A lifting line model to investigate the influence of tip feathers on wing performance

Abstract

Bird wings have been studied as prototypes for wing design since the beginning of aviation. Although wing tip slots, i.e. wings with distinct gaps between the tip feathers (primaries), are very common in many birds, only a few studies have been conducted on the benefits of tip feathers on the wing's performance, and the aerodynamics behind tip feathers remains to be understood. Consequently most aircraft do not yet copy this feature. To close this knowledge gap an extended lifting line model was created to calculate the lift distribution and drag of wings with tip feathers. With this model, is was easily possible to combine several lifting surfaces into various different birdwing-like configurations. By including viscous drag effects, good agreement with an experimental tip slotted reference case was achieved. Implemented in C++ this model resulted in computation times of less than one minute per wing configuration on a standard notebook computer. Thus it was possible to analyse the performance of over 100 different wing configurations with and without tip feathers. While generally an increase in wing efficiency was obtained by splitting a wing tip into distinct, feather-like winglets, the best performance was generally found when spreading more feathers over a larger dihedral angle out of the wing plane. However, as the results were very sensitive to the precise geometry of the feather fan (especially feather twist) a careless set-up could just as easily degrade performance. Hence a detailed optimization is recommended to realize the full benefits by simultaneously optimizing feather sweep, twist and dihedral angles.

Literature Review: Biomimetic and Conventional Aircraft Wing Tips

“…When it comes to stability and control considering bird wing tips, only the yawing moment of bird feather found some attention, but very few studied the effect of the pitching and rolling moments. The mathematical model available for an airplane in the form of lifting line theory is not yet developed for bird flight except what has been done by Fluck (2014).…”

“…During each half-stroke total force production produces a force that supports 115% of body weight, and during upstroke force is generated at 36% of body weight. According to Fluck and Crawford (2014), an increase in wing efficiency by splitting the wing tip like birds feather wingtip is possible and found that the best performance can be achieved through spreading the wing tip like the spreading of feathers over a large angle of the wing planform. Hua et al (2014) have shown that bionic wing aerodynamics performance is superior to the conventional airfoil wing.…”

A Brief Review on Aerodynamic Performance of Wingtip Slots and Research Prospect

“…Fluck and Crawford [26] created an extended lifting line model considering the viscous drag effect to calculate the lift distribution, and drag of wings varying with cant angles, tip twist angle and number of wingtip slots, (Fig. 13).…”

“…It was found that slotted wings with appropriate Fig. 13 The is bird wing compared with the simplified wing in the bird wing for the lift line model [26] Fig. 14 Lift-to-drag ratio and drag polar for an elliptic wing versus base wing with five twisted feathers [26] Fig.…”

A fast stochastic solution method for the Blade Element Momentum equations for long‐term load assessment

“…However, repeatedly solving this equation for multiple candidate designs is still fairly costly, even for an aerodynamic model as simple as BEM. A more complicated aerodynamic model (eg, a Lagrangian vortex model as would be used to analyze advanced blade geometries) might not allow to express blade loads explicitly as a function of the random variable. Hence, the next section presents the steps necessary to project Equation onto the stochastic space.…”