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Hooray, I have a basic grasp of VD. Now.... on to harmonics :-(In this case you have a long final circuit, so you are going to see significant VD on that segment. As Lucian has said you generally want to spread the VD around (sorry if that phrase has unfortunate medical connotations...) so you don't have the sub-main or the final as being close to 5% and the other unrealistically heavy cable to keep down the rest.
You have a bit of fact-finding to do, but I suspect you are going to be better with a larger sub-main (such as 50mm 4C and parallel 25mm earth) so you have a bit more leeway at the Barn A for any extensions out (maybe even future feed to another building, etc) without needing to depend on decent 3P balance.
Get the facts together first!
I'm joking please don't go on to harmonics, baby steps required.
Could I ask why you are suggesting a separate earth? Is it purely for cost, as it would be cheaper than a 5 core? Also, would my new thread make a difference to this? The new thread is talking about TT'ing the installation and whether it is necessary. If it was TT'd then could I just run a 4 core SWA as you suggest and no earth? The armour would be earthed (PME) giving the cable fault protection, and then it would be a TT at the barn.
Ps.. The customer is a nice chap but near impossible to get any facts from. @plugsandsparks post was highly insightful and accurate with regards this client!