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Interpolating derating factors for multicore cables

I'm looking at table 4B5 and am musing on interpolation of the de-rating values for differing numbers of cores from those tabulated.  I have an application I have been asked to look at with 16 loaded cores, and if I use the tabulated value for 14 loaded cores I can use the 30% rule, but if I use the value for 19 loaded cores I (just) can't.  At the factor of 19 loaded cores I am .005A the wrong side of less than 30%!


The challenge this gives me is that the OCPD is 10A rated, the design current is 2.826A, the 30% rule based on the multicore derating alone is 2.821A, and the fully de-rated capacity of the cores (allowing for a further group of the multicores in the installation) in the multicore cable cores is 6.11A.  If I can apply the 30% rule so no derating for the multicore cable then we are in the clear.  The cable is already installed and in all other respects calculates out fine.


The graph of derating factor vs number of cores isn't quite linear: 1711d4446663643ccb8ed6c700e2cdc2-huge-image-20210412170544-1.png


It nearly is in my region of interest though!  Does anyone have a formula for this calculation (if there is one?).


I know this is so marginal as to not normally be worth bothering about, but we may be dealing with a particularly picky client organisation here.


Practically, the chances of someone going up a tower, replacing some or all of the 650W lanterns with 2kW lanterns and leaving them all turned on to the point where the cable is damaged is so close to b***** all as to really but be worth considering, but right is right and wrong is wrong!


It's also not so easy to replace the OCPDs with 6A ones, as these are in a theatrical dimmer unit so modifying that would likely void the warranties, never mind the approvals!


Any other creative solutions welcomed.


As a complete aside I wonder how they chose the numbers of cores to put in the table - multiple single phase circuits would always be an even number, as would multiple TPN circuits - only 3-phase delta circuits would get you a multiple of 3 loaded cores so how you get to 7,19 or 37 cores baffles me unless you put part of the circuit in one multicore and part in another which is a bad idea, or it's some kind of control application.

  • Chris Pearson:



    That said, do you want to do it linearly, geometrically, or exponentially? By my reckoning, linearly, the answer is 0.486 Ω - closer to 14 then 19, but it won't make any significant difference.



    Ah - Yes - my error on the maths, and I prefer your answer to mine!  That would round to 0.49 at the same precision in the table.


    Mike's answer rounds to 0.48.  Either may be enough to squeeze the numbers to allow the use of the 30% rule.  This is one of those silly situations where it's either one side of the line or the other, so even though the raw data isn't that good, and enhanced 'precision' is practically meaningless but can make that theoretical difference that helps.


    Jason.


  • jbrameld


    You seem to have come across some kind of nutter, who obviously has no experience of theatre. Are these cables on Socapex or really 8 circuits wired in, thus only six circuits and 6 Earth wires? Whilst this may interest him (her?) the idea that such a cable could overheat sufficiently to be damaged under normal use is beyond belief. Operating 8 (6) 2k lanterns on full brightness for a significant period is highly unlikely, and even if you did the cable might be damaged but not melted. Almost all theatre lanterns are never operated at 100%, and this lot would be sufficient to light a Professional theatre stage, let alone a school-sized one. After one hour at 80 (60) A this cable would be pretty warm, probably above 70C, but not melted. If stressed it might cause a short circuit between a couple of cores, but cannot start a fire. What size cores does the cable have (1.5 or 2.5 m)? Whilst all this may seem to be unimportant and not following BS7671 to the letter, it is important. Was it you who discussed this with some emails to me previously, I had another similar question about cable ratings, it may have been (too much correspondence!). A diversity factor of 50% should probably be applied, then you certainly have no problem.  My phone 07578 997199 if that would help you out or we can continue here more slowly.


    Regards

    David CEng etc.
     

  • Former Community Member
    0 Former Community Member
    if the factor for 14 loaded cores is 0.51 and the factor for 19 loaded cores is 0.45 then what should the factor for 16 loaded cores be?  An interpolation would give me 0.474.  Is that good enough?


    Awake now, or I think I am!


    Another aspect to consider is that the tabulated figures are to 2 decimal places so could have been "laboratory" determined as between 0.505 to 0.514 and 0.445 to 0.454 


    Regards


    BOD
  • davezawadi (David Stone):

    jbrameld


     Was it you who discussed this with some emails to me previously, I had another similar question about cable ratings, it may have been (too much correspondence!). A diversity factor of 50% should probably be applied, then you certainly have no problem. 


    Regards

    David CEng etc.
     



    Hi David - Yes it's the same jbrameld who spoke to you with a similar problem a while ago.


    We haven't actually been pulled up on this yet, and I have got involved too late (as usual...) but in this case I want to make sure we are on solid ground before we send the paperwork as it is the same organisation we are dealing with, and the same idiot as before may well get involved.


    To answer your questions:

    It is 8 circuits (25-core cable) per bar and 3 x bars.  If I can't apply the 30% rule on the multicores then the fully de-rated CCC of the 1.5mm2 cores is around 6A and they are protected by 10A MCBs - and that is my issue.  Practically it won't be an issue as you say, but I really need some supporting calcs that give me the right answer. With an interpolated value for the 16 loaded cores along the lines of figures quoted above, it does get me the right side of the line.


    Jason.