1. Trajectory of a Discus
Acknowledgments
I would to thank Professor Dan Briotta, for his aid with this project.
Schnayder Termidor
Department of Physics and Astronomy
Ithaca College
Introduction
The discus throw is an ancient track-and-field event in which a thrower throws a heavy disc, with a large amount
of spin perpendicular to it’s plane, in an attempt to out throw his or her competitors The purpose of this project was
to numerically model the 2D trajectories in order to determine the conditions in which maximum distances are
reached.
Figure 1. Discus and its
parameters midflight
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References
Danby, J. Computer Modeling: From Sports to Spaceflight… From
Order to Chaos. 1997
Rouboa, A. Analysis of wind velocity and release angle effects on discus
using computational fluid dynamics: Computer Methods in
Biomechanics and Biomedical Engineering
Forces and Equations of
Motion
The discus is subject to
three forces while in flight. The
force due to gravity, the drag
force and the lift force. The
equation of motion depends on
the initial conditions of the
discus and the angle between
the velocity of the discus and
horizontal.
Figure 2. Extended free body
diagram and equations of motion
discus in flight with wind.
Figure 3. Trajectory and
positions of discus released at
a 32 degree angle at 25 m/s;
angle of attack of 15 degrees
with no wind (RED); Without
drag and lift forces (BLUE).
Conclusion
The trajectory of a discus is heavily dependent on the
drag and lift forces. An angle of attack between 5 and 10
degrees, and an initial release angle of 32 degrees is
recommended in order to maximize the lift force and
minimize the drag force. Further distances will be achieved
when a thrower releases the discus with a greater initial
velocity or, if he or she throws into a headwind.
Drag and Lift
Coefficients
The drag and lift
coefficients are both
functions of the angle of
attack of the discus .
Figure 4. Plots of drag and lift
coefficients vs. angle of attack.
Figure 5. Trajectory of discus; with
headwind of 20 m/s (RED); with no
wind (BLUE).
Throwing a Discus with Wind
By varying the initial conditions of the throw, the trajectories of the discus also varied.
Specifically when varying the velocity of the wind. The discus traveled a further distance with a
headwind rather than with a tailwind.