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Eric Meulemans
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PostPosted: Mon 11 May, 2009 5:41 pm    Post subject: Velocity of an arrow - Mounted vs. Ground?         Reply with quote

An upcoming Mythbusters episode sparked a friendly debate regarding the outcome as the the question they are to ask: "Did Hungarian archers get twice the penetration shooting a bow from a galloping horse?" (Episode #120 - "Exploding Bumper" Airing 13 May, 2009).

I think it clear enough that twice the penetration cannot be expected, but what amount of energy - if any - is additionally applied to an arrow (or other projectile) cast from a moving firing platform (in this case, a horse)? This would harken back to the old physics query involving a gun fired from a train traveling as fast as the bullet, and as I understand it the answer is dependent upon one's frame of reference. In this case, I think the only frame of reference we need to worry about is the target's...

Common sense would seem to dictate that the speed of one's mount would be applied directly to the speed of the arrow, but somehow I feel this isn't wholly true. Perhaps in a pen-and-paper world it is, but I am curious about any variables which would reduce or negate such ideal results, such as:

1. Ultimate velocity of the projectile - if it's already going as fast as the bow can push it, does it go faster? Faster than is aerodynamically permissible by its design?

2. At what point is the arrow considered cast?

3. What effect does the various angles of fire have on any added energy? If an arrow shot straight ahead increases in speed relative to a target, then a parting shot must decrease...

4. ...unless of course one's target is also mounted and traveling at the same speed.

5. The frames of reference can get confusing - what would a stationary chronometer say of the arrow's velocity?

Etc., etc., etc. I'm curious about this question because while the answer to the original question may be simple (or perhaps not?) it raises a number of potentially interesting real-world questions related to mounted archery not usually addressed.
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Jim Mearkle




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PostPosted: Mon 11 May, 2009 6:57 pm    Post subject:         Reply with quote

In a vacuum, the horse's speed would be added to the arrow's speed. In reality, this would be true as it left the string, but air drag would bleed off the arrow's speed. When it hit the target. it would still be moving faster than it would if shot from a stationary horse, but not as much faster.
Jim
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Jared Smith




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PostPosted: Mon 11 May, 2009 7:32 pm    Post subject:         Reply with quote

Quarter horses race at a speed of around 60 feet per second (40 mph.) A mounted rider in a controlled speed shoot situation would probably be going slower (maybe half this speed.) In comparison, arrows leave medium to war bows at very roughly around 200 feet per second . A lot of the higher initial arrow speed is lost between 20 to 50 yards of flight. At head on, short range shots, I would guess high speed horse speed could contribute enough extra arrow energy to be worth calculating/ considering. I doubt many professional jockeys / archers would want the task of performing such a feat though.
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Dan Howard




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PostPosted: Mon 11 May, 2009 11:30 pm    Post subject:         Reply with quote

IIRC the Mythbusters crew found that the arrows penetrated around 30% more when fired from a moving horse compared to when stationary.
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Robert Subiaga Jr.





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PostPosted: Tue 12 May, 2009 7:26 am    Post subject:         Reply with quote

That's why I love the Mythbusters crew. Oldest principle of science: "Nothing ruins a good hypothesis like an experiment." (Or in this case supports a hypothesis, but you get the drift.)
Starting in a hollowed log of wood—some thousand miles up a river, with an infinitesimal prospect of returning! I ask myself "Why?" and the only echo is "damned fool!...the Devil drives...
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Joel Minturn





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PostPosted: Tue 12 May, 2009 8:39 am    Post subject:         Reply with quote

30% increased penetration makes sense if the horse and rider are going 60ft/s and the bow shoots around 200ft/s. But I would like to see the episode before I take there experiment as proof, It wouldn't be the first time the I have had issues with how they did something. That said, the math backs up the theory, with in limits.

Basically, if the target is stationary, the relative velocity of the arrow would be the horse speed + the arrow speed. In the case above the arrow velocity at release would be 260ft/sec which is a 30% increase in velocity. And yes if the rider was riding away from the target (or the target was fleeing) then yes the relative velocity would decrease.

This is definatly true (and easier to deal with) in a vacuum. With air and drag there is an issue that the faster the arrow goes the more drag on the arrow and the more relative cross wind to throw the arrow off target. So there is a point of diminishing returns since drag increases by velocity squared.

As an aside I did try to figure out at what point the drag on the arrow would be greater than the force of the bow. Its around mach 28 give or take.
Ok that more than enough from me.
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Glen A Cleeton




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PostPosted: Tue 12 May, 2009 2:10 pm    Post subject:         Reply with quote

Contrary and contentious of much premise is that the arrows were most often being shot in a lateral plane to that of which the archers were travelling. Is their historical information indicating the archers were shooting in a direct charge and in the direction of travel?

