Figure 1
From: On the role of tail in stability and energetic cost of bird flapping flight
(a) Bird model for describing the flight dynamics in the longitudinal plane. The state variables are expressed with respect to the moving body-frame located at the flier’s center of mass \(G(x',z')\). These state variables are the component of forward flight velocity, u, the velocity component of local vertical velocity, w, the orientation of this body-centered moving frame with respect to the fixed frame, \(\theta\) and its angular velocity, q. A second frame \(O(x'_{w}, z'_{w})\) is used to compute the position of the wing, relative to the body. The wings (dark gray) and the tail (red) are the surfaces of application of aerodynamic forces. (b) Top view of the bird model. The left wing emphasizes a cartoon model of the skeleton. The shoulder joint s connects the wing to the body via three rotational degrees of freedom (RDoF), the elbow joint e connects the arm with the forearm via one RDoF and the wrist joint w connects the forearm to the hand via two RDoF. Each feather is attached to a bone via two additional RDoF, except the most distal one ”1” which is rigidly aligned with the hand. The right wing further emphasizes the lifting line (red) which is computed as a function of the wing morphing. The aerodynamic forces generated on the wing are computed on the discretized elements \(P_{i}\). The tail is modelled as a triangular shape with fixed chord \(c_{t}\) and maximum width \(b_{t}\) that can be morphed as a function of its opening angle \(\beta\). (c) Wing element i between two wing profiles, identifying a plane \(\Sigma\) containing the lifting line (red). (d) Cross section of the wing element, containing the chord point \(\mathbf {P_i}\) where the velocities are computed (Color figure online).
