scholarly journals Precision of the Nebra Disc in Astronomical and Geometric Aspect

2021 ◽  
Vol 20 ◽  
pp. 97-107
Author(s):  
Piotr Banasik ◽  
Władysław Góral
Keyword(s):  
Horizontal Plane ◽  
Vertical Plane ◽  
Linear Measure ◽  
The Moon ◽  
Geometric Constructions ◽  
Geometric Aspect ◽  
Analytical Geometry ◽  
Turn On ◽  
Angular Measurements ◽  
Digital Disc

The astronomical knowledge on the disc has been coded on two planes: horizontal and meridian. The range of sunrise and sunset directions during the year has been described on the horizontal plane. In turn, on the meridian (vertical) plane, the range of changes in the horizontal height and declination of the Sun in the upper culmination during the year and the Moon in its 18.61-year cycle were described. The relationships between the latitude of the place of observation, the horizontal height of the celestial body and its declination were described by means of geometric constructions. The presented article is a continuation of two publications [1] and [2], which describe the decryption of the Nebra disc. These publications were based on the interpretation of the results of angular measurements, made using a protractor with a scale of 0.5 degrees, without the use of a computer. The presented publication is based on a digital disc image obtained by means of its digitization. The obtained data was used for further calculations based on analytical geometry and graphic programs. This allowed to obtain results in a linear measure with a precision of less than 1 mm. PRECYZJA DYSKU Z NEBRY W ASPEKCIE ASTRONOMICZNYM I GEOMETRYCZNYM Wiedza astronomiczna na dysku została zakodowana na dwóch płaszczyznach: horyzontalnej i południkowej. Na płaszczyźnie horyzontalnej (poziomej) opisano zakres kierunków wschodu i zachodu Słońca w ciągu roku. Z kolei na płaszczyźnie południkowej (pionowej) opisano zakres zmiany wysokości horyzontalnej i deklinacji Słońca w kulminacji górnej w ciągu roku oraz Księżyca w jego 18,61-rocznym cyklu. Za pomocą konstrukcji geometrycznych opisano związki między szerokością geograficzną miejsca obserwacji, wysokością horyzontalną ciała niebieskiego i jego deklinacją. Prezentowany artykuł jest kontynuacją dwóch publikacji: [1], [2], w których opisano deszyfrację dysku z Nebry. Publikacje te były oparte na interpretacji wyników pomiarów kątowych, wykonanych za pomocą kątomierza o podziałce 0,5 stopnia, bez użycia komputera. Prezentowana publikacja bazuje na cyfrowym obrazie dysku, uzyskanym za pomocą jego digitalizacji. Uzyskane dane wykorzystano do dalszych obliczeń opartych na geometrii analitycznej oraz programach graficznych.

scholarly journals Dielectric anisotropy as indicator of crystal orientation fabric in Dome Fuji ice core: method and initial results

2021 ◽  
pp. 1-12
Author(s):  
Tomotaka Saruya ◽  
Shuji Fujita ◽  
Ryo Inoue
Keyword(s):  
Crystal Orientation ◽  
Horizontal Plane ◽  
Ice Core ◽  
Vertical Plane ◽  
Vertical Direction ◽  
Core Sample ◽  
Dielectric Anisotropy ◽  
Principal Axes ◽  
Polycrystalline Ice ◽  
Initial Results

Abstract Polycrystalline ice is known to exhibit macroscopic anisotropy in relative permittivity (ɛ) depending on the crystal orientation fabric (COF). Using a new system designed to measure the tensorial components of ɛ, we investigated the dielectric anisotropy (Δɛ) of a deep ice core sample obtained from Dome Fuji, East Antarctica. This technique permits the continuous nondestructive assessment of the COF in thick ice sections. Measurements of vertical prism sections along the core showed that the Δɛ values in the vertical direction increased with increasing depth, supporting previous findings of c-axis clustering around the vertical direction. Analyses of horizontal disk sections demonstrated that the magnitude of Δɛ in the horizontal plane was 10–15% of that in the vertical plane. In addition, the directions of the principal axes of tensorial ɛ in the horizontal plane corresponded to the long or short axis of the elliptically elongated single-pole maximum COF. The data confirmed that Δɛ in the vertical and horizontal planes adequately indicated the preferred orientations of the c-axes, and that Δɛ can be considered to represent a direct substitute for the normalized COF eigenvalues. This new method could be extremely useful as a means of investigating continuous and depth-dependent variations in COF.

scholarly journals A New Method for the Calculation of Energy and Power Requirements of Bucket Wheel Excavators

