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33-569: The Tanum Tunnel is 3,590 meters (11,778 ft) long and has a cross section varying between 105 and 115 square meters (1,130 and 1,240 sq ft). The tunnel consists of a 2,718-meter-long (8,917 ft) blasted section and an 800-meter-long (2,600 ft), cut-and-cover section—the latter the easternmost part of the tunnel. It carries the double-tracked Asker Line between Jong and Åstad. The tunnel runs mostly through Cambrian - Silurian sedimentary slate , nodular limestone and shale , with local occurrences of Permian igneous rock. There

66-423: A cardinal or ordinal utility function u ( w , v ) gives the degree of satisfaction of a consumer obtained by consuming quantities w and v of two goods. If a plane section of the utility function is taken at a given height (level of utility), the two-dimensional result is an indifference curve showing various alternative combinations of consumed amounts w and v of the two goods all of which give

99-405: A contour line ; for example, if a plane cuts through mountains of a raised-relief map parallel to the ground, the result is a contour line in two-dimensional space showing points on the surface of the mountains of equal elevation . In technical drawing a cross-section, being a projection of an object onto a plane that intersects it, is a common tool used to depict the internal arrangement of

132-407: A cross section is the non-empty intersection of a solid body in three-dimensional space with a plane , or the analog in higher- dimensional spaces. Cutting an object into slices creates many parallel cross-sections. The boundary of a cross-section in three-dimensional space that is parallel to two of the axes , that is, parallel to the plane determined by these axes, is sometimes referred to as

165-406: A four-dimensional object passed through our three-dimensional space, we would see a three-dimensional cross-section of the four-dimensional object. In particular, a 4-ball (hypersphere) passing through 3-space would appear as a 3-ball that increased to a maximum and then decreased in size during the transition. This dynamic object (from the point of view of 3-space) is a sequence of cross-sections of

198-443: A polyhedron is a polygon . The conic sections – circles , ellipses , parabolas , and hyperbolas – are plane sections of a cone with the cutting planes at various different angles, as seen in the diagram at left. Any cross-section passing through the center of an ellipsoid forms an elliptic region, while the corresponding plane sections are ellipses on its surface. These degenerate to disks and circles, respectively, when

231-436: A probability density function of two random variables in which the cutting plane is at a fixed value of one of the variables is a conditional density function of the other variable (conditional on the fixed value defining the plane section). If instead the plane section is taken for a fixed value of the density, the result is an iso-density contour . For the normal distribution , these contours are ellipses. In economics ,

264-425: A production function f ( x , y ) specifies the output that can be produced by various quantities x and y of inputs, typically labor and physical capital. The production function of a firm or a society can be plotted in three-dimensional space. If a plane section is taken parallel to the xy -plane, the result is an isoquant showing the various combinations of labor and capital usage that would result in

297-425: A 3-dimensional object in two dimensions. It is traditionally crosshatched with the style of crosshatching often indicating the types of materials being used. With computed axial tomography , computers can construct cross-sections from x-ray data. If a plane intersects a solid (a 3-dimensional object), then the region common to the plane and the solid is called a cross-section of the solid. A plane containing

330-423: A cross-section of the solid may be referred to as a cutting plane . The shape of the cross-section of a solid may depend upon the orientation of the cutting plane to the solid. For instance, while all the cross-sections of a ball are disks, the cross-sections of a cube depend on how the cutting plane is related to the cube. If the cutting plane is perpendicular to a line joining the centers of two opposite faces of

363-574: A few. The Asker Line allows regional and intercity trains to by-pass local stations east of Asker while local and freight trains remain on the Drammen Line. The Asker Line was built in two stages: the first, from Asker to Sandvika, was constructed between 2001 and 2005. The second stage, from Sandvika to Lysaker, was constructed between 2007 and 2011. The other two tunnels on the Asker Line are the 3,590-meter-long (11,780 ft) Skaugm Tunnel and

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396-486: A surface in a three-dimensional space is defined by a function of two variables, i.e., z = f ( x , y ) , the plane sections by cutting planes that are parallel to a coordinate plane (a plane determined by two coordinate axes) are called level curves or isolines . More specifically, cutting planes with equations of the form z = k (planes parallel to the xy -plane) produce plane sections that are often called contour lines in application areas. A cross section of

