1. 3.2.3 Elongated twills 1) The density ratio changes the fabric appearance. (See Fig.3.14)

2. Tan α= / = P o /P y The inclination angle depends on the density ratio: P o = P y ; tan α= 1; α=45 0 P o ＜ P y ; tan α ＜ 1; α< 45 0 P o ＞ P y ; tan α ＞ 1; α> 45 0 See Fig.3.14

3. 2) The shift changes the fabric appearance. (See Fig.3.15, Fig.3.17)

4. 3) weave drawn: (1) Calculate the repeats, R O & R y R y =R yB Where, R OB, R yB are basic twill repeats. (2) Draw the first end according to the formula of the basic twill (3) Draw the other ends according to the same formula, but with the changed shift

5. 4) Applications and sample Some fabrics made from the diagonal weave are: whipcord, lady’s cloth.

6. 3.2.4 Curved twills

7. 1) Concept Curved twills produce a curvilinear appearance when the inclination angle of diagonal increases gradually. As we know, the inclination angle of the diagonal may be changed by changing the shift. The curved twill can be constructed by alternating shift of the basic twill in either vertical or horizontal direction. The alternation of shifts is made by the wish of the designer.

8. 2) two points in designing: The sum of shifts must equal 0 or can be divided by a repeat without remainder. The biggest shift must be less than the biggest overlaps, for avoiding the curved line breaking.

9. Example 1: The basic twill is twill : The curved twill with the alternating vertical shifts having the following succession: S o =2 、 2 、 2 、 1 、 1 、 1 、 1 、 0 、 1 、 0 、 0 、 1 、 0 、 0 、 0 、 1 、 0 、 0 、 1 、 0 、 1 、 1 、 1 、 1 、 2 、 2 、 2 、 2  (Where the sum of shifts equals 26, two times of 13 which is the weave repeat )

10. Example 2: The basic twill is still twill: The alternating vertical shifts are 2 、 2 、 1 、 1 、 0 、 1 、 0 、 0 、 1 、 1 、 0 、 1 、 1 、 1 、 -1 、 –1 、 –1 、 0 、 -1 、 -1 、 0 、 0 、 -1 、 0 、 - 1 、 -1 、 -2 、 -2.

11. 3) Weave drawn Drawing vertically curved twill weaves are as following: 1) Calculating the repeats: R o = numbers of the alternating shifts. R y = weft repeat of basic twill 2) Drawing the first end according to the formula of the basic weave. 3) Drawing the other ends based on the shifts designed. Horizontally cured twill weaves can be drawn in a similarly way

12. 4) Applications Curved twill weaves are widely used for decorative fabrics and apparel fabrics.

13. Home works: 1. Whipcords made from weave formula (1) S o =2 (2) S o =2 drawing the above weaves. 2. Drawing the curved weave, the basic twill is, the vertical shift S 0 =2, 2, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, -1, -1, -1, 0, -1, -1, 0, 0, -1, 0, -1, -1, -2, -2,and drawing the weaving plan using as small number of shafts as possible.