2019 ◽  
Vol 10 (1) ◽  
pp. 15-20
Author(s):  
József András ◽  
József Kovács ◽  
Endre András ◽  
Ildikó Kertész ◽  
Ovidiu Bogdan Tomus
Keyword(s):  
Energy Consumption ◽  
Numerical Method ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
New Method ◽  
Energy Requirements ◽  
Belt Conveyor ◽  
Analytical Formulas ◽  
Power And Energy ◽  
Continuous Working

Abstract The bucket wheel excavator (BWE) is a continuous working rock harvesting device which removes the rock by means of buckets armoured with teeth, mounted on the wheel and which transfers rock on a main hauling system (generally a belt conveyor). The wheel rotates in a vertical plane and swings in the horizontal plane and raised / descended in the vertical plane by a boom. In this paper we propose a graphical-numerical method in order to calculate the power and energy requirements of the main harvesting structure (the bucket wheel) of the BWE. This approach - based on virtual models of the main working units of bucket wheel excavators and their working processes - is more convenient than those based on analytical formulas and simplification hypotheses, and leads to improved operation, reduced energy consumption, increased productivity and optimal use of available actuating power.

Many-legged maneuverability: dynamics of turning in hexapods

1999 ◽  
Vol 202 (12) ◽  
pp. 1603-1623 ◽  
Author(s):  
D.L. Jindrich ◽  
R.J. Full
Keyword(s):  
Horizontal Plane ◽  
Center Of Mass ◽  
Vertical Plane ◽  
Force Production ◽  
The Body ◽  
Mean Velocity ◽  
Blaberus Discoidalis ◽  
Body Design ◽  
Reaction Forces ◽  
Straight Ahead

Remarkable similarities in the vertical plane of forward motion exist among diverse legged runners. The effect of differences in posture may be reflected instead in maneuverability occurring in the horizontal plane. The maneuver we selected was turning during rapid running by the cockroach Blaberus discoidalis, a sprawled-postured arthropod. Executing a turn successfully involves at least two requirements. The animal's mean heading (the direction of the mean velocity vector of the center of mass) must be deflected, and the animal's body must rotate to keep the body axis aligned with the heading. We used two-dimensional kinematics to estimate net forces and rotational torques, and a photoelastic technique to estimate single-leg ground-reaction forces during turning. Stride frequencies and duty factors did not differ among legs during turning. The inside legs ended their steps closer to the body than during straight-ahead running, suggesting that they contributed to turning the body. However, the inside legs did not contribute forces or torques to turning the body, but actively pushed against the turn. Legs farther from the center of rotation on the outside of the turn contributed the majority of force and torque impulse which caused the body to turn. The dynamics of turning could not be predicted from kinematic measurements alone. To interpret the single-leg forces observed during turning, we have developed a general model that relates leg force production and leg position to turning performance. The model predicts that all legs could turn the body. Front legs can contribute most effectively to turning by producing forces nearly perpendicular to the heading, whereas middle and hind legs must produce additional force parallel to the heading. The force production necessary to turn required only minor alterations in the force hexapods generate during dynamically stable, straight-ahead locomotion. A consideration of maneuverability in the horizontal plane revealed that a sprawled-postured, hexapodal body design may provide exceptional performance with simplified control.

Latencies of Tee Eye and Herd to Targets in the Vertical and Horizontal Planes

1988 ◽  
Vol 32 (19) ◽  
pp. 1424-1428
Author(s):  
William P. Janson ◽  
Gloria L. Calhoun
Keyword(s):  
Head Movement ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
Small Sample ◽  
Tracking Task ◽  
Manual Tracking ◽  
Verbal Command ◽  
Latency Data ◽  
Oculomotor Responses ◽  
Small Sample Sizes

Past studies involving oculomotor responses have typically been limited to refixations along the horizontal plane, small sample sizes, and little data pertaining to head movement. The study reported herein addresses these data voids by collecting both eye and head latency data for refixations in the horizontal and vertical planes. The subjects' task was to perform a central manual tracking task while periodically responding to a verbal command to classify a target on one of four peripheral monitors. Two targets were displayed along the horizontal plane and two along the vertical plane. Results from 620 trials indicated similar trends for the eye and head latency across all four monitor locations, suggesting no significant differences in eye or head latency as a function of target plane.

scholarly journals Comparison of Maxillary Occlusal Plane with Various Craniofacial Reference Lines in Nepalese and Indian Young Adults

2011 ◽  
Vol 1 (1) ◽  
pp. 16-19
Author(s):  
Binod Acharya
Keyword(s):  
Horizontal Plane ◽  
Vital Role ◽  
Occlusal Plane ◽  
Age Group ◽  
Complete Dentures ◽  
Facial Growth ◽  
Degree Of Separation ◽  
Angular Measurements ◽  
Natural Teeth ◽  
Frankfort Horizontal Plane

