Mathematical Modeling of Aircraft Flying Qualities with Varying Tail Dihedral

Abstract—V-tail is a tail geometry setup that provides stability and controllability about longitudinal and directional axes simultaneously. In addition, the setup has less wetted area and interference, thus producing less drag as compared to conventional tails. The dihedral angle of a V-tail determines its contribution to both longitudinal and directional dynamics. However, there is no well-defined empirical method to compute the most suitable dihedral angle for a V-tail in order to meet the required flying qualities. This work presents a method to select the most appropriate dihedral angle of a V-tail to fulfill the requirements of aircraft flying qualities. Numerical calculations were used to generate a complete flight dynamics model with different tail dihedral angles. Subsequently, damping ratios for longitudinal and lateral-directional modes were extracted from these models. Using a curve fitting technique a polynomial was generated for longitudinal and lateral-directional damping ratios against tail dihedral angle. It was observed that by increasing the tail dihedral the longitudinal damping ratio was reduced. In addition, the lateral-directional damping ratio increased with the increase in tail dihedral angle. The lower bound of the tail dihedral angle was obtained using the lateral-directional damping limit in accordance to the flying qualities. Similarly, the upper bound of the tail dihedral angle was obtained using the longitudinal damping limit. The tail dihedral angle in between these bounds was found to be optimal for adequate longitudinal and lateral-directional flying qualities. In addition, it was observed that the mathematical model was not valid for a different flight dynamics model. This is due to the change in aerodynamic behavior of the aircraft.

Index Terms—Athena VLM, curve fitting, damping ratio, flight dynamics, flying qualities, mathematical modelling, tail dihedral, vortex lattice, v-tail.

M Uzair Khan, Naveed Akmal Din are with Mechanical Engineering Department EME. National University of Sciences and Technology, Islamabad, Pakistan (e-mail: uzair01994@gmail.com, naveeddin@ceme.nust.edu.pk).
M Diyan Khan and M Fawad Hussain are with Flight Controls Team, AvRID, Pakistan Aeronautical Complex, Kamra, Pakistan (e-mail: diyankhan@aerospace.pk, hussain.fawad@gmail.com).

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Cite: M. Uzair Khan, Naveed A. Din, M. Diyan Khan, and M. Fawad Hussain, "Mathematical Modeling of Aircraft Flying Qualities with Varying Tail Dihedral," International Journal of Materials, Mechanics and Manufacturing vol. 7, no. 5, pp. 224-229, 2019.

Copyright © 2019 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).