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Dear Members,

I have a doubt regarding track circuit calculation.

Given : The minimum ballest resistance RB= 2.5 ohm.km

To calculate the length of track circuit L,

The formula is RB=(ρL)/a

where
ρ = Resistivity ohm meter
L = Length in meter
a = Cross sectional area in square meter

if we know the ballest resistance, how to find the length of track circuits.

i have verified in one of the calculations

the sample calculation conveys me

RB=ρ/L

how this is derived?
what abt the cross sectional area?

I got confused regarding this kindly clarifiy and also
what is the difference between ohm.km & ohm/km ?

Regards,

Murugesan
Where have you got the formula from?

Normally in these queations, you end up with a min value that the total resistance and you need to work out the length of TC that will achieve it. The cross sectional area does not come into this.

Can you post a copy of your working?

Peter
(12-09-2012, 10:02 AM)Murugesan india Wrote: [ -> ]I got confused regarding this kindly clarifiy and also
what is the difference between ohm.km & ohm/km ?

Sorry, I missed this when I read your post before.

The difference is that one is the correct units for ballast resistance and one is not, but is often wrongly quoted as the units!

What we call ballast resistance is the total effective leakage between rails caused by the fact that the sleepers and ballast are not perfect insulators. An individual sleeper and ballast bed will have very low leakage (high resistance) but because there are a lot of them, you effectively end up with lots of high value resistors in parallel. From basic electrical theory, you will know that if you have two resistors of value R ohm in parallel, the total resultant resistance will be R/2 ohm. In a 1000m track, you will have around 1500 sleepers, meaning that you have 1500 parallel resistors resulting in a value of 1/1000th of the single sleeper.

So, what has this got to do with what you asked? Because we are talking about resistors in parallel, the more you have, the lower the value. The unit for the constant needs to reflect this. We are interested in the resistance (units ohm) over a given length (units km).

The equation in words is:
Value we want = characteristic value / length

Or written in terms of the units of measure:
Ohm = (ohm . km) / km

[If you do not understand the line above, look up dimensional analysis which is one of the most useful mathematical / engineering things that I was taught in physics at school].

I think it is because there are not many units of measure that need to be expressed as a product of units (a common example is Nm), but we are used to the ones that are given as a quotient (eg m/s, £ / kg, joules / sec), people tend to quote composite units as quotients. Strictly speaking quoting ballast resistance as ohm / km would mean that as the track circuit increases in length, the resistance would go up (ie that means that for every km of track you have n ohm of resistance) so this is clearly wrong. However, it is a very very common error to find it quoted thus.

Peter