Simulation of Opening Angle of Archimedes Wind Turbine Design Based on the Fibonacci Series

The configuration of new type of turbine is the Archimedes wind turbine with a spiral structure whose design is inspired by logarithmic spirals. This type of wind turbine uses lift and drag to harness the kinetic energy of the wind. The eccentric design has aerodynamic characteristics that have been the focus of previous research. The design is made from the arrangement of the Fibonacci sequence (1x1, 2x2, 3x3, 5x5, 8x8) or commonly known as the golden ratio. This study aims to analyze the coefficient of lift (CL) and coefficient of drag (CD) with variations opening angle of 35°, 45°, 65°, air fluid, turbulent flow, Re 1200, pressure distribution 1 atm, wind speed 5, 5 and 15 m/s. The results is at wind speed of 5.5 m/s, an angle of 35°, the CL value is 1.07E+02, the CD value is 4.02E+04. At wind speed of 5.5 m/s, an angle of 45°, the CL value is 1.08E+04, the CD value is 1.77E+01. At wind speed of 5.5 m/s, an angle of 65°, the CL value is 1.84E+06, the CD value is 3.68E+04. At wind speed of 15 m/s, an angle of 35°, the CL value is 2.20E+03, the CD value is 9.76E+02. At wind speed of 15 m/s, an angle of 45°, the CL value is 5.51E+04, the CD value is 4.12E+02. At wind speed of 15 m/s, an angle of 65°, the CL value is 5.96E+01, the CD value is 1.33E+03. Based on this, it can be concluded that at wind speed of 5.5 m/s the higher the opening angle, the higher CL produced. At wind speed of 15 m/s the larger the opening angle the CD increases. This is because the higher the angle, the more it receives sweeps or catches the wind. While the unstable value generated in this simulation is generally a weakness in the wind turbine design.

The Use of a Spiral Band Model to Estimate Tropical Cyclone Intensity

Spiral cloud-rain bands (SCRBs) are some of the most distinguishing features inherent in satellite and radar images of tropical cyclones (TC). The subject of the proposed research is the finding of a physically substantiated method for estimation of the TC’s intensity using SCRBs’ configuration parameters. To connect a rainband pattern to a physical process that conditions the spiraling feature of a rainband, it is assumed that the rainband’s configuration near the core of a TC is governed primarily by a streamline. In turn, based on the distribution of primarily forces in a TC, an analytical expression as a combination of hyperbolic and logarithmic spirals (HLS) for the description of TC spiral streamline (rainband) is retrieved. Parameters of the HLS are determined by the physical parameters of a TC, particularly, by the maximal wind speed (MWS). To apply this theoretical finding to practical estimation of the TC’s intensity, several approximation techniques are developed to “convert” rainband configuration to the estimation of the MWS. The developed techniques have been tested by exploring satellite infrared imageries and airborne and coastal radar data, and the outcomes were compared with in situ measurements of wind speeds and the best track data of tropical cyclones.

Hyperbolic Rules in Genomes, the Harmonic Progression and Recurrence Sequences in Algebraic Biology

The article is devoted to biological models using recurrence sequences, which are connected with the harmonic progression 1, 1/2, …, 1/n, and some cooperative properties of genomes. The harmonic progression is itself one of the recurrence sequences based on the harmonic mean. This progression appears in the hyperbolic rules of oligomer cooperative organization in eukaryotic and prokaryotic genomes. This allows thinking that the harmonic progression is also related to inherited physiological systems, which must be structurally consistent with the genetic coding system for their transmission to descendants and survival in evolution. The harmonic progression is one of historically known mathematical series, whose features were studied by Pythagoras, Leibniz, Newton, Euler, Fourier, Dirichlet, Riemann. It is widely used in many known algorithms and is closely related to some other important mathematical objects, for example, the function of the natural logarithm and harmonic numbers. Accordingly, the article describes the possibilities of using these interrelated mathematical objects to model biological structures, including logarithmic spirals and some other. Modeling inherited spiral configurations seems to be a particularly urgent task, since they are extremely common at all levels of organization of living bodies and, according to Goethe, are lines of life. The principle of a recurrence similarity, that is a special similarity of parts and transformations presented in recurrence sequences of numbers and matrix operators (the scale similarity and scale transformations are only particular cases of such similarity), is considered as one of the key principles of structural organization of living bodies.

