How physics can improve the urinal

Restroom visitors can expect cleaner knees and tidier floors, if they happen to use a new urinal inspired by curves in nature.                                                        The key to making a splashless urinal is ensuring that a person’s pee stream hits the porcelain at a shallow angle no matter where it is aimed, researchers report November 22 at the American Physical Society’s Division of Fluid Dynamics meeting in Indianapolis.  “For a small enough angle, there is no splash,” says mechanical engineer Zhao Pan of the University of Waterloo in Canada. Pan calls the angle where splashing ceases “the critical angle.” Keeping the angle that a fluid strikes the surface at the critical angle or lower prevents the splash.                                                            Pan and colleagues’ design — a tall, narrow urinal with a curving inner surface — employs the same geometry as a nautilus shell (SN: 4/1/05). “There’s a smooth flow across the surface,” says Waterloo mechanical engineering student Keesha, prevents droplets from flying out.            In experiments involving dyed fluids sprayed into conventional urinals, the team found significant splash that, in the real world, would have ended up on a person’s legs and feet and on the floor nearby. When the researchers repeated the experiments with prototypes of the new design and inspected the surrounding surfaces, “I couldn’t find even a single droplet,”       It’s unclear whether people using the new urinals will still somehow find a way to make a mess. To tell how well the urinals work in eventual real-world tests, Pan says, just look at the floor.    The tightly packed florets at a daisy’s center have an intriguing arrangement. The florets get larger at greater distances from the center. And there are hints of clockwise and anticlockwise spirals in the pattern.       One way to model such a pattern is to start with a curve called Fermat’s spiral. This curve is also known as a parabolic spiral. It’s given by the polar equation.                                                    The origin, k is a constant that determines how tightly wound the spiral is, an AI the polar angle.                This type of spiral has the property of enclosing equal areas with every turn.    By placing points (disks or polygons) centered at regular angular intervals along such a spiral, you can create a variety of intriguing patterns—depending on the angle you choose to use. Using the angle 222.49 degrees, a value related to the golden ratio, 1.618034. . .  You get a pattern with an even packing of polygons (or disks). It closely resembles a daisy’s florets.   By choosing other angles, you get intriguing variants. Each choice gives a different pattern of secondary spirals, some winding clockwise and others anticlockwise, which form an interlocking system. Robert Dixon explores some of these possibilities in his book Orthographies.                        Using larger numbers of points and smaller angles produces patterns with a variety of secondary spirals and, often, with radial lines that become evident toward the edges. Michael Naylor of Western Washington University has investigated a variety of such patterns (see “Golden Blossoms, Pi Flowers” at Golden Blossoms, Pi Flowers).                                                        By placing points at fixed angular intervals along these curves, he gets very elaborate patterns that show a variety of features.