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Momentum of an arrow or a sword thrust?

  1. Nov 11, 2012 #1
    Can someone tell me what generates more momentum, an arrow fired from a yew long bow at its peak strength or a sword thrust from a longsword and rapier too at its strongest?

    Thank you.
  2. jcsd
  3. Nov 12, 2012 #2

    Simon Bridge

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    There are a lot of variables here - what is this for?

    Bows store the energy from drawing your arm back.
    Thus energy from your arm is stored in the spring.

    Swords increase your reach - a thrust delivers energy from your arm directly.

    Guessing that the energy from pulling the arm back is about the same is pushing it forward, then a simple bow can be expected to introduce the same energy to the arrow as the thrust does to the sword. ##p=\sqrt{2mE}## so the more massive sword gets the more momentum. (wow!) You already know you want a heavy weapon in melee if you are interested in delivering damage. But that's making a lot of assumptions.

    However - the sword thrust has to be quick -while you can take your time on the draw.
    So there would be an upper limit to the sword thrust that is lower than what you could store in a bow.

    Then there are compound bows which can vastly magnify the stored energy.
    For a random bow vs a random sword - I'd bet on the bow having more momentum than the sword, for the same arm... assuming maximum draw weight is being used.

    Short answer: it depends.
    You sound like someone with access to archery and fencing equipment ... so you can do an experiment.
    You can measure how fast the rapier thrust and the arrow flight is and weigh both.
    Last edited: Nov 12, 2012
  4. Nov 12, 2012 #3


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    The first reference I Googled up for the arrow case talked about arrow energies in the 65 foot-pound range at the high end and mentioned a 400 grain (~ 1 ounce) arrow at 250 feet per second as typical. This would be for a modern hunting bow, NOT a yew bow.

    The momentum of the arrow in such a case would be 14 pound feet/second.

    The first reference I Googled up for the rapier case was from the "Deadliest Warrier" TV show and talked about a measured thrust speed of 5.9 feet per second at the high end. A different reference talked about weights of around 1 kilogram.

    Accepting both figures, a rapier thrust would be about 13 pound feet/second.

    I am unable to find speed figures for a long sword. Apparently rapiers are in the 2 to 2.5 pound range and longswords are in the 3 to 3.5 pound range. One would expect the deliverable momentum for the longsword to be somewhat higher, perhaps 15 pound feet/second.

    Given the low accuracy of these figures, I would say that the result is a tie.

    Like Simon, I am unclear on why you are after momentum figures. At first glance, it does not seem like a useful statistic.
  5. Nov 12, 2012 #4


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    I think you'll find that it is the standard way to specify things like Air Guns. I guess it's a convenient way of defining / designing a suitable spring construction for propulsion. It's never easy to describe the utility of a device with just one figure.
  6. Nov 12, 2012 #5


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    Yes, it is common to see projectiles rated in "foot-pounds". This is a unit of energy where the pounds are taken as pounds-force.

    The figures that I computed were for momentum in "pounds feet/second" where the pounds are taken as pounds-mass.

    An air gun spring or the propellant in a cartridge would most naturally be rated in units of energy rather than units of momentum. Or so I would have expected. I can Google up lots of ratings for projectile energy in foot pounds and for muzzle velocity in feet per second, but not so much for momentum.
  7. Nov 12, 2012 #6
    It's not really useful to compare the total energy as the wounding characteristics of each weapon are very different.

    Consider a draw cut where the blade of the longsword is placed against the surface to be cut, and drawn backwards. Like a saw. Or a person eating steak. The blade will cut, and is it meaningful to compare the energy of that (almost zero) that with a gun shot?

    A high power bullet will often pass straight through a target, making it less useful than a less energetic one, which will be stopped and transfer all of its energy into the target. Through penetration with a broadhead arrow is less of a problem since the arrowhead will have 3 inch long blades coming out of the side and make a much larger wound than any bullet.

    Suffice to say that despite popular belief, it's still not a good idea to discount the effectiveness of ancient weapons.
  8. Nov 12, 2012 #7
    Thank you.
  9. Nov 12, 2012 #8


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    High powered bullets can do much more damage than larger arrows because they will create a powerful shockwave in the body, since flesh is mostly incompressible.
  10. Nov 12, 2012 #9
    Did you also know that most kevlar vest will protect you from a pistol round but not from a knife stab, on account of a knife placing so much force on such a small surface (its tip)? In fact when you are shot while wearing a vest I suspect your body absorbs more energy than when you get shot without a vest, but it's less lethal. As you said, it's not just about the energy an attack delivers, it's about delivering that energy in a meaningful (i.e. lethal) way.
  11. Nov 12, 2012 #10

    Simon Bridge

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    Do not attend gsw scenes if you can help it. Exit wound is bigger than the entry.

