Troposkein
Encyclopedia
In physics
and geometry
, the troposkein is the curve an idealized rope
assumes when anchored at its ends and spun around its long axis at a constant angular velocity
. This shape is similar to the shape assumed by a skipping rope, and is independent of rotational speed in the absence of gravity, but varies with respect to rotational speed in the presence of gravity. The troposkein does not have a closed-form
representation; in the absence of gravity, though, it can be approximated by a pair of line segments spanned by a circular arc (tangential to the line segments at its endpoints). The form of a troposkein can be approximated for a given gravational acceleration, rope density and angular velocity by iterative approximation
. This shape is also useful for decreasing the stress experienced by the blades of a Darrieus
vertical axis wind turbine
.
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
and geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, the troposkein is the curve an idealized rope
Rope
A rope is a length of fibres, twisted or braided together to improve strength for pulling and connecting. It has tensile strength but is too flexible to provide compressive strength...
assumes when anchored at its ends and spun around its long axis at a constant angular velocity
Angular velocity
In physics, the angular velocity is a vector quantity which specifies the angular speed of an object and the axis about which the object is rotating. The SI unit of angular velocity is radians per second, although it may be measured in other units such as degrees per second, revolutions per...
. This shape is similar to the shape assumed by a skipping rope, and is independent of rotational speed in the absence of gravity, but varies with respect to rotational speed in the presence of gravity. The troposkein does not have a closed-form
Closed form
-Maths:* Closed-form expression, a finitary expression* Closed differential form, a differential form \alpha with the property that d\alpha = 0-Poetry:* In poetry analysis, a type of poetry that exhibits regular structure, such as meter or a rhyming pattern;...
representation; in the absence of gravity, though, it can be approximated by a pair of line segments spanned by a circular arc (tangential to the line segments at its endpoints). The form of a troposkein can be approximated for a given gravational acceleration, rope density and angular velocity by iterative approximation
Iterated function
In mathematics, an iterated function is a function which is composed with itself, possibly ad infinitum, in a process called iteration. In this process, starting from some initial value, the result of applying a given function is fed again in the function as input, and this process is repeated...
. This shape is also useful for decreasing the stress experienced by the blades of a Darrieus
Darrieus wind turbine
The Darrieus wind turbine is a type of vertical axis wind turbine used to generate electricity from the energy carried in the wind. The turbine consists of a number of aerofoils usually—but not always—vertically mounted on a rotating shaft or framework...
vertical axis wind turbine
Vertical axis wind turbine
Vertical-axis wind turbines are a type of wind turbine where the main rotor shaft is set vertically and the main components are located at the base of the turbine...
.