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Conical spiral with an archimedean spiral as floor projection Floor projection: Fermat's spiral Floor projection: logarithmic spiral Floor projection: hyperbolic spiral. In mathematics, a conical spiral, also known as a conical helix, [1] is a space curve on a right circular cone, whose floor projection is a plane spiral.
For <, spiral-ring pattern; =, regular spiral; >, loose spiral. R is the distance of spiral starting point (0, R) to the center. R is the distance of spiral starting point (0, R) to the center. The calculated x and y have to be rotated backward by ( − θ {\displaystyle -\theta } ) for plotting.
In mathematics, a conchospiral a specific type of space spiral on the surface of a cone (a conical spiral), whose floor projection is a logarithmic spiral. Conchospirals are used in biology for modelling snail shells, and flight paths of insects [1] [2] and in electrical engineering for the construction of antennas. [3] [4]
Two well-known spiral space curves are conical spirals and spherical spirals, defined below. Another instance of space spirals is the toroidal spiral. [8] A spiral wound around a helix, [9] also known as double-twisted helix, [10] represents objects such as coiled coil filaments.
A conic helix, also known as a conic spiral, may be defined as a spiral on a conic surface, with the distance to the apex an exponential function of the angle indicating direction from the axis. A curve is called a general helix or cylindrical helix [4] if its tangent makes a constant angle with a fixed line in space.
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A spiral antenna is a type of radio frequency antenna shaped as a spiral, [1]: 14‑2 first described in 1956. [2] Archimedean spiral antennas are the most popular, while logarithmic spiral antennas are independent of frequency: [3] the driving point impedance, radiation pattern and polarization of such antennas remain unchanged over a large bandwidth. [4]
The relatively recently developed conical screw compressor is a type of rotary-screw compressor using a different topology from the typical dual-screw type. In effect it can be thought of as a conical spiral extension of a gerotor , although the exact geometry is somewhat different due to the angular offset.