How to Calculate Helical Length

How to Calculate Helical Length
••• hroe/iStock/Getty Images

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.

    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 = \text{ Radius} \\ H = \text{ Rise of helix in one revolution} \\ N = \text{ Number of turns}

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

    L = \sqrt{H^2 + C^2}

    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 \text{ 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 = \sqrt{2^2 + 6.29^2} = \sqrt{4 + 39.6} = 6.60 \text{ meters}

    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 \text{ meters}

Related Articles

How to Calculate the Length of Wire to Make a Coil
How to Calculate Wheel Speed
How to Calculate the Henrys in a Coil
How to Find the Length of the Sides of an Octagon Based...
How to Calculate Volume of a Circular Cylinder
How to Calculate Conveyor Belt Speed
How to Calculate Electrical Winding Wires by Weight...
How to Calculate the Radius of a Pipe
How to Calculate a Spiral
How to Calculate Mechanical Advantage Screws
How to Calculate the Obtuse Triangle
How to Find the Circumference of an Octagon
How to Calculate the Chord of a Circle
How to Calculate the Volume and Circumference of a...
How to Calculate the Square Meters in a Triangle
How to Calculate the Perimeter of Combined Shapes and...
How to Calculate Tire Turns Per Mile
What Are the Rungs on the DNA Double Helix Made Of?
How to Calculate Toroidal Transformers
How to Calculate the Outside Length of a Circle

Dont Go!

We Have More Great Sciencing Articles!