Two-dimensional-braid geometry is analyzed. The cover factor of a fabr
ic braided on a particular braider depends on three variables: braid a
ngle, helical length, and braid diameter; however, only two of the thr
ee are independent because of an equation of constraint. The cover fac
tor of an existing braid is a function of braid angle and diameter and
maintains a constant helical length between its tensile and compressi
ve jammed states. A stable jammed state with maximum crimp is found to
exist when the braid angle is 45 degrees and the helical length is a
minimum. When the braid diameter is held constant by braiding on a con
stant-diameter mandrel, the cover factor is increased by decreasing th
e helical length or increasing the braid angle. The cover factor is di
rectly related to the fabric width as a single independent variable. W
hen the yam cannot be considered as a flat strip hut must instead be c
onsidered to have a circular cross-section, the maximum cover factor i
n the jammed state is shown to be 0.82.