Lawrence Wu Biology 438 April 15 th 2014 Act of raising ones center of gravity higher in the vertical plane solely with the use of ones own muscles Vertical Jump Lees et al 2004 ID: 1046881
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1. Biomechanics of Vertical JumpLawrence WuBiology 438April 15th, 2014
2. Act of raising one's center of gravity higher in the vertical plane solely with the use of one's own musclesVertical JumpLees et al., 2004 Journal of Biomechanics
3. Muscles involvedhttp://www.verticaljumpcenter.com/wp-content/uploads/2012/06/legmuscles.jpghttp://www.calworkouts.com/images/lifting/Muscles_anterior_upper_labeled.png
4. Fast twitch musclesOverall: Produce great amount of work in small amount of timeOptimal balance between high velocity of contraction and force generated to maximize powerKnees flex and muscles become increasingly stiffBody halts the fast stretch of the muscleGreat amount of force produced in the muscle and a rise in elastic energy storage in the musclesMuscles Involved
5. Analyze components of vertical jumpMuscles involvedPhysicsElasticityRotational motion1D KinematicsHow does the counterswing arm movement affect height of jump?Other factors involvedPower, energyThe Study
6. Calculated center of mass based on average segment weight for different parts of bodyhttp://www.exrx.net/Kinesiology/Segments.htmlNo arm movementKnee, Foot, HipModel: mass (upper body) on spring (legs)Arm movementTracked movement ofKnee, Foot, Hip, Shoulder, ElbowModel: mass (upper body) on spring (legs) with a force applied upwards (arm movement)Methods
7. Simplified modelUpper body (Mass)Legs (Spring)Arm movement(“External force”)
8. videoNo arm movement
9. Movement of center of masscompression(+) restoration (-) restoration*Simple harmonic motionMinor CompressionAnd restoration
10. Movement of all modeled body partscompression(+) restoration (-) restorationMinor CompressionAnd restoration
11. Apparent “spring constant” of legs: 1465 N/mEi=Ef= 345JoulesAssumption: PEelastic,legs=PEgravity 0.5kx2=mghx=0.95-0.26m=0.69m (change in ycm of whole body during compression)m=68.04 kg, h=0.52m (change in ycm of whole body after restoration)) No arm movementRestCompressionRestorationRestCompression
12. Average Power: 495.7 WattsWork=345 Joules=0.696 sWork generated by contraction of muscle groups in legs No arm movement
13. Arm movementvideo
14. Center of Mass movement compression(+) restoration (-) restoration*Simple harmonic motionMinor CompressionAnd restoration
15. Movement of all modeled body parts compression(+) restoration (-) restorationMinor CompressionAnd restoration
16. Ei=Ef== 543 JoulesAssumption: PEelastic, legs+KE rotational=PEgravity0.5kx2+ 0.5I 2 =mghk=1465 N/m, h=.81m, x=.54m Arm movement*Estimated center of mass since arms are not visibleRestorationRestCompression
17. Rotational energyIarm=MforearmR2forearm+Mupper armR2upper arm+MforearmR2forearmIarm=.19 kg m2=, =5.236 radians, t=.472, = 11.09 rad/sKErotational=11.7 JoulesPEelastic, legs+KE rotationalPEgravityNew equation: PEelastic, legs+KE rotational+ PEelastic, arms to legs=PEgravityPEelastic, arms to legs=317.7 JoulesNew “apparent spring constant” .5kx2+.5I 2=mgh.5kx2=543 J-11.7 JoulesK=3644 N/m Arm movement
18. Average Power: 742 WattsWork=543 Joules=0.732 sAverage power of arm movement: 24.8 WattsWorkarm= 11.7 Joules=0.472 s Arm movement
19. Difference in Maximum height above ground*Not maximum height of center of massArm movement (1.10 m)No Arm movement (0.53m)
20. Arm movement contributes significantly to the height of the vertical jump (1.10m to .52m)Energy as wellThe time of jump with arm movement, from bottom to maximum height, is only 5% longer (0.732s to 0.696s)However arm movement increases the energy of system by 57% (345 Joules to 543 Joules)Mainly potential energy (96% of increased energy)Some rotational kinetic energy (4% of increased energy)Conclusions
21. Center of mass is accurately modeled Same expected trajectory as a point particleFull body movement is most efficient and produces most powerRecruits additional muscle groups above the torso to increase force generation Body-leg spring system is complex Can be modeled with relatively simple mechanicsConclusions
22. Decompose my mass-spring model into smaller systems to analyze in greater detailSpecific sections of the legCalves, feet, etc.Analyze how the positioning of the arm adds potential energy to the whole body systemElectromyogram to analyze individual muscle activity in real timeFuture Directions