Within the initial modulus region of the yarn’s load- elongation profile, there is direct proportionality of the yarn tension to the shed opening angle. That tension or load may be determined either by dividing the base warp tension at closed shed by the cosine of the appropriate opening angle or it may be found by using the Pythagorean theorem to find the yarn extension during opening. It is important to note that the opening point of the rear shed is determined by the position of the stop motion and not by the whiproll of the weaving machine. Since warp let-off is governed by reaction of the whiproll or tensioner rolls, the slack shed is advanced by the same length as that demanded by the more heavily loaded shed. As a result, longer floats are generated in the fabric than would be present in symmetrical shed weaves. These long floats create structural variations on a fabric surface that are utilized by designers to produce billows, waves, rows and similar textures. A heavier twill known as serge has a smooth surface and is frequently used for stylish outerwear such as trench coats. Thicker versions made of wool and cotton are used for work clothing. Serge de Nîmes (serge from the city of Nîmes in southern France) was, some argue, the orig- inal name of denim, the heavy cotton twill now used for blue jeans. Levi Strauss, the inventor of blue jeans, was initially using tent canvas (a plain weave), but switched to denim because of its superior strength. For similar rea- sons, in 1908 the U.S. Army began to issue soldiers denim work uniforms. These were popular and widely used un- til they were phased out during World War II

Satin weaving was invented in China more than two thousand years ago. Although elaborate textiles such as brocade (a figured satin produced on a draw loom) were expensive and in many cases restricted to the upper classes, the cultivation of silk was widespread. By the late second millennium Ordinary peasant women were expert in the special techniques associated with silk weaving; silk was produced in quantity and worn, at least on some occasions, by a wide range of people, not just the aristocracy” (Steele and Major, p. 22). Silk weaving was a treasured secret, but eventually the technology spread to Japan, Korea, India, Thailand, and other parts of southern Asia. Limited amounts of silk fabric were ex- ported to the West as early as the time of ancient Greece, but satin was not produced in Europe until the Middle Ages. The scarcity of silk restricted the use of this mate- rial to the church, nobility, and upper classes. During the late Renaissance, silk weaving expanded from Italy to Spain, the Netherlands, France, England, and the American colonies. Variations of satin acquired several new names including peau de soie (literally “skin of silk,” a matte fabric with tiny diagonal lines) and charmeuse (a lightweight, pebbly satin, sometimes called crepe-backed satin). Sateen, made of finely spun cotton threads (often long-staple Egyptian cotton), has floats in the filling instead of the warp. These sideways floats drape in the opposite direction from a standard warp satin; when used for an elegant ball gown or full skirt they help the fabric stand away from the body. Slipper satin, a strong, compactly woven material is mainly used for footwear.