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

2. 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

3. Shooting Without Jumping

4. Shooting With Jumping

5. 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

6. 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

7. 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

8. Arc of Standing Shot Y = -4.755t2 + 14.10 t – 6.804 meters
X = t – meters

9. Tangent Angle of Y Curve
Tan-1 (5.222) = degrees

10. Arc of Jump shot Y = -4.651t2 + 13.61 t – 6.328 meters
X = t – meters

11. Tangent Angle of Y Curve
Tan-1 (4.135) = degrees

12. Standing Shot Velocities
Vy = t m/s
Vx = t m/s

13. Jump Shot Velocities Vy = -9.340 t + 13.68 m/s
Vx = t m/s

14. Initial KE and PE Mass of basketball – 0.624 Kg KE: Gravity PE:
Standing shot –
0.5*0.624 Kg *( m/s)2 = 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 * m = J
0.624 Kg * 9.8 m/s2 * m = J

15. 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 * Kg = J

16. Change in Rotational Energy
Standing Shot
Jump Shot

17. 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 s
7.42 rad/sec J
Post-release
146
0.559 rad s
2.65 rad/sec
1.651 J

18. 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

19. 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 degrees
Velocity of the shots
The jump shot was more affected by air resistance
Vy : t to t

20. 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 J
PE: to 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.

21. 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 J

22. 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

23. References:
1. Is Outside Shooting an Lost Art?
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),
3. Muscles Used During Basketball html
4. Muscles Used in Shooting a Basketball html
5. Moment of Inertia of Body Parts. s/208A/body_segment_mass.txt
6. Shooting Angles and Their Effect on Scoring. dyn/content/article/2010/03/15/AR html