Aerodynamic modelling of flapping flight using lifting line theory

Abstract

Purpose

The purpose of the work is to design a flapping wing that generates net positive propulsive force and vertical force over a flapping cycle operating at a given freestream velocity. In addition, an optimal wing is designed based on the comparison of the force estimated from the quasi‐steady theory, with the wind‐tunnel experiments. Based on the designed wing configuration, a flapping wing ornithopter is fabricated.

Design/methodology/approach

This paper presents a theoretical aerodynamic model of the design of an ornithopter with specific twist distribution that results generation of substantial net positive vertical force and thrust over a cycle at non‐zero advance ratio. The wing has a specific but different twist distribution during the downstroke and the upstroke that maintains the designed angle of attack during the strokes. The wing is divided into spanwise strips and Prandtl's lifting line theory is applied to estimate aerodynamic forces with the assumptions of quasi‐steady flow and the wings are without any dihedral or anhedral. Spanwise circulation distribution is obtained and hence lift is calculated. The lift is resolved along the freestream velocity and perpendicular to the freestream velocity to obtain vertical force and propulsive thrust force. Experiments are performed in a wind tunnel to find the forces generated in a flapping cycle which compares well with the theoretical estimation at low flying speeds.

Findings

The estimated aerodynamic force indicates whether the wing geometry and operating conditions are sufficient to carry the weight of the vehicle for a sustainable flight. The variation of the aerodynamic forces with varying flapping frequencies and freestream velocities has been illustrated and compared with experimental data that shows a reasonable match with the theoretical estimations. Based on the calculations a prototype has been fabricated and successfully flown.

Research limitations/implications

The theory does not take into account the unsteady effects and estimates the aerodynamic forces at wing level condition. It doesn’t predict stall and ignores structural deformations due to aerodynamic loads. The airfoil section is only specified by the chord, zero lift angle of attack, lift slope, profile drag coefficient and angle of attack as given inputs. To fabricate a light weight wing that maintains a very accurate geometric twist and camber distribution as per the theoretical requirement is challenging.

Practical implications

Useful for designing ornithopter wing (preferably bigger) involving an unswept rigid spar with flapping and twisting.

Originality/value

The novelty of the present wing design is the appropriate spanwise geometric twisting about the leading edge spar.

Citation

Bhowmik, J., Das, D. and Ghosh, S.K. (2013), "Aerodynamic modelling of flapping flight using lifting line theory", International Journal of Intelligent Unmanned Systems, Vol. 1 No. 1, pp. 36-61. https://doi.org/10.1108/20496421311298134