Academic literature on the topic 'Vertical curve'

Existing highway vertical curves may be grouped into two categories: symmetrical vertical curves and unsymmetrical vertical curves. In the past vertical curves design, parabolic arc was used as the vertical curve. This paper presents the new single-arc unsymmetrical vertical curve which is include only one cubic parabola. This curve has the gradual change of the rates of change in grade so that it can provide more comfort to the driver. This paper mainly presents the method by which to find the minimum length for a new single-arc unsymmetrical crest vertical curve based on the minimum sight distance . The discussion will be divided into two situations: the sight distance is longer than the curve length and the sight distance is not longer than the curve length.

Several studies have shown that the perception of horizontal curves can be influenced by an overlapping vertical alignment. A previous two-phase study investigated the hypothesis that a horizontal curve appears flatter when overlapping with a vertical sag curve and sharper when overlapping with a vertical crest curve. The study concluded that the hypothesis was valid. The study also developed several statistical models to estimate the perceived radius of horizontal curves in a combined alignment. This study extends the earlier work by investigating the effect of additional geometric parameters on the perception. The parameters examined include the presence of spiral curves, the length of the spirals, and the position of the vertical curve midpoint relative to the horizontal curve. It was found that (1) driver misperception of the horizontal curvature increases as the radius of the horizontal curve increases, (2) the presence of a spiral curve affects driver perception of the horizontal curvature in the case of crest combination only, (3) the length of the spiral curve has no effect on the perception whether on crest or sag combinations, and (4) while the effect of the position of the vertical curve midpoint relative to the horizontal curve is not statistically significant, it seems that the perception problem appears to diminish as the positive offsets increases.Key words: highway geometric design, visual perception, combined alignment.

OBJECTIVE: To find the mean curve spee depth and association in three different skeletal vertical patterns (Hypodivergent, Normodivergent and Hyperdivergent). METHODOLOGY: Orthodontic models of mandibular arch and Lateral cephalogram of 110 patients with the mean age of 17.16±4 years, 26.4% (N=29) males and 73.6% (N=81) females were taken from the patients who visited for the orthodontic treatment, to the Department of Orthodontics of Karachi Medical and Dental College. Skeletal divergence defined by the mandibular plane (Lower border of mandible) to sella-nasion line angle (SN-MP). It was measured on lateral cephalogram and Curve of spee depth measured on mandibular cast. RESULTS:Out of 110 patients 20.9% (N= 23) were hypodivergent, 29.1% (N=32) were normodivergent and 50% (N=55) were hyperdivergent. The curve of spee among these three groups were 3.39±0.30mm, 2.62±0.23mm and 2.02±0.45mm. One-way ANOVA has been applied and it showed highly significant differences in the value of curve of spee depth among three vertical skeletal patterns with the p-value of 0.000. Moving from Hypodivergent to Hyperdivergent cases, the curve of Spee depth reduces. CONCLUSION: It has been found that there is a significant difference in curve of spee among hypodivergent, normodivergent and hyperdivergent patients. KEYWORDS: Dentistry, Curve of Spee, Vertical Skeletal Patterns, Orthodontic Diagnosis. HOW TO CITE: Rehman SA, Rizwan S, Faisal SS, Hussain SS. Association of curve of spee with vertical skeletal patterns. J Pak Dent Assoc 2020;29(4):254-258.

Traditional unsymmetrical vertical curves consist of two parabolic arcs smoothly connected at the point of common curvature. A new single-arc unsymmetrical vertical curve that takes the form of a cubic instead of parabolic function has been recently developed. The curve has a rate of change in grade that gradually varies between the start and end of the vertical curve. The single-arc curve eliminates the sudden change that exists in curvature of traditional two-arc unsymmetrical vertical curves. This paper first develops the sight distance (SD) relationships for the new single-arc curve (crest type). With these relationships, the SD profile for the new curve is established and its shape shows a substantial improvement over the abrupt-type SD profiles of the two-arc curves. The length requirements that satisfy stopping, passing, and decision SD guidelines of AASHTO are then presented. Some examples are used to illustrate the use of the developed design aids. The new single-arc curve builds on previously developed unsymmetrical vertical curves to improve curve characteristics that hopefully will promote road safety.

In this paper, an electronic calculator for vertical curve computations is developed in Microsoft Windows. The developed calculator used is successfully for vertical curve computations and requires entering the curve length, tangent grades, setting out interval, and the elevation of the intersection points. Computations of vertical curves by the developed calculator are faster, easier, accurate, and less subject to errors comparable to the traditional method of calculations. Finally, the results obtained by the traditional and developed methods are presented for checking the behavior of the developed calculator.

