Great Western Coffee Shop

Question I've been asked ... and I don't know the answer: "Just wondering how much usage of electric one train will use per km"

I suspect the answer is complicated by speed, gradient, length of train, acceleration / deceleration (might consumption be negative with regenerative braking?) and whether the heaters are turned on.

Anyone have a simple answer / formula to give a general answer?

Complex - yes as it depends on -

What type of train; a class 315 will use less energy than a 395; a class 165/0 will use less energy than a class 253
Is it passenger or freight; freight what is the Tonnage

etc

There is a commonly-used formula for the drag versus speed of a train - the Davis formula - and that can be readily turned into power vs speed. Getting the right parameter values for that for a given train is, however, less easy. I've found some for a class 220: 3.4537 + 0.0767.v + 0.0043.v², gives force in kN for v in m/s. Multiply by v in m/s to give kW - it's that simple!

There is a fuller version that derives those parameter values from the size, number of axles, weight etc. and I've done some estimates (though that term may be a bit complimentary) for class 800/801. In that case, for a 9-car, the power goes up as: 17 kW at 10 km/hr, 128 at 50, 438 at 100, and 2133 at 200. That's only drag at constant speed, there's also the power that goes into accelerating it. That stores up energy that increases as v², up to 183 kWhr at 200 km/hr. Gradients are similar, storing energy with height.

Then you need to know what a TOC pays for its electricity, don't you?

E&OE, as this is something I only did recently.

Who does initially pay for the energy used from the wires? And how is it apportioned to each train/TOC?

That is some sort of record - I'm lost after the third post.  But then I did fail Physics O Level - only to discover after I had sat the exam that my father had helped set the paper! 

Isn't there a meter on each unit that's read once a quarter and used to calculate the TOC's bill?

In all seriousness, I've gotten lost in the formulae too - spectacularly, and I take my hat off to those who present or understand them.   If someone could work an example out for me that would be fantastic - let's say for a 9 coach electric train off class 80? running from London to Bristol Temple Meads with stops at Reading, Didcot, Swindon, Chippenham, Corsham, Bath Spa and Bristol at some date in the future. And (as I'm not a great one for the physics) give me a comparison of how many of the same units it takes to run (say) a tumble dryer for an hour.

There is but as things stand currently (no pun intended) the electricity is wrapped up in the track access charge, the energy meters are used to help agree these charges.  If NR / HMG have their way with the NR electrical power systems being sold off (remember the railways have pylons up and down the country  ::) )  TOC's n FOCs may well be buy their electricity the same as we all do at home, by having a contract with an energy supplier

A bit more often - for details see Railway Group Standard GM/RT2132 "On-board Energy Metering for Billing Purposes".

Network Rail publish consumption rates by stock type and TOC for the purposes of charging.

http://www.networkrail.co.uk/cp5-access-charges/traction-electricity-modelled-consumption-rates-list.xls

Generically the area is known as 'EC4T' - Electric Current for Traction. There's a whole raft of stuff about it on Network Rail's web site http://www.networkrail.co.uk/using-our-network/on-train-metering/ (http://www.networkrail.co.uk/using-our-network/on-train-metering/).

As to actual usage, a modern train like the Pendolino has a maximum power consumption of around 6MW. Allowing for acceleration, regenerative braking, air-conditioning power and dwell time at stations one could guesstimate that, over a one hour period, it might use a third of the maximum, that is 2 Megawatt-hours.

A tumble-dryer has a rating of about 2.5kW, so used for an hour the consumption is 2.5kW-hours. This means that a Pendolino is equivalent to some 800 tumble-dryers.

This is a physicist's approach to an approximation - sometimes called Milkmaid's arithmetic!

Your mileage may vary! (But it won't be far out - the orders of magnitude are certainly correct!)

I have to either go online or go to a PayPoint outlet to top up a smartkey before inserting it into my meter. It'd be fun seeing a Class 801 driver having to do that!  :P ;) ;D

Yep - I was lost at that stage!  :o ::) ;D

I think one of the points that comes across is that on train metering is very much a statistical thing based on averages across the whole fleet,   only a certain proportion of units actually have the metering systems fitted and there's a presumption that repeated occurrences of the same daily diagrams will use the same amount of power to a first approximation.

So presumably the subset of SWT's EMU fleets fitted with 'meters' have to be rotated round all the routes.  I found this on NR's website, it includes a table of unit numbers that suggests that the numbers of metered trains are relatively small:

56th TG Supplemental Agreement
 (http://www.networkrail.co.uk/browse%20documents/track%20access/2%20completed%20consultations/2014/2014.11.13%20swt%2056th%20sa%20-%20closes%2012%20december%202014/56th%20tg%20sa.pdf?cd=6)
I also reckon that once a particular fleet is moved onto metering then there is no longer a traction element to the track access charge.

Paul

From what I remember from a talk about this issue at the IMechE a couple of years ago there is an issue with metering multiple unit stock as each unit needs its own meter. So one can get cases that one unit is metered and the other not. If I recall correctly all recent (in the last dozen years or so) 25kV new builds have meters and meters have been retrospectively fitted to all the Pendolino sets.

Metering on the SWT area is not so critical as essentially SWT is the only consumer.

Apparently the system used to work as you suggest, average use per diagram was summed over the year and the total cost of the electricity then divvied up among the operators. However, with the advent of metering those operators with meters would only pay for the electricity they had actually consumed and the rest was divvied up between those that that were not fitted with meters - the so-called 'wash-up' meetings or agreements.

This had the side effects that those operators without meters fitted them quickly which then tended to make people aware of the scale of the losses in the distribution system (the main interest in the 3rd rail metering) and that older electric locomotives (Class 86 and similar) tended not to have meters - apparently because the circuits are less suitable for fitting them. This meant that the FOCs tended to get lumbered with the 'wash-up' making their electricity very expensive and encouraging them to use diesels. (As I said, this was all a couple of years ago so things may have changed since).