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 Minimizing Friction Adhesive to base
Wax
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) - µgcos(ø) 5CpAv^2/2m
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 99 X=Dcosß Km/h X=Vxt
Facts
Biggest:
cliff drop 230 ft gap jump 300 ft half pipe 30 ft