Examples of engineering problems to be analyzed:

• turning radii considering inward lean, edging angle, ski geometry and snow properties
• turning forces and moments, influence of arc shape, calculation of arc length
• mechanics of acceleration (change in direction and speed) in ski racing by stepping
• fastest path between to non-vertical points on an inclined plane (e.g., optimizing line in speed events, escaping from the path of an avalanche)
• forces for the machining of snow and the relation to edge grip (shear strength to hardness ratio, based on Merchant’s theory of chip formation in conventional machining)
• trajectories of skidding bodies
• friction of skis on snow - sliding mechanics
• loads on the ACL in backwards falls as a function of boot stiffens
• beam deflection, relation between camber and the pressure distribution under the ski
• epidemiology, statistical interpretation of injuries and the population at risk

Working Course Outline (November 1997)

0. Introduction

0.0 alpine ski competition - objective: optimize speed and line to minimize time to complete a course

0.1 ski racing: over 60mph on a narrow path down a mountain

• a fascinating control problem
• development of equipment and technique

0.2 energy conservation and ski racing

• potential energy at the start (altitude & chemical), kinetic energy of motion, lost work
• technique: stay on line, minimize frictional loss (aerodynamic and ski-snow friction), maximize skier's muscle contribution
• line: conserve speed, shorten distance, convert potential energy of altitude into kinetic energy of motion as quickly as possible
• equipment: minimize friction, facilitate technique

1. Mechanics of ski-snow interactions

1.1 what is snow, mechanical and chemical properties

1.2 skis (first look): basic geometry and base material

1.3 mechanics of sliding, heat, electricity...

• base preparation: waxing and roughness

1.4 machining snow and ice

• origins of control

2. Mechanical analysis of ski technique

2.0 mechanics of turning, skidding and carving

2.1 ski-snow interaction: weighting (forces and moments), edging

2.2 knees, hips, ankles, arms

2.3 coaching

 

3. Skis

3.0 a beam for transmitting loads to the snow

3.1 flex distribution, torsion, damping

3.2 measuring properties (ASTM, ISO), lab testing, on-slope testing

 

4. Boots and bindings

4.0 transmitting loads and stiffness testing

4.1 boots, the human-equipment interface

4.2 bindings, retention and release

4.3 binding tests (ASTM, ISO) (lab mechanical testing)

 

5. Ski injuries - epidemiology and mechanisms

5.1 historical trends and mechanisms

5.2 reduction of fractures

5.3 current problems: the knee

5.4 loss of control, inadvertent release and fall trajectories

5.5 trail design and collisions

5.6 litigation, the cost of injuries, equipment and trail design