How long are the carbon fibre rods for a Travelling Kossel? TL;DR - For a given Kossel frame size (w.r.t. the vertical and horizontal frame lengths of the aluminium extrusion), what would the length of the carbon fibre rods be?



A case in point, from RepRapWiki - Kossel, there is an intriguing note about a scaled down Kossel:


  Optionally scale down to a Traveling RepRap that fits within IATA hand
  luggage size limit (see transportation):
  
  
  Frame height: 550&nbsp;mm.
  Footprint: triangle, 270&nbsp;mm width, 250 mm across (210&nbsp;mm 15 x 15&nbsp;mm aluminium extrusion like OpenBeam + printed corners).
  


However, there is no mention of the length of the carbon fibre rods (carbon tubes).

Now, as per my previous question, For a larger build volume, what lengths of 2020 aluminium do I need?, is there a formula or ratio by which one needs to abide? Whereas in my previous question, the answer was along the lines of: Not really, you can use any lengths, within reason, and account for it later in the firmware, I would imagine that the Delta aspect of the printer is somewhat more exacting.

I have tried googling for further information on this Travelling Kossel, but found nothing, except for the information of RepRapWiki.

Looking at the corresponding lengths (vertical/horizontal) of the aluminium versus those of the carbon fibre rods for the Mini and XL:


600/240 mm versus 180 mm
750/360 mm versus 300 mm


I really can not see what the (trigonometric) relationship is, and therefore can not deduce the lengths of the carbon rods for the Travelling Kossel. 

Unless it is simply that the carbon rods are 60&nbsp;mm shorter than the aluminium horizontals? Is it really as simple as that, or is this just a coincidence? In which case, would the carbon rods be (210 - 60 =) 150&nbsp;mm?

By extension, imagine if you wanted to build a Kossel XXXL, with a horizontal aluminium extrusion length of, let's say, 1000&nbsp;mm, would the length of the carbon rods be 940&nbsp;mm?

Any ideas?
Most information I was able to find was the arms are 80% the length of the horizontal structure.  I did find a copy of the original Google Sheets that everyone used a few years ago here.  The source of that link did mention that there may have been some issues with it but all of those links were dead ends.  

Some things to note:

The height doesn't matter, it has no relationship with the arms other than you are losing approximately the arm length from the height when figuring print area as some arms will approach vertical when reaching the outsides of your print area.

The arm length isn't terribly important from what I could find.  Longer arms = less travel of the carriages and possibly lower resolution.  Shorter arms = more travel of the carriages and possibly lower print speed due to required movement.