Calculate helix
Online calculator and formulas for calculating a helix curve
This calculator is used to calculate the slope, curvature, torsion and arc length of a helix. For the calculation, enter the radius, the height and the number of turns.
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Formulas for a helix curve
A helix is a curve that is created by a combination of rotation and translation along the axis of rotation. It can be seen as a curve which winds around the surface of a cylinder with a constant gradient.
A helix or helical lines play a role in the representation of spiral stairs, threads and twist drills, for example. The development of a helix is a straight line.
The helix becomes a straight line when the cylinder surfave with the helix is developed into a plane.
Slope
The slope is calculated by dividing the height of the turns by the circumference of the cylinder.
\(\displaystyle k=\frac{h}{2·π·r} \)
Curvature
\(\displaystyle κ= \frac{1}{r·(1+k^2)}\)
Torsion
The torsion kappa is the measure how much a wire is twisted when it is formed into a helix.
\(\displaystyle w= \frac{k}{r·(1+k^2)}\)
Arc length
\(\displaystyle s=2·π·r·\sqrt{1+k^2}*t\)
r Radius h Height of a turn t Number of turns k Slope κ Curvature (kappa) w Torsion s Arc length
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