Spur calculation confusion!

[saucyjack]

Hi guys, I wonder if someone would be kind enough to help me understand the answer to this question from a well known guide-book on 'Inspection, testing and certification of Electrical Installations', 'cos I can't work it out for the life of me!

Q: A ring circuit is wired in 4mm[SUP]2[/SUP] singles in conduit. The circuit is 87 metres in length and is protected by a 32A BS 3871 type 2 circuit breaker, the maximum Z[SUB]s [/SUB]permissible is 1.07 ohms and the actual Z[SUB]e [/SUB]is 0.63 ohms.
Calculate:

(i) The expected Z[SUB]s
[/SUB](ii) The maximum permissible length that could be allowed for a spur in 4mm[SUP]2 [/SUP]cable.

A: (i) From Table 9A in the On-site-Guide 4mm[SUP]2 [/SUP]copper conductors have a resistance of 4.61 m-ohms/M.
R[SUB]1[/SUB]+R[SUB]2 [/SUB]for the phase and CPC both in 4mm[SUP]2[/SUP] is 9.22 m-ohms/M

R[SUB]1[/SUB]+R[SUB]2[/SUB]:

9.22 x 67 = 0.061 ohms
1000

As it is a ring:

0.61 = 0.15
4

The R[SUB]1[/SUB]+R[SUB]2[/SUB] value is 0.15 ohms.

Z[SUB]s [/SUB]= Z[SUB]e[/SUB] + R[SUB]1[/SUB]+R[SUB]2

[/SUB]0.63 + 0.15 = 0.78 ohms. As the maximum permissible given as 0.86 ohms this value is acceptable.


(ii) As the maximum permissible Z[SUB]s[/SUB] is given as 0.9 and is taken from the On-Site-Guide, no correction for temperature is required. We must subtract the Z[SUB]e[/SUB] from the actual Z[SUB]s[/SUB] to find the maximum permissible R[SUB]1[/SUB]+R[SUB]2[/SUB] value.

R[SUB]1[/SUB]+R[SUB]2 [/SUB]= 0.9-0.63 = 0.27 ohms


We must now subtract the actual R[SUB]1[/SUB]+R[SUB]2[/SUB] value from the maximum permissible value.

0.27-0.15 = 0.12


The maximum resistance that our spur could have is 0.12 ohms. To calculate the length we must transpose the calculation:

mV x length = R
1000

to find the total length transpose to

R x 1000 = length
mV

Therefore:

length =
0.12 x 1000 = 13 metres
9.22

Total length of cable for the spur will be 8.67 metres.



Now, this is typed out pretty much exactly as per the book, and the first thing is that although the question is talking about an 87M run, the answer is based on 67M. So i figure presumeably a typo, and go with the value of 67metres for the purposes of the calculations, and I follow all the thinking (even allowing for the fact that the quoted maximum Z[SUB]s[/SUB] for a 32A 3871 type 2 CB in the current OSG is 0.83 ohms, not 0.90), right up 'till point number (ii). The answer states that the maximum Z[SUB]s[/SUB] is given as 0.9?!! (A rounded-up 0.86?), and I understand that you would take away the Z[SUB]e[/SUB] to get your max R[SUB]1[/SUB]+R[SUB]2[/SUB], and then subtract the previously worked out R[SUB]1[/SUB]+R[SUB]2[/SUB] value, to find out what R[SUB]1[/SUB]+R[SUB]2[/SUB] you've got left to 'play with', but how is the final figure of 8.67 metres arrived at? I can't see what I'm missing, and it's driving me mental!! :crazy: Cheers to all in advance for any insight into this!

 

[Doug]

If you use max Zs of 0.86, subtract Zs for the ring of 0.78, this gives max R1+R2 for the radial of 0.08. Use this in the final calculation instead of 0.12 and you get 8.677m!

The question gives max Zs from the regs as 1.07. 80% of this is 0.856. They used 0.86. Like you said, the current OSG gives 0.83. The difference could be due to older regs using 240V as nominal voltage.

 

[saucyjack]

Many thanks for the reply, which suggests that really the quoted method of working out the answer from '(ii)' onwards is a bit erroneous, 'cos the whole 'R[SUB]1[/SUB]+R[SUB]2'[/SUB] part of the calculation is really redundant, given the the way you've applied the Zs figures to the problem, which actually makes more sense. It would've helped if the books' explanation was a bit clearer; jumping from 13 to 8.67 metres in the space of two sentences with no explanation is a bit confusing!