Equivalent diameter of a group of round objects

For multiple cables twisted or bound together, a combined diameter circumscribing all cables can be calculated. The resulting value is also approximatively correct for three loose cables in touching trefoil formation.

For multiple unequal round objects, possibly non-touching, finding the smallest circle that encompasses all other circles is not easy and we consider following approximation as presented in stackoverflow.com

  1. Take the average of all your centers of the circles call this point X
  2. Let R1 be the maximum distance from X to a circle center.
  3. Let R2 be the maximum radius of the circles
  4. Then all the circles must fall inside the circle centered at X with radius R1+R2

$F_{eq} D_e$multiple cables
$F_x D_{core}$pipe-type cables
$f{\left(\right)}$air-filled pipe with ducts