Rotating furnace

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Axially symmetrical paraboloid. The inside surface is concave Paraboloid of Revolution.svg
Axially symmetrical paraboloid. The inside surface is concave

A rotating furnace is a device for making solid objects which have concave surfaces that are segments of axially symmetrical paraboloids. Usually, the objects are made of glass. The furnace makes use of the fact, which was known already to Newton, that the centrifugal-force-induced shape of the top surface of a spinning liquid is a concave paraboloid, identical to the shape of a reflecting telescope's primary focusing mirror.

Contents

Paraboloids can be used in various ways, including (after being silvered) as primary mirrors in reflecting telescopes and solar cookers. [1]

Design

Parabolic shape formed by a liquid surface under rotation. Two liquids of different densities completely fill a narrow space between two sheets of plexiglass. The gap between the sheets is closed at the bottom, sides and top. The whole assembly is rotating around a vertical axis passing through the center. Parabola shape in rotating layers of fluid.jpg
Parabolic shape formed by a liquid surface under rotation. Two liquids of different densities completely fill a narrow space between two sheets of plexiglass. The gap between the sheets is closed at the bottom, sides and top. The whole assembly is rotating around a vertical axis passing through the center.

The furnace includes a mechanism that rotates an open-topped container at constant speed around a vertical axis. A quantity of glass sufficient to make the mirror is placed in the container, heated until it is completely molten, and then allowed to cool while continuing to rotate until it has completely solidified. When the glass is solid, the rotation is stopped and the paraboloidal shape of its top surface is preserved. [2] [3] This process is called spin casting.

The same process can be used to make a lens with a concave paraboloidal surface. The other surface is shaped by the container that holds the molten glass acting as a mold. Lenses made this way are sometimes used as objectives in refracting telescopes.

The axis of rotation becomes the axis of the paraboloid. It is not necessary for this axis to be in the center of the container of glass, or even for it to pass through the container. By placing the container away from the axis, off-axis paraboloidal segments can be cast. This is done in the making of very large telescopes which have mirrors consisting of several segments.

Mathematical model

Rotation speed and focal length

The focal length of the paraboloid is related to the angular speed at which the liquid is rotated by the equation: , where is the focal length, is the rotation speed, and is the acceleration due to gravity. On the Earth's surface, is about 9.81 metres per second-squared, so meters per second-squared. [3] Equivalently, as 1 radian per second is about 9.55 rotations per minute (RPM), , where is the focal length in metres, and is the rotation speed in RPM.

Uses

Generally, a spin-cast paraboloid is not sufficiently accurate to permit its immediate use as a telescope mirror or lens, so it is corrected by computer-controlled grinding machines. The amount of grinding done, and the mass of glass material wasted, are much less than would have been required without spinning.

Spin casting can also be used, often with materials other than glass, to produce prototype paraboloids, such as spotlight reflectors or solar-energy concentrators, which do not need to be as exactly paraboloidal as telescope mirrors. Spin casting every paraboloid that is made would be too slow and costly, so the prototype is simply copied relatively quickly and cheaply and with adequate accuracy.

Liquid-mirror telescopes have rotating mirrors that consist of a liquid metal such as mercury or a low-melting alloy of gallium. These mirrors do not solidify and they are used while liquid and rotating. The rotation shapes them into paraboloids that are accurate enough to be used as primary reflectors in telescopes. Compared with spin-cast glass mirrors which need correction due to the distortions that arise during and after solidification, these mirrors require no such correction.

See also

Related Research Articles

Isaac Newton's rotating bucket argument was designed to demonstrate that true rotational motion cannot be defined as the relative rotation of the body with respect to the immediately surrounding bodies. It is one of five arguments from the "properties, causes, and effects" of "true motion and rest" that support his contention that, in general, true motion and rest cannot be defined as special instances of motion or rest relative to other bodies, but instead can be defined only by reference to absolute space. Alternatively, these experiments provide an operational definition of what is meant by "absolute rotation", and do not pretend to address the question of "rotation relative to what?" General relativity dispenses with absolute space and with physics whose cause is external to the system, with the concept of geodesics of spacetime.

