Serpentines are nothing more than half circles joined by straight lines. How do we calculate them? In this instance we are talking about serpentines which go out to the edge of the arena like in the diagram provided.

First you take the arena length, then divide it by the number of loops to give you the diameter of the half circles. Then you can work out the connecting straight line by deducting the diameter of one circle from 20m

EXAMPLE 1

20m x 40m Arena - 3 Loops

40m / 3 = 13.33M Half Circles

Straight Line = 20M - 13.33 = 6.66M

In plainer English we can say the following:
A 3 loop serpentine in a 20M x 40M arena consists of approx. 13M diameter half circles joined by approx. 7M straight lines.

EXAMPLE 2

20m x 60m Arena - 4 Loops

60m / 4 = 15M Half Circles

Straight Line = 20M - 15M = 5M

In plainer English we can say the following:
A 4 loop serpentine in a 20M x 60M arena consists of 15M diameter half circles joined by 5M straight lines.