CN Cycloid Conduits

CN cycloid conduits are the core geometry of FR2716123, the Ravatin fluid-activation patent. The conduits through which fluid is circulated are shaped as a CN curve, where N ≥ 2, defined by a recursive relation:

• C1 is a left-handed cycloid in the orthonormal reference frame;
• for any integer N ≥ 1, CN+1 is a left-handed cycloid in the curved reference frame bound to CN.

A left cycloid is the curve followed by a point on a ray of a circle as the circle rolls on a straight line and simultaneously turns about that line. The cycloid is "stringent" when the point lies on the circle, "lengthened" when the point's distance from the centre exceeds the radius, and "shortened" when it is less. The preferred embodiment uses elongated left cycloids.

Claimed maximum: C3

The source states that activation is maximum for C3 conduits — an elongated left cycloid C3 rolled around an elongated left cycloid C2 itself rolled around the starting elongated left cycloid C1. The claimed physical rationale is that each element of fluid at a point P3 of C3 "behaves as if it were at the same time in P1, P2 and P3," where P1 and P2 lie at distances from the respective origins O1 and O2 of C1 and C2 equal to the distance separating O3 from P3 — even though C1 and C2 "do not exist materially in the installation."

Not a strict fractal

The source is explicit that this is not a strict fractal construction. The laying out of C2 involves a slight modification of the form of C1, and likewise at each recursion, so "there is not thus a stringent construction like that which one applique in the theory of the said objects fractals but it is to some extent a generalization of the concept of fractal object. One is presented with a new class of objects." The source nevertheless retains the denomination "cycloid" for C1, C2, C3 and so on.

Conduit details

• Circulation conduits have a hexagonal transverse section, or the section of a third-degree curve with inflection points.
• To stabilize the activation, conduits are made of copper alloyed with ~2% by weight of heavier metals — atomic number Z between 38 and 45, or rare earths; indium and molybdenum are named.
• Compressed-gas supply conduits are also formed as C3 curves, since the compressed gas is itself activated and then activates the fluid more strongly; this is stated not to be an absolute requirement.

See FR2716123 — Device for Activating Fluids & Solids and Fluid Activation (Ravatin).