Biomechanics of Jumping during a Basketball Shot Ziang

Biomechanics of Jumping during a Basketball Shot Ziang (John) Lu BIOL 438 4/24/14

Background A Basketball Shot: • The most common type of field goal attempt (~63%) in the NBA 1. • Uses both upper and lower body muscles. • Does not require jumping: free-throws comprise of 20% of points scored in Division I NCAA Basketball 2 • Most successful when ball is released between 47 to 52 degrees 6

Shooting Without Jumping

Shooting With Jumping

Muscles Used – Lower Body 1) Hip hyperextension: a) Gluteus maximus (back of hips) hyperextends the hip to move thighs backwards 2) Knee extension: a) Quadriceps (front of thighs) straighten the knee joint during jump b) Hamstrings (back of thighs) bend knees before shot Source: ESPN. com 3) Calf muscles*: a) Soleus (lower) and gastrocnemius (upper) muscles contract to bring body on toes before liftoff.

Muscles Used – Upper Body 4) Wrist extensors: a) Forearm muscles move the wrist and control the opening and closing of fingers. 5) Elbow: a) Triceps extend the elbow during shooting. b) Biceps flex the elbow for aiming and returning the arm to its normal position. 6) Shoulders: a) The trapezius (collarbone muscle) and deltoid (shoulder joint) muscles raise the arm and rotate the shoulder to aim and shoot. Source: ESPN. com

Question and Parameters �Does jumping change the arc and energy of the basketball as it travels toward the rim? �Parameters to measure: ◦ Arc equation of the ball trajectory ◦ Horizontal and vertical Velocity of the ball ◦ Initial linear KE and gravity PE of the ball ◦ Change in body center of mass from jumping ◦ Change in rotational KE of forearm

Arc of Standing Shot Y = -4. 755 t 2 + 14. 10 t – 6. 804 meters X = 3. 826 t – 2. 762 meters

Tangent Angle of Y Curve Tan-1 (5. 222) = 79. 16 degrees

Arc of Jump shot Y = -4. 651 t 2 + 13. 61 t – 6. 328 meters X = 3. 778 t – 2. 705 meters

Tangent Angle of Y Curve Tan-1 (4. 135) = 76. 40 degrees

Standing Shot Velocities Vy = -9. 567 t + 14. 18 m/s Vx = -0. 635 t + 4. 727 m/s

Jump Shot Velocities Vy = -9. 340 t + 13. 68 m/s Vx =-0. 646 t + 4. 690 m/s

Initial KE and PE �Mass of basketball – 0. 624 Kg �KE: ◦ Standing shot – � 0. 5*0. 624 Kg *( 6. 609 m/s)2 = 13. 63 J ◦ Jump shot – � 0. 5*0. 624 Kg * (4. 949 m/s)2 = 6. 30 J �Gravity PE: ◦ Standing shot – � 0. 624 Kg * 9. 8 m/s 2 * 2. 148 m = 13. 16 J ◦ Jump shot – � 0. 624 Kg * 9. 8 m/s 2 * 2. 305 m = 14. 10 J

Change in Center of Mass & PE Change in Center of Mass = 1. 27 m – 1. 07 m = 0. 20 m Change in PE = 0. 20 m * 9. 8 m/s 2 * 65. 77 Kg = 128. 91 J

Change in Rotational Energy Standing Shot Jump Shot

Change in Rotational Energy �Rotational Energy = ½ Iω2 ◦ I 5 = Mass of body*0. 0076 �Standing Position Prerelease Postrelease �Jump Position Prerelease Postrelease ; shot Starting Angle Ending Angle Angular Change Time of Change 99 140 0. 716 rad 0. 155 s 140 163 0. 401 rad 0. 184 s Angular Velocity (ω) 4. 63 rad/sec 2. 17 rad/sec Forearm Rotational Energy 5. 024 J 1. 112 J Shot Starting Angle Ending Angle Angular Change Time of Change Angular Velocity (ω) Forearm Rotational Energy 72 114 0. 733 rad 0. 0988 s 7. 42 rad/sec 12. 891 J 114 146 0. 559 rad 0. 2108 s 2. 65 rad/sec 1. 651 J

Total Energy Type of Shot Initial Linear KE Standing Shot Jump Shot Initial Gravity PE Rotational KE Total Energy 13. 63 J 13. 16 J 6. 14 J 32. 93 J 6. 30 J 14. 10 J 14. 54 J 34. 94 J 40 32. 93 Energy (Joules) 35 34. 94 30 25 20 15 10 13. 63 6. 3 13. 16 14. 1 Standing Shot 14. 54 Jump Shot 6. 14 5 0 Linear Kinetic Energy Gravity Potential Angular Rotational Energy Type of Energy Total Energy

Conclusion �Arc of the shots ◦ The jump shot had a slightly flatter and, in theory, more successful arc than the standing shot. � 76. 40 degrees to 79. 16 degrees �Velocity of the shots ◦ The jump shot was more affected by air resistance �Vy : -9. 340 t to -9. 567 t

Conclusion �KE and PE of the shots ◦ The jump shot had slightly more PE but much less linear KE at release than the standing shot �KE: 6. 30 to 13. 63 J �PE: 14. 10 to 13. 16 J �Rotational Energy ◦ The jump shot produced much more rotational energy than the standing shot. ◦ Most of the energy (~90%) can be accounted for during the pre-release phase.

Conclusion �Total Energy ◦ The jump shot produced about 6. 07% more total energy than the standing shot ◦ This increase in energy is small compared to the increase of PE from jumping � 2. 01 J compared to 128. 91 J

Future Direction �Measuring different types ◦ Fadeaway, pull-up, etc �Measuring ball of jump shots different times of releasing the ◦ Beginning, apex, or end of jump �Measuring muscle changes ◦ Knee and hip angles in lower body

References: � � � 1. Is Outside Shooting an Lost Art? http: //www. 82 games. com/comm 23. htm 2. Kozar, B. , Vaughn, R. E. , Lord, R. H. , & Whitfield, K. E. (1995). Basketball free-throw performance: practice implications. Journal of Sport Behavior, 18(2), 123 -129. 3. Muscles Used During Basketball. http: //getfit. jillianmichaels. com/muscles-used-during-basketball 1937. html 4. Muscles Used in Shooting a Basketball. http: //healthyliving. azcentral. com/muscles-used-shooting-basketball 10577. html 5. Moment of Inertia of Body Parts. http: //www. phys. washington. edu/users/jeff/courses/ken_young_web s/208 A/body_segment_mass. txt 6. Shooting Angles and Their Effect on Scoring. http: //www. washingtonpost. com/wpdyn/content/article/2010/03/15/AR 2010031502017. html