Many Cables on Perforated trays

Horizontally, most of the influence on a cable comes from its closest immediate neighbours, and progressively less from those further away, By the time you get to 4,5,6 cables wide the ones in the middle may as well be part of an infinite array of cables. If you look at the tables you see that the effect of one more cable when you go from 5 to 6 is quite small.

This does not work vertically, as the heat from the cables below rises and pre-heats the ones above. If you do it properly the lower cables are not derated as much as the ones at the top of the stack. The cables at the top get all of the heat of all of those in levels below. Ideally minimise vertical stacking, and arrange some offset or arrange enough air flow sideways that they are more or less independent,

Realise that the formulae in the regs are an approximation, to a small sub-set of all possible wiring layouts, and to a degree you are on your own. There are also reports by ERA that you may be able to get hold of that cover a few more arrangements.

Mike.

To mapj1

Thank you for your well-reasoned explanation. According to your logical explanation, if we know the nature of the circuits which has less load, these cables should be installed on lower trays. And group rating factors applied to lower tray cables are smaller than cables on top tray. Also thank  you for your information about ERA.

eizo

'group rating factors applied to lower tray cables are smaller than cables on top tray. 'msut be correctd. Smaller must be larger.

Indeed - lightly loaded stuff at the bottom saves heating the cables above- unless of course the top layer is jammed against the ceiling.  The regs assume your tray is on an infinitely high wall and the risk of a hot air trap at the top is overlooked - but there is a reason for the regions of bootscraper style mesh flooring on cable troughs on some industrial sites and the positioning of vent louvres at the sides of connection boxes.   It is the same reason we use perforated tray or basket and not solid shelves. All the hot air has to go somewhere, ideally out. I have in the past walked along on service trays near the ceiling of  factory hanger, and after a few mins I was dripping sweat, even though the doors were open and floor level was decidedly chilly. And no, not fear of heights or rusting support studs, just that the top 6 foot or so of the space to the ceiling was essentially a heat trap.

And the assumption that a cable diameter spacing has the same de-rating factor for both thick and thin cables is also a bit off, in practice the way chimney convection currents start to form eddies in larger gaps, means that rule of thumb  tends to over-cook thin cables while fat ones run a bit cooler than expected. The saving grace is that very rarely are all cables at full load at the same time. Indeed quite often we know the total supply to the building or the dis-board or whatever, and can know an upper bound of how many can be fully loaded at once.

For the original query, look at how similar 6 is to 5, add a similar bit more for luck, or just round to the next cable size, and that will cover you for 7-10, and probably beyond. ;-)

Mike.