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Geodesy
Published in Basudeb Bhatta, Global Navigation Satellite Systems, 2021
Conical projections result from projecting a spherical surface onto a cone (Figure 9.10). A cone may be imagined to touch the globe of a convenient size along any circle (other than the great circle), but the most useful case is the normal one in which the apex of the cone lies vertically above the pole on the earth’s axis produced and the surface of the cone is tangent to the sphere along some parallel of latitude. It is called ‘standard parallel’. The meridians are projected onto the conical surface, meeting at the apex of the cone. Parallel lines of latitude are projected onto the cone as rings. The cone is then ‘cut’ along any meridian to produce the final conic projection which has straight converging lines for meridians, and concentric circular arcs for parallels. The meridian opposite the cut line becomes the central meridian.
Theoretical background for pressure moulding of concrete tunnel lining
Published in Ya. I. Marennyi, R.B. Zeidler, Tunnels with In-Situ Pressed Concrete Lining, 2020
The reduced pressure p′ at any point of the generating line OD of the conical surface reads p′=(q+H)(1−sinφg)sin(Δ+δ)sinδ(rODr0D−E)2Btanφg××(D−r0rODE)−2Atanφgexp[(π−ωOD)2tanφg]
Design and Mounting of Small Mirrors
Published in Paul Yoder, Daniel Vukobratovich, Opto-Mechanical Systems Design, 2017
A concept for mounting a single-arch mirror to a hub with a spherical clamp interfacing with a conical interface in the mirror is shown in Figure 9.59. The clamp constrains the mirror in all six degrees of freedom near its CG and at its thickest and strongest section with a large area contact. This reduces stresses that could disturb the optical surface. A flat surface is provided on the back of the mirror; the axis of the cone is perpendicular to that flat surface and the apex of the cone coincides with it. A metal insert with an external conical surface and a concave spherical inner surface fits into the substrate’s conical surface. The hub has a convex spherical surface forming a bearing in conjunction with the insert. This spherical bearing ensures contact of the conical surfaces. Slight slippage can occur between the conical surfaces, but expansion/contraction of the mount will not alter coincidence of the cone apex with the plane of the mirror’s back.
Physical features’ characterization of the water-in-mineral oil macro emulsion stabilized by a nonionic surfactant
Published in Journal of Dispersion Science and Technology, 2022
Cone and plate geometry is the fixation of a conical vertex perpendicular to a flat plate. The cone is in point contact with the flat plate and determination of viscosity is made possible by rotation of the cone at a constant speed and measurement of the torque over the conical surface. The mathematical relationships for this specific type of viscometer are as follows:[24] where T is the % full-scale torque (dyne-cm), r is the cone radius (cm), is the cone speed (rad/s), is the cone angle (degrees), is shear stress (dyne/cm2), is the shear rate (1/s), and is viscosity (cp or mPa s).
Influence of attached inertia and resonator on the free wave propagation in 2D square frame grid lattice metamaterial
Published in Waves in Random and Complex Media, 2021
Gandharv Mahajan, Avisek Mukherjee, Arnab Banerjee
Dirac cone takes the shape of the upper and lower halves of a conical surface, meeting at Dirac point. Dirac cone occurs at all variants of the square lattice abundantly, at point O (). The formation of dirac cone at any point other than O is purely accidental. From all the variants of the square lattice the dirac cone has been observed at the A and B points of the IBZ traverse. An example of the dirac cone has been shown for SqMT in Figure 19. In Dirac-like point, the attenuation band gap becomes diminutive known as a deaf band, as presented in Figure 7(b). The dirac cone observed in SqMT is fragmented into several points and corresponding mode shapes have been plotted to show the wave idiosyncrasy before (points 1–4) and after (points 7–9) the dirac point. Points 5 and 6 shows the dirac point which falls at the edge of deaf band. The variation of the band-structure near the Dirac-point is similar to that of the veering because the bands are similarly approaching and then veer away from the Dirac point; however, instead of only two bands in case of veering, numerous bands participate in the formation of the Dirac-cone. Moreover, the transition of mode-shape of multiple bands are analogous to that of veering phenomena as shown in Figure 19. Interestingly the mode-shape of point 5 and 6 are mutually orthogonal which indicates the orthogonal wave transportation phenomena as elucidate in Ref. [36].
Tangential developable and hydrodynamic surfaces for early stage of ship shape design
Published in Ships and Offshore Structures, 2023
A surface is called a developable surface if it can be developed on a plane without any lap fold or break. During this parabolic bending, the length of the curves and the angles between two curves belonging to the developable surface remain unchanged. Any developable surface is a cylindrical surface, or a conical surface, or else a surface of tangent lines of arbitrary space curve (torse). They are ruled surfaces with only parabolic points in which K = k1k2 = 0. So, an equality of Gaussian curvature K to zero is the sufficient and necessary condition for a developable surface.