## Forces at play during "Cutting"?

I'm involved in a debate over the broadheads (arrowheads using multiple razor-sharp metal blades) for bow hunters. I need a little help in the physics dept.

I'm arguing that the sharpness of a blade is less important than than the fact that there IS a cutting surface (of some kind) AND, more importantly, the force exerted by the cutting surface against whatever is being cut- in this case bone, flesh, etc.

The argument arose because a new company is claiming that their arrowheads using a relatively dull flexible wire will cut as effectively as the traditional 3 and 4-bladed broadheads. The designer of these new heads claims that physics says even a dull edge, given sufficient force and velocity will cut as well as, if not better than, a sharp blade. Is there any truth to this? Is there a specific law that would explain this claim?

Nick
Austin, TX

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 Recognitions: Gold Member There are a couple of different aspects to this. Bear in mind that I'm neither a physicist nor an expert in archery. The wires (and I'd like to know just how they're set up) sound like a reasonable idea, as long as they're not too flexible or too wide. If you've ever seen a whip or broken support cable in action, you know that they can be very dangerous and indeed will cut things. A lot will depend upon the bow itself, of course, as well as the target. A wimply little beginner's unit might not give enough speed to go into something like a grizzly with a thick hide. Sharpness there would be an advantage. On the other hand, a honkin' huge compound could probably fire a chunk of 1/2" dowel through a small deer. One reason that bow hunters have to be more precise than rifle hunters is that you need almost surgically accurate placement of the arrow to effect a humane kill. There's no (okay, very little) hydrostatic shock, whereas that's one of the major effects of a bullet. Likewise for secondary projectiles. I'd be happier with a compromise myself. I always keep my fighting knives the way my uncle told me to... the way he did his bayonette in WWII. The tip is razor-sharp top and bottom for about an inch, then dull and a bit notched. It'll go in very easily, but the rough bit causes a lot of damage while it's in there and when it's coming back out. I think that an arrowhead set up that way would be more effective than either a dull or a sharp one. There's also the consideration that an arrow is spinning, so it sort of drills its way in. I'm thinking that a dull head would put the brakes on that spin upon impact, but I don't know for sure. And by the way... welcome to PF. You'll be getting more responses from people who are more expert at this than I am.

Recognitions:
Homework Help
The law is Newton's second law, F=ma.

If the force keeping molecules together in the area of the target struck by the cutting surface is less than the force required to accelerate the target out of the way of the cutting object, then the cutting object will cut through (assume the target cannot stop the cutting object),

The amount of time available for the target to move out of the way depends on the speed of the cutting object. As the speed of the cutting object increases, the force required to displace the whole target (without cutting) increases dramatically.

Lets suppose the target is grass. If the centre of mass of the grass blade must move distance d to deflect out of the way of the blade to avoid being cut, the force required is:

$$F = 2dm/t^2$$ where t is the time of contact, m is the mass of the blade, d is the distance to move.

By decreasing t (ie. increasing the speed of the cutter) the force increases - as $1/t^2$. You can achieve huge cutting forces with a blunt blade by simply decreasing the time of contact (increasing speed).

AM

## Forces at play during "Cutting"?

I hope this helps in some measure!

Cheers

 I'm arguing that the sharpness of a blade is less important than than the fact that there IS a cutting surface (of some kind) AND, more importantly, the force exerted by the cutting surface against whatever is being cut- in this case bone, flesh, etc. The argument arose because a new company is claiming that their arrowheads using a relatively dull flexible wire will cut as effectively as the traditional 3 and 4-bladed broadheads. The designer of these new heads claims that physics says even a dull edge, given sufficient force and velocity will cut as well as, if not better than, a sharp blade. Is there any truth to this? Is there a specific law that would explain this claim?
Jeez, can't we just all be friends? It all has to do with pressure and impact the way I see it. Force/area. If you want a better cut, put more force on a smaller area.

 Recognitions: Gold Member Then again, I've designed exploding arrows that take the guesswork out of it. Razor broadhead 'floating' on an impact fuse... hollow aluminum arrow full of explosives...
 Think about this: you have a thin-wire arrangement that impacts a target. As that thin-wire arrangement goes through "flesh-and-bone" what is the physical support for those wires? Without a base support(other than end-to-end), what would stop those wires from breaking?
 Recognitions: Gold Member Thanks for tuning me in on something, Palladin. This whole thing sounded somehow familiar, and I couldn't figure out why. Your post reminded me; there use to be (still are?) fishing arrows that had wire guards around the head to prevent it from snagging on rocks or seaweed or whatever for retrieval by the built-in cord.