The fiber slippage of spun yarns depends on the spinning parameter. From the practical point of view., This paper has studied the relationship between the Fiber slippage and fibre property, i.e., fiber dimensions, coefficient of friction of single fiber and compressibility of a fiber assembly. The region of frictional slip has been predicted by applying the studies of D.R. Cox, P.A. Smith. and M. Hannah. On the assumption of the orientation of the fiber assembly and by using, as a parameter, the apparent density ρ_v0 of a fiber assembly under the pressure of 1 gf/cm², the region of frictional ship (_??_ t) is given by :
_??_t=2 ((K^b₁·ρ_v0/ρ_f) (K₂-cLN/K₃μLNd)) ^{1/2 (1-b)}
where,
d =fiber diameter (cm),
L =fiber length (cm),
N= number of fibers in a yarn cross-section,
μ =coeficient of inter-fiber friction (non dimension),
c = cohesion term in inter-fiber friction (gf/cm),
ρ_f = fiber density (gf/cm³),
ρ_v0 =apparent density of fiber assembly under the pressure 1 gf/cm².
b = coeficient of compressibility of fiber assembly (non dimension),
K₁= 2 π f/P₀, K₂ = 6f, K₃ = 4 πf,
f = maximum draft force when a yarn is considered to be in the slipping state, during the untwisting and drafting system. In this case, f= 20 gf.
P₀= standard pressure. In this case, P₀= 1 gf/cm².
Experimental data obtained by the untwisting and drafting system developed by one of authors have agreed well with the values of _??_t for both polyester (15d × 38mm, 1.5d × 44mm) and acrylic (1.5d × 38mm, 3d × 44mm) fibres.

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It is necessary for a clothing design to predict and control the compound bending rigidity of the reinforced composite. The compound bending rigidity relates to the formability and form retention of the reinforced fabrics on a curved surface of garments. This paper aims to predict the compound bending rigidity of reinforced fabrics from those of each constitutional component. The results are summarized as follows :
(1) On the assumption that a face fabric, fusible interlinings and their composite fabrics are elastic, the compound bending rigigity can be predicted by applying the bending equation of combined beams. Correcting coefficients have been given for each construction of base fabrics of interlinings to predict the compound bending rigidity.
(2) The compound ratio of the bending rigidity is varied from 2.0 to 9.7 depending on the structure of base cloth of interlinings. These values are found to be closely related to the tensile properties of face fabrics and interlinings. An equation has been derived to represent the compound ratio by tensile strain at 100 gf/cm. The compound ratio tends to be lower as the tensile strain ε₁ of interlinings is greater and the ratio ε_f2/ε_f1 of weft to warp tensile strains of face fabric is larger.

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