Cheers

GC
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Dan Howard




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PostPosted: Tue 12 May, 2009 3:25 pm    Post subject:         Reply with quote

Yep. The horses were galloping stright towards the target. It seems to have limited practicality in a combat situation though that is beyond the scope of the test. They were simply trying to discover whether an arrow fired from a gallpoing horse would achieve greater penetration. And it did. I agree that the results tell us little about historical situations.
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Jared Smith




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PostPosted: Tue 12 May, 2009 4:08 pm    Post subject:         Reply with quote

I figure this has some applicability to cultures that used horse-archers. (Mongols, Turkish tribes, Samurai, others? I don't study any of them.)

I would expect this kind of horse speed and accuracy of straight line shots to be useful within a range of roughly 50 yards. At the kind of speeds we have been discussing (~ 41 mph or 66 km/hr horse) some room is needed to turn unless the tactic was to charge completely through an enemy line. I would want at least 20 yards to perform a right angle turn at this kind of speed. It does seem plausible for hit and run tactics on reasonable terrain, or for raids passing straight through scattered enemy lines.

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Jeff Demetrick





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PostPosted: Tue 12 May, 2009 4:13 pm    Post subject:         Reply with quote

Remember penetrating energy is proportional to the kinetic energy. The kinetic energy is proportional to the velocity squared. I will let you do the math but, roughly only a 10-15 % increase in speed will give a 30 % increase in energy or penetration.

Jeff

P.S. the Mongols and Magyars rode what we would consider ponies, no where near the speeds of the modern quarter horse.
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Joel Minturn





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PostPosted: Tue 12 May, 2009 4:30 pm    Post subject:         Reply with quote

Well penetration is a lot more complicated than just kinetic energy. KE is how much energy is available to dump on the target but how far it penetrates seems to be more a function of impulse and momentum (and surface friction, cross sectional area, aerodynamic shape and the medium being hit). Momentum is just mass X velocity. Just because something hits with a higher KE doesn't mean it will penetrate more. Case and point. an arrow may penetrate a bucket of sand but a the same buck will stop a bullet with in inches.
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Jeff Demetrick





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PostPosted: Tue 12 May, 2009 4:50 pm    Post subject:         Reply with quote

Joel Minturn wrote:
Case and point. an arrow may penetrate a bucket of sand but a the same buck will stop a bullet with in inches.


Hi Joel,

Not if they are the same mass and shape, which I assume applies to the arrow test above. The best bang for your penetrating buck comes from velocity, which as mentioned is proportional to the speed square. Mass increases directly proportional, so I would not be surprised by the mythbuster results.

Jeff
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Nat Lamb




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PostPosted: Tue 12 May, 2009 5:53 pm    Post subject:         Reply with quote

Dan Howard wrote:
. I agree that the results tell us little about historical situations.

That isn't really what the show is about though, in this case they have shown that , yes, an arrow fired while moving can have more speed, under optimal conditions, so the question about efficacy remains open. What they are normally looking for is where under optimal conditions there is no effect, and the idea can then be discounted. And then you can make something explode.
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Joel Minturn





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PostPosted: Tue 12 May, 2009 7:40 pm    Post subject:         Reply with quote

Jeff Demetrick wrote:

Not if they are the same mass and shape, which I assume applies to the arrow test above. The best bang for your penetrating buck comes from velocity, which as mentioned is proportional to the speed square. Mass increases directly proportional, so I would not be surprised by the mythbuster results.


I do agree that I am not surprised by the mythbuster results , well maybe a little till I did the math. If the two objects have the same shape and mass, then yes, the faster one would result in better penetration. Unless the object is going fast enough to break apart, or deform more. And yes that is an issue with some bullets. From shooting experiment that I have done velocity can be detrimental to penetration. The best penetrating bullets are the ones that are heavy solids and travel at a moderate velocity. Light weight, high velocity rounds tend to dump lots of energy quickly and don't penetrate well. But I think this may be getting a little to far off topic.
Back on topic, Since arrows don't deform on impact, it would be expected the same arrow going faster should penetrate more, but not necessarily from higher kinetic energy.
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Jared Smith




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PostPosted: Tue 12 May, 2009 8:18 pm    Post subject:         Reply with quote

Joel Minturn wrote:

Light weight, high velocity rounds tend to dump lots of energy quickly and don't penetrate well. But I think this may be getting a little to far off topic.


I am wondering where these velocity regimes tend to start and end? (Credible velocity for most historic archery is under 300 fps, although, at least a couple of modern enthusiasts have made extremely heavy war bow reproductions generating very close to 300 feet per second/ 100 meters/second.) Severe disintegration is something I assume pairs up with speeds of several thousand feet per second. Around 10,000 fps, unhardened projectiles can become gaseous vapor upon impact. But, a 7 mm magnum traveling at 3000 fps can make a nice clean pencil sized hole (can see daylight right through it) through a pretty large pine tree! I would have just guessed a bodkin style point would have been used if this was the true objective. That does not seem to be what I am finding as I look into arrowhead styles of those who were horse archers.

