CEAS Aeronautical Journal

, Volume 9, Issue 1, pp 93–112 | Cite as

Unsteady aerodynamics of a diamond wing configuration

  • Stefan PfnürEmail author
  • Christian Breitsamter
Original Paper


The damping derivatives associated with the pitching, yawing, and rolling motion of the SAGITTA flying wing configuration at low Mach number conditions are presented. A tailless variant of the configuration and a variant with attached double vertical tail are investigated. The damping derivatives are determined by means of the aerodynamic response to forced harmonic oscillations. The required data for the determination of the damping derivatives are obtained from time-accurate Reynolds-averaged Navier–Stokes computations. The calculation methodology for the pitch-, yaw-, and roll-damping derivatives for arbitrary freestream conditions is described and a short evaluation of the approach is presented. Angle of attack and sideslip angle trends as well as the effect of the double vertical tail on the dynamic stability are investigated. The damping derivative of every considered type of motion exhibits significant non-linearities with respect to the freestream condition for angles of attack larger than \(8^\circ\). The pitch-damping and roll-damping derivative indicate a dynamically stable behavior at all considered freestream conditions for the configuration with and without vertical tail. The yaw-damping characteristic is more critical. Both configurations exhibit unstable behavior at several freestream conditions. The vertical tail, however, considerably improves the yaw-damping characteristic of the SAGITTA configuration.


Diamond wing Unsteady aerodynamics Dynamic derivatives CFD UAV Vortex flow 

List of symbols


Wing aspect ratio


Wing span (m)


Arbitrary aerodynamic coefficient

\(C_{\nu \dot{\zeta }}\)

Arbitrary dynamic derivative


Rolling moment coefficient, \(M_x/\left( \frac{\rho _\infty }{2}U_\infty ^2S_\mathrm{ref}s\right)\)


Roll-damping derivative, \(\mathrm{d}C_{mx}/\mathrm{d}p\)

\(C_{mx\beta }\)

Rolling moment derivative, \(\mathrm{d}C_{mx}/\mathrm{d}\beta\)


Pitching moment coefficient, \(M_y/\left( \frac{\rho _\infty }{2}U_\infty ^2S_\mathrm{ref}l_\mu \right)\)

\(C_{my\alpha }\)

Pitching moment derivative, \(\mathrm{d}C_{my}/\mathrm{d}\alpha\)

\(C_{my\dot{\alpha }}+C_{myq}\)

Pitch-damping derivative , \(\mathrm{d}C_{my}/\mathrm{d}\dot{\alpha }+\mathrm{d}C_{my}/\mathrm{d}q\)


Yawing moment coefficient, \(M_z/\left( \frac{\rho _\infty }{2}U_\infty ^2S_\mathrm{ref}s\right)\)

\(C_{mz\beta }\)

Yawing moment derivative, \(\mathrm{d}C_{mz}/\mathrm{d}\beta\)

\(C_{mzr}-C_{mz\dot{\beta }}\)

Yaw-damping derivative, \(\mathrm{d}C_{mz}/\mathrm{d}r-\mathrm{d}C_{mz}/\mathrm{d}\dot{\beta }\)


Pressure coefficient, \(\left( p-p_\infty \right) /q_\infty\)


Root chord (m)


Tip chord (m)


Frequency (Hz)


Prism layer stretching factor


Initial prism layer thickness (m)


Reduced frequency, \(\left( \omega l_\mu \right) /U_\infty\)


Mean aerodynamic chord (m)


Freestream Mach number


Rolling moment (body-fixed COS) (Nm)


Pitching moment (body-fixed COS) (Nm)


Yawing moment (body-fixed COS) (Nm)


Roll rate (rad/s)


Freestream static pressure (N/m\(^{{2}}\))


Pitch rate (rad/s)


Freestream dynamic pressure (N/m\(^{{2}}\))


Yaw rate (rad/s)


Reynolds number


Reference area (m\(^{{2}}\))


Semi wing span (m)


Temperature (K)


Physical time (s)


Freestream velocity (m/s)


Moment reference point (m)


Cartesian coordinates (m)


Dimensionless wall distance


Angle of attack (\(^\circ\))


Sideslip angle (\(^\circ\))


Wing taper ratio

\(\varphi _\mathrm{le}\)

Leading-edge sweep angle (\(^\circ\))

\(\varphi _\mathrm{te}\)

Trailing-edge sweep angle (\(^\circ\))

\(\rho _\infty\)

Freestream density (kg/m3)


Arbitrary degree of freedom


Roll angle (\(^\circ\))


Yaw angle (\(^\circ\))


Pitch angle (\(^\circ\))


Dimensionless time


Angular velocity (rad/s)



Body fixed




\(j{\mathrm{th}}\) harmonic


Leading edge


Trailing edge










The support of this investigation by Airbus Defence and Space is gratefully acknowledged. Furthermore, the authors thank the German Aerospace Center (DLR) for providing the DLR TAU-Code, which is used for the numerical investigations. Moreover, the authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. ( for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (


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Copyright information

© Deutsches Zentrum für Luft- und Raumfahrt e.V. 2018

Authors and Affiliations

  1. 1.Chair of Aerodynamics and Fluid Mechanics, Department of Mechanical EngineeringTechnical University of MunichGarching bei MünchenGermany

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