Skip to main content
×
×
Home

Dynamics and Control of Single-Line Kites

  • G. Sánchez (a1)
Abstract

This paper presents a dynamic analysis of a single-line kite with two degrees of freedom. A Lagrangian formulation is used to write convenient equations of motion. The equilibrium states of the system and their stability are studied; Eigenvalues and eigenmodes are calculated by using linear theory. The stability in the parametric plane δ – W0 is discussed, where δ defines the bridle geometry and W0 is wind velocity. The system goes through a Hopf bifurcation and periodic branches of solutions appear. The orbits and their stability have been calculated numerically using Floquet theory and wind velocity seems to play an important role in their existence. Finally the kite response against gusts is considered and an open loop control system developed to keep the flight altitude invariant under changing atmospheric conditions. Modifying the bridle’s geometry seems to be a convenient way to control a kite’s performance.

Copyright
References
Hide All
1. Glauert, H., The stability of a body towed by a light wire, RM, 1930, 1312, Aeronautical Research Council, UK.
2. Bairstow, L., Relf, E.F. and Jones, R., The stability of kite ballons: mathematical investigation, RM, December 1915, 208, Aeronautical Research Council, UK.
3. Bryant, L.W., Brown, W.S. and Sweeting, N.E., Collected research on the stability of kites and towed gliders, RM, February 1942, 2303, Aeronautical Research Council, National Physical Lab, Teddington Middlesex, UK.
4. Adomaitis, R.A., Kites and bifurcation theory, SIAM Review, September 1989, 31, (3), pp 478483.
5. Alexander, K. and Stevenson, J., Kite equilibrium and bridle length, Aeronaut J, September 2001, pp 535541.
6. Veldman, S., Bersee, H., Vermeeren, C. and Bergsma, O., Conceptual design of a high altitude kite, 2002, 43rd AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Denver, Colorado, 22-25 April, 2002.
7. Diehl, M., Magni, L. and De Nicolao, G., Efficient NMPC of unstable periodic systems using approximate infinite horizon closed loop costing, Annual Review in Control, 2004, 28, pp 3745.
8. Delaurier, J.D., Influence of ballonet motions on the longitudinal stability of tethered aerostats, J Aircr, May 1980, 17, (5), pp 305312.
9. Fluid forces and moments on flat plates, September 1970, ESDU International, Engineering Science Data Unit 70015.
10. Doedel, E.J., Champmeys, A.R., Fairgrieve, T.F., Kuznetsov, Y., Sanstede, B., Wang, X.J., AUTO 97: Continuation and bifurcation software for ordinary differential equations, 1997, pub/doedel/auto at ftp.cs.concordia.ca.
11. Ermentrout, B. Xppaut, Dynamical systems software with continuation and bifurcation capabilities, 2000, /pub/bardware at ftp.math.pit.edu.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

The Aeronautical Journal
  • ISSN: 0001-9240
  • EISSN: 2059-6464
  • URL: /core/journals/aeronautical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed