Tents: a paradigm of lightness and sustainability in vernacular architecture and in Frei Otto's work

PurposeThe aim of this paper is to explore the relationship between vernacular architecture and Frei Otto's work, searching for shared principles and specific singularities, and testing whether lightness and sustainability can be identified as a common goal.Design/methodology/approachThe study is focused on tents and yurts, as archetypal examples of traditional architecture, and membrane structures and gridshells, as two types of light structures developed by Frei Otto. A comparative analysis of their behavior, form, elements, types, materials and strength has been carried out.FindingsThe survey carried out shows that Frei Otto's innovative tents and gridshells were not based on form imitation of vernacular architecture, but rather on a thorough understanding of physical form-generating processes, driving specific materials to optimal form, like his experiments with soap film models to generate tensioned minimal surfaces or his experiments with hanging chain net models to generate compressive antifunicular lattice shells.Originality/valueThis paper highlights how Frei Otto's endeavor to get the maximum with the minimum, to achieve a lot from a little, is also a key target of lightness and sustainability, and an essential feature of vernacular architecture.

Camera Calibration Using Catenary

In this work, we introduce a novel calibration technique based on a hanging chain curve replacing the checkerboard-based methods. It is a known physical phenomenon that a hanging chain or a flexible rope under gravity can be modeled by a special curve called catenary. Therefore, instead of the commonly-used planar calibrator, we propose using multiple shots of a catenary-shaped chain for calibration. This approach can solve the out-of-focus problem which is faced in checkerboard calibration methods when the size of the board is not large enough. Although enlarging a planar calibrator increases the manufacturing time and cost, a simple label chain can create large planar areas as precise as a rigid checkerboard, is easily foldable and transportable. We compare the results of our proposed approach against the widely used checkerboardbased calibration as well as the state-of-the-art calibration methods and show that catenary-based calibration is much more accurate than checkerboard-based calibration by a very large margin and is also very competitive among the other approaches.<br>

Camera Calibration Using Catenary

In this work, we introduce a novel calibration technique based on a hanging chain curve replacing the checkerboard-based methods. It is a known physical phenomenon that a hanging chain or a flexible rope under gravity can be modeled by a special curve called catenary. Therefore, instead of the commonly-used planar calibrator, we propose using multiple shots of a catenary-shaped chain for calibration. This approach can solve the out-of-focus problem which is faced in checkerboard calibration methods when the size of the board is not large enough. Although enlarging a planar calibrator increases the manufacturing time and cost, a simple label chain can create large planar areas as precise as a rigid checkerboard, is easily foldable and transportable. We compare the results of our proposed approach against the widely used checkerboardbased calibration as well as the state-of-the-art calibration methods and show that catenary-based calibration is much more accurate than checkerboard-based calibration by a very large margin and is also very competitive among the other approaches.<br>

Shapes of large, static soap bubbles

Standard predictions induced by the balance of surface tension and pressure dictate that static soap bubbles must be spherical. However, definite non-spherical shapes appear in large bubbles, where noticeable oblate or prolate deformations occur. Gravity is the principal cause of such deformations, and multiple approaches for including its influence appear in recent literature. This paper derives a general surface-theoretic model by applying asymptotic and variational methods to a fully three-dimensional set-up where the soap bubble is a finite-thickness film. The procedure illuminates implicit assumptions, clarifying the discrepancies seen in previous models. Then the model is studied in four physical situations. In three of these situations, results show that there is a maximum stable span and volume of the soap bubbles, implying that their behaviour is qualitatively more similar to liquid drops than standard soap bubbles. Also, the model presented is directly analogous to the two-dimensional version of a hanging chain, and the derived predictions give practical insights into the construction of heavy containment vessels.

A Machine Vision-Based Method for Monitoring Broiler Chicken Floor Distribution

The proper spatial distribution of chickens is an indication of a healthy flock. Routine inspections of broiler chicken floor distribution are done manually in commercial grow-out houses every day, which is labor intensive and time consuming. This task requires an efficient and automatic system that can monitor the chicken’s floor distributions. In the current study, a machine vision-based method was developed and tested in an experimental broiler house. For the new method to recognize bird distribution in the images, the pen floor was virtually defined/divided into drinking, feeding, and rest/exercise zones. As broiler chickens grew, the images collected each day were analyzed separately to avoid biases caused by changes of body weight/size over time. About 7000 chicken areas/profiles were extracted from images collected from 18 to 35 days of age to build a BP neural network model for floor distribution analysis, and another 200 images were used to validate the model. The results showed that the identification accuracies of bird distribution in the drinking and feeding zones were 0.9419 and 0.9544, respectively. The correlation coefficient (R), mean square error (MSE), and mean absolute error (MAE) of the BP model were 0.996, 0.038, and 0.178, respectively, in our analysis of broiler distribution. Missed detections were mainly caused by interference with the equipment (e.g., the feeder hanging chain and water line); studies are ongoing to address these issues. This study provides the basis for devising a real-time evaluation tool to detect broiler chicken floor distribution and behavior in commercial facilities.

Stretching a Hanging Chain without Work

We study a variation of the hanging chain problem. If one end (or both) of a hanging chain moves with stretching the chain along a path such that an external force(s) supporting the chain does not do any work, what path does the movable end draw? Sketching the path (“the workless curve”) will help students to acquire a qualitative understanding of work. In its mathematical derivation, one has to solve transcendental equations under an approximation including the Lambert [Formula: see text] function. It is suitable for undergraduate students in calculus-based physics courses.

The ‘hanging flag’ problem: on the heaving motion of a thin filament in the limit of small flexural stiffness

We investigate the fluid–structure interaction of a vertically hanging filament immersed in uniform incompressible high Reynolds number flow. The filament is subject to small-amplitude harmonic heaving at its upstream edge, and to a gravity-induced (‘hanging chain’) tension force. We focus on the limit of small bending rigidity to examine the differences between a highly elastic beam (where bending rigidity is small but finite) and a membrane (where bending rigidity vanishes). The problem is analysed by means of thin airfoil theory, in conjunction with a discrete vortex model for the downstream wake. Denoting the filament non-dimensional rigidity (normalized by the tension force) by $\bar{\unicode[STIX]{x1D700}}$, it is first verified that the beam deflection and associated flow field converge to the membrane solution at $\bar{\unicode[STIX]{x1D700}}\rightarrow 0$. At low actuation frequencies, the differences between the membrane and beam motions are small, and both follow a nearly rigid-body motion parallel to the upstream-edge actuation. With increasing frequency, the differences between the beam and membrane become visible at increasingly lower values of $\bar{\unicode[STIX]{x1D700}}$, and the stabilizing effect of beam flexural rigidity, resulting in reduced flapping amplitudes, is apparent. Examining the beam motion near its edge points at non-small frequencies, semi-analytic approximations for the associated time-periodic displacements are obtained. Close to the actuated end, a layer of width $\bar{\unicode[STIX]{x1D700}}^{1/2}$ is found, where the flexural rigidity term in the equation of motion is balanced by the tension term. Here, the differences between the beam and membrane deflections are attributed to the additional zero-slope condition satisfied by the former. In the vicinity of the free end, a local Taylor expansion is carried out. A balance between the bending and inertia terms results in a layer of width $\propto \bar{\unicode[STIX]{x1D700}}^{1/4}/\bar{\unicode[STIX]{x1D714}}_{h}^{1/2}$, where $\bar{\unicode[STIX]{x1D714}}_{h}$ denotes the scaled heaving frequency. The layer is therefore thicker than the upstream layer for $\bar{\unicode[STIX]{x1D714}}_{h}\approx 1$, and becomes thinner with increasing $\bar{\unicode[STIX]{x1D714}}_{h}$. Within the layer, the beam deflects linearly with the distance from the edge, in marked difference from a membrane and in accordance with the free-end conditions satisfied by the former.

Catenary optics for achromatic generation of perfect optical angular momentum

The catenary is the curve that a free-hanging chain assumes under its own weight, and thought to be a “true mathematical and mechanical form” in architecture by Robert Hooke in the 1670s, with nevertheless no significant phenomena observed in optics. We show that the optical catenary can serve as a unique building block of metasurfaces to produce continuous and linear phase shift covering [0, 2π], a mission that is extremely difficult if not impossible for state-of-the-art technology. Via catenary arrays, planar optical devices are designed and experimentally characterized to generate various kinds of beams carrying orbital angular momentum (OAM). These devices can operate in an ultra-broadband spectrum because the anisotropic modes associated with the spin-orbit interaction are almost independent of the incident light frequency. By combining the optical and topological characteristics, our approach would allow the complete control of photons within a single nanometric layer.