KEVOS® MAKEOS · Geometry
Helix (Coil) Developed Length
How long is the wire, tube or strip wound into this helix?
Developed length, helix angle and lead of a helix such as a coil, spring, cooling coil or spiral guard, from its mean diameter, pitch and number of turns.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Mean coil diameter | mm | Diameter to the centre of the wire or tube. |
| Pitch (axial advance per turn) | mm | Axial distance between adjacent turns, centre to centre. |
| Number of turns | turns | Number of complete (or fractional) turns. |
| Straight end allowance (total) | mm | Extra straight length for tails and connections. |
Method and formulas
- Length per turn = √((π D)² + p²).
- Developed length = turns × length per turn + end allowance.
- Helix angle (from a plane normal to the axis) = atan(p ÷ π D); coil height = turns × p.
- Example: 10 turns at 300 mm diameter and 50 mm pitch need 9.438 m.
Limitations
- Uniform helix; transitions at the ends are covered only by the end allowance.
- Bending stretches the outside and compresses the inside; the centre-line length is used.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Estimate tube length for a cooling or heating coil
- Find wire length for a spring or guard
- Find the helix angle of a coil
Who it is for
- Design engineers
- Toolmakers
- Estimators
What you get
- Length per turn
- Developed length
- Helix angle
- Coil height
Interpreting the result
- Add cutting and bending allowances before ordering material.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 2060–2062, 304–320. Topic reference; no source tables or recommended settings are reproduced.
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