Who can tell me more about Geotangent domes?
norm...@gmail.com
norm...@gmail.com
One of the disadvantages associated with such previously known structures is that the geodesic alignment of the structural elements creates fold lines about which the entire structure can collapse when subjected to sufficiently severe stresses. Regularity in the structural design is advantageous from the point of view of enabling the use of a small number of different modules, i.e., different sizes and shapes of component elements, for the composition of the structure, but this structural regularity can be disadvantageous, from the point of view of overall strength of the structure, if the regularity produces structural weaknesses such as fold lines along great circles of the sphere which the structure approximates.
norm...@gmail.com
norm...@gmail.com
TaffGoch
norm...@gmail.com
What are geotangent domes?
[Keyed in by Patrick G. Salsbury.]The following is quoted from ``Scientific American'' in the September 1989 issue. (Pages 102-104)
Surpassing the Buck(Geometry decrees a new dome)``I started with the universe--as an organization of energy systems of which all our experiences and possible experiences are only local instances. I could have ended up with a pair of flying slippers.'' -R. Buckminster Fuller
Buckminster Fuller never did design a pair of flying slippers. Yet he became famous for an invention that seemed almost magical: the geodesic dome, an assemblage of triangular trusses that grows stronger as it grows larger. Some dispute that Fuller originated the geodesic dome; in Science a la Mode, physicist and author Tony Rothman argues that the Carl Zeiss Optical Company built and patented the first geodesic dome in Germany during the 1920's. Nevertheless, in the wake of Fuller's 1954 patent, thousands of domes sprung up as homes and civic centers--even as caps on oil-storage tanks. Moreover, in a spirit that Fuller would have heartily applauded, hundreds of inventors have tinkered with dome designs, looking for improved versions. Now one has found a way to design a completely different sort of dome.
In May, J. Craig Yacoe, a retired engineer, won patent number 4,825,602 for a ``geotangent dome,'' made up of pentagons and hexagons, that promises to be more versatile that its geodesic predecessor. Since Fuller's dome is based on a sphere, cutting it anywhere but precisely along its equator means that the triangles at the bottom will tilt inward or outward. In contrast, Yacoe's dome, which has a circular base, follows the curve of an ellipsoid. Builders can consequently pick the dimensions they need, Yacoe Says. And his design ensures that the polygons at the base of his dome always meet the ground at right angles, making it easier to build than a geodesic dome. He hopes these features will prove a winning combination.
Although Fuller predicted that a million domes would be built by the mid-1980's, the number is closer to 50,000. Domes are nonetheless still going up in surprising places. A 265-foot-wide geodesic dome is part of a new pavilion at Walt Disney World's Epcot Center in Florida. A bright blue 360-foot-high dome houses a shopping center in downtown Ankara, Turkey. Stockholm, Sweden, boasts a 280-foot-high dome enclosing a new civic center.
Dome design is governed by some basic principles. A sphere can be covered with precisely 20 equilateral triangles; for a geodesic dome, those triangles are carved into smaller ones of different sizes. But to cover a sphere or ellipsoid with various sizes of pentagons and hexagons required another technique, Yacoe says.
Yacoe eventually realized that he could build a dome of polygonal panels guided by the principle that one point on each side of every panel had to be tangent to (or touch) an imaginary circumscribed dome. With the assistance of William E. Davis, a retired mathematician, he set out to describe the problem mathematically.
They began with a ring of at least six congruent pentagons wrapped around the equator of an imaginary ellipse. The task: find the lengths of the sides and the interior angles of the polygons that form the next ring.
To do so for an ellipsoidal dome, they imagined inscribing an ellipse inside each polygon. Each ellipse touched another at one point; at these points, the sides of the polygons would also be tangent to a circumscribed ellipsoid. But where, precisely, should the points be located? Yacoe and Davis guessed, then plugged the numbers into equations that describe ellipses and intersecting planes. Aided by a personal computer, they methodically tested many guesses until the equations balanced. Using the tangent points, Yacoe and Davis could then calculate the dimensions and interior angles of the corresponding polygons and so build the next ring of the dome.
After receiving the patent, Yacoe promptly set up a consulting firm to license his patents. He says dome-home builders have shown considerable interest, as has Spitz, Inc., a maker of planetariums located near Yacoe in Chadds Ford, Pa. Yacoe has also proposed that the National Aeronautics and Space Administration consider a geotangent structure as part of a space station. -E.C.