<span class="mw-page-title-main">Coriolis force</span> Force on objects moving within a reference frame that rotates with respect to an inertial frame

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<span class="mw-page-title-main">Lens</span> Optical device which transmits and refracts light

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<span class="mw-page-title-main">Paraboloid</span> Quadric surface with one axis of symmetry and no center of symmetry

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<span class="mw-page-title-main">Vortex</span> Fluid flow revolving around an axis of rotation

In fluid dynamics, a vortex is a region in a fluid in which the flow revolves around an axis line, which may be straight or curved. Vortices form in stirred fluids, and may be observed in smoke rings, whirlpools in the wake of a boat, and the winds surrounding a tropical cyclone, tornado or dust devil.

<span class="mw-page-title-main">Parabolic reflector</span> Reflector that has the shape of a paraboloid

A parabolicreflector is a reflective surface used to collect or project energy such as light, sound, or radio waves. Its shape is part of a circular paraboloid, that is, the surface generated by a parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave travelling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis.

<span class="mw-page-title-main">Spherical aberration</span> Optical aberration

In optics, spherical aberration (SA) is a type of aberration found in optical systems that have elements with spherical surfaces. Lenses and curved mirrors are prime examples, because this shape is easier to manufacture. Light rays that strike a spherical surface off-centre are refracted or reflected more or less than those that strike close to the centre. This deviation reduces the quality of images produced by optical systems. The effect of spherical aberration was first identified by Ibn al-Haytham who discussed it in his work Kitāb al-Manāẓir.

<span class="mw-page-title-main">Reflecting telescope</span> Telescopes which utilize curved mirrors to form an image

A reflecting telescope is a telescope that uses a single or a combination of curved mirrors that reflect light and form an image. The reflecting telescope was invented in the 17th century by Isaac Newton as an alternative to the refracting telescope which, at that time, was a design that suffered from severe chromatic aberration. Although reflecting telescopes produce other types of optical aberrations, it is a design that allows for very large diameter objectives. Almost all of the major telescopes used in astronomy research are reflectors. Many variant forms are in use and some employ extra optical elements to improve image quality or place the image in a mechanically advantageous position. Since reflecting telescopes use mirrors, the design is sometimes referred to as a catoptric telescope.

<span class="mw-page-title-main">Newtonian telescope</span> Type of reflecting telescope

The Newtonian telescope, also called the Newtonian reflector or just a Newtonian, is a type of reflecting telescope invented by the English scientist Sir Isaac Newton, using a concave primary mirror and a flat diagonal secondary mirror. Newton's first reflecting telescope was completed in 1668 and is the earliest known functional reflecting telescope. The Newtonian telescope's simple design has made it very popular with amateur telescope makers.

<span class="mw-page-title-main">Euler's Disk</span> Scientific educational toy

Euler's Disk, invented between 1987 and 1990 by Joseph Bendik, is a trademark for a scientific educational toy. It is used to illustrate and study the dynamic system of a spinning and rolling disk on a flat or curved surface. It has been the subject of several scientific papers.

<span class="mw-page-title-main">Solar cooker</span> Device for cooking with the heat of sunlight

A solar cooker is a device which uses the energy of direct sunlight to heat, cook or pasteurize drink and other food materials. Many solar cookers currently in use are relatively inexpensive, low-tech devices, although some are as powerful or as expensive as traditional stoves, and advanced, large scale solar cookers can cook for hundreds of people. Because they use no fuel and cost nothing to operate, many nonprofit organizations are promoting their use worldwide in order to help reduce fuel costs and air pollution, and to help slow down deforestation and desertification.

<span class="mw-page-title-main">Aspheric lens</span> Type of lens

An aspheric lens or asphere is a lens whose surface profiles are not portions of a sphere or cylinder. In photography, a lens assembly that includes an aspheric element is often called an aspherical lens.