Existing unsymmetrical vertical curves consist of two parabolic arcs smoothly connected at the point of common curvature. As such, each arc has a constant rate of change in grade. This paper presents a new and improved single-arc unsymmetrical vertical curve for highways that takes the form of a cubic function. The curve has a rate of change in grade that varies gradually between the beginning and end of the curve. The new curve lies below the sharper arc and above the flatter arc of the existing equal-arc unsymmetrical (EAU) vertical curve, thus smoothing out the EAU curve. In addition, the new curve slightly improves highway sight distance in most of the cases studied. The single-arc curve exhibits several interesting properties. The forward and backward offsets are not equal, nor are the basic and reverse offsets. The offsets of the new and EAU curves are equal at the mid-point of the curve. Also, the rate of change in grade of the new curve at the mid-point equals the average of the rates of change in grade of the two arcs of the EAU curve. The new curve exhibits several important properties and, as such should be of interest to highway designers.Key words: unsymmetrical vertical curves, single arc, highways, offset, sight distance, driver comfort.

Free-flow speeds were collected at both a control section and a curve section at 14 surburban sites with horizontal curves and 10 suburban sites with vertical curves. The scatter plots of the 85th percentile speed versus approach density indicate that when the approach density is between 3 and 15 approaches per km, approach density does not influence speed. Regression analysis indicated that the curve radius for horizontal curves and the inferred design speed for vertical curves can be used to predict the 85th percentile speed on curves for vehicles on the outside lane of a four-lane divided suburban arterial. For horizontal-curve sites, a curvilinear relationship exists between curve radius and the 85th percentile speed. A linear relationship provided the best fit between the inferred design speed and the 85th percentile speed for the vertical curve sites. For the horizontal and vertical curve sites, the speed at which 85th percentile speed becomes less than the inferred design speed is lower for suburban arterials than for rural highways. Drivers on suburban horizontal curves operate at speeds greater than the inferred design speed for curves designed for speeds of 70 kph or less, whereas on rural, two-lane roadways, drivers operate at speeds greater than the inferred design speed for curves designed for speeds of 90 kph or less. For vertical curves, the speeds at which drivers operate greater than the inferred design speed are 90 kph for suburban arterials and 105 kph for rural highways. These results are within 12 kph of the observed 85th percentile speeds on nearby control sections (approximately 80 kph for suburban arterials and 100 kph on rural highways).

Highway profile information may not be available or may not be up to date, especially for old highways. In these cases, profile data are collected using global positioning systems (GPS) or by extracting them from digital images. This paper presents an optimization model for estimating the parameters of continuous vertical alignments, involving multiple parabolic vertical curves that best fit existing highway profile data using the least-squares method. The optimization involves two levels: single-curve optimization and multiple-curve optimization. The former is used to obtain the approximate length of each vertical curve based on the approximate tangent parameters determined from the outline controlling points. The latter is used to obtain the global optimal parameters for tangents and vertical curves. The model is validated and applied using actual data of a vertical alignment. The proposed model presents a useful extension to existing methods for estimating simple vertical alignments and therefore should be of interest to highway engineering professionals.

The purposes of this dissertation were to examine the phase characteristics of the countermovement jump force-time curve between athletes based on jumping ability, examine the influence of maximal muscular strength on the countermovement jump force-time curve phase characteristics of athletes, and to examine the behavior of the countermovement jump force-time curve phase characteristics over the course of a training process in athletes of varying strength levels. The following are the major findings of these dissertations. The analysis of athletes by jumping ability suggested that proficient jumpers are associated with greater relative phase magnitude and phase impulse throughout the phases contained in the positive impulse of the countermovement jump force-time curve. Additionally, phase duration was not found to differ between athletes based on jumping ability or between male and female athletes. The analysis of athletes based on maximal muscular strength suggested that only unweighted phase duration differs between strong and less-strong athletes. Interestingly, in both investigations based on jumping ability and maximal strength indicated the relative shape of the stretching phase representing the rise in positive force was related to an athlete’s jumping ability (jump height). The results of the longitudinal analysis of countermovement jump force-time phase characteristics identified that these variables can be frequently assessed throughout a training process to provide information of regarding an athlete performance state. Furthermore, based on the contrasting behaviors of many of the countermovement jump force-time curve phase characteristics over time, an athlete’s level of muscular strength may influence how these characteristics are expressed in the context of a training process.

Full scale lateral load tests were performed on five piles located at various distances behind MSE walls. Three of the five test piles were production piles used to support bridges, and the other two piles were located behind a MSE wing walls adjacent to the bridge abutment. The objective of the testing was to determine the effect of spacing from the wall on the lateral resistance of the piles and on the force resisted by the MSE reinforcement. Tentative curves have been developed showing p-multiplier vs. normalized spacing behind wall for a length to height ratio of 1.1 and 1.6. The data suggest that with a L/H ratio of 1.6, a p-multiplier of 1 can be used when the normalized distance from the back face of the MSE wall to the center of the pile is at least 3.8 pile diameters. When the L/H ratio decreases to 1.1 a p-multiplier of 1 can be used when the pile is at least 5.2 pile diameters behind the wall. A plot showing the induced load in the reinforcement as a function of distance from the pile has been developed. The data in the plot is normalized to the maximum lateral load and to the spacing from the wall to the pile. The best fit curve is capped at a normalized induced force of approximately 0.15. The data show that the induced force on the reinforcement when a lateral load is applied to the piles decreases exponentially as the normalized distance from the pile increases. The plot is limited to the conditions tested, i.e. for the reinforcement in the upper 6 ft. of the wall with L/H values ranging from 1.1 to 1.6.

