speed. The vertical scale is MJ per Cabin-km, ie, the amount of energy needed to move one Cabin one kilometer and the horizontal scale is km per hour.

Fig 2 shows the breakdown of the various types of energy loss at specific speeds.

PAT and PAT convoy

The drag coefficients are from wind tunnel tests on a model based on the ULTra vehicle.

Putting the rolling resistance coefficient to a value of 0·03, ie, somewhat greater than is obtained with the best rubber tyre, accounts for 50% of published power requirements of the ULTra vehicle.

ULTra

This is the published figure for ULTra.

"Best PAT"

This is the curve for a PAT vehicle with aerodynamics the same as a saloon car and the best achievable rolling resistance coefficient for steel on steel of 0.001.

Cowled Convoy

The aerodynamic drag on a PAT vehicles in a convoy could be further reduced by filling the gaps between them with a cowl so as to give a more continuous surface. This curve is estimated on the basis that the skin friction drag predominates and that the gaps between the cowl and the Cabins result in a degradation by a factor of 4. The rolling resistance is arbitrarily set at 0·002.

In-line

A novel carrier in which a single Cabin fits in the cross-section. The articulation is designed with a minimal gap so that the outline is aerodynamically smooth. The major advantage of this proposed type of carrier is that the load per unit length on the guideway is minimised (at least a factor of four less than rail) so that the cost of the guideway, the major component of system cost, can be minimised.

Saloon car

For the sake of comparison this curve, derived from the same series of wind-tunnel tests as above is included. The illustrated rolling resistance coefficient is 0.02, which is typical for the average tyre and road surface.

Real car

As a reality check, data was taken from a graph of mpg vs speed for a "typical" car has been included . The curve is sum of the aerodynamic and rolling resistance losses the same as the Saloon car above, plus a constant, speed independent energy loss. By adjusting the constant energy loss and the efficiency a reasonable fit to the data was obtained.

Coach

This point is based on a journey from London to Glasgow which is 411 miles and takes about 8·5 hours. The Neoplan Skyliner Megabus takes 91 passengers with a fuel consumption of 2·3kg of fuel per passenger for this journey

ICE

The curves for ICE and Transrapid are taken from a web site of the International Union of Railways and gives energy consumption in energy per km for a square meter of floor space. This is translated into 2.6 m² per Cabin.

The same source gives the energy consumption for Transrapid which is very close to ICE

Best possible

The curve "best possible" is calculated for skin friction drag of a vehicle with similar dimensions to the Transrapid and an aerodynamically smooth surface.

This curve gives a boundary to what is reasonably achievable, at least without using evacuated tubes.

Air

The data for cars and trains came from the web site of the German Airports Association, which gives comparative fuel consumption per passenger km for airliners, cars and rail. I have used the a conversion factor 41 MJ per litre for aviation fuel.

Estimation of energy losses.

We consider three components of energy loss: Rolling resistance, Form drag and Skin friction drag.

Rolling resistance

is a constant force opposing movement. Energy is lost to friction and hysteresis effects arising from the deformation of the wheel and the surface on which it rides

Cr is the rolling resistance coefficient. This is defined as the ratio of the force needed to roll the wheel to the force on the wheel. It depends on the type of wheel.

Er = energy in MJ to move against rolling resistance for 1km

Where M is the mass of the vehicle in kg

Form drag

is the aerodynamic resistance caused by pushing air out of the way of a body. At the speeds and dimensions we are considering the flow is turbulent.

Ed = energy in MJ to move against form drag for 1km

Where Cd is the drag coefficient which is typically between 0.2 for a very streamlined shape and 1 for a flat surface.

A is the cross sectional area in m²

V is the velocity in msec^-1

Skin friction drag

is the aerodynamic resistance due to pulling a long body with uniform cross section through the air without displacement.

L = length

Pr = length of outline of cross-section

Renolds number, is given by

For the velocity and dimensions we are considering Renolds number is large and the flow will be turbulent. The skin friction drag coefficient is given by:

The dynamic pressure:

The drag for the surface area is:

Where:

This would be for a smooth surface with no protuberances or gaps. Real surfaces, such as the outside of a high speed train, will have gaps between the coaches to allow articulation and projections such as wheels and power pick-up. To allow for this we have introduced

R_f = roughness coefficient. Has a value of 1 for a smooth surface and gets larger as the surface gets rougher.

E_f = energy in MJ needed to move against skin friction for one km:

Total Energy to move one cabin:

Last updated: 15 February 2008 webmaster@maitint.org