Category Archives: Edges

Path & Presentation: Understanding The Cutting Stroke

Note: This work is a living document and will continue to see updates as we have the opportunity to write them.

In cutting tools today the most common topics stem around steels, heat treatment, and (in folding knives) locking mechanisms. If you’re lucky, you might see some discussion around cross-sectional geometry and its impact on cutting performance. However, one aspect of edged tool design that seems to almost never be discussed is the impact of the profile of the tool on its optimum stroke pattern, or even how strokes themselves behave. This is a fundamental and profoundly important aspect of edged tool design, and culturing a deep understanding of it can greatly assist in matching the correct tools to their best functional contexts.

Any stroke of a rigid object consists of two variables: the path and the presentation. In the following diagrams, the path is shown as a red line, and for clarity’s sake the heel of the blade is bound to it, riding along it as if affixed to a track.


Presentation is the orientation of the blade relative to the path. A green line is used to represent the path traced by the toe of the blade and the depth of the swath made by the total stroke, though the red line is considered the dominant path of the two. In this case there is no path (just a single point at the heel) and the presentation of the blade is being altered by pivoting it at that point.KnifePresentation

Here the two actions are combined. The heel rides the path while the presentation shifts through rotation relative to the path.KnifeRotationAlongStraightPath

You can see how an object presented as a target to the blade would only be cut by this motion if it existed in the space between the first and second frames of the animation, after which the spine begins to precede the edge, and the edge is pulled away from the target instead of moving into it. This brings us to the subject of edge engagement and stroke optimization.

To begin, let’s demonstrate using this straight-edged knife cutting a target against a flat anvil surface. As before, the red line represents the path of the stroke, while the green line described by the toe helps visualize how the presentation of the blade is affecting the depth of the swath (the area the edge actively passes through during the stroke.) The act of cutting consists of a combination of pushing and sliding forces, in varied degrees. Here we see an isolation of sliding force, without any pushing.

A fully neutral slice. The edge glides along the target medium without any downward force to give depth to the cut.

As you can see, no green line is visible because the edge is running perfectly on top of the path itself, and as a result, there is no depth to the swath. In order for the knife to cut the target, the path and presentation need to be altered to add depth to the swath and place the target within its boundaries.  However, the edge can be considered as fully engaged because its full length is sliding along the surface of the target, albeit with no penetration at all. This unusual situation will become important later as we delve into more complicated aspects of cutting strokes, and will be referred to as a “neutral slice” from this point onward.

Shifting from a neutral slice, let’s switch to the opposite extreme by rotating the path 90°. This happens to switch this blade to what is, from here on out, referred to as a “fully open” presentation, in that the depth of the swath cannot be increased any further. Rotating the blade in either direction would result in the depth of the swath narrowing, but would cause either the toe of the blade or the heel of the blade to be leading the stroke depending on the direction of rotation. Regardless of the shape of the edge itself, the fully open presentation will always create a swath as deep as the straight-line distance between the heel and the most distal point of the edge.

A fully pushing cut. The blade passes fully through the material, but only a small region of the edge is engaged in the cut.

The problem here is that only a small part of the blade is doing all of the work, which–in addition to causing more wear on one region of the blade in repeated cuts–is less efficient than spreading out the work over more edge length. As an edge is effectively a slope, this is much like how climbers tackle otherwise unscalable inclines by zig-zagging up them. It stretches elevation over a longer distance, effectively making it like climbing a longer ramp to the same elevation. So let’s see what happens by altering the presentation of the blade to narrow the swath, bringing more edge to bear on the target.

An angled push cut. More edge length is used in the cut, but the presentation means that the target must be in open space for the cut to be performed, like hanging off the edge of a table.

This angled pushing cut is the same principle employed by the infamous guillotine, spreading the cutting force required over a longer length of edge than possible in a perpendicular cut. However, it obviously produces a notable limitation: you need to have empty space for the tool to pass into. This cut works fine if a target were hanging off the edge of a table, but if cutting in the middle of a broad, flat surface like a cutting board, you cannot force the handle through the board. A different approach would have to be used.

