The second additional aspect that needs to be taken into account for practical
situations is that the arc does not necessarily hug the surface of the insulator over
its entire length – an example is illustrated in Figure 6.14. The sparkover of the air
gaps between sheds and the ribs of a shed can effectively shorten the arc’s length,
and buoyancy forces can result in either its shortening or its lengthening, depending
upon the part of the insulator’s surface under consideration. Mathematically, this can
be represented by stating that the arc’s length X(a) is related to the corresponding
spanned length X(i) of the insulator by