Scalability of resonant motor-driven flapping wing propulsion systems

This work aims to develop an integrated conceptual design process to assess the scalability and performance of propulsion systems of resonant motor-driven flapping wing vehicles. The developed process allows designers to explore the interaction between electrical, mechanical and aerodynamic domains in a single transparent design environment. Wings are modelled based on a quasi-steady treatment that evaluates aerodynamics from geometry and kinematic information. System mechanics is modelled as a damped second-order dynamic system operating at resonance with nonlinear aerodynamic damping. Motors are modelled using standard equations that relate operational parameters and AC voltage input. Design scaling laws are developed using available data based on current levels of technology. The design method provides insights into the effects of changing core design variables such as the actuator size, actuator mass fraction and pitching kinematics on the overall design solution. It is shown that system efficiency achieves peak values of 30–36% at motor masses of 0.5–1 g when a constant angle of attack kinematics is employed. While sinusoidal angle of attack kinematics demands more aerodynamic and electric powers compared with the constant angle of attack case, sinusoidal angle of attack kinematics can lead to a maximum difference of around 15% in peak system efficiency.

Isophote curves on spacelike surfaces in Lorentz–Minkowski space

An isophote curve consists of a locus of surface points whose normal vectors make a constant angle with a fixed vector (the axis). In this paper, we define an isophote curve on a spacelike surface in Lorentz–Minkowski space [Formula: see text] and then find its axis as timelike and spacelike vectors via the Darboux frame. Besides, we give some relations between isophote curves and special curves on surfaces such as geodesic curves, asymptotic curves or lines of curvature.

The slant helices according to N-Bishop frame of the spacelike curve with spacelike principal normal in Minkowski 3-space

If the principal normal vector field of a curve makes a constant angle with constant direction, this curve is called as slant helix. In this paper, a slant helix is defined according to N-Bishop frame of the spacelike curve with a spacelike principal normal. Some characterizations of the slant helices are obtained according to spacelike curve N-Bishop frame with a spacelike principal normal, benefiting from the definition of the slant helices.