A destruição causada por um terremoto depende de muitos fatores, como características e profundidade da fonte, magnitude, distância epicentral e da configuração geológica da área. A destruição causada devido à configuração geológica da área é denominada como efeito local. A modelagem do efeito local implica na determinação do tempo e nível de vibração e do efeito de amplificação do deslocamento. As propriedades elásticas dos materiais geológicos (velocidade das ondas de compressão e de cisalhamento, densidade, espessura da camada de solo, etc.) podem ser obtidas por diversos métodos geofísicos. O conhecimento dessas propriedades elásticas ajuda a melhor projetar as infraestruturas e reduzir as chances de danos. Este procedimento é denominado de microzoneamento. Os parâmetros mais importantes para realizar o microzoneamento são as espessuras dos sedimentos que recobrem o embasamento e o perfil das velocidades das ondas S (cisalhamento). Esses dois parâmetros são adequadamente caracterizados pelo uso de várias técnicas geofísicas como perfilagens em furos de sondagem, reflexão e refração sísmica. Esses métodos geofísicos trazem algumas restrições como a necessidade da execução de um furo, emprego de fontes sísmicas artificiais que muitas vezes são dispendiosas e por vezes de uso restrito em áreas urbanas, além de muitas vezes estarem limitadas a investigações de apenas algumas dezenas de metros. Os métodos que substituíram esses métodos geofísicos convencionais nas últimas décadas são a análise do ruído sísmico produzido por fontes naturais e culturais. Este ruído sísmico ambiental pode ser registrado com menor custo e esforço e com boa cobertura lateral. Várias técnicas que se utilizam do ruído sísmico podem ser empregadas, no entanto, aquela que obteve maior atenção nos últimos anos é a técnica da razão do espectro horizontal sobre o espectro vertical da onda de superfície (H/V). A curva da razão espectral H/V é uma ferramenta rápida, fácil e de baixo custo para a caracterização da subsuperfície rasa. Existem vários estudos realizados sobre o tema que tentaram cobrir todos os aspectos e problemas associados ao método. Aqui neste estudo são aprofundados alguns aspectos ainda não avaliados em detalhe. Diferentes procedimentos para a modelagem e as associações entre os fenômenos físicos envolvidos e as características da curva H/V são discutidos e os resultados numéricos desses estudos são comparados com informações extraídas de perfis de sondagens de um dos locais estudados. O pico e a forma da curva H / V são modelados para encontrar o desvio na frequência de pico a partir da frequência de ressonância da onda de cisalhamento considerando diferentes campos de onda em torno do pico, assim como sua relação com a forma dominante da curva. A frequência de pico das curvas H/V é utilizada para estimar a relação entre a frequência a espessura através de análise de regressão. O estudo mostra que a curva de dispersão obtida a partir de um ensaio MASW pode ser usada para estimar a velocidade da onda S a um metro de profundidade e sua tendência de aumento com a profundidade. Esses valores podem ser usados para estimar a relação frequência-espessura para uma área. Esses resultados são comparados com a relação frequência-espessura derivada experimentalmente para a mesma área. A sensibilidade da forma da curva H/V à estrutura de velocidade do meio é analisada através de duas técnicas de modelagem (elipticidade da onda Rayleigh e campo difuso baseado na curva H/V). Diferentes partes da curva H/V são invertidas visando avaliar qual a parte da curva H/V contém as informações mais importantes sobre a estrutura subterrânea. As lições aprendidas dessas análises são aplicadas a três dados experimentais de locais distintos. As ondas Love podem contaminar o resultado da curva H/V. Duas técnicas diferentes para remover o efeito das ondas amorosas são discutidas. Em seguida, são discutidos os resultados da inversão conjunta das curvas de dispersão e da curva H/V após remoção do efeito da onda Love, ou seja, a curva de elipticidade. Alguns aspectos novos da técnica H/V são discutidos no final.
The destruction caused by an earthquake at a site depends on many factors like source characteristics such as magnitude, epicentral distance from the site, depth of the source, and on the geological setting of the area. The destruction caused due to the geological setting of an area is termed as site effect. To model the site effect of an area is to determine the shaking level longevity and its displacement amplification. The elastic properties (shear and compressional wave velocities, density, thickness of soil layer, etc.) of the site are required to find out by employing various geophysical procedures. The knowledge of these elastic properties help in better designing the infrastructure, which reduces the chances of destruction caused by a local geological setting due to an earthquake occurrence. This procedure is widely termed as microzonation. The most important parameters for the microzonation are the thickness of soft sediments over the seismic bedrock and its shear wave velocity profile. These two parameters are properly characterized by employing various geophysical techniques like borehole measurement, seismic reflection and seismic refraction. The conventional geophysical methods bring some hindrance to the picture such as, the drilling of a borehole and artificial seismic sources deployment for the reflection and refraction survey, which are both expensive and time consuming, difficult or even in some case impossible to implement in urbanized environment, the investigation is depth limited to few tens of meter. The methods which replaced this conventional geophysical method from the last decades or so is the analysis of Earth vibration caused by the seismic noise which is produced by both natural and cultural sources. This ambient seismic noise can be recorded with less cost and effort with good lateral coverage. Various seismic noise techniques are employed for this job; however, the one which got the most attention in recent years is the horizontal over vertical spectral ratio (H/V) technique. The H/V spectral ratio curve is a fast easy and cheap tool for the near-subsurface characterization. There are various study performed on the topic which has tried to cover almost all the aspects and problems associated with the method. Here in this study, we try to detail the aspects of this technique, which are not been evaluated fully. The different modelling procedures presented to model and physically link the H/V curve with some physical phenomenon will be discussed and its numerical result with the experimental H/V curve will be compared for a borehole test site. The peak and the shape of the H/V curve will be modelled to find its peak frequency deviation from the shear wave resonance frequency by considering different wave-field around the peak. Similarly, the shape dominancy of the H/V curve linkage will be find out. The peak frequency of the H/V curve is used to estimate the thickness-frequency relation by regression analysis. Here we will show that the dispersion curve obtained from multi-channel analysis of surface waves (MASW) can be used to estimate the velocity at one meter and the shear wave velocity increase trend with depth. These values can be used to estimate the thickness frequency relation for an area and its result will be compared with the experimentally derived thickness-frequency relationship for the same area. The sensitivity of the H/V curve shape to the subsurface velocity structure will find out for two main modelling techniques (Rayleigh wave ellipticity and diffused field based H/V curve). The different parts of the H/V curve are inverted (back modelled) to find out the part of H/V curve which is carrying the most important information about the subsurface structure. The lesson learned from all this analysis will be applied to experimental data of three different sites. The Love waves might contaminate the result of the H/V curve. Two different techniques to remove their effects will be discussed. Then, the joint inversion result of the dispersion and this Love effect removed H/V for more precisely ellipticity curve is discussed. Some new aspects of the H/V curve technique are also discussed at the end.