Some of the broad head and diamond shaped, whistling, etc. type arrow points (mercenary's taylor has a medieval Mongol arrow head on one of their web pages) of applicable era horse archer peoples do not look like particularly good penetrator designs to me. Several period art examples I stumbled across while looking into it (Assyrians, Mongols, etc.) seem to most commonly show horse archers shooting backwards.

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Eric Meulemans
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PostPosted: Tue 12 May, 2009 9:08 pm    Post subject:         Reply with quote

How much energy is really needed for an arrow of a particular type to penetrate a body? It would seem that if you're generating enough force to get the arrowhead into or through the target, why use more? It's not as if - like a bullet - that energy can/will be substantially transfered to the target (as in the bucket of sand example). I'm thinking in terms of material/technological limitations that might bring about diminishing returns.

Obviously there are gains to be made as far as range, flatter trajectory, better energy downrange if using a heavier shaft or shortening time to target with with a lighter one (in relation to draw weight). And of course against armour more "punch" is desired, but if the predominate type of arrowhead is not optimized for armour-piercing then surely the intended targets were principally exposed flesh? If this is the case, then it would make sense to not bother pushing the envelope with regards to materials - if the shaft is buried in them at 160 fps, then why bother pushing it to 300?
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Lukasz Papaj




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PostPosted: Wed 13 May, 2009 12:15 am    Post subject:         Reply with quote

You cannot compare arrows to bullets -
first thing is that bullet is more or less blunt projectile - it crushes the target. Arrow with broadhead or "flat diamond" head cuts through target . Bodikin is something in the middle, some piercing, some crushing, but not much cutting. So given same speed and SOFT target, broadhead would cut through, but bodikin would likely stuck. Now, i'm not hunting with a bow, so I cannot say if there is any truth at that, but one fellow I know that did some bowhunting in US said that broadhead from 60 pounder bow (think a compound) at a 30m range would cut right through a deer's ribcage, and one can have troubles recovering arrow after successful shot, cause it just flies through. Never did that meself, so I cannot say if he was boasting or not , just heard that statement, but since there are many arrowheads designed just to limit penetration and maximize damage, think he wasn't colourizing much.
Second thing is mass - low end for arrow for warbow is 60 gram (923 grains), IIRC turkish bows of war variety are thought to be most efficient with arrows weighting some 90 g (1385 grains). Now NATO 5.56/ .223/SS109 projectile weights 3.95 gram (61 grains), .357Magnum 8-11.7 gram(123-180 grain). Speeds are completly different too - bow will max out 100 m/s , SS109 -1005 m/s., 357 Mag - 442-332 m/s. Not to even mention completly different aerodynamics of those projectiles. Apples and oranges too boot.

As for shooting straight ahead - simple physics says the results are plausible, though as far as my knowledge goes training for hungarian horse archer is rather hitting target that's on left side on the horse, close, and then second shot when target is in back-left quarter of the rider. Reason is that when shooting ahead, the body alignments are quite wrong, and the counterbalancing after shot quite hard to do. Closest thing to shooting ahead would be something like that: Or like in that "Lajos Kassai in action" Shooting back is meant for pursuing enemy, that would move at speed matching the rider, so the speeds would even out. There is that diagram of training for Hungarian horsearchery : http://www.diesteppenreiter.de/img/ungarische_variante.jpg

One thing that comes to mind that in the beginning of XVc in Poland, when there were a horse - banners, and part of the tactics (supposedly) was a shower of bolts in direction of charge - it was crossbow that was used, not the bow.
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Lafayette C Curtis




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PostPosted: Sat 16 May, 2009 7:20 am    Post subject:         Reply with quote

Jared Smith wrote:
Quarter horses race at a speed of around 60 feet per second (40 mph.) A mounted rider in a controlled speed shoot situation would probably be going slower (maybe half this speed.)


Probably a fair bit more than half speed; too fast was apparently better than too slow, since the horse becomes a more stable archery platform at higher speeds (up to a certain limit).
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Lafayette C Curtis




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PostPosted: Sat 16 May, 2009 7:25 am    Post subject:         Reply with quote

Glen A Cleeton wrote:
Contrary and contentious of much premise is that the arrows were most often being shot in a lateral plane to that of which the archers were travelling. Is their historical information indicating the archers were shooting in a direct charge and in the direction of travel?


Jared Smith wrote:
I figure this has some applicability to cultures that used horse-archers. (Mