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Volume Measurement
Published in Joanne Kirkpatrick Price, Basic Math Concepts, 2018
Calculations of the cone and sphere volume do not use the general volume equation since there is no “representative surface area.” Both of these volume calculations, however, are based on the volume of a cylinder. The cone volume is one-third the volume of a cylinder and the sphere volume is two-thirds the volume of a special cylinder, as described in this section.
Constituent Materials
Published in B. T. Åström, Manufacturing of Polymer Composites, 2018
The reinforcements tried include SiC, carbon, and metal wires. Since CMCs are likely to contain microcracks, the oxidation problem of carbon reinforcement at temperatures above 400°C must be considered. Some CMCs perform well up to 1,000°C. There are currently very few commercial applications of CMCs and they must still be considered as being in the early stages of development. Potential applications include rocket nose cones and engine parts.
Color fundamentals for digital imaging
Published in Sharma Gaurav, Digital Color Imaging Handbook, 2017
The cones are responsible for color vision. Observers with normal color vision† have three different types of cones, with photosensitive pigments that differ in their spectral absorption characteristics and, consequently, in their spectral sensitivities. The three types of cones are commonly called S, M, and L cones, which are abbreviated forms of short, medium, and long wavelength sensitive cones, respectively.‡ Under a fixed set of viewing conditions, the response of these cones can be accurately modeled by a linear system defined by the spectral sensitivities of the cones. If the spectral distribution of light incident on the retina is given by f(λ), where λ represents wavelength (we are ignoring any spatial variations in the light for the time being), the responses of the three cones can be modeled as a three vector with components given by
Manufacturability evaluation of parts using descriptor-based machining feature recognition
Published in International Journal of Computer Integrated Manufacturing, 2021
Changmo Yeo, Sanguk Cheon, Duhwan Mun
This study introduces the concept of base face of machining feature. The base face is regarded as the basis for identifying a feature, even if the topology and geometry constituting an individual feature partially change. In other words, among the many faces that make the feature, the base face most represents the feature characteristic. Table 2 defines the base faces of the defined features. The base face varies, depending on whether two or more different rotational shapes are combined for creating holes. The base face of a simple hole or taper hole consisting of a single rotational shape is a cylindrical face or a conical face, respectively, of the hole feature. A cylinder (cone) can be represented by one cylindrical (conical) face, or two half-cylindrical (half-conical) faces. In this study, it is assumed that a cylinder (cone) consists of two half-cylindrical (half-conical) faces. The base face of a countersink hole or a counterdrilled hole is a conical face as the base face. The base face of a counterbore hole is the planar face between two cylindrical faces. For slots, the base face is a bottom or side face, depending on whether the bottom surface exists. For pockets and islands, the base face is the bottom face of the pocket. For fillets and chamfers, the base face is a cylindrical face or planar face.
Simultaneous distribution and sizing optimization for stiffeners with an improved genetic algorithm with two-level approximation
Published in Engineering Optimization, 2019
Shenyan Chen, Tianshan Dong, Xiaofang Shui
In this example, a conical shell stiffened by longitudinal (stringer) and circumferential (ring) stiffeners is optimized. A cylindrical coordinate is used when constructing the cone model in MSC Patran, and the length unit of the model is metres. As shown in Figure 14, the radii of the cone at the small end and at the base are 0.8128 m and 1.7526 m, respectively, and the cone apex angle is 20 degrees. Thirty stringers and 30 rings are equally distributed on the ground structure. A 1000 kg non-structural mass is set above the cone and connected to the small end of the cone using multi-point constraints. In practical engineering applications, the mass point can be replaced by a satellite or other payloads. The material of the shells, stringers and rings is magnesium, with a Young’s modulus of 4.06 GPa, density of 1827.9 kg/m3 and Poisson’s ratio of 0.33. The cone thickness is 5.08 mm, and all of the stringers and rings have the same cross-sectional dimensions, 12.7 mm in width and 12.7 mm in height. The initial structural weight is 300.55 kg. The first two order frequencies of the initial structure are both 16.941 Hz along the radial and lateral direction, and the constraint defined in Formula (21) is that the first two orders of natural frequencies should not be lower than 15 Hz.
An alternative way of defining integration in multivariable calculus
Published in International Journal of Mathematical Education in Science and Technology, 2022
Fix r>0. Suppose that we want to find the volume of the region E bounded by the cylinder , the cone and the plane . The desired volume can be obtained by subtracting the volume of the cone from the volume of the cylinder.