be defined from the condition that expansion forces for expansion by each swage should be equal equating forces f 1 from equation 14 and f 2 from equation 16 and ignoring changes in wall thickness equation 24 is obtained equation 24 defines the relationship between diameters of first and second expansion swages 62 and 64 equation 24 also provides the minimum expansion force for tubular radial expansion by two swages if diameters of the swages are selected according to equation 24 the expansion force calculated using equation 14 becomes equation 25 the expansion force to expand the same tubular to the same diameter d 2 using a conventional swage technique calculated by equation 1 with dc d 2 and d f do is shown by equation 26 comparison of equations 25 and 26 shows that the force for tubular expansion by tubular expansion apparatus 5 may be half of the force for expansion of the same tubular to the same degree of expansion by a conventional expansion technique selecting the diameters of swages according to equation 24 and using the expansion ratio defined as equation 27 the limitation on maximum degree of expansion due to the constraint of connector efficiency shown by constraint 10 may be obtained by substituting expansion force from equation 25 in constraint 10 and shown by equation 28 for the.