Helix

Called the helix (plural helices or helices ), and screw, helix, spiral or cylindrical spiral is a curve that winds with a constant slope to the surface of a cylinder. The naming of the winding ( helicity ) follows the right- fist rule, the helix is right-handed if it winds up (as seen in the direction in which they are located away from the viewer ), otherwise left-handed clockwise. In botany are left writhing called because they viewed from above grow counterclockwise turning up as a right-handed helix growing plants.

• 2.1 Helical structures
• 2.2 screw and wedge action 2.2.1 Seilerei

Mathematical Description

The vectorial description of a helix in Cartesian coordinates is

• Here, the number of windings of the traversed
• Here, the pitch, so that distance by which the screw in a full revolution to the top (in the direction of the cylinder axis, the z-direction ) overcomes the radius of the screw, and the displacement in the z direction.
• Is the pitch of the helix: the helix is ​​a straight line with a slope, if the unwinding of the helix in a cylinder surface with the layer.
• This is called the transition angle of the helix.

Pitch and thread angle are two basic applications of the helix in the technical parameters, such as for the standardization of threads.

• For left-handed helices h is negative.
• The arc length of the helix is calculated to
• Constant, the curvature of the radius of curvature ( the curvature of the second term is related to the defect in wound cylinder ), and the winding
• The torsion refers to the measure of how strongly a wire is twisted in itself, if one overcomes a helix it.

The helix is a chiral curve, because she and her reflection can not be accommodated by rotating and shifting to cover (for example, right and left- hand thread).

Multi-start screws

Putting two congruent helixes by a half pitch displaced together (), there is a two-start screw. The same result is obtained if it is mixed, the second helix about a half turn. The two helices have constant distance and never touch each other, so the resulting curve is divided into two branches. Analog formation with several helices produces correspondingly more hand helices. These definitions play an important role in the art.

Helix and Spiral

In the central projection of a helix in the direction of the axis on a flat surface produces a hyperbolic spiral. This is also the view of a screw along the axis ( see picture examples below, Helix and spiral and spiral staircase), because the eye follows this projection type (perspective ).

Examples of helical forms in nature and technology

Two reasons come helices in nature and technology often before:

• The space savings through the " wind-up " of the straight line on a cylinder
• The analog to the screw wedge effect

Helical structures

Chemistry: The molecular helix in (M ) - ( -)- heptahelicene has helicity in the counterclockwise direction.

Spiral staircase in the Vatican Museum in Rome as an example of a two-start helical structure for comparison. The symmetry of the corresponding (P) - heptahelicene.

The screw rotation of this climbing plant corresponds to the direction of rotation of (M ) - heptahelicene.

The best known biopolymer is spirally constructed, the DNA is also referred to as a double- helix due to the two umeinanderlaufenden complementary DNA single strands. Furthermore, sections of many proteins, especially those that are integrated into biomembranes ( integral proteins ) composed of helically. This type of structure of the secondary structure is referred to as α - helix. Also from about 6 per turn α -D - glucose units constructed polysaccharide amylose, the amylopectin is contained in addition to strength, the form of a helix.

In chemistry there are hydrocarbons - the helicenes - with schraubenartigem construction, which are chiral.

In art, a spiral is an often cantilevered helical wire member ( incandescent filament, a helical antenna, wire wound resistor, coil heater ). Another typical helix, the helical spring, which houses the spring forces of a spring on the long small space. The spiral staircase takes advantage of the space savings, because the outer dimension of the conquered height is independent. The same applies to the helical ramps around in underground garages and parking garages. The wire of a light bulb is a double helix, ie a helix to a more helical runs ( rack configuration examples). Other examples are the outer edge of the auricle or the peptide chains of collagen.

Screw and wedge action

The wedge effect due to the fact that the pitch angle of a movement along the long cathetus in a normal movement along the short cathetus "translated ". Due to the lever principle, the resulting normal force is then the ratio of the short sides is greater than the force used. The smaller the angle of slope ( the shallower, the wedge ), the stronger the effect.

This applies to the analogous helix. Therefore, a relatively small torque to the center axis (small tangential force ) can be converted into a large force along the axis. On this principle, the thread of a screw with nut based, like that of the Archimedean screw and the screw conveyor. The operation of the propeller or the threaded spindle in mechanical engineering is based on conversion of rotation into forward / feed. The adjusting screw uses Conversely, the reduction of the path, which makes a fine setting possible. Also corkscrew with and without " soul " are helical.

The flutes of drills are arranged helically around the drill casing. Colloquially, the drills are mistakenly called twist drill.

Seilerei

Another application is the rope factory. While the breaking load for a single thread or a parallel fiber bundle is only dependent on the cross-section, and therefore rise sharply thickness and heaviness, with a rope, the individual fibers or strands are twisted ( "beaten" ). Under load, the tensile force converts to a normal to the fiber force - because the pitch of the helices is close to 90 ° and the wedge effect is reversed - is significantly lower. In addition, it is transmitted as a compressive stress to the neighboring fibers and / or soul. Here, the forces between the individual fibers or strands pick up, the soul becomes extremely compressed (hence for elastic materials are used) and absorbs the energy.

Image examples

Helix, slightly perspective

Helix ( green) and hyperbolic spiral ( black)

A screw along a screw, double helix

Two -Hand Screw and model of the DNA double helix

Helix structure in the facade of the Art Tower Mito

Toroidal continuous helix

Coil spring

Right-handed helix of the Real bindweed, incline about 60 °

Left-handed helix of Commons Schmerwurz

Right-handed twist drill; From left to right: 8- mm drill bit for wood, metal and concrete, as well as a center drill