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?
Frisbee Flight
 Forces in flight include:
 Drag
 Lift
 Gyroscopic rotation
Hammond, pg. 6
Figure 1: COM: Center of Mass;
COP: Center of Pressure; D
(Drag); L (Lift); v (velocity); mg
(gravity)
 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
How?
Solution:
 Must be able to see the
rotation of the arm and
rotation of the frisbee
 Take view from above!
 Must be able to see
overall velocities of arm
movement and frisbee
flight
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
Anatomy Involved
 Normal 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
Overall linear velocity is
shown to increase with
distance from the shoulder.
This produces the initial
velocity of the frisbee.
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
Equations/Calculations


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
Mass of Frisbee: 0.175 grams
Radius of Frisbee: 0.27305 meters
Mass of Arm: 2.52% of body mass = 1.886 grams
Radius of Arm: 0.4402 meters
Mass of Hand: 0.65% of body mass = 0.486 grams
Radius of Hand: 0.137 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: 0.162 kg•m2
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).
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
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θ=ωot+½αt2
ω=ωo+αt
τ=Iα
KE = ½Iω2 or ½mv2
Throw by the numbers
Fast throw
Slow throw
Angular
displacement
θ (radians)
1.571
Angular
displacement
θ (radians)
1.134
Time
t (seconds)
0.12
Time
t (seconds)
0.2
Angular
acceleration
 (radians/s2)
Angular
acceleration
 (radians/s2)
Torque
t (newtons)
Torque
t (newtons)
Angular velocity
w (radians/s)
13.09
Angular velocity
w (radians/s)
11.344
KE (rotational)
J (Joules)
47.97
KE (rotational)
J (Joules)
10.441
109.083
15.269
56.723
9.204
Post-release spin
Slow Throw
Fast Throw

Angular Velocity: 15.3 rad/sec

Angular Velocity: 34.9 rad/sec

Angular KE: 0.764 J

Angular KE: 3.973 J

Linear Velocity: 6.996 m/s

Linear Velocity: 11.258 m/s

Linear KE: 4.282 J

Linear KE: 11.09 J
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
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
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
References
 Plagenhoef, S., Evans, F.G. and Abdelnour, T. (1983) Anatomical data for
analyzing human motion. Research Quarterly for Exercise and Sport 54,
169-178.
 http://biosport.ucdavis.edu/research-projects/frisbee-flightsimulation-and-throw-biomechanics/8thISCSB_Frisbee_throws.pdf
 http://biosport.ucdavis.edu/research-projects/frisbee-flightsimulation-and-throw-biomechanics/HummelThesis.pdf