INTRODUCTION Merchant's model (1945) for chip formation in machining is applied to the interaction of an edged ski with the surface of snow. Forces for turning while skiing are generated by this interaction, and these forces depend on the shear strength of the snow, the depth of penetration, and the shear angle in the snow. Previously, Leiu and Mote (1985) and Brown and Outwater (1989) have applied cutting experiments and models to edge ice and snow interactions in order to model turning skis and to determine the properties relating to ski-ability of snow. METHODS In the analogy with orthogonal machining, the base of the ski is considered to be the rake face of the tool, and the snow is the workpiece. The depth of penetration (p) of the edge into the snow is analogous to the depth of cut. The skidding is the cutting velocity. The edge angle (O) is measured between the base of the ski and the snow, and is the ninety degrees plus rake angle (o). In this analogy, a is always negative. According to Merchant, the snow will shear under the action of the ski in a zone approximated by a plane extending from the edge of the ski to the snow surface, at an angle (o) to the skid direction. Merchant derived the relation between the rake angle and the shear angle as: o=45-ß'/2+a/2, where ß' is the friction angle (tanß'=u, the transverse friction coefficient on the ski base). Substituting the edge angle (a= 0-90), the shear angle is given as o=(0-ß')/2. The shearing force Fs and the cutting force Fc, i.e., the force perpendicular to the ski that can be used for turning, can be calculated in terms of 0 and the shear strength of the snow o. RESULTS and DISCUSSION The shear force is Fs=paL/sino, where L is the length of the ski segment. The cutting force is Fc=Fscoso+Fnsino, where Fn is the normal force on the shear plane, which can be shown to be equal to Fs/tan(0-ß'-o). Substituting, this becomes Fc=(poL)(cot(0-ß')/2+cot(0-3ß')/2)). Therefore, increasing the edge angle for the same penetration decreases the turning force. Decreasing the transverse friction coefficient also decreases the turning force. These relations apply to a skidding ski and could be limiting conditions on carving. This suggests that there is an Optimum edge angle for generating the maximum turning forces when skidding. The penetration depth can be modeled as p=/(0)Fp/o), where Fp is the force normal to the snow, and the function f(0) describes an inverse relation with ski-snow contact area. During carving, the sidewall of the ski is in contact with the snow and limits the penetration. During skidding, the side wall of the ski is not in contact with the snow, thereby the penetration and hence the turning forces can increase. This suggests that instabilities of edge-penetration depth could arise from transitioning between carving and skidding conditions, and could cause Charter. CONCLUSIONS Merchant's model of Chip formation in machining provides insights for determining turning forces from edge-snow interactions. There is an optimum edge angle for generating maximum turning forces. The transverse friction coefficient improves turning forces. The transition between carving and sliding conditions could lead to instabilities in the depth of the edge penetration.
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