ABSTRACTLateral Resistance of Piles near 15 Foot Vertical MSE AbutmentWalls Reinforced with Ribbed Steel StripsJarell Jen Chou HanDepartment of Civil and Environmental Engineering, BYUMaster of ScienceA full scale MSE wall was constructed and piles were driven at various distances behind the wall. Lateral load tests were conducted to determine the effect of pile spacing from the wall on the lateral resistance of the piles and the force resisted by the MSE reinforcement. The piles used for this study were 12.75 inch pipe piles and the reinforcements were ribbed steel strips.Load-deflection curves were developed for piles located behind the wall at 22.4 inches (1.7 pile diameters), 35.4 inches (2.8 pile diameters), 39.4 inches (3.1 pile diameters) and 49.9 inches (3.9 pile diameters). Data results show that the lateral resistance of the pile decreases as the spacing behind the wall decreases. Measured load-deflection curves were used to compare with computed curves from LPILE with p-multiplier developed for the lateral resistance of piles closer to the wall. A curve was created showing the variation of p-multiplier with normalized pile spacing behind the wall. The curve suggests that a p-multiplier of 1 (no reduction in lateral resistance) can be used when a pile is placed at least four pile diameters from the back face of the wall.

Dans cette thèse, nous proposons une approche méthodologique et algorithmique pour la reconnaissance visuelle d'intentions, basée sur la rotation et le mouvement vertical de la tête et de la main. Le contexte dans lequel cette solution s'inscrit est celui d'une personne handicapée, dont la mobilité est assurée par un fauteuil roulant. Le système proposé constitue une alternative intéressante aux interfaces classiques de type manette, boutons pneumatiques, etc. La séquence vidéo, composée de 10 images, est traitée en utilisant différentes méthodes pour construire ce qui dans cette thèse est désigné par « courbe d'intention ». Une base de règles est également proposée pour classifier chaque courbe d'intention. Pour la reconnaissance basée sur les mouvements de la tête, une approche utilisant la symétrie du visage est proposée pour estimer la direction désirée à partir de la rotation de la tête. Une Analyse en Composantes Principales (ACP) est utilisée pour détecter l'intention de varier la vitesse de déplacement du fauteuil roulant, à partir du mouvement vertical de la tête. Pour la reconnaissance de la direction basée sur la rotation de la main, une approche utilisant à la fois la symétrie verticale de la main et un algorithme d'apprentissage (réseaux neuronaux, machines à vecteurs supports ou k-means), permet d’obtenir les courbes d'intentions exploitées par la suite pour la détection de la direction désirée. Une autre approche, s’appuyant sur l'appariement de gabarits de la région contenant les doigts, est également proposée. Pour la reconnaissance de la vitesse variable basée sur le mouvement vertical de la main, deux approches sont proposées. La première utilise également l'appariement de gabarits de la région contenant les doigts, et la deuxième se base sur un masque en forme d'ellipse, pour déterminer la position verticale de la main. Les résultats obtenus montrent de bonnes performances en termes de classification aussi bien des positions individuelles dans chaque image, que des courbes d'intentions. L’approche de reconnaissance visuelle d’intentions proposée produit dans la très grande majorité des cas un meilleur taux de reconnaissance que la plupart des méthodes proposées dans la littérature. Par ailleurs, cette étude montre également que la tête et la main en rotation et en mouvement vertical constituent des indicateurs d'intention appropriés
In this thesis, a methodological and algorithmic approach is proposed, for visual intention recognition based on the rotation and the vertical motion of the head and the hand. The context for which this solution is intended is that of people with disabilities whose mobility is made possible by a wheelchair. The proposed system is an interesting alternative to classical interfaces such as joysticks and pneumatic switches. The video sequence comprising 10 frames is processed using different methods leading to the construction of what is referred to in this thesis as an “intention curve”. A decision rule is proposed to subsequently classify each intention curve. For recognition based on head motions, a symmetry-based approach is proposed to estimate the direction intent indicated by a rotation and