# With a machete, why is a diagonal cut more effective than a right angle one?

When cutting back some thick growth in the garden a question that always nagged me. Why is cutting diagonally seemingly more effective than cutting at right angles? Part of the answer is obviously to do with the ease of cutting vertically as opposed to horizontally (with vertical stems), but this also seems to be true at most other growth angles as well.

• I can't tell you off hand, but this might also have to do with the fact that if you cut at a right angle, then some of your energy is going into moving the bushes, rather than cutting them. Since they can't move downward, putting downward energy ito the bushes causes them to be cut more directly. – Jerry Schirmer Jul 10 '15 at 20:08
• I would assume that when cutting at an angle, the stems will transmit more of the force from the machete into the ground, and the stem will act more rigid than a right-angle cut, where the stem can bend, and absorb more force before being cut. – CoilKid Jul 10 '15 at 20:10
• Looks like I just restated Jerry's comment :P Such things happen when you both say something at the same time, I guess. – CoilKid Jul 10 '15 at 20:11
• Maybe the internal structure of what you are cutting plays a role as well? – Bernhard Jul 10 '15 at 20:12
• I think less to do with internal structure, since I have also cut multiple materials with a katana - and that is also usually a diagonal cut – user56903 Jul 10 '15 at 20:26

The flexural rigidity of a vertical beam will be greater with a diagonal cut. This allows more of the force to be channeled into cutting the target as opposed to bending the target.

The determinants of flexural rigidity affected by a diagonal as opposed to a horizontal cut are the cross section of the beam and distance from the supported end of the beam. The elasticity of the material is measured by Young's modulus, but that's not at issue here as it applies to the material itself, not to its positioning or structure.

A diagonal cut effectively increases the beam's cross section, which increases rigidity.

A diagonal cut transmits more force into the ground (as Jerry Shirmer and CoilKid noted in their comments), which effectively shortens the distance to the supported end of the beam.

For a beam in tension or compression (as one would expect of a vertical beam), the axial stiffness is:

k = A * E / L

where:

A is cross section area,

E is Young's modulus or the modulus of elasticity (Bending stiffness is also a function of the modulus of elasticity, cross section, and length: https://en.wikipedia.org/wiki/Bending_stiffness),

L is length (effectively length to the ground).

The diagonal cut effectively increases A and decreases L, resulting in greater k and more force put into cutting, less into deforming the target.

• I'm pretty sure you'd want the shear modulus to describe the transverse flexing of the beam. Or do I misunderstand? – dmckee Jul 11 '15 at 1:37
• @dmckee: It depends on the angle of the diagonal cut. I see your point: if the diagonal angle to the surface were small, shear stress might come into play. Shear modulus applies when a force is parallel to one face, while the opposite face is supported by an opposing force (like cutting with dull scissors). Young's modulus applies to compression of the beam rather than to bending or to shear deformation. My thought is that a diagonal cut would tend to compress the target, whereas a horizontal cut would tend to deflect it. But you're right, the diagonal cut may tend to shear the target. – Ernie Jul 11 '15 at 7:44
• Isn't there something to do with depth of cut versus length of blade being engaged in cutting? Parabolic versus circular section... – user56903 Jul 11 '15 at 10:01
• @Dirk Bruere: The diagonal section of a cylinder is an ellipse, and presents a deeper cross section in the direction of the cut (major axis). But its minor axis equals the diameter of a circular cut, so the blade length need only be at least the diameter of a circular cross section. BUT a longer blade provides greater leverage to make the cut easier (particularly if you snap down your wrist in the direction of the cut). So you're right, it's important to gauge the length of the blade to the angle of the cut (longer major axis, longer blade) and the toughness of the material you are cutting. – Ernie Jul 11 '15 at 14:06