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.