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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.