<span class="mw-page-title-main">Liquid-mirror telescope</span>

Liquid-mirror telescopes are telescopes with mirrors made with a reflective liquid. The most common liquid used is mercury, but other liquids will work as well. The liquid and its container are rotated at a constant speed around a vertical axis, which causes the surface of the liquid to assume a paraboloidal shape. This parabolic reflector can serve as the primary mirror of a reflecting telescope. The rotating liquid assumes the same surface shape regardless of the container's shape; to reduce the amount of liquid metal needed, and thus weight, a rotating mercury mirror uses a container that is as close to the necessary parabolic shape as feasible. Liquid mirrors can be a low-cost alternative to conventional large telescopes. Compared to a solid glass mirror that must be cast, ground, and polished, a rotating liquid-metal mirror is much less expensive to manufacture.

The Pfund telescope, originated by A.H. Pfund, provides an alternative method for achieving a fixed telescope focal point in space regardless of where the telescope line of sight is pointed.

<span class="mw-page-title-main">Curved mirror</span> Mirror with a curved reflecting surface

A curved mirror is a mirror with a curved reflecting surface. The surface may be either convex or concave. Most curved mirrors have surfaces that are shaped like part of a sphere, but other shapes are sometimes used in optical devices. The most common non-spherical type are parabolic reflectors, found in optical devices such as reflecting telescopes that need to image distant objects, since spherical mirror systems, like spherical lenses, suffer from spherical aberration. Distorting mirrors are used for entertainment. They have convex and concave regions that produce deliberately distorted images. They also provide highly magnified or highly diminished (smaller) images when the object is placed at certain distances.

A liquid-mirror space telescope is a concept for a reflecting space telescope that uses a reflecting liquid such as mercury as its primary reflector.

<span class="mw-page-title-main">Free surface</span> Surface of a fluid that is subject to zero parallel shear stress

In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere. Unlike liquids, gases cannot form a free surface on their own. Fluidized/liquified solids, including slurries, granular materials, and powders may form a free surface.

The spinning drop method or rotating drop method is one of the methods used to measure interfacial tension. Measurements are carried out in a rotating horizontal tube which contains a dense fluid. A drop of a less dense liquid or a gas bubble is placed inside the fluid. Since the rotation of the horizontal tube creates a centrifugal force towards the tube walls, the liquid drop will start to deform into an elongated shape; this elongation stops when the interfacial tension and centrifugal forces are balanced. The surface tension between the two liquids can then be derived from the shape of the drop at this equilibrium point. A device used for such measurements is called a “spinning drop tensiometer”.

<span class="mw-page-title-main">Centrifugal casting (industrial)</span> Casting technique that is typically used to cast thin-walled cylinders

Centrifugal casting or rotocasting is a casting technique that is typically used to cast thin-walled cylinders. It is typically used to cast materials such as metals, glass, and concrete. A high quality is attainable by control of metallurgy and crystal structure. Unlike most other casting techniques, centrifugal casting is chiefly used to manufacture rotationally symmetric stock materials in standard sizes for further machining, rather than shaped parts tailored to a particular end-use.

Spin casting is a technique for constructing large parabolic mirrors by using the curved surface formed by a rotating liquid. It is distinct from the spin casting or centrifugal rubber mold casting (CRMC) technique used for casting metal or plastics.

References

  1. "Using Spinning Liquids to Simplify the Construction of parabolic Solar Concentrators".
  2. Dierickx, P. (2000). "Optical fabrication in the large". European Southern Observatory Conference and Workshop Proceedings. 57: 224. Bibcode:2000ESOC...57..224D.
  3. 1 2 Ninomiyaa, Yuichi (1979). "Parabolic mirror made by the rotation method: its fabrication and defects". Applied Optics. 18 (11): 1835–1841. Bibcode:1979ApOpt..18.1835N. doi:10.1364/AO.18.001835. PMID   20212558. S2CID   122277262.