We humans like to measure and measurement is the key of science. We tend to understand more about physical non-living things well by measurement we even measure sound, air pressure, frequency of light and nearly everything that nature has to offer. Yet we don't seem to have a measurement for Sharpness of a blade.
Of course blade is a physical object which has a capacity to cut. But again the capacity to cut also depends on many other factor angle at which blade is making contact, the force of cutting, type of material etc. The degree to which it has the capacity is called sharpness of the blade. Sharpness is more of a comparative term than measurement. We can only say which blade is sharp when compared to some other.
There are lots of things that contribute to a blade's sharpness, but no unit for "sharpness" itself. Part of the reason for this is that there are different "kinds" of sharpness, suitable for different purposes.
At its most basic level, a blade is an application of the simple machine known as the wedge. Any wedge's mechanical advantage is its length divided by its width. For knives, this is usually expressed as the grind angle. The lower the angle, the greater the mechanical advantage, so sharpness increases. Razors have angles of around 15 degrees, and are thus sharper than axes, which may have angles of 45 degrees or more.
So why don't we grind all tools with a very low edge angle? Just try chopping down a tree with a straight razor! The thinner the edge (lower edge angle, higher mechanical advantage), the more the blade is prone to deformation and chipping. These two actions account for dullness in most blades. Whether the blade deforms or chips is dependent on the hardness of the blade.
Hardness is usually measured on the Rockwell scale. Harder blades will deform less, and so keep their edge longer. Edge retention is an important measure of the sharpness of a blade, since most people do not want to sharpen their tool before every cut. Stainless steels are generally softer than carbon steels, and so have less edge retention and are more prone to deformation. Blades made from flint, obsidian, and ceramic are very hard, and retain a very sharp edge very well, but are brittle and prone to chipping. A chipped edge may still cut, due to micro serrations, but it will not be as "sharp" as a smooth edge. High carbon steels can also chip and deform, but generally strike a good balance between the two.
But still there is a machine which counts sharpness.
Enjoy reading and be open to the things that world has to offer.
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