Constant Force Spring System With a Spiral

The paper is devoted to the theory of a mechanism called constant force spring system. The system consists of a linear helical spring, a spiral drum, a take-up pulley, and two cords. The spiral drum and the take-up pulley are attached rigidly to each other. One of the cords connects the spring with the spiral drum, and at the initial position of the system fills the entire spiral groove on the drum. During the operation of the system, the spiral drum may rotate about its center, and the cord may gradually unwind from the spiral and wind again. The process of winding/unwinding causes the spring to change its length and change the force it exerts on the spiral drum. Due to the shape of the spiral, the distance of the cord from the center of the drum changes, so that the force in the other cord which is wound on the take-up pulley remains constant. Creation of that constant force is the goal of the system. The heart of the system is a specially designed spiral. The solution to the associated differential equation is provided. The system may allow to eliminate weight towers in exercise machines; eliminate counterweights in elevators, as well as in windows that open by moving upwards. The landing path of fighter planes’ landing on aircraft carriers may be reduced. The spiral of the system exhibits an important property which may interest mathematicians; its behavior is compared with that of the Archimedes’ and logarithmic spirals. Because of this property, the spiral may find other applications.

A family of discrete spirals

Most spirals are continuous spirals, certainly those famous in history such as the traditional Archimedean spiral (r = a + bθ) and the logarithmic spirals (r = aebθ. Here we consider ‘discrete spirals’.

Logarithmic Spirals and Right-angled Triangles

This article presents some recurrent functions which we can use to make Right-angledTriangles and through their special arrangement we can obtain logarithmic spirals,and their discrete form. The recurrent functions are obtained through recurrencerelations which can be expressed as a linear combination of fibonacci numbers.

Automatic standardized shape analysis of the sagittal profiles (J-Curves) of the femoral condyles based on three-dimensional (3D) surface data

The sagittal geometry of the articular surfaces of the femoral condyles, also called J-Curves because of the letter J-shaped profiles, is one of the main factors affecting knee kinematics in the normal knee[1] as well as artificial knee [2]. For example, Clary et al. [2] showed that large changes in the J-curves’ radii cause abrupt changes in the center of rotation, leading to decreased anterior-posterior stability. In literature, the sagittal profile has been described mathematically by different geometric figures, such as arcs, circles, involutes of a circle, and Archimedean and logarithmic spirals [3]. The circular approximation has been often followed in the different concepts of knee implant designs, such as single- radius-, dual-radius-, or multiple-radius-designs. Single-radius-designs have a fixed flexion-extension axis. Dual-radius-designs consist of a larger distal and smaller posterior radius aiming a higher congruence during low flexion (high loading) and lower congruence at high flexion angles (high mobility). Multi-radius-designs try to mimic a physiological roll-glide ratio. However, the description of these circles is usually not standardized. A summary of different measurement methods was given by Nuno and Ahmed [4].Thereby, the radii are very sensitive regarding the length of the fitting arc [5] and position of the sagittal plane [3]. Nuno and Ahmed [3] found that medial and lateral condyles can be adequately described by two-circular arcs and proposed a quantitative description. However, the posterior limits of their arcs were not considered individually, the anterior limits were defined based on soft-tissue measurements (anterior margins of the menisci), and the sagittal plane was positioned at the posterior extreme points, which might be inadequate in arthritic knees.The goal of this study was to automatically analyse the medial and lateral sagittal profiles of the femoral condyles mathematically by two-circular arcs in a standardized and robust fashion.

Asymptotics of the entire functions with $\upsilon$-density of zeros along the logarithmic spirals

Let $\upsilon$ be the growth function such that $r\upsilon'(r)/\upsilon (r) \to 0$ as $r \to +\infty$, $l_\varphi^c = \{z=te^{i(\varphi+c \ln t)}, 1 \leqslant t < +\infty\}$ be the logarithmic spiral, $f$ be the entire function of zero order. The asymptotics of $\ln f(re^{i(\theta +c \ln r)})$ along ordinary logarithmic spirals $l_\theta^c$ of the function $f$ with $\upsilon$-density of zeros along $l_\varphi^c$ outside the $C_0$-set is found. The inverse statement is true just in case zeros of $f$ are placed on the finite logarithmic spirals system $\Gamma_m = \bigcup_{j=0}^m l_{\theta_j}^c$.