1. Biomechanics of Throwing a Frisbee
Jesse Rappaport
BIOL 438
4/12/12

2. Types of Frisbee Throws
Backhand
Forehand
Overhead
All Include flick of the wrist/arm to rotate the frisbee
Focus on rotation
Research Focus
What is the rotational kinetic energy in a frisbee throw?
What is the angular velocity needed to produce a steady frisbee toss?
What are the major differences in slow versus fast throws?

3. Frisbee Flight Forces in flight include: Gyroscopic rotation Drag Lift
Rotation is needed to keep frisbee in flight
Difference between Center of Mass and Center of Pressure creates wobble
Wobble is diminished by increased angular velocity
Hammond, pg. 6
Figure 1: COM: Center of Mass; COP: Center of Pressure; D (Drag); L (Lift); v (velocity); mg (gravity)

4. How?
Solution:
Must be able to see the rotation of the arm and rotation of the frisbee
Must be able to see overall velocities of arm movement and frisbee flight
Take view from above!

5. Technique overview Two throws
First: attempt a quick throw with adequate spin
Second: attempt a slower throw with more wobble
Analyze direction of arm and wobble of frisbee qualitatively
Analyze rotation of the arm and frisbee quantitatively
Measure/calculate the following:
Mass
Moment of Inertia
Angular Momentum
Angular Acceleration
Torque
Kinetic Energy

6. Anatomy Involved Normal throw Focused throw Use of whole body
Step with legs
Turn with torso
Turn with arm
Flick with wrist
Focused throw
Use of arm
Extend arm
Rotate forearm
Flick wrist

7. Overall linear velocity is shown to increase with distance from the shoulder. This produces the initial velocity of the frisbee.

8. Biggest Observational Difference:
Slower throw uses more of an arc in the arm and less of a rotational change by the end.
Why is this important?
- Quick rotation allows for increased velocity over short amount of time, allowing for a faster resulting angular KE during flight

9. Equations/Calculations
Mass of Frisbee: grams
Radius of Frisbee: meters
Mass of Arm: 2.52% of body mass = grams
Radius of Arm: meters
Mass of Hand: 0.65% of body mass = grams
Radius of Hand: meters
Moment of Inertia for throwing system (frisbee and arm)
Treat frisbee as thin disk and arm as rod with rotation about the elbow
Use parallel axis theorem (Iz= Icm + m(rarmlength)2) for frisbee where Icm= ½m(rfrisbee)2
Add Iarm= ⅓m(Larm)2
Moment of Inertia using arm: kg•m2

10. Equations/Calculations
Using digital protractor, angular displacement, θ, was measured with the initial point where angular velocity, ω0, was zero.
The following equations were used to calculate angular acceleration (α), angular velocity (ω), torque (τ), and Kinetic Energy (KE).
θ=ωot+½αt2
ω=ωo+αt
τ=Iα
KE = ½Iω2 or ½mv2

12. Throw by the numbers Fast throw Slow throw Angular displacement
θ (radians)
1.571
Time
t (seconds)
0.12
Angular acceleration
α (radians/s2)
Torque
t (newtons)
15.269
Angular velocity
w (radians/s)
13.09
KE (rotational)
J (Joules)
47.97
Angular displacement
θ (radians)
1.134
Time
t (seconds)
0.2
Angular acceleration
α (radians/s2)
56.723
Torque
t (newtons)
9.204
Angular velocity
w (radians/s)
11.344
KE (rotational)
J (Joules)
10.441

13. Post-release spin Slow Throw Fast Throw Angular Velocity: 15.3 rad/sec
Angular KE: J
Linear Velocity: m/s
Linear KE: J
Angular Velocity: 34.9 rad/sec
Angular KE: J
Linear Velocity: m/s
Linear KE: J

14. Results
The increased angular acceleration lead to a larger final angular velocity
The fast throw added significantly more angular velocity and therefore more angular kinetic energy than the slow throw or the overall movement of the faster throw.
The lack of angular velocity lead to wobble in the slow throw, whereas the fast throw had initially no wobble.
Not all KE was converted to frisbee- arm still continues forward and along same path

15. Conclusions
In order to have a more effective frisbee throw, be sure to generate a high angular acceleration to create a strong angular velocity in the frisbee during flight
Creating a more drastic rotation in less time towards the end of the throw will help to generate the KE needed
Full body usage will aid to the amount of force generated in both the x-direction and rotation

16. Future Considerations
Camera angles
Having multiple cameras taking images of the same shot (or one camera with mirrors rigged up) would allow for further analysis of relationship between the degree of wobbling and the angular velocity generated
Compute many more trials to gauge the direct relationship between angular velocity and amount of wobble
Calculate elasticity in arm as it whips forward
Calculate rotational and linear KE using entire body to throw

17. References
Plagenhoef, S., Evans, F.G. and Abdelnour, T. (1983) Anatomical data for analyzing human motion. Research Quarterly for Exercise and Sport 54,
simulation-and-throw-biomechanics/8thISCSB_Frisbee_throws.pdf
simulation-and-throw-biomechanics/HummelThesis.pdf