1. Kite Flight Dynamics Sean Ganley and Z! Eskeets Calculus 114

2. Kites Fly Kites are very sensitive aerodynamic systems. Mathematics can provide various models to predict kite behavior in a variety of conditions.

3. 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.

4. 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.

5. Terms Area (A)-the area of the kite, not always of the entire kite. c-cord length C L -Lift coefficient C D -Drag coefficient X COM -Distance to Center of Mass from leading edge. X COP -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

7. Models of Interaction Lift Coefficient: C L = L /.5*  V 2 A Drag coefficient: C D =D /.5*  V 2 A Resultant aerodynamic force: R =  ( L 2 +D 2 ) Line Tension T e =  (h-Mg) 2 +b 2 Moment arm length for wt force Mg from COP: X W =(x com -x cop )cos(  +  )

8. 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: X L T e =X w Mg

9. 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.