Let’s try “opening” the presentation of the blade relative to the path and trying a pure slice again.

A fully engaged lateral slice. A change in the presentation of the blade and the run of the path allow the whole edge to be put to work. However, the hand has little clearance of the anvil surface and the anvil surface itself is not being used to best advantage.

Now we’re getting somewhere. We’re now able to engage the full length of the edge in the stroke. However, you may notice that there’s now little room for the hand, and if the edge didn’t sit so far forward of the handle we would have to lift the heel of the blade instead of the toe and make a drawing cut to provide this effect. Additionally, the anvil surface is no longer opposing the direction of force, and so isn’t lending a helping hand in immobilizing the target as we cut into it. Let’s try a combination of slicing and pushing forces instead.

A fully engaged cut that combines slicing and pushing actions to give the hand good clearance and support of the target from the anvil surface.

The edge is now fully engaged with good clearance for the hand and the anvil surface is opposing the applied force from the cut, helping to immobilize the target as we cut into it. Chances are that this resembles the action of how you already use a knife in the kitchen, because it’s what you’ve found to provide the best results. Now you know why!

[To Be Continued]

Why convex edges are awesome–it’s not why you think!

If there’s one thing that everyone likes, it seems to be convex edges. Users often state how impressed they are with their performance. However, the oft-touted belief is that a convex edge has more material supporting the blade, and thus has better edge retention than a conventional “V” edge. This makes sense at a cursory glance because the shortest distance between two points is a straight line, and so a convex would mean there was more material and a concave would have less, right? 

Sort of. A convex edge traversing those two points (the apex of the bevel and where the bevel transitions into the primary grind or blade stock) would have more material supporting the edge…but would also have a broader effective edge angle meaning it would have to displace more material during the cut and at a more rapid pace. This is really the dynamic of the old broad vs. thin edge angle tradeoff, and you can’t add material back onto the blade anyway so the only way to increase the supporting material is by diminishing the blade height through sharpening so we push the red lines back into the thicker region of the blade. You can see that that would start removing a lot of blade pretty quick, and at the cost of cutting performance as well. What we really need to be looking at is a “V” edge being converted to a convex of equal effective edge angle. What you get is something like this:

So you can see that what you’re really getting is a reduction of the transitional shoulder, giving you a thinner geometry but maintaining the same edge angle and without significantly reducing the material supporting the edge where it typically needs it most. This makes for a smoother cut (increasing controllability due to the more gradual shift in geometry) but also reduces the amount of material that must be displaced by the blade as it passes through the cutting medium. This means that your cuts require less energy, yet the edge is still almost as well-supported as a conventional “V” edge.

Given the actual realistic benefit provided by a convex edge, this is why I tell folks to not worry too much about maintaining a perfect convex edge when out in the field. If you’re a perfectionist you can always restore it to “true” when you get back to the house. Besides–freehand sharpening results in slight variation in angle from stroke to stroke so you end up with a very slight convex form anyhow. 

Most tests in which folks have been impressed with the edge-holding abilities of convex edges have been batoning their knife through a bunch of wood and then still been able to shave their arm at the end. Impressive, right? Well once the edge goes in the edge rarely actually touches the wood! The parts of the bevel either side of the edge and the bevel of the primary grind take the brunt of the action since the wood splits ahead of the edge itself. The convex edge doesn’t significantly play a role in this effect other than perhaps allowing the split to start a little easier. Cross-grain batoning would be another matter, but little comparative testing has been done between two otherwise identical knives of equal edge angle with “V” and convex edges to provide substantive evidence for any sort of improvement in edge retention. If there is one it’s simply that for equal amounts of force applied to each blade the thinner convex one will be able to cut deeper, and thus cut more material for equal energy expenditure, but the actual sharpness of the edge (or the thickness of the apex on the terminal “edge” bevel) will be affected about the same since it has the same edge angle and degree of wear resistance.