    I read someplace that it is not desirable to kill-outright a soldier on a battlefield since a dead soldier will be picked up by a stretcher team later while an incapacitated one will occupying at least one of his mates who tries to help, affects the morale of the others with his screams, and occupies a medic, medevac, a medical team and their support people and equipment that all this implies ... all of which is resources not being spent on killing your guys. If you inflict a lot of injuries you can overwhelm the enemy ability to cope with the influx of wounded. I'm not very fond of military reasoning.

    @d3mm - ancient soldiers wore armor for a reason yep. But your best point is reinforced by Amok - it is the means of delivery that counts.

    @Amok: a bullet deforms as it passes through kevlar while the knife does not - so the knife penetrates further. You'll have see the Mythbusters ep. on a lawmans badge stopping a bullet - it worked if the badge had two layers. The bullet deforms on hitting the first layer making it easier for the second layer to stop it.

    Though a stopped bullet delivers more energy than a through-and-through bullet - the bullet that enters the body dissipates energy in soft tissue while the bullet stopped in the vest dissipates energy through the vest across a wider area, through padding (lengthening the stopping distance) and the vest is supported on the body's frame (bones, stronger muscles etc) more capable of absorbing the energy without damage.

    All this is diverting enough - but is it on-topic?
    I suppose it is entertainment until OP gets back to us.
  12. Nov 12, 2012 #11

    Simon Bridge

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    Back on topic: I am happy that the "typical" figures provided by jbriggs444 (post #3) have borne out my reasoning. I did have a google for them and found the variation to be very wide so gave up. Someone with more patience could probably compile the statistics.

    This question has the smell of a "settle a bet" type of thing - it can come up in RPG sessions sometimes. Fact is, these weapons would be used in very different situations and so a direct comparison is seldom useful IRL.

    In an RPG you want to be able to assign damage to different attacks... which naturally leads to comparisons...
    A quick look at D&D, AD&D, RQ and GURPS shows that they all give a bow about the same damaging ability as a average rapier in each of their systems. GURPS assigns damage based on character STR score, so a strong character with a rapier does about the same damage as the same character with the strongest bow they can draw.
  13. Nov 13, 2012 #12
    There was a video wayback of someone using a greatsword and cutting a large pig carcass into two parts with a single swing. It's vanished from youtube now.

    We're quite lucky the katana fanclub hasn't descended on this thread. They seem to invade every sword thread on every internet site. As a weapon optimised for duelling, it's comparable in role to the rapier so it would probaby be the first legitmate invasion they ever made ;-) The longsword had a different function and comes from a different era (to the rapier).
  14. Nov 13, 2012 #13

    Simon Bridge

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    Mythbusters did a test of a katana's ability to cut heads off (wielder reports, "like butter") that was pretty scary.

    I don't know that it was "optimized" for dueling - "katana" is just Japanese for "a sword" and like western swords there were/are many kinds. Your standard Samurai thing (like you see mocked up on display stands in people's homes) was a battlefield weapon... but they did get used for dueling much as javelins and discus get used for sports and, similarly, people got special ones made.

    People do tend to obsess over them ...

    Can we further derail the thread? How about those longbow legends?
  15. Nov 14, 2012 #14
    I don't know much about longbow legends. I know the pull was about 300 newtons and the range for massed volley fire was over 200 yards. They are easy to debunk with a modern bow.

    For samurai at war there was a shift towards spears (eg Battle of Shizugatake) because there were so many peasant levies with spears so it was hard to get close, and because they had a longer reach when charging from horseback.

    Curved bladed swords have the curve so they can cut flesh in one direction. As you can imagine from the physics, the curve increases the cutting ability if the weapon is drawn across the target - that unique "backward" sword motion you see in japanese martial arts where they stick the sword out and pull it towards themselves.

    That doesn't work as well with a straight blade, but the straight blade is doubled edged and has a backswing. It's also designed for stabbing through heavy armor. Everytime you see a warrior (not duellist) with a curved weapon, he usually has lighter armor. Only the guys with full metal plate armor use those straight swords.

    A duellist would prefer light or no armor, and a fast weapon (rapier, not longsword). Armor is for the battlefield where you can be ganked in the arse by a 2nd man or archer.
    Last edited: Nov 14, 2012
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