429-408: Is "visible" from the perspective of the viewer. For a convex body , each ray through the object from the viewer's perspective crosses just two surfaces. For such objects, the integral may be taken over the entire surface ( A {\displaystyle A} ) by taking the absolute value of the integrand (so that the "top" and "bottom" of the object do not subtract away, as would be required by

462-422: Is a circle if the cutting plane is perpendicular to the cylinder's axis of symmetry, or an ellipse if it is neither parallel nor perpendicular to that axis. If the cutting plane is parallel to the axis the plane section consists of a pair of parallel line segments unless the cutting plane is tangent to the cylinder, in which case, the plane section is a single line segment. A plane section can be used to visualize

495-474: Is also a 400-meter-long (1,300 ft) section of less stable sedimentary rock in the Asker Group. The tunnel had a cover most of the way of between 50 and 100 meters (160 and 330 ft); however at Billingstad there was a much lower margin, laying for the most at 10 to 15 meters (33 to 49 ft) and at the least at 1.5 meters (4 ft 11 in). At Åstad, the line runs 600 meters (2,000 ft) in

528-404: Is perpendicular to the base it consists of a rectangle (not shown) unless it is just tangent to the cylinder, in which case it is a single line segment . The term cylinder can also mean the lateral surface of a solid cylinder (see cylinder (geometry) ). If a cylinder is used in this sense, the above paragraph would read as follows: A plane section of a right circular cylinder of finite length

561-571: The Divergence Theorem applied to the constant vector field r ^ {\displaystyle \mathbf {\hat {r}} } ) and dividing by two: In analogy with the cross-section of a solid, the cross-section of an n -dimensional body in an n -dimensional space is the non-empty intersection of the body with a hyperplane (an ( n − 1) -dimensional subspace). This concept has sometimes been used to help visualize aspects of higher dimensional spaces. For instance, if

594-448: The partial derivative of a function with respect to one of its arguments, as shown. Suppose z = f ( x , y ) . In taking the partial derivative of f ( x , y ) with respect to x , one can take a plane section of the function f at a fixed value of y to plot the level curve of z solely against x ; then the partial derivative with respect to x is the slope of the resulting two-dimensional graph. A plane section of

627-444: The 4-ball. In geology , the structure of the interior of a planet is often illustrated using a diagram of a cross-section of the planet that passes through the planet's center, as in the cross-section of Earth at right. Cross-sections are often used in anatomy to illustrate the inner structure of an organ, as shown at the left. A cross-section of a tree trunk, as shown at left, reveals growth rings that can be used to find

660-487: The 5.5-kilometer-long (3.4 mi) Bærum Tunnel . The Norwegian National Rail Administration awarded the contract to build the Tanum Tunnel to AF Spesialprosjekt, part of AF Gruppen. The tunneling cost NOK 370 million, including the open section between Solstad and Åstad, but excluding superstructure. The main part of the tunnel was built using the drilling and blasting method, using two points of entry. Work on

693-491: The National Rail Administration appealed the requirements and was permitted to allow up to 32 dBA. In March 2004, a test was done in the tunnel to insure that the requirements would be met, as low-frequency sound is difficult to predict. Measurements after the opening of the tunnel showed background noise of 30 dBA, that no-one was subject to 32 dBA or higher, and that it was nearly impossible to measure

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726-592: The ballast with limestone. By 2011, the emergency lighting system had to be replaced because of the high humidity. The National Rail Administration has stated that savings made to the specifications in the water and frost methods have caused higher maintenance costs because the small leaks which are present do a lot of harm. In addition, areas with leaks suffer from icing. This has been part of a national trend where older tunnels are nearly maintenance-free, while newer tunnels have incurred high maintenance costs. Cross section (geometry) In geometry and science ,

759-420: The cube, the cross-section will be a square, however, if the cutting plane is perpendicular to a diagonal of the cube joining opposite vertices, the cross-section can be either a point, a triangle or a hexagon. A related concept is that of a plane section , which is the curve of intersection of a plane with a surface . Thus, a plane section is the boundary of a cross-section of a solid in a cutting plane. If

