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Physics in Skiing
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LisaB1982
Physics in Skiing By Philip Martin and Jack McQuiston Where is Physics in Skiing? Design and manufacturing of Equipment Snow qualities The Turn in Skiing Terrain Design and Effects Ski Shape Hour glass shape Effects on turning radius Camber Length Width: shovel(S), waist(W), tail(T) Sidecut Equation: Rsc=C^2/(8SC) C is contact length and SC=1/4(S-2W+T) Camber Equation: Rflex=C^2/*8SCtanø ø is angle between ski and surface Ski Materials and Structure Effects on: Flex Torsion Ski Base Material Durable Little Friction Wax Minimizing Friction Adhesive to base Ski Edge Construction Turning Radius Types of Skis Powder Wider, longer, little side cut Example: Dimensions: 130-110-120 Sidecut: 44.8 m at 193 cm All-Mountain Skis everywhere Example: Dimensions 119-87-111 Sidecut: 22.4 m at 185 cm Park Tricks on jumps and rails Example: Dimensions: 113-85-104 Sidecut: 23m @ 179 Race Groomed Runs Example: Equations to Keep in Mind -fc=(h)/(l)*FN Rsc=C^2/(8SC) Rflex=C^2/*8SCtanø Dimensions: 113-64-97 Sidecut: 12.2 m at 150 cm Forces on Skiers Straight Line Motion Gravity Force(mg*sinø) Friction Force(ƒk=µmg*cosø) Drag Force(.5Capv^2) Plow force(Fplow) Lift Force(5Capv^2) How fast has a skier gone? 156 MPH or 251 KM/H Skier’s Movement Force during turn(load force) Gravity’s Effect Changing momentum Rotation of a turn Edging Terrain’s Effect on Skiing Effect from Pitch and fall-line Techniques for different degree slope Moguls(Decreasing impact force with knees) Good skiers keep center of mass along straight line during descent Maintaining turn through run Radius in deep snow Rt=l^2/(2∆sinø) Projectile Motion Equations x=(cosø)vt y=(sinø)vt+.5(-9.8)t^2 p=mv and F=ma PE=mgh E=.5mv^2+mgh L,D=.5CpAv^2 Iw^2+I’w’^2=0 L=rxp and T=rxf Landing angle designed to minimize change in momentum(Slope of Parabola) Bigger jumps need steeper landing(F=ma) Maximum lift, low drag Design Aspects Do Big People Do Faster? Equations F =ma ƒk = µmgcos(ø) D=.5CpAv^2 Fg = mgsin(ø) Answer? Yes A = gsin(ø) 5CpAv^2/2m µgcos(ø) - Example of Projectile Motion Distance traveled: 300 feet Angle of slope: 28˚ Angle of jump: 45˚ Time: 4.2 Seconds Vx=Vcosø 61 MPH or X=Dcosß Km/h X=Vxt 99 Facts Biggest: cliff drop 230 ft gap jump 300 ft half pipe 30 ft
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