Transcript Kite Flight Dynamics

Kite Flight Dynamics
Sean Ganley and Z! Eskeets
Calculus 114
Kites Fly
• Kites are very
sensitive aerodynamic
systems.
• Mathematics can
provide various
models to predict kite
behavior in a variety
of conditions.
History
• The studies of kites began
with many assumptions.
• Many kite studies are
very recent. Some of the
earlier ones occuring in
the 1970’s
• Most early kite models
don’t include some very
important effects on kite
flight and stability.
Effects On the Kite
• Drag
• Wind
• Center of pressure and
mass
• Bridle Position
• Line tension
• Lift
• Resultant aerodynamic
force
• Weight force.
• Angle from the ground
of the cord.
Terms
• Area (A)-the area of the kite,
not always of the entire kite.
• c-cord length
• CL-Lift coefficient
• CD-Drag coefficient
• XCOM-Distance to Center of
Mass from leading edge.
• XCOP-Distance to Center of
Pressure from leading edge.
•  azimuth angles at kite (k) and
at the ground (g)
•  angle between front bridle and
kite chord line.
• Mg- Weight force
• h-height of force vector triangle
• M-mass of the kite
• R-resultant aerodynamic
force.
• V-relative velocity
between the kite and the
air.
•  -angle of attack
•  -density of air
•  -angle from horizontal
to apparent wind direction
• LTD-corrected lift to drag
ratio.
• b=base length of force
vector triangle
Models of Interaction
• Lift Coefficient: CL
= L / .5* V2A
• Drag coefficient: CD
=D / .5* V2A
• Resultant aerodynamic
force: R
=( L2+D2)
• Line Tension Te
= (h-Mg)2+b2
• Moment arm length
for wt force Mg from
COP: XW
=(xcom-xcop)cos( + )
Conditions for Equilibrium
• The R force and the
Mg force create a
moment rotating the
kite about the bridle
point, changing 
• As  changes the
center of pressure
moves, modifying the
moment acting around
the bridle point.
• The kite must rotate until
the moments vanish, and
match the LTD with the
k.
• For stability, the kite must
be arranged so the sum of
the moments is zero,
according to:
XLTe=XwMg
Conclusion
• Kites are fun to fly
• Kites are very
aerodynamic. They are
complex mathematical
systems.
• Kites tend to fly at
equilibrium values
determined by the
characteristics of the
kite and the
environment.