Orientation of occlusal plane for complete dentures play a vital role as it affects all the basic requirements of complete dentures. Depending on soft tissue landmarks for orienting occlusal plane seems to be unreliable. Cephalometrics were introduced in Prosthodontics to orient the occlusal plane in the same position as it was with the lost natural teeth. In the present study, 60 lateral cephalometric radiographs of a group of male and female dentulous subjects of Indian and Nepali origin (30 subjects in each group) were obtained and tracings were made. All the subjects selected were in the age group of 20-30 years in whom the facial growth was completed. Angular measurements were made between FH (Frankfort Horizontal plane)- CP (Camper's Plane), FH-OP (Occlusal Plane) and CP-OP and subjected to statistical analysis to determine the degree of separation between these planes in Indian and Nepalese ethnic groups. The absolute parallelism between the natural occlusal plane and Camper's plane were not proven in both Indian and Nepalese subjects involved in this study. This significantly reduces the reference values of these planes in Prosthodontics.

Instrumental expertise and musical timbre modulate the spatial representation of pitch

2020 ◽  
Vol 73 (8) ◽  
pp. 1162-1172 ◽  
Author(s):  
Carlotta Lega ◽  
Zaira Cattaneo ◽  
Noemi Ancona ◽  
Tomaso Vecchi ◽  
Luca Rinaldi
Keyword(s):  
Mental Representation ◽  
Horizontal Plane ◽  
Spatial Representation ◽  
Vertical Plane ◽  
Unified Framework ◽  
Instrumental Training ◽  
Younger Age ◽  
Bottom Side ◽  
The One ◽  
Pitch Space

Humans show a tendency to represent pitch in a spatial format. A classical finding supporting this spatial representation is the Spatial–Musical Association of Response Codes (SMARC) effect, reflecting faster responses to low tones when pressing a left/bottom-side key and to high tones when pressing a right/top-side key. Despite available evidence suggesting that the horizontal and vertical SMARC effect may be differently modulated by instrumental expertise and musical timbre, no study has so far directly explored this hypothesis in a unified framework. Here, we investigated this possibility by comparing the performance of professional pianists, professional clarinettists and non-musicians in an implicit timbre judgement task, in both horizontal and vertical response settings. Results showed that instrumental expertise significantly modulates the SMARC effect: whereas in the vertical plane a comparable SMARC effect was observed in all groups, in the horizontal plane the SMARC effect was significantly modulated by the specific instrumental expertise, with pianists showing a stronger pitch–space association compared to clarinettists and non-musicians. Moreover, the influence of pitch along the horizontal dimension was stronger in those pianists who started the instrumental training at a younger age. Results also showed an influence of musical timbre in driving the horizontal, but not the vertical, SMARC effect, with only piano notes inducing a pitch–space association. Taken together, these findings suggest that sensorimotor experience due to instrumental training and musical timbre affect the mental representation of pitch on the horizontal space, whereas the one on the vertical space would be mainly independent from musical practice.

Two Egyptian Construction Tools

1993 ◽  
Vol 86 (2) ◽  
pp. 166-167
Author(s):  
John F. Lamb
Keyword(s):  
Horizontal Plane ◽  
Vertical Plane ◽  
The Other

Among the objects in the Ramses II exhibition at Fair Park in Dallas in 1989 were two tools from the tomb of Sen-nedjem, one of Ramses II's workmen. One was a level for determining the horizontal plane, the other was a plumb level for determining the vertical plane.

Tempest in a glass tube: A helical vortex formation in a complex plasma

2014 ◽  
Vol 80 (6) ◽  
pp. 869-876 ◽  
Author(s):  
Yoshifumi Saitou ◽  
Osamu Ishihara
Keyword(s):  
Horizontal Plane ◽  
Vortex Formation ◽  
Vertical Plane ◽  
Glass Tube ◽  
Disk Center ◽  
Dust Particles ◽  
Experimental Conditions ◽  
Complex Plasma ◽  
Dust Disk ◽  
Helical Vortex

A collective behavior of dust particles in a complex plasma with a magnetic field (up to 4 kG) is investigated. Dust particles form a dust disk which is rotating in a horizontal plane pushed by ions rotating with the E × B drift as a trigger force. The thickness of the disk is determined by controlling the experimental conditions. The disk rotates in a horizontal plane and forms a two-dimensional thin structure when the pressure pAr is relatively high. The dust particles are ejected from near the disk center and form a rotation in the vertical plane and, hence, forms a helical vortex when the disk is thick for relatively low pAr. The reason the dust disk has the different thickness is due to the neutral pressure. Under a higher (lower) neutral gas pressure, the disk becomes two (three) dimensional due to the influence of the neutral drag force.