a Principal Component Analysis (PCA) is used to classify speed variation intents of the wheelchair indicated by a vertical motion. For recognition of the desired direction based on the rotation of the hand, an approach utilizing both a vertical symmetry-based approach and a machine learning algorithm (a neural network, a support vector machine or k-means clustering) results in a set of two intention curves subsequently used to detect the direction intent. Another approach based on the template matching of the finger region is also proposed. For recognition of the desired speed variation based on the vertical motion of the hand, two approaches are proposed. The first is also based on the template matching of the finger region, and the second is based on a mask in the shape of an ellipse used to estimate the vertical position of the hand. The results obtained display good performance in terms of classification both for single pose in each frame and for intention curves. The proposed visual intention recognition approach yields in the majority of cases a better recognition rate than most of the methods proposed in the literature. Moreover, this study shows that the head and the hand in rotation and in vertical motion are viable intent indicators

Vertical-axis wind turbines (VAWTs) have with time been outrivaled by the today more common and economically feasible horizontal-axis wind turbines (HAWTs). However, VAWTs have several advantages which still make them interesting, for example, the VAWTs can have the drive train at ground level and it has been argued that they have lower noise emission. Other proposed advantages are suitability for both up-scaling and floating offshore platforms. The work within this thesis is made in collaboration between Halmstad University and Uppsala University. A 200-kW semi-guy-wired VAWT H-rotor, owned by Uppsala University but situated in Falkenberg close to Halmstad, has been the main subject of the research although most results can be generalized to suit a typical H-rotor. This thesis has three main topics regarding VAWTs: (1) how the wind energy extraction is influenced by turbulence, (2) aerodynamical noise generation and (3) eigenfrequencies of the semi-guy-wired tower. The influence from turbulence on the wind energy extraction is studied by evaluating logged operational data and examining how the power curve and the tip-speed ratio for maximum Cp is impacted by turbulence. The work has showed that the T1-turbine has a good ability to extract wind energy at turbulent conditions, indicating an advantage in energy extraction at turbulent sites for VAWTs compared to HAWTs.The noise characteristics are studied experimentally, and models of the two most likely aerodynamic noise mechanisms are applied. Here, inflow-turbulence noise is deemed as the prevailing noise source rather than turbulent-boundary-layer trailing-edge noise (TBL-TE) which is the most important noise mechanism for HAWTs. The overall noise emission has also been measured and proven low compared to similar sized HAWTs. The eigenfrequencies of a semi-guy-wired tower are also studied. Analytical expressions describing the first-mode eigenfrequency of both tower and guy wire has been derived and verified by experiments and simulations.

The subject of my thesis is a variant I/57 in the section Semetín-Bystřička. The proposed route of communication, was part of an existing communications maintained for its full utilization. Were drawn four proposed variants of the solution, 3 variants are trying their best to use existing communication Jablůnka the village, one suggested option B that leads outside the existing road.

This graduation thesis deals about researching study of by-pass road of city Hustopeče, district of Břeclav, Southmoravian region. This city passes main road number 425, which should be connected with the by-pass road. The by-pass road will be designed as road of category S9,5/70 and will be situated west of the city. Terrain is undulated and composed of agricultural parcels. The main purpose of this by-pass road is significant burden of region traffic.

The textbook describes the physical foundations, theory, principles of selection and calculation of the main parameters of spring suspension schemes, discusses the issues of fitting crews into curves, vertical dynamics of the traction drive, the use of coupling weight and vibrations of electric rolling stock. It is intended for the training of certified specialists in the direction of "Railway rolling stock".

