Helix is a type of curve in three-dimensional space formed by a straight line drawn on a plane. The curve can become a straight line if the surface were unrolled into a plane, with the distance to the apex is an exponential function of the angle indicating direction from the axis. Helix is also called as 'Helices', 'helixes'.

π = 3.1415926 r = Radius h = Height required for Helix to complete one revolution

For example, consider that an antenna is constructed in XF7 using the helix script. It will expand along the Z-axis and will have a radius of 50 cm. In addition, height of the helix curve is 2 cm and the angle made by the curve is 360.Calculate the circumference, length, handrail radius of the curve.

Radius = 50, Height = 2, Angle = 360

Circumference Height (h) Length Unit Rise Handrail Radius

Let us calculate the circumference, length, handrail radius of the helix curve.

Let us first calculate the value of circumference.

Circumference | = 2πr |

= (2 x 3.1415926 x 50) | |

= 314.15926 |

Calculate the value of height by substituting the values in the formula,

h | = (height of helix x 360) / angle |

= (2 x 360) / 360 | |

= 2 |

Calculate the length of helix by substituting the values in the formula,

Length | = √h2 + circumference2 |

= √22 + 314.159262 | |

= √4 + 98696.04064 | |

= 314.1656 |

Find the value of Unit Rise.

Unit Rise | = h / circumference |

= 2 / 314.15926 | |

= 0.00637 |

Finally, let us calculate the handrail radius of the helix curve,

Handrail Radius | = (4π^{2}r^{2} + h^{2}) / 4π^{2}r |

= ((4 x 3.1415926^{2} x 50^{2}) + 2^{2}) / (4 x 3.1415926^{2} x 50)) | |

= (98696.040643748 + 4) / 1973.920812875) | |

= 50.00203 |