792-406: The cutting planes are perpendicular to a symmetry axis. In more generality, the plane sections of a quadric are conic sections. A cross-section of a solid right circular cylinder extending between two bases is a disk if the cross-section is parallel to the cylinder's base, or an elliptic region (see diagram at right) if it is neither parallel nor perpendicular to the base. If the cutting plane

825-412: The following surface integral: where r ^ {\displaystyle \mathbf {\hat {r}} } is the unit vector pointing along the viewing direction toward the viewer, d A {\displaystyle d\mathbf {A} } is a surface element with an outward-pointing normal, and the integral is taken only over the top-most surface, that part of the surface that

858-409: The level of output given by the height of the plane section. Alternatively, if a plane section of the production function is taken at a fixed level of y —that is, parallel to the xz -plane—then the result is a two-dimensional graph showing how much output can be produced at each of various values of usage x of one input combined with the fixed value of the other input y . Also in economics,

891-460: The municipalities of Bærum and Asker. The line was built to allow increased railway traffic though the main corridor west of Oslo . Previously, the only railway west of Oslo was the Drammen Line , which has limited capacity and is used by a mix of local, regional, intercity and freight trains. This caused many delays and poor utilization of tracks, as some trains make many stops and others only

924-567: The open before entering the Skaugum Tunnel . The line is electrified at 15 kV  16.7 Hz AC and allows a maximum speed of 160 kilometres per hour (100 mph). The tunnel has frost insulation 300 meters (980 ft) into the tunnel form each end. The tunnel has frost fans which ensure that the air stays put in the middle of the tunnel, thus hindering cold air from flowing past the frost isolation. The Asker Line runs from Lysaker Station via Sandvika Station to Asker Station, in

957-621: The passing of trains. Among the major concerns was leaks; during the construction on the Romerike Tunnel , there was a one-year delay and severe cost overruns due to improper leak handling methods. Therefore, one of the main focuses in the Skaugum Tunnel project was to avoid similar leaks. The contract specified a maximum leakage of 4 liters (0.88 imp gal; 1.1 U.S. gal) per minute per 100 meters (330 ft). The contractor attempted to achieve this by extending

990-978: The specified level of utility. Cavalieri's principle states that solids with corresponding cross-sections of equal areas have equal volumes. The cross-sectional area ( A ′ {\displaystyle A'} ) of an object when viewed from a particular angle is the total area of the orthographic projection of the object from that angle. For example, a cylinder of height h and radius r has A ′ = π r 2 {\displaystyle A'=\pi r^{2}} when viewed along its central axis, and A ′ = 2 r h {\displaystyle A'=2rh} when viewed from an orthogonal direction. A sphere of radius r has A ′ = π r 2 {\displaystyle A'=\pi r^{2}} when viewed from any angle. More generically, A ′ {\displaystyle A'} can be calculated by evaluating

1023-412: The time used for pre-injection of concrete. However, there was still water dripping into the tunnel, which caused several types of damage. Some places the water dripped onto the track, causing rust; other places water dripped onto electrical equipment. There was also issues with water running down the walls and collecting in the cable conduit , and the water with limestone dripping on the ballast and mixing

Tanum Tunnel - Misplaced Pages Continue

1056-478: The tunneling started in 2002 and was concluded in February 2004. Construction included the removal of 486,000 cubic meters (17,200,000 cu ft) of earthwork and the laying of 160,000 tonnes (160,000 long tons; 180,000 short tons) of ballast . Laying of tracks, signaling, power supply and other superstructures were done by Baneservice . The cost of superstructures for the entire section from Asker to Sandvika

1089-419: Was NOK 70 million. The work was completed by November 2004. The opening of the tunnel and the rest of the section from Asker to Sandvika took place on 27 August 2005. A concern from people living along the tunnel was that they would be subject to low-frequency noise . Originally the municipalities of Asker and Bærum had demanded that residents be subject to a maximum of 27 decibel A-weighting (dBA), but

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