The Illusion of Smooth Surfaces: Decoding the Intricacies of Surface Roughness

 In essence, we as human beings are symbolically inclined. We often streamline and idealize various aspects of reality to interpret them more straightforwardly within our abstract cognitive realm. This process initiates from a young age, pairing tangible and concrete objects with ideal geometric shapes that don't naturally occur. For instance, we might liken a billiard ball to an ideal sphere, among countless other examples. Although it may seem that there's a precise correlation between the actual object (the billiard ball) and its idealized depiction (the sphere), this isn't the case.

No object on Earth, or likely in the entire cosmos, possesses the attributes to perfectly emulate a sphere. Indeed, every object deviates to some extent from flawless sphericity. Currently, the most spherical object known to exist in the universe resides on Earth, a silicon ball valued at over two million dollars. These silicon balls are part of the International Avogadro project, a research initiative aiming to assist metrology scientists in redefining the kilogram - the fundamental unit of mass in the International System of Measurements. Despite the unmatched precision in creating these metal spheres, they still fall short of being termed ideal spheres.

The surface roughness

Returning to the example of the billiard ball, we said that this-as well as the most spherical object of which we have knowledge-is not perfectly assimilable to an ideal sphere. This deviation from perfect sphericity has basically two origins: the first is the actual geometric deviation from the shape of the sphere, for example, when the ball has a shape of a slightly flattened sphere; while the second-which is what we will focus on in the article-is the surface deviation from a perfectly smooth surface. All objects we experience, even those produced to the highest standards of accuracy, have an irregular surface full of peaks and valleys.

To stay on the case of round objects-but clearly the concept can be extended to any other shape-you can imagine the surface of the billiard ball somewhat like that of the Earth: full of mountains and ocean floors. So you have realized that no object is really smooth, not even when its surface seems to us to be polished to a mirror finish. This deviation of the real surface from the ideal one is very important in the technical field, so much so that quantifying and controlling its extent is crucial for many applications.

From a formal point of view, the deviation from a perfectly smooth surface is called surface roughness and can be quantified by a number of different parameters, including the average roughness Ra which is one of the most common. The Ra parameter basically gives an indication of what the average deviation of the actual surface is from the ideally smooth surface. Therefore, the lower this parameter is, the smoother the surface is.

To give you a more concrete idea about the typical surface roughness values achievable with the most common industrial processes, know that typically the average roughness can range from 25 micrometers - thousandths of a millimeter - down to even below a micrometer in the case of very controlled processes. To give you a term of comparison, a human hair has a diameter of about 75 micrometers.

The practical consequences of surface roughness

As mentioned earlier, surface roughness is a very important parameter in engineering. For example, a pipe with a particularly high surface roughness requires more powerful pumps to transport water. In aerodynamics, on the other hand, surface roughness affects the aerodynamic forces experienced by a body moving through the air. In this regard, golf balls are intentionally manufactured with a higher surface roughness so as to reduce the braking action of air during flight.

Moving into the more mechanical realm, surface roughness becomes particularly important in determining the fatigue life of components subjected to intense vibration: the higher the surface roughness value, the lower the fatigue strength of an object. This is because the presence of irregularities acts as a "catalyst" for crack nucleation, which then grow over time to cause component failure.

Staying with the mechanical theme, wear on moving components is facilitated by higher values of surface roughness, as well as the coefficient of friction. As a result, mechanisms characterized by high surface roughness will exhibit higher energy losses and will therefore be less efficient, as well as spoil quickly. This was only meant to be a short list - certainly not exhaustive - of the concrete effects that surface roughness of objects can cause, but we hope it will serve to give you an idea of the complexity behind every smallest aspect of the world around us.