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Length of a Spiral

Calculate the length of a spiral or the length of material contained in a roll.

spiral length

The length of a spiral can be calculated as

L = 3.14 n (D + d) / 2                  (1)


L = length of spiral (m, ft ...)

n = number of rings

D = spiral outside diameter (m, ft ...)

d = spiral inside diameter or opening (m, ft ...)

The equation can be used to calculate the length of a material of uniform thickness. Typical examples may be belts, garden hoses or ropes in a roll.

Spiral Length Calculator

Example - Water Solar Heater

A solar heater is made like a coil with 20 mm pipe inside a 1 m x 1 m window frame. The coil is done like a doughnut with an outer radius of 0.5 m and an inner radius of 0.1 m due to the bending limits of the pipe. If the coil is made with no space between the pipes the number of turns can be calculated as   

n = ((0.5 m) - (0.1 m)) / (0.02 m)

  = 20

The length of the water pipe in the solar heater can be calculated as

L = 3.14 (20) ((1 m) + (0.2 m)) / 2 

  = 37.7 m

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