OVERVIEW OF TEXTILES
Figure 2-17. 3D unit cell for 1x1, 4-step braid.
Because yarn carriers on the surface of the rectangle travel less distance in a given
cycle, the surface yarns incline at different angles. Furthermore, the apparent angle seen on
the surface of a braid is actually the projection of the angle of inclination onto the plane of
the surface. The relations between the surface yarn angle of inclination,
β
, the projected
surface angle,
α
, and the internal yarn angle of inclination,
γ
, are
tan α = tan
γ
/ 8 = tan
β
/ 5
(2.14)
The yarn volume fraction is
V
y
=
π
sec(
γ
)/8 (2.15a)
or
(2.15b)
These relations are shown in Fig. 2-19.
The ratio of surface yarns to internal yarns is a function of the aspect ratio of the
rectangle, m/n, and the total number of carriers, N. Figure 2-20 shows this relationship for
a series of aspect ratios.
