Physics in Skiing

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