Maths question

[studentspark]

If I wanted to calculate the maximum length of a circuit, in relation to its Zs
would the following transposition be correct..

So if it was a 2.5mm2 T&E cable on a 20 amp MCB.
I would use 2.19Ω (BS7671) as my Max Zs, as this is at the maximum operating temperature. Not 1.75Ω as in the 80% value

I have a Ze of 0.35
Im correcting the 19.51 mΩ/m to 70 oC with the factor of 1.2

R1+R2 = 19.51
L = Length
F = Temperature correction 1.2


Zs = Ze + (R1+R2) x L x F / 1000

2.19 = 0.35 + 19.51 x ? x1.2 /1000

Transposed to

L= Zs - Ze / R1+R2 x F
x 1000

So...

2.19 -0.35 = 1.84
19.51 x 1.2 = 23.41

1.84 / 23.41 = 0.07

0.07 x 1000 = 70m

But this would give a volt drop of 25.2 volts.
If my maths are correct !! I presume in the design stage, using Zs as a guide to maximum length of a circuit, is not a good idea?

I hope that makes some sense...


Thanks

 

[EFLImpudence]

So if it was a 2.5mm2 T&E cable on a 20 amp MCB.
I would use 2.19Ω (BS7671) as my Max Zs, as this is at the maximum operating temperature. Not 1.75Ω as in the 80% value.

Well the Max Zs allowed IS 2.185Ω (2.19). That doesn't change whatever the temperature.
230 / 100 x 0.95.
It should be 230 /100 x 0.94; i.e. 216.2 /100 = 2.162Ω but it isn't for some reason.

I have a Ze of 0.35

Ok. So R1+R2 is max of 2.19 - 0.35 = 1.84Ω

Im correcting the 19.51 mΩ/m to 70 oC with the factor of 1.2

Ok. 19.51 x 1.2 = 23.4mΩ/m.

R1+R2 = 19.51
L = Length
F = Temperature correction 1.2

Ok.

Zs = Ze + (R1+R2) x L x F / 1000
2.19 = 0.35 + 19.51 x ? x1.2 /1000

Ok.

Transposed to
L= Zs - Ze / R1+R2 x F
x 1000

Ok.

So...
2.19 -0.35 = 1.84
19.51 x 1.2 = 23.41

1.84 / 23.41 = 0.07
0.07 x 1000 = 70m

Yes, that's all you needed in the first place.

But this would give a volt drop of 25.2 volts.
If my maths are correct !! I presume in the design stage, using Zs as a guide to maximum length of a circuit, is not a good idea?

If the actual load is 20A and IF the temperature will be 70° which it won't with 20A (or less) on 2.5mm².
You don't have to use the MCB rating.

 

[EFLImpudence]

Also - the volt drop might not matter.

 

[JohnW2]

If I wanted to calculate the maximum length of a circuit, in relation to its Zs
would the following transposition be correct.. So if it was a 2.5mm2 T&E cable on a 20 amp MCB. I would use 2.19Ω (BS7671) as my Max Zs, as this is at the maximum operating temperature.

OK

I have a Ze of 0.35 ... Im correcting the 19.51 mΩ/m to 70 oC with the factor of 1.2

Before I move on to the rest of your maths ..... where does that 19.51 mΩ/m come from?? Table 4D2B (or 4D5) of BS7671 gives 18 mΩ/m for 2.5mm² cable at 70°C.

Kind Regards, John

 

[ericmark]

A long time ago I tried to transpose and calculate volt drop, the correction factor with sq root etc made the calculation rather complex, so I used java script and built myself a calculator and tested it using the published 106 meter limit for a ring final when using 26 amp as Ib.
I started to enter details and get something like this

Does that help?

 

[JohnW2]

... Before I move on to the rest of your maths ..... where does that 19.51 mΩ/m come from?? Table 4D2B (or 4D5) of BS7671 gives 18 mΩ/m for 2.5mm² cable at 70°C.

@studentspark Ah, having looked at the rest of your maths, I see that you are talking about the R1+R2 resistivity (not R1+Rn, per BS7671 VD tables). That being the case, R1+R2 for 2.5/1.5 mm² T+E not be (18/2)+(29/2) = 23.5mΩ/m - which is essentially your 19.51 x 1.2 - but I still wonder where the 19.51 comes from? OSG perhaps?