In this chapter it is shown how to calculate the force which arises due to the hydrostatic pressure distributed over a submerged surface or object. The vertical component of force is shown to be equal in magnitude to the weight of fluid which would occupy the volume directly above the surface and to act vertically downwards through the centroid of this volume. For a curved surface, the magnitude of the horizontal component of the hydrostatic force is shown to equal the hydrostatic force on the projection of the surface onto a vertical plane. This force is equal to the product of the area of the surface and the pressure at its centroid. The buoyancy force exerted on a submerged or floating object is shown to equal the weight of the fluid displaced by the object (Archimedes’ principle) and to act vertically upwards through the centroid of the displaced fluid. Stability of floating objects is discussed and the concept of metacentric height introduced.

This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree ofmathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactlywhat is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.

Bones are multifunctional passive organs of movement that supports soft tissue and directly attached muscles. They also protect internal organs and are a reserve of calcium, phosphorus and magnesium. Each bone is covered with periosteum, and the adjacent bone surfaces are covered by articular cartilage. Histologically, the bone is an organ composed of many different tissues. The main component is bone tissue (cortical and spongy) composed of a set of bone cells and intercellular substance (mineral and organic), it also contains fat, hematopoietic (bone marrow) and cartilaginous tissue. Bones are a tissue that even in adult life retains the ability to change shape and structure depending on changes in their mechanical and hormonal environment, as well as self-renewal and repair capabilities. This process is called bone turnover. The basic processes of bone turnover are: • bone modeling (incessantly changes in bone shape during individual growth) following resorption and tissue formation at various locations (e.g. bone marrow formation) to increase mass and skeletal morphology. This process occurs in the bones of growing individuals and stops after reaching puberty • bone remodeling (processes involve in maintaining bone tissue by resorbing and replacing old bone tissue with new tissue in the same place, e.g. repairing micro fractures). It is a process involving the removal and internal remodeling of existing bone and is responsible for maintaining tissue mass and architecture of mature bones. Bone turnover is regulated by two types of transformation: • osteoclastogenesis, i.e. formation of cells responsible for bone resorption • osteoblastogenesis, i.e. formation of cells responsible for bone formation (bone matrix synthesis and mineralization) Bone maturity can be defined as the completion of basic structural development and mineralization leading to maximum mass and optimal mechanical strength. The highest rate of increase in pig bone mass is observed in the first twelve weeks after birth. This period of growth is considered crucial for optimizing the growth of the skeleton of pigs, because the degree of bone mineralization in later life stages (adulthood) depends largely on the amount of bone minerals accumulated in the early stages of their growth. The development of the technique allows to determine the condition of the skeletal system (or individual bones) in living animals by methods used in human medicine, or after their slaughter. For in vivo determination of bone properties, Abstract 10 double energy X-ray absorptiometry or computed tomography scanning techniques are used. Both methods allow the quantification of mineral content and bone mineral density. The most important property from a practical point of view is the bone’s bending strength, which is directly determined by the maximum bending force. The most important factors affecting bone strength are: • age (growth period), • gender and the associated hormonal balance, • genotype and modification of genes responsible for bone growth • chemical composition of the body (protein and fat content, and the proportion between these components), • physical activity and related bone load, • nutritional factors: – protein intake influencing synthesis of organic matrix of bone, – content of minerals in the feed (CA, P, Zn, Ca/P, Mg, Mn, Na, Cl, K, Cu ratio) influencing synthesis of the inorganic matrix of bone, – mineral/protein ratio in the diet (Ca/protein, P/protein, Zn/protein) – feed energy concentration, – energy source (content of saturated fatty acids - SFA, content of polyun saturated fatty acids - PUFA, in particular ALA, EPA, DPA, DHA), – feed additives, in particular: enzymes (e.g. phytase releasing of minerals bounded in phytin complexes), probiotics and prebiotics (e.g. inulin improving the function of the digestive tract by increasing absorption of nutrients), – vitamin content that regulate metabolism and biochemical changes occurring in bone tissue (e.g. vitamin D3, B6, C and K). This study was based on the results of research experiments from available literature, and studies on growing pigs carried out at the Kielanowski Institute of Animal Physiology and Nutrition, Polish Academy of Sciences. The tests were performed in total on 300 pigs of Duroc, Pietrain, Puławska breeds, line 990 and hybrids (Great White × Duroc, Great White × Landrace), PIC pigs, slaughtered at different body weight during the growth period from 15 to 130 kg. Bones for biomechanical tests were collected after slaughter from each pig. Their length, mass and volume were determined. Based on these measurements, the specific weight (density, g/cm3) was calculated. Then each bone was cut in the middle of the shaft and the outer and inner diameters were measured both horizontally and vertically. Based on these measurements, the following indicators were calculated: • cortical thickness, • cortical surface, • cortical index. Abstract 11 Bone strength was tested by a three-point bending test. The obtained data enabled the determination of: • bending force (the magnitude of the maximum force at which disintegration and disruption of bone structure occurs), • strength (the amount of maximum force needed to break/crack of bone), • stiffness (quotient of the force acting on the bone and the amount of displacement occurring under the influence of this force). Investigation of changes in physical and biomechanical features of bones during growth was performed on pigs of the synthetic 990 line growing from 15 to 130 kg body weight. The animals were slaughtered successively at a body weight of 15, 30, 40, 50, 70, 90, 110 and 130 kg. After slaughter, the following bones were separated from the right half-carcass: humerus, 3rd and 