Tapered spiral welded structure
A method for creating a tapered spiral welded conical structure where the overall shape of the cone is first graphically slit axially and unwrapped, and then a series of construction arcs and lines are created to form the edge lines of a strip that can then be wrapped (rolled) to form a tapered conical structure. The edges of the spirally wound strip can be welded together, and a very large conical structure can thus be achieved. Various construction options are presented from a constant width strip to strip made from straight segments. Equations are given for the formation of the strips to enable those skilled in the art of spiral welded tubing to practice the invention.
1. A method comprising:
obtaining a plurality of planar sheets, wherein:
each one of the plurality of planar sheets has a first edge and a second edge;
the plurality of planar sheets are collectively dimensioned such that, in a particular planar configuration, the first edges of the plurality of planar sheets collectively comprise a first curve that is not a single straight line and the second edges of the plurality of planar sheets collectively comprise a second curve; and
there exists a rotation about an axis such that the first curve coincides with the second curve when rotated by the rotation; and
at least one point along the first curve has a different minimum distance to the second curve than at least one other point along the first curve; and
spiral-welding the plurality of planar sheets sequentially so that at least one first edge of one of the plurality of planar sheets contacts a second edge of another one of the plurality of planar sheets to form a frusto-conical structure.
2. The method of claim 1 , wherein spiral-welding the sheets is performed at a use site of the frusto-conical structure.
3. The method of claim 1 , in which spiral welding the plurality of sheets to form the frusto-conical structure does not introduce in-plane deformation to any of the sheets.
4. The method of claim 1 wherein the second curve is a rotated copy of the first curve.
5. The method of claim 1 wherein the rotation includes a rotation about a vertex of a flat wedge-shaped segment formed by splitting and unwrapping the shape of the frusto-conical structure.
6. The method of claim 5 further comprising forming the first curve as a construction curve in one or more adjacent instances of the flat wedge-shaped segment.
7. The method of claim 6 further comprising forming the second curve as a copy of the first curve rotated about the vertex.
8. The method of claim 1 wherein the plurality of sheets form the frusto-conical structure in a single wrap.
9. The method of claim 1 wherein the plurality of sheets form the frusto-conical structure in a plurality of wraps.
10. The method of claim 1 wherein the plurality of sheets have equal width.
11. The method of claim 1 wherein the plurality of sheets are formed from straight strips of metal stock.
12. A method comprising:
obtaining a collection of planar sheet means for assembly into a frusto-conical structure; and
assembling the sheet means into the frusto-conical structure, without introducing in-plane deformation to any of the planar sheet means, the sheet means including a plurality of sheets such that:
each sheet has a first edge and a second edge;
the plurality of sheets are collectively dimensioned such that, in a particular planar configuration, the first edges of the plurality of sheets collectively comprise a first curve and the second edges of the plurality of sheets collectively comprise a second curve; and
there exists a rotation about an axis such that the first curve coincides with the second curve when rotated by the rotation.