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Dynamic modeling, testing, and stability analysis of an ornithoptic blimp

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Abstract

In order to study ornithopter flight and to improve a dynamic model of flapping propulsion, a series of tests are conducted on a flapping-wing blimp. The blimp is designed and constructed from mylar plastic and balsa wood as a test platform for aerodynamics and flight dynamics. The blimp, 2.3 meters long and 420 gram mass, is propelled by its flapping wings. Due to buoyancy the wings have no lift requirement so that the distinction between lift and propulsion can be analyzed in a flight platform at low flight speeds. The blimp is tested using a Vicon motion tracking system and various initial conditions are tested including accelerating flight from standstill, decelerating from an initial speed higher than its steady state, and from its steady-state speed but disturbed in pitch angle. Test results are used to estimate parameters in a coupled quasi-steady aerodynamics/Newtonian flight dynamics model. This model is then analyzed using Floquet theory to determine local dynamic modes and stability. It is concluded that the dynamic model adequately describes the vehicle’s nonlinear behavior near the steady-state velocity and that the vehicle’s linearized modes are akin to those of a fixed-wing aircraft.

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Abbreviations

φ:

Instantaneous wing heaving angle

Ch:

Amplitude of flapping oscillation

Ct:

Amplitude of wing twist at the tip

f:

Frequency of flapping

t:

Time

r:

Coordinate along span of a wing

η:

Instantaneous wing twist

φ 0 :

Phase of flapping oscillation

φ η0 :

Phase of twisting oscillation

Γ:

Circulation around the airfoil

CL:

Translational lift coefficient

CR:

Rotational lift coefficient

c(r):

Local chord value

u:

Local section velocity parallel to chord

ν:

Local section velocity normal to chord

Fν:

Viscous force

ρ:

Air density

CD(0):

Drag coefficient at zero angle of attack

CD(π/2):

Drag coefficient at 90° angle of attack

dFu:

Local force on the wing parallel to chord

dFv:

Local force on the wing normal to chord

mw:

Wing mass

α:

Angle of attack

R:

Wing length

τ:

Airfoil moment

U:

Vehicle forward velocity

W:

Vehicle velocity normal to forward velocity

Q:

Vehicle pitch rate

θ:

Vehicle pitch angle

g:

Gravitational constant

FU:

Total aerodynamic force on vehicle in forward direction

FW:

Total force on vehicle in downward normal to forward direction

m:

Vehicle mass

I y :

Moment of inertia about pitching axis

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Authors and Affiliations

  1. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, New York, USA

    John Dietl, Thomas Herrmann & Ephrahim Garcia

  2. Air Force Research Laboratory, Wright-Patterson AFB, OH, 45433-7542, USA

    Gregory Reich

Authors
  1. John Dietl
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  2. Thomas Herrmann
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  3. Gregory Reich
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  4. Ephrahim Garcia
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Corresponding author

Correspondence to John Dietl.

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Dietl, J., Herrmann, T., Reich, G. et al. Dynamic modeling, testing, and stability analysis of an ornithoptic blimp. J Bionic Eng 8, 375–386 (2011). https://doi.org/10.1016/S1672-6529(11)60043-7

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  • DOI: https://doi.org/10.1016/S1672-6529(11)60043-7

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