4th metatarsal bone, femur, tibia and fibula as well as 3rd and 4th metatarsal bone. The features of bones were determined using methods described in the methodology. Describing bone growth with the Gompertz equation, it was found that the earliest slowdown of bone growth curve was observed for metacarpal and metatarsal bones. This means that these bones matured the most quickly. The established data also indicate that the rib is the slowest maturing bone. The femur, humerus, tibia and fibula were between the values of these features for the metatarsal, metacarpal and rib bones. The rate of increase in bone mass and length differed significantly between the examined bones, but in all cases it was lower (coefficient b <1) than the growth rate of the whole body of the animal. The fastest growth rate was estimated for the rib mass (coefficient b = 0.93). Among the long bones, the humerus (coefficient b = 0.81) was characterized by the fastest rate of weight gain, however femur the smallest (coefficient b = 0.71). The lowest rate of bone mass increase was observed in the foot bones, with the metacarpal bones having a slightly higher value of coefficient b than the metatarsal bones (0.67 vs 0.62). The third bone had a lower growth rate than the fourth bone, regardless of whether they were metatarsal or metacarpal. The value of the bending force increased as the animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. The rate of change in the value of this indicator increased at a similar rate as the body weight changes of the animals in the case of the fibula and the fourth metacarpal bone (b value = 0.98), and more slowly in the case of the metatarsal bone, the third metacarpal bone, and the tibia bone (values of the b ratio 0.81–0.85), and the slowest femur, humerus and rib (value of b = 0.60–0.66). Bone stiffness increased as animals grew. Regardless of the growth point tested, the highest values were observed for the humerus, tibia and femur, smaller for the metatarsal and metacarpal bone, and the lowest for the fibula and rib. Abstract 12 The rate of change in the value of this indicator changed at a faster rate than the increase in weight of pigs in the case of metacarpal and metatarsal bones (coefficient b = 1.01–1.22), slightly slower in the case of fibula (coefficient b = 0.92), definitely slower in the case of the tibia (b = 0.73), ribs (b = 0.66), femur (b = 0.59) and humerus (b = 0.50). Bone strength increased as animals grew. Regardless of the growth point tested, bone strength was as follows femur > tibia > humerus > 4 metacarpal> 3 metacarpal> 3 metatarsal > 4 metatarsal > rib> fibula. The rate of increase in strength of all examined bones was greater than the rate of weight gain of pigs (value of the coefficient b = 2.04–3.26). As the animals grew, the bone density increased. However, the growth rate of this indicator for the majority of bones was slower than the rate of weight gain (the value of the coefficient b ranged from 0.37 – humerus to 0.84 – fibula). The exception was the rib, whose density increased at a similar pace increasing the body weight of animals (value of the coefficient b = 0.97). The study on the influence of the breed and the feeding intensity on bone characteristics (physical and biomechanical) was performed on pigs of the breeds Duroc, Pietrain, and synthetic 990 during a growth period of 15 to 70 kg body weight. Animals were fed ad libitum or dosed system. After slaughter at a body weight of 70 kg, three bones were taken from the right half-carcass: femur, three metatarsal, and three metacarpal and subjected to the determinations described in the methodology. The weight of bones of animals fed aa libitum was significantly lower than in pigs fed restrictively All bones of Duroc breed were significantly heavier and longer than Pietrain and 990 pig bones. The average values of bending force for the examined bones took the following order: III metatarsal bone (63.5 kg) <III metacarpal bone (77.9 kg) <femur (271.5 kg). The feeding system and breed of pigs had no significant effect on the value of this indicator. The average values of the bones strength took the following order: III metatarsal bone (92.6 kg) <III metacarpal (107.2 kg) <femur (353.1 kg). Feeding intensity and breed of animals had no significant effect on the value of this feature of the bones tested. The average bone density took the following order: femur (1.23 g/cm3) <III metatarsal bone (1.26 g/cm3) <III metacarpal bone (1.34 g / cm3). The density of bones of animals fed aa libitum was higher (P<0.01) than in animals fed with a dosing system. The density of examined bones within the breeds took the following order: Pietrain race> line 990> Duroc race. The differences between the “extreme” breeds were: 7.2% (III metatarsal bone), 8.3% (III metacarpal bone), 8.4% (femur). Abstract 13 The average bone stiffness took the following order: III metatarsal bone (35.1 kg/mm) <III metacarpus (41.5 kg/mm) <femur (60.5 kg/mm). This indicator did not differ between the groups of pigs fed at different intensity, except for the metacarpal bone, which was more stiffer in pigs fed aa libitum (P<0.05). The femur of animals fed ad libitum showed a tendency (P<0.09) to be more stiffer and a force of 4.5 kg required for its displacement by 1 mm. Breed differences in stiffness were found for the femur (P <0.05) and III metacarpal bone (P <0.05). For femur, the highest value of this indicator was found in Pietrain pigs (64.5 kg/mm), lower in pigs of 990 line (61.6 kg/mm) and the lowest in Duroc pigs (55.3 kg/mm). In turn, the 3rd metacarpal bone of Duroc and Pietrain pigs had similar stiffness (39.0 and 40.0 kg/mm respectively) and was smaller than that of line 990 pigs (45.4 kg/mm). The thickness of the cortical bone layer took the following order: III metatarsal bone (2.25 mm) <III metacarpal bone (2.41 mm) <femur (5.12 mm). The feeding system did not affect this indicator. Breed differences (P <0.05) for this trait were found only for the femur bone: Duroc (5.42 mm)> line 990 (5.13 mm)> Pietrain (4.81 mm). The cross sectional area of the examined bones was arranged in the following order: III metatarsal bone (84 mm2) <III metacarpal bone (90 mm2) <femur (286 mm2). The feeding system had no effect on the value of this bone trait, with the exception of the femur, which in animals fed the dosing system was 4.7% higher (P<0.05) than in pigs fed ad libitum. Breed differences (P<0.01) in the coross sectional area were found only in femur and III metatarsal bone. The value of this indicator was the highest in Duroc pigs, lower in 990 animals and the lowest in Pietrain pigs. The cortical index of individual bones was in the following order: III metatarsal bone (31.86) <III metacarpal bone (33.86) <femur (44.75). However, its value did not significantly depend on the intensity of feeding or the breed of pigs.

