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 NBA1. Uses both upper and lower body muscles. Does not require jumping: free-throws comprise of 20% of points scored in Division I NCAA Basketball2 Most successful when ball is released between 47 to 52 degrees6

Shooting Without Jumping

Shooting With Jumping

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

Muscles Used – Upper Body 4) Wrist extensors: Forearm muscles move the wrist and control the opening and closing of fingers. 5) Elbow: Triceps extend the elbow during shooting . Biceps flex the elbow for aiming and returning the arm to its normal position. 6) Shoulders: 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 = -4.755t2 + 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 = -4.651t2 + 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: Gravity PE: 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: 0.624 Kg * 9.8 m/s2 * 2.148 m = 13.16 J 0.624 Kg * 9.8 m/s2 * 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/s2 * 65.77 Kg = 128.91 J

Change in Rotational Energy Standing Shot Jump Shot

Change in Rotational Energy Rotational Energy = ½ Iω2 ; I5 = Mass of body*0.0076 Standing shot Jump Shot Position Starting Angle Ending Angle Angular Change Time of Change Angular Velocity (ω) Forearm Rotational Energy Pre-release 99 140 0.716 rad 0.155 s 4.63 rad/sec 5.024 J Post-release 163 0.401 rad 0.184 s 2.17 rad/sec 1.112 J Position Starting Angle Ending Angle Angular Change Time of Change Angular Velocity (ω) Forearm Rotational Energy Pre-release 72 114 0.733 rad 0.0988 s 7.42 rad/sec 12.891 J Post-release 146 0.559 rad 0.2108 s 2.65 rad/sec 1.651 J

Total Energy Type of Shot Initial Linear KE Initial Gravity PE Rotational KE Total Energy Standing Shot 13.63 J 13.16 J 6.14 J 32.93 J Jump Shot 6.30 J 14.10 J 14.54 J 34.94 J

Conclusion Arc of the shots Velocity 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 Rotational Energy 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 of jump shots Fadeaway, pull-up, etc Measuring different times of releasing the ball Beginning, apex, or end of jump Measuring muscle changes in lower body Knee and hip angles

References: 1. Is Outside Shooting an Lost Art? http://www.82games.com/comm23.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/208A/body_segment_mass.txt 6. Shooting Angles and Their Effect on Scoring. http://www.washingtonpost.com/wp- dyn/content/article/2010/03/15/AR2010031502017.html