Kind Regards, John

 

[EFLImpudence]

OK
Before I move on to the rest of your maths ..... where does that 19.51 mΩ/m come from?? Table 4D2B (or 4D5) of BS7671 gives 18 mΩ/m for 2.5mm² cable at 70°C.

Resistance per metre of 2.5/1.5mm² cable.

Edit - didn't see your next post.

 

[JohnW2]

Resistance per metre of 2.5/1.5mm² cable.

Indeed - see my message posted simultaneously with yours!

Kind Regards, John

 

[EFLImpudence]

2.5 is 7.32mΩ
1.5 is 12.2mΩ
at 20°C

Hence 19.51 (19.52) x 1.2.

 

[JohnW2]

If I wanted to calculate the maximum length of a circuit, in relation to its Zs
would the following transposition be correct.......

(after my initial misunderstanding!) Your maths is correct, other than (as a matter of detail) ...

1.84 / 23.41 = 0.07 .... 0.07 x 1000 = 70m

1.84/23.41 is actually 0.0786, which therefore becomes 78.6m.

But this would give a volt drop of 25.2 volts.

It would - although, as EFLI has said, 20A through 2.5mm² cable will not result in a conductor temp of 70°C - so resistance, hence VD at 20A , will be less than you have calculated.

If my maths are correct !! I presume in the design stage, using Zs as a guide to maximum length of a circuit, is not a good idea?

I think you'll find that, for any circuit (and with 'usual' values of Ze), calculations of 'maximum length' based on the guidance VD figures (at maximum circuit current) will always resulkt in shorter 'maximum lengths' than would be necessary to satisfy ADS (i.e. Zs) requirements.

However, the thing to remember is that satisfying the ADS/Zs requirement is the important, safety-critical, issue, whereas VD is only a matter of guidance, and is rarely of any importance at all. Don't forget that, in order to satisfy BS7671, all that is required of VD is that it is not so great as to 'impair the safe operation of connected equipment' - and, frankly, I can thing of nothing whose 'safe operation' will be impaired by under-voltage -0 it might not work properly (maybe not at all), if voltage is too low, but it won't become 'unsafe' because of low voltage.

Kind Regards, John

 

[JohnW2]

2.5 is 7.32mΩ ... 1.5 is 12.2mΩ ... at 20°C ... Hence 19.51 (19.52) x 1.2.

Indeed - as I wrote ..

... That being the case, R1+R2 for 2.5/1.5 mm² T+E not be (18/2)+(29/2) = 23.5mΩ/m - which is essentially your 19.51 x 1.2 - but I still wonder where the 19.51 comes from? OSG perhaps?

However, although now slightly re-worded, I still have to ask where those 20°C figures come from. If the OSG, I didn't think you read that

Kind Regards, John

 

[EFLImpudence]

1.84/23.41 is actually 0.0786, which therefore becomes 78.6m.

D'oh. I didn't check that one.

 

[EFLImpudence]

I still have to ask where those 20°C figures come from.

Not sure originally. Just standard values ???

https://www.tlc-direct.co.uk/Book/5.3.6.htm

As the figures do not all match, I always start from 1.83mΩ/m for 10mm² and calculate from there.

 

[JohnW2]

Not sure originally. Just standard values ???

As I said, I suspect you're quoting the publication that you'd prefer not to read

Kind Regards, John

 

[JohnW2]

As the figures do not all match, I always start from 1.83mΩ/m for 10mm² and calculate from there.

Yes, that's probably sensible. The rounding in 'VD' figures in BS7671 means that they don't all exactly correspond. For example ...

10mm² (2 conductors) is tabulated as 4.4 mΩ/m ... 4.4 x 4 = 17.6, but 2.5mm² is tabulated as 18 mΩ/m
16mm² (2 conductors) is tabulated as 2.8 mΩ/m ... 2.8 x 4 = 11.2, but 4mm² is tabulated as 11 mΩ/m.
6mm² (2 conductors) is tabulated as 7.3 mΩ/m ... 7.3 x 4 = 29.2, but 1.5mm² is tabulated as 29 mΩ/m.

All trivial 'errors', but conceivably relevant if one wants, for whatever reason, one feels a need to undertake 'accurate' calculations.

However, any attempt ('fooling oneself'!) at 'accurate calculations' are really a total joke, since one will very rarely have any good idea of what the conductor temperature actually will be in any given situation

Kind Regards, John