A new method for the “horizontal and vertical curve negotiation angle calculation” is developed and presented in this paper. The new method greatly reduces the complexity of the current procedure while maintaining the accuracy of the final result. An example is given to illustrate the difference between the current and the alternate method. The accuracy of the new method is shown as well. Discussion and conclusions are given in the final part of this paper.

Based on the principle of no car vibrations interference when trains pass grade section from the end of front vertical curve to the start of latter vertical curve, using railway wheel/rail simulation NUCARS™ software, some dynamics simulation studies for minimum grade lengths on high speed railway lines were made. The dynamics simulation results show that, the minimum tangent lengths between vertical transition curves should be more than 0.43V in meters (V is speed of train, km/h). So the minimum length is 800 meters when the vertical curve radius is 25000 meters, and 900 meters when radius is 30000 meters for the Chinese Dedicated Passenger Railway lines (PDLs) on which maximum speed is 350 km/h and ruling gradient is 12‰.

<p>Can we establish the guidelines that make our designs into a success? Is there something like the Golden Ratio for shaping the curve? The Golden Ratio is a common mathematical ratio found in nature, which can be used to create pleasing, organic-looking compositions. This is used for the overall shape and proportions in bridge design. In our practice and in modern-day bridge design we see more and more curved bridges.</p><p>Especially with the rise of parametric design a whole world opened up for (more) complex curved designs. Curviness (either vertical, horizontal or both) is not just a nice aesthetic feature. We encounter design principles that need to be taken into account to get to the ultimate elegancy that we thrive for in our bridge design.</p><p>In our practice, shaping the curve of a bridge is a recurrent topic in the design process – from concept to realisation. From the forming of the (3D) <i>alignment, </i>it’s about how curves fluidly connect. It’s all about the radius, diameter, arcs, splines, offsets and the way to connect with tangents and sinusoids. This is best shown by the Lucky Knot and the Zaligebrug by NEXT architects. We also experienced the difficulties during construction phase and learned to control dealing with the unexpected.</p><p>With a series of case studies from our own bridges we show the importance of precision in shaping curves to make a design that is both natural and understandable to the eye of the user. If done right, curves seem logic and right; but if done improperly, it ends up as a disaster.</p>

A Soloflex machine was analyzed mathematically. Dimensions of the components of the machine were measured, and calculations were made to determine a resistance curve. The machine consists of a mainframe bent into an L-shape, having a vertical post height of 6 ft. A loading post with 27 drilled holes is attached along the back of the vertical post. The loading piece receives a bench pin and the barbell arm pin. To perform an exercise, the barbell arm is attached with the barbell arm pin to the loading piece. Weight straps of equal rating are placed on both sides of the load and barbell arm pins. Pushing upward on the barbell arm will stretch the weight straps which provides resistance to the motion of the barbell arm. The weight straps behave like springs. The straps were stretched with a Tinius-Olsen machine to determine the force vs deflection behavior for a standard set of weight straps, including one pair each of 2.5 lb, 5 lb, 10 lb, 25 lb, 50 lb and 100 lb weight straps. The objective of this study was to make measurements of force versus deflection for each matched pair of weight straps, and then to calculate the force required at the barbell arm to perform an exercise for a particular "weight." Although several different exercises can be performed, the focus here is on a simple bench press, for which the resistance curve was determined.