kite flight dynamics
DESCRIPTION
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. - PowerPoint PPT PresentationTRANSCRIPT
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.