Hydraulic Fracture Geometry: Fracture Containment in Layered Formations

1982 ◽  
Vol 22 (03) ◽  
pp. 341-349 ◽  
Author(s):  
H.A.M. van Eekelen
Keyword(s):  
Stress Field ◽  
Cross Section ◽  
Horizontal Plane ◽  
Fluid Pressure ◽  
Vertical Plane ◽  
Fracture Propagation ◽  
In Situ Stress ◽  
Design Procedures ◽  
Fracture Height

Abstract One of the main problems in hydraulic fracturing technology is the prediction of fracture height. In particular, the question of what constitutes a barrier to vertical fracture propagation is crucial to the success of field operations. An analysis of hydraulic fracture containment effects has been performed. The main conclusion is that in most cases the fracture will penetrate into the layers adjoining the pay zone, the depth of penetration being determined by the differences in stiffness and in horizontal in-situ stress between the pay zone and the adjoining layers. For the case of a stiffness contrast, an estimate of the penetration depth is given. Introduction Current design procedures for hydraulic fracturing of oil and gas reservoirs are based predominantly on the fracturing theories of Perkins and Kern, Nordgren, and Geertsma and de Klerk. In the model proposed by Perkins and Kern, and improved by Nordgren, the formation stiffness is concentrated in vertical planes perpendicular to the direction of fracture propagation, The fracture cross section in these planes is assumed elliptical, and the stiffness of the formation in the horizontal plane is neglected. In the model proposed by Geertsma and de Klerk, the stiffness of the formation is concentrated in the horizontal plane. The fracture cross section in the vertical plane is assumed rectangular, and the stiffness in the vertical plane is neglected. In both models, the fluid pressure is assumed a function of the distance from the borehole, independent of the transverse coordinates. The theory by Perkins and Kern is more appropriate for long fractures (L/H >1, where L and H are length and height of the fracture), whereas the model by Geertsma and de Klerk is applicable for short fractures, L/H less than 1. The main shortcoming of these fracture-design procedures is that they assume a constant, preassigned fracture height. H. The value of H has a strong influence on the result, for fracture length, fracture width, and proppant transport. Usually, the estimated fracture height is based on assumed "barrier action" of rock layers above and below the pay zone. This situation is rather unsatisfactory. Moreover, if these layers do not contain the fracture, large volumes of fracturing fluid may be lost in fracturing unproductive strata, and communication with unwanted formations may be opened up. Whether an adjacent formation will act as a fracture barrier may depend on a number of factors: differences in in-situ stress, elastic properties, fracture toughness, ductility, and permeability; and the bonding at the interface. We analyze these factors with respect to their relative influence on fracture containment. Differences in in-situ stress and differences in elastic properties affect the global or overall stress field around the fracture, and, hence, the three-dimensional shape of the fracture. This shape, together with the horizontal and vertical fracture propagation rates, determines the fluid pressure distribution in the fracture, which in turn affects the stress field around the fracture. Consequently, the elastic stress field, the fluid pressure field, and the fracture propagation pattern are intimately coupled, which makes the fracture propagation problem a complicated one. Whether at a certain point of the fracture edge the fracture will propagate is determined by the intensity of the stress concentration at that point. This stress concentration depends on the global stress distribution in and around the fracture, but it also is affected directly by local ductility, permeability, and elastic modulus in the tip region. SPEJ P. 341^

Secondary Surveillance Radar and Airborne Transponder System

1961 ◽  
Vol 65 (606) ◽  
pp. 407-411
Author(s):  
G. G. Roberts
Keyword(s):  
Traffic Control ◽  
Horizontal Plane ◽  
Vertical Plane ◽  
Beam Width ◽  
Vertical Axis ◽  
High Coverage ◽  
Beam Shape ◽  
Height Range ◽  
Cathode Ray Tube ◽  
Position Indicator

The use of primary pulsed radar as a surveillance instrument in Air Traffic Control is familiar to most, and is a direct development of the various ground radars current in the last war. The wavelengths generally employed are 10 cms. for more local control, and 50 cms. for long range and high coverage. The primary radar depends for its information on reflection from the target aircraft of sequences of pulses of electromagnetic energy radiated by the aerial, and displays this information as a “paint” on a P.P.I. (Plan-Position Indicator) cathode ray tube giving range and bearing relative to the radar site. The radar beam is fan-shaped, narrow in the horizontal plane to a few degrees, and wide in the vertical plane to provide adequate vertical cover. The beam is made to scan through the target by a rotation of the aerial about a vertical axis up to a rate of 14 r.p.m. The beam width in the horizontal plane is necessarily kept narrow to provide adequate discrimination between targets at the same range but different bearings. The primary radar is frequently associated with a height-finding radar in which the beam shape is reversed, having a narrow angular cross section in the vertical plane. In this case the aerial is made to nod up and down along an appropriate azimuth selected by the controller, and the height of an aircraft is displayed on a height-range cathode ray tube.

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