The relation is investigated between the wave number k0 of a twisted polypropylene filament and the wave number k1 of the double helix composed of the filaments. The sum of the wave numbers is zero, illustrating the rule of wave number conservation unless the product t = ka of the wave number k and radius a of the filament is large. The deviation from the rule Δt is proportional to t03 ≡ k03a3, and the proportionality constant y is equal to the elasticity/rigidity ratio E/G.
Bennett, J.M. , and Postle, R., TheTorque Generated in Single and Multi-Ply Yarns as a Function of Changes in Yarn Tension, Textile Res. J.49, 499-506 (1979).
3.
Hearle, J.W.S. , Theoretical Analysis of the Mechanics of Twisted Staple Fiber Yarns, Textile Res. J.35, 1060-1071 (1965).
4.
Hearle, J.W.S. , Structural Mechanics of Torque-Stretch Yarns: The Mechanism of Snarl Formation, J. Textile Inst.57, T441-T455 (1966).
5.
Hearle, J.W.S. , and Yegin. A.E., The Snarling of Highly Twisted Monofilaments. Part I: The Load-Elongation Behaviour with Normal Snarling , J. Textile Inst.63, 477-489 (1972).
6.
Hearle, J.W.S. , and Yegin. A.E., The Snarling of Highly Twisted Monofilaments, Part II: Cylindrical Snarling. J. Textile Inst.63, 490-501 (1972).
7.
Kilby, W.F., TheMechanical Properties of Twisted Continuous-Filament Yarns, J. Textile Inst.53, T589-T632 (1964).
8.
Maruko, A., Onuki. M., Ougizawa, M. and Aikawa, Y., Helix Structure and its Property, J. Human Env. Eng.4, 168-169 (2002).
9.
Maruko, A., Onuki, M., Ougizawa, M., and Aikawa, Y., Curvature and Torsion, J. Human Env. Eng.4, 164-167 (2002).
10.
Platt, M.M. , Klein, W.G., and Hamburger , W.J., Mechanics of Elastic Performance of Textile Materials, Part XI, Textile Res. J.24, 907-939 (1954).
11.
Tayebi, A., and Backer, S.. TheMechanics of Self-Plying Structures, Part I: Monofilament Strands , J. Textile Inst.64, 704-710 (1973).
12.
Tayebi, A., and Backer, S., TheMechanics of Self-Plying Structures, Part II: Multifilament Strands, J. Textile Inst.64, 711-717(1973).
13.
Woods, H.J., "Physics of Fibers," The Institute of Physics, London, 1955, p. 10.
