# Calculating load requirement for light rail

Hi all, my first post here so first, I'll say hello. Hello.

My question is this. I'm trying to figure out how to go about getting an approximate power requirement for an expanding light rail design. The idea is to figure out what it takes to propel a single self propelled train car based on it's weight so that I can continue adding cars and still be able to calculate the required power.

Now I know this is a very complicated question but maybe someone can give me a general sense as to where I can start.

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You could start with a simple approximation. First, the power to accelerate the train:

work = force X distance
power = force X velocity
force = mass X acceleration

So,

Power = mass X acceleration X velocity

Or if you want to look at the average power:

Pavg = Energy / time = (1/2 mass vel^2) / time

where vel would be your final velocity.

To improve the calculation, you could consider the drag force:

F drag = 1/2 * air density * drag coefficient * vel^2 * projected area

and also the "rolling resistance" of the wheels:

F-roll = ur X F-normal

where ur = 0.002 (about) for steel wheels on rails.

The power for the rolling resistance is:

P-rolling = F-roll X vel

This simple treatment would allow you to do some very approximate initial studies.

I think the Pavg is going to be my best bet to go about calculating what I need to know.

If I run the calculation using an 8,000 lb train at an average speed of 60 mph for 1 minute, it reveals 3 things:

1. I get Pavg=14,400,000 (Watts?)
2. 1,800 Watts per lb of train
3. My understanding of basic physics is at about a high school level (or what I remember of it).

So, assuming I calculated this correctly, am I correct that the unit of power I just solved for is watts?

The other thing I'm wondering about is that once I know the requirement, is there a loss of overall efficiency involved in transferring the electricity from the rail (as in the 3rd rail) to the train and it's motor such as in a system like a subway or light rail? I think the efficiency of a motor runs at something like 85%, but I wonder if they lose anything more when the conductors are dragging across each other.

Double check your units. 14,400,000 watts is 19,311 horsepower. This is way too high.

To establish a baseline, look at this site:

http://ecotopia.com/ulr/

It talks about a 13,500 lb light rail train with 90 horsepower. Now using our formulas, it would take about 33 seconds to reach 60 mph. I crunched the numbers and units in Mathcad - I don't know how to cut and paste them here. But see if you can match my number.

85% is a decent motor efficiency assumption for preliminary calculations.

In San Francisco. The cable car routes each run on a single 300 HP electric motor at the substation. This motor pulls the underground cable that all the cars use. It is important that there should always be a cable car going down a hill whenever another car on the same cable is going up. In this way, each cable car does not need the power to propel itself up the hills. Also, at the end of each route, the passengers need to get out and manually turn the car around on the turnstyle.

 This is very light rail.
Bob S

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