Chapter 14 471 not find data for ellipticity versus age for African type hair. Current studies show no effects of age on ellipticity of the scalp hair for Japanese females, ages 10 to 70, and no effects for Caucasian males and females over a similar age range however, we would not speculate on what to find among those of African descent because of the very high ellipticity among that geo-ethnic group. Stretching, bending and torsional properties of hair fibers and age: Equations for the moduli for elastic stretching, bending, and torsional shear all suggest that the stresses to deform human hair fibers increase with hair fiber diameter: • E s = H g L /A ΔL where Es is the elastic modulus for stretching H is the Hookean slope g is the gravitational constant A is the fiber cross-sectional area (increases with fiber diameter) and ΔL isthe distance the fiber is stretched • E b = 64/ ∏ D4 where Eb is the bending modulus and D is the fiber diameter and • E t = 128 ∏ I L/ P2 D4 where Et is the torsional modulus I is the moment of inertia of the pendulum L is the fiber length P is the period of oscillation of the pendulum and D is the fiber diameter. Robbins and Scott27 have shown that the Hookean slope and the dry breaking stress determined by tensile elongation, and the bending stiffness index28 are proportional to hair fiber diameter. Also, tensile properties have been shown by Robbins and Crawford29 to be controlled primarily by the cortex, and thus the outer layers of the fiber do not provide a disproportionate contribution to the stretching and bending properties of the fiber as they do with torsion.30 Therefore, changes in hair fiber diameter will provide changes in tensile, bending, and torsional resistance or stiffness of hairs as diameter changes with age. For Caucasian and Asian women who do not damage their hair, tensile stresses and bending stiffness will on average increase with age through the late 30s, but for men the available data on hair diameter versus age suggests that the peak in