Airborne Wind Energy

Flight navigation and maneuvering

Roland Schmehl

21 November 2024

CC BY 4.0

Outline

Kitepower

Review of AWE workshop

  • Quasi-Steady Model (QSM) revisited
  • Loyd recapitulation
  • Trim condition and longitudinal stability
  • Inclusion of the angle of attack
  • Modeling crosswind trajectories
  • Jupyter Notebook Workshop
  • Q&A

Learning objectives

Use the developed theory to describe specific idealized flight maneuvers, such as

  • straight crosswind flight (motion along a great circle, and
  • turning maneuvers (motion along a small circle), and
  • retraction of the kite (motion in a plane and eventually on a radial line).

For that purpose also the steering behavior of the kite is taken into account. The navigation strategies and resulting maneuvers are building blocks to construct flight paths of which the basic aspects are introduced together with flight control.

Before we do this, we first recapitulate where we stand in terms of theory development.

Theory recapitulation

  • Developed 2d-theories of Loyd (1980) for
    • ideal crosswind operation during reel-out \((\beta=\phi=0)\), and
    • asymptotic steady-state reel in \((\beta=\const, \phi=0)\)
  • Extended theory to 3d by considering an elevation angle \(\beta>0\) during reel out
  • Developed full 3d-theory using spherical coordinates, acounting for a course angle \(\chi\) and the gravitational effect of mass
  • Computed achievable net power for pumping cycle operation, considering single reel-out and reel-in flight states
  • So far, the analysis was focused on the tether force and the available power output
  • Transverse (to the tether) force components are important for steering of the kite
  • This is relevant for flight navigation and maneuvering

Flight test

Flight test on 9 October 2025

Content

  • Forces on the kite transverse to the tether
  • Turn rate law theory
  • Compare to the turning law of untethered fixed wing aircraft.
  • Flight navigation vs flight control
  • Radial navigation
  • Tangential navigation
  • Small earth analogy (Jehle 2012; Jehle and Schmehl 2014)
  • Point mass models (3 DoF) (Vermillion et al. 2021)
  • Point mass models (4 DoF)
  • Rigid body models (6 DoF)

Kite-fixed reference frames

Up to this point, we have considered the kite as a point mass with a velocity.

Aerospace convention

Following the convention used for aircraft and spacecraft, the kite-fixed reference frame is aligned with the principal axes of the kite.

Flight control of flexible membrane wings

Skysails roll control (2013)

Flight control mechanism for parafoils

Parafoil vehicles in maneuvering flight differ significantly from other, conventional aircraft types in that control input produces turn rate, rather than roll rate, and also in that turning is associated with side-slip (Brown 1993).

Soft-kite turning maneuver

Turning maneuver

Composite photo of 6 m\(^2\) kite during a tow test, photographed
from the towing vehicle (Elfert and Schmehl 2023).


Figure-of-eight maneuver

Schelbergen and Schmehl (2024)

Figure-of-eight maneuver




Test flight on 30 March 2017.

Schelbergen and Schmehl (2024)

Kite performing turning maneuver

Kite performing turning maneuver

Turn rate law

Analysis from Elfert paper, leading to

\[ \dot{\psi} = g_k \frac{v^2_a}{v_k} \us + \frac{\vec{g}\cdot\vec{e}_{y,k}}{v_k}, \qquad \text{where} \]
\(\dot{\psi}\) is the turn rate,
\(g_k\) is the steering gain,
\(\us\) is the nondimensional steering input.

Experimental identification

Roullier (2020)

Flight navigation

  • We now know how to control the kite to perform certain flight maneuvers
    • Turning flight maneuvers, while reeling out (strong crosswind component)
    • Straight flight, while reeling out (strong crosswind component)
    • Reeling in (weak to vanishing crosswind component)
  • But how to construct the entire flight path for the pumping cycle?
  • This task is denoted as flight path planning

Great and small circles

Figure of eight from circular segments

Kinematics in spherical coordinates

  • Develop the time derivatives
  • Distinguish between derivative of magnitudes and base vectors
  • How does curvature and compression/stretching of space influence the derivatives
  • Interpret the different contributions
  • Compare these curvilinear

Parametrisation of flight path

  • Introduce path vector base with radial direction, path-aparallel and path-orthogonal (side) contributions
  • For performance analysis we only look at radial direction
  • For steering we look at path-orthogonal (side) contributions

Concept of quasi-steady motion

Further reading

The planning of the flight path for pumping cycle operation is detailed in Section 15.3 “Flight Path Planner” of this book chapter.

References

Brown, G.: Parafoil steady turn response to control input. In: Aerospace design conference, Irvine, CA, USA (1993
Elfert, C., Schmehl, R.: Measurement of the turning behaviour of tethered membrane wings using automated flight manoeuvres. Wind Energy Science. (2023)
Jehle, C.: Automatic flight control of tethered kites for power generation, https://mediatum.ub.tum.de/1185997, (2012)
Jehle, C., Schmehl, R.: Applied tracking control for kite power systems. Journal of Guidance, Control, and Dynamics. 37, 1211–1222 (2014). https://doi.org/10.2514/1.62380
Loyd, M.: Crosswind kite power. Journal of Energy. 4, 106–111 (1980). https://doi.org/10.2514/3.48021
Roullier, A.: Experimental analysis of a kite system’s dynamics, (2020)
Schelbergen, M., Schmehl, R.: Swinging motion of a kite with suspended control unit flying turning manoeuvres. Wind Energy Science. 9, 1323–1344 (2024). https://doi.org/10.5194/wes-9-1323-2024
Vermillion, C., Cobb, M., Fagiano, L., Leuthold, R., Diehl, M., Smith, R.S., Wood, T.A., Rapp, S., Schmehl, R., Olinger, D., Demetriou, M.: Electricity in the air: Insights from two decades of advanced control research and experimental flight testing of airborne wind energy systems. Annual Reviews in Control. (2021). https://doi.org/10.1016/j.arcontrol.2021.03.002

Questions?





kitepower.tudelft.nl

// reveal.js plugins