Skier and Toboggan Apply Weights

1. Skier and Toboggan Apply Weights • Assumption: • Skier =200lb • Toboggan = 300lb • Slop = 20 degree • No chain is used • No friction force is used 200 lb 300 lb 20’

2. Forces Apply to Skier on 20 degree slope 200xSinß=68 200xCosß=188 300xSinß=102 300xCosß=282 102 lb 68 lb 188 lb 200 lb 282 lb 300 lb ß=20’

3. Forces Apply to Skier on 20 degree slope 102 lb 102+68=170 lb 188 lb 200 lb 282 lb 300 lb 20’

4. Forces Apply to Skier on 20 degree slope 102 lb 102+68=170 lb 188 lb Graph #1 200 lb 282 lb 20’ 300 lb Pushing force (lb) Slop angle degree

5. Forces Apply to Skier on 20 degree slope 102 lb 102+68=170 lb 188 lb Graph #1 200 lb 282 lb 20’ 300 lb Pushing force (lb) Slop angle degree

6. Forces Apply to Skier on 20 degree slope 102 lb 102+68=170 lb 188 lb Graph #2 200 lb 282 lb 20’ Toboggan weight (lb) 300 lb Pushing force (lb) Slop angle degree

7. Forces Apply to Skier on 20 degree slope 48’ 102 lb 170 lb 188 lb 282 lb 300 lb 254 lb 20’

8. Pushing Force: Total Pushing Force that Applies to Skier Graph #1 and 2 shows this force in different slopes and toboggan weights 48’ 102 lb 170 lb 188 lb 282 lb 300 lb 254 lb 20’

9. Stopping Force: Reaction Force that applies to the skier to stop the toboggan This force must be equal to the pushing force in order to stop the toboggan. Graph #1 and 2 shows this force in different slope and toboggan weight conditions 48’ 102 lb 188 lb 170 lb 282 lb 300 lb 254 lb 20’

10. Tip-over Torque: Pushing force causes a tipping torque over the edge of front ski • Tip-Over Torque=P×Z • The taller Z is the bigger the Tip-Over moment is • Note: by lowering the Center of Gravity of the body the Tip-over torque is decreasing. 48’ 102 lb P=170 lb Z 188 lb 282 lb 300 lb 254 lb 20’

11. Balancing Torque: Skier normal weight force causes a balancing torque to prevent skier tip over front ski • Balancing Torque=N×Y • By leaning back the CG moves back, by adjusting Y distance we can balance the tip-over torque • To balance the torques we have to have NxY=PxZ 48’ 102 lb P=170 lb N=188 lb Z 282 lb 300 lb 254 lb Y 20’

12. Balancing Angle: Is the angle that body has to be in order to balance Tip-over torque • Balancing line: is the line that pass through CG of the body and middle of two skies on snow. • Balancing Angle: Is the angle between the balancing line and slope. • The sum of P and N vectors must be in line with balance line in order to balance the Tip-over torque. 48’ 102 lb P=170 lb N=188 lb 282 lb 300 lb 254 lb 20’

13. Forces Apply to Skier on 20 degree slope in balance position 102 lb 48’ 170 lb 188 lb 282 lb 254 lb 300 lb 20’

14. Forces Apply to Skier on 20 degree slope in balance position 102 lb 48’ 170 lb 188 lb Toboggan weight (lb) 282 lb Skier body balance angle (degree) 254 lb 300 lb 20’

15. Forces Apply to Skier on 20 degree slope in balance position 102 lb 48’ 170 lb Graph #3 188 lb 282 lb 254 lb 300 lb 20’ Skier body balance angle (degree) Toboggan weight (lb)

16. Forces Apply to Skier on 20 degree slope in balance position 102 lb 48’ 170 lb 188 lb 282 lb 254 lb 300 lb 20’

17. Forces Apply to Skier on 30 degree slope in balance position • By lowering and moving back the CG of the body skier can balance tip-over torque in higher slope angles. • The balancing Angle in different slope angles and toboggan weights is shown in Graph #3 150 lb 35’ 260 lb 250 lb 173 lb 300 lb 304 lb 30’

18. Forces Apply to Skier on 20 degree slope 48’ 102 lb 170 lb 188 lb 282 lb 300 lb 254 lb 20’

19. Forces Apply to Skier on 20 degree slope 102 lb 48’ 170 lb 188 lb 282 lb 254 lb 300 lb 20’

20. Forces Apply to Skier on 20 degree sloope 102 lb 48’ 170 lb 188 lb 282 lb 254 lb 300 lb 20’

21. Graph #1 Pushing force vs. slope angle, Skier 200lb, Toboggan 300lb • Assumption: • No Chain or frictions are applied Tiger slope Pushing force (lb) Slop angle degree

22. Graph#2: Pushing force from toboggan vs. slope angle with variant toboggan weight • Assumption: • No Chain or frictions are applied Toboggan weight (lb) Tiger slope Pushing force from Toboggan (lb) Slop angle degree

23. Graph #3: Skier balancing angle to overcome tip-over moment vs. slope angle • Assumption: • No Chain or frictions are applied Skier body balance angle (degree) Toboggan weight (lb) Slop angle degree