About: Focus-Balanced Paraboloidal Reflector

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Clock mechanisms don't produce much torque, so preferably the dish should have its centre of gravity (or centre of mass) located on the polar axis so it can be easily turned. To make the centre of gravity remain on the polar axis as the dish is tilted about the perpendicular one, the perpendicular axis should also pass through the centre of gravity. The two axes should intersect at the centre of gravity of the dish.

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rdfs:label	Focus-Balanced Paraboloidal Reflector
rdfs:comment	Clock mechanisms don't produce much torque, so preferably the dish should have its centre of gravity (or centre of mass) located on the polar axis so it can be easily turned. To make the centre of gravity remain on the polar axis as the dish is tilted about the perpendicular one, the perpendicular axis should also pass through the centre of gravity. The two axes should intersect at the centre of gravity of the dish.
dcterms:subject	Solar cooker designs Solar calculations Parabolic solar cooker designs
dbkwik:solarcookin...iPageUsesTemplate	dbkwik:resource/fNTiBPcj8fe2KcC8wF_ung== dbkwik:resource/oHtQwMp34zyeWUyPt0neVw==
abstract	Clock mechanisms don't produce much torque, so preferably the dish should have its centre of gravity (or centre of mass) located on the polar axis so it can be easily turned. To make the centre of gravity remain on the polar axis as the dish is tilted about the perpendicular one, the perpendicular axis should also pass through the centre of gravity. The two axes should intersect at the centre of gravity of the dish. The two preceding paragraphs imply that the centre of gravity of the dish and its focus should be the same point. The dimensions of the dish must be such that its centre of gravity coincides with its focus. Assuming that the dish is made of material of uniform thickness, i.e. mass density, I calculated its required dimensions. (See below.) Using F to denote the focal length of the paraboloid, it turns out that the depth of the dish, measured along the axis of the paraboloid from the vertex to the plane of the rim, which is perpendicular to the axis, is 1.8478 times F. The radius of the rim of the dish is 2.7187 F. (The closeness of this number to the value of "e", the base of natural logarithms, is just an accidental coincidence, but it does make a useful mnemonic.) The angular radius of the rim as seen from the focal point is 72.68 degrees. A simple solar cooker would have such a dish, rotated by a clock about a polar axis. A second axis, perpendicular to both the polar one and the axis of the paraboloid, would be provided to allow the dish to be turned to follow the sun's seasonal movements. Both of the rotation axes would pass through the focal point of the dish. A stationary arm, attached to some support external to the dish, would reach into the dish to its focus, and would hold the cooking pot at its end, at the focal point. Ideally, this arm would coincide with the axis of symmetry of the paraboloid when it is pointing at the sun at noon on an equinox. The dish would be able to turn 72.68 degrees before the edge of the dish collides with the fixed arm. At 15 degrees per hour, this would take nearly five hours. The cooker would therefore be able to be used from about 7:15 a.m. to 4:45 p.m. without moving the arm. In tropical latitudes, this corresponds to more or less the whole part of the day when the sun is high enough above the horizon for solar cooking to be practicable. At times of year other than the equinoxes, there would be little difference to the period when the cooker can be used.

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