How To Calculate Helical Length

A helix is defined as a spiral that also has a linear dependence upon a third dimension. Found both within nature and within the man-made world, examples of helices include springs, coils and spiral staircases. The length of a helix can be calculated using a simple formula.

Step 1

Write down the quantities that define the helix. A helix can be defined by three quantities: the radius, the rise of the helix in one revolution and the number of turns. For this example, we will define the following symbols:

r= Radius
H= Rise of helix in one revolution
N= Number of turns

Step 2

Calculate the length associated with one turn within the helix. To do this use the following formula:

L=H2+C2

In this nomenclature, H^2 means "H multiplied by H" or "H squared." C is the circumference of the circle and is equal to :

C=2×3.145×R

For example, if a spiral staircase has a radius of 1 meter, then the circumference is equal to :

C=2×3.145×1=6.29 meters

If the staircase rises by approximately 2 meters after each turn (H = 2) then the length associated with one turn around the staircase is:

L=22+6.292=4+39.6=6.60 meters

Step 3

Calculate the total helical length (T). To do this use the formula:

T=NL

Following the example, if the staircase has 10 turns:

T=10×6.60=66 meters

Cite This Article

MLA

Markings, Samuel. "How To Calculate Helical Length" sciencing.com, https://www.sciencing.com/calculate-helical-length-7808380/. 26 October 2020.

APA

Markings, Samuel. (2020, October 26). How To Calculate Helical Length. sciencing.com. Retrieved from https://www.sciencing.com/calculate-helical-length-7808380/

Chicago

Markings, Samuel. How To Calculate Helical Length last modified March 24, 2022. https://www.sciencing.com/calculate-helical-length-7808380/

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