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There’s a case to be made that the sharpest object in the world can’t cut anything. Which seems weird, right? If you’ve ever sliced an apple with a knife or sewn a badge with a needle, sharpness probably seems pretty straightforward. If a tool is sharp…it cuts. Right?
But, like most other things, scientists have tried to pin down a way of measuring sharpness. And the weird thing is, they haven’t found a universal way to do it! There are a lot of ways to define sharpness depending on what thing you’re trying to do. And those things could be important practices, from surgery to scientific research.
And even if no one agrees on exactly how to measure it, our search for better tools has recently led to some of the sharpest objects we’ve ever created. Before we get to the sharpest object in the world, let’s start with the first thing that probably comes to mind when you hear “sharp”: a knife blade. Part of the reason it sticks out as such a vivid example is the distinct shape of a blade. Studying the exact details of that shape, its geometric properties, gives us a starting point for defining sharpness.
The two sides of a blade’s edge are usually straight and flat. And if we zoom in to the very edge, there’s a kind of wedge shape where the two sides meet. Intuitively, the “sharpness” of the wedge seems to come down to two main properties: how pointy it is and how narrow it is. So, scientists have created specific measures of “pointiness” and “narrowness”, to try and define sharpness!
Starting with the former, if we zoom in on the edge of a blade, called the “apex”, the tip of the wedge doesn’t shrink to an infinitely small point. Instead, it ends in a tiny curve. Think of that curve as forming part of a circle. The radius of that circle can tell us how tight the curve is, which ultimately defines how small the edge of a blade is. There’s a word for this, it’s called the edge radius, and it’s the geometric way we describe the “pointiness” of a knife’s edge. A smaller edge radius means a tighter curve, closer to an ideal, perfectly pointy shape.
But edge radius isn’t the whole story of sharpness because even blades with the same radius can be thicker or thinner. So for “edge-radius” to be helpful, we first have to pin down the “narrowness” part as well. That’s defined by what’s called the wedge angle: the angle the between the two flat sides of the wedge. A smaller angle means a thinner wedge, which usually means a sharper blade.
The upshot of all this is that edge radius is only a helpful way of defining sharpness if the wedge angle is small. In practice, that means the things we call “blades” tend to be objects with wedge angles of about 20 degrees or less. If we do have a small wedge angle, then edge radius is a helpful start at determining sharpness.
For instance, certain surgical scalpels have sapphire blades with an edge radius as thin as 25 nanometers, which is only a couple hundred atoms in width! And with a blade that sharp, the scars left behind by sapphire scalpels actually heal faster than steel scalpels thanks to the incredibly precise, clean cuts it leaves in the skin. Plus, being made of hard sapphire and all, the blades are also super durable.
But even these ultra-sharp scalpels aren’t the cutting edge of … cutting edges. That title belongs to blades made of obsidian, a kind of volcanic glass that can be crafted into an edge with an edge radius just 3 nanometers across. That’s just dozens of atoms thick, making it one of the sharpest objects we know of in terms of edge radius. Remarkably, we’ve been using these sharpest tools as a species since the Stone Age! And we still use obsidian blades today for certain kinds of surgery, since their ultra sharpness means they can make cuts without needing to apply much pressure. Obsidian blades are so sharp that they can even cut individual cells in half, and wedge angle and edge radius are two properties used to describe their incredible cutting power. However, these geometric properties have some shortcomings when it comes to defining sharpness, such as needles and pins.
In addition, the size of the edge radius doesn’t always indicate sharpness. For instance, the tungsten nanoneedle has the smallest edge radius ever achieved on a man-made tool, yet it is not able to cut or pierce anything because it is too brittle.
Rather than defining sharpness in terms of geometry, it can be defined in terms of the amount of force needed to cut something. For example, a 2007 study found that the distance between a blade and a material before it initiates a cut reflects the amount of force needed to make a cut. Therefore, the less force needed to press a blade, the sharper it is. Better still, the same researchers found that the familiar geometric properties of blades were correlated with an alternative definition of sharpness. Other studies have found similar results, connecting the wedge angle and edge radius definitions of sharpness to a lower amount of force needed to cut with a given blade, including those stone-age tools. A 2022 study led by an archaeologist at the University of Cambridge found that stone tools with a smaller edge radius needed less mechanical force to cut a PVC pipe.
So for stone tools at least, both the geometric and mechanical definitions of sharpness make sense. But even if we use both definitions, there’s still something missing from our picture of sharp tools. As it turns out, the mechanical force needed to cut a material depends on what that material is! We can’t just focus on the tool itself.
A 2018 study by Italian researchers at the University of Parma demonstrated this using a measure of sharpness that incorporated both the geometry of the tool and the material properties of the thing being cut. In the study, they used both a brittle, polystyrene plastic and a soft, silicone rubber. The sharpness metric behaved as expected in the polystyrene, with narrower tools needing less force to initiate a cut and form a crack in the material. But with the softer rubber, the shape of the blade didn’t matter much. The force needed to make a cut was really similar for the blades that the researchers defined as “sharp” and “blunt” for that material. That’s because unlike a brittle one, softer materials have to be “squished into” a lot more before a cut starts to appear, and that “squishing”, which researchers call “large deformations” follow the broader shape of the tool rather than just the very edge.
So “sharpness” depends on the thing you’re applying sharpness to. And it gets even weirder than that. The mechanical definitions we’ve just talked about broadly assume that only the forces and distances in the process determine cutting sharpness. But that doesn’t always hold true either! The way you cut also determines the apparent sharpness of a blade.
For instance, one 1996 study by researchers at North Carolina State University found that increasing the speed of scissor blades cutting a plastic film reduced the amount of force needed to cut it! They suspected that this was because the film crinkled up and became harder to cut at slower speeds, while at fast speeds the material was smooth and easier to cut for the same blade. Kind of like how cutting wrinkled up saran wrap is a whole lot harder than slicing through a smooth sheet. And a 2007 study by French researchers found that when they used carving knives to cut into a foam that had similar properties to meat, the angle at which the blade cut into the foam affected the amount of force needed to cut into it.
All told, “sharpness” isn’t just about an object’s shape or how easily you can cut into something because the multiple definitions don’t always overlap, and they interact with each other in complicated ways. So how do we define how sharp a tool is? How can we make a video about the sharpest object ever? Ultimately, it depends on the thing you’re trying to cut, and how you’re planning on cutting it. As well as the shape of the tool, you have to consider everything from the speed, angle, and the material of the object. In other words, to make a tool sharp, engineers have to stay pretty sharp, too.
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