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Forces at play during Cutting ?

  1. Jun 9, 2006 #1
    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?

    Thanks, in advance, for any helpful relies I get.

    Austin, TX
  2. jcsd
  3. Jun 9, 2006 #2


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    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.
  4. Jun 9, 2006 #3

    Andrew Mason

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    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:

    [tex]F = 2dm/t^2[/tex] 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 [itex]1/t^2[/itex]. You can achieve huge cutting forces with a blunt blade by simply decreasing the time of contact (increasing speed).

  5. Jun 10, 2006 #4
    mmm I think I would cut the fat off of my steaks and chicken with a good knife rather that whacking it with a textbook... The reason an arrow cuts in the first place is the following. The arrow has a certain momentum based on its mass and velocity, and it maintains that momentum based on its aerodynamics and the condition and composition of the fluid through which it is moving, air in our case. The arrow will experience an inelastic collision with its intended target, exerting a force equal to the time rate of change of its momentum. This force is applied to the target over the area of the cutting surface, resulting in a large pressure over that area. The higher the pressure, the higher the likelihood that I begin to sever the ionic, molecular, and van der Waals bonds that hold tissue together. This is precisely why one would prefer an extremely sharp arrowhead, i.e. smaller surface area on the cutting edge, to a dull head. It should also be noted that the tissue first encounters the point of the arrowhead where the surface area is at an absolute minimum. As the arrow penetrates, there is increasing frictional drag of the tissue against the sides of the arrowhead. To reduce this drag, broadheads have a large amount of their blade centers removed. So here is the deal... frictional drag against the wire tip arrow is going to be reduced, I wager cutting will be worse, The structural constitution of the broad heads is probably much better( I add probably only because I havent seen the wire poop), and the stopping power will be less if the mass of the arrow is substantially reduced by the different head. In short, the greatest utility of these new arrows on a hunting trip would probably be to hold your toilet paper on :wink:
    I hope this helps in some measure!

  6. Jun 10, 2006 #5


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    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.
  7. Jun 10, 2006 #6


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    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... :biggrin:
  8. Jun 12, 2006 #7
    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?
  9. Jun 12, 2006 #8


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    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.
  10. Mar 9, 2007 #9
    In basic formula sense...to Cut something is based upon three variables.

    Cutting = Edge + Pressure + Velocity

    It isn't that I agree with shooting animals with "Dull" broadheads...the point is that given sufficienty velocity and pressure...even something perceived as "Dull" can cut.. Fishing line for example is round...yet when yanked on can cut you to the bone.

    The razor wire spoken about on The Atom broadhead is perceived as dull in that you can't easily shave hair nor cut your finger...yet when launched from a bow and being forced thru an animal...there are easily sufficient magnitudes of velicity and pressure on the edge of the razor wire to cause the "Cutting" to occur.
    Consider that the same machine that grinds, hones and strops medical blade scalpels also grinds, hones and strops the edge on the razor wire...same edge..just a less steep grind angle...in this manner I was able to create an extremely durable edge that wasn't dulled as it passed thru bone to get to the soft tissue vital organs and thus was still able to achieve capillary cutting action to occur. The bonus was that the Atom broadhead then became exponentially more re-usable and thus quite cost effective.
    As for the "Flexibility" portion of the discussion...The razor wire is basically a titanium spring...quite strong and requires significant pressure to compress when locked into the body of the broadhead. Typically the density of bone is required to compress the "Spring" to a minimal width...whereas the soft tissue vitals, muscle, skin, hair are not of sufficient density to cause this compression. For example the skin of a buffalo measured one inch thick. We compressed the razor wire 3/32 of an inch while cutting thru it. that is some tough hide and we easily cut thru it both going in and going out as we obtained a complete pass thru on the buffalo. No wimpy spring for sure.
    While this may not cover all the particular items discussed on this forum string...its late and I've got to get some work done. Any questions...I'll have a look when I can...enjoyed discovering a forum such as this!
  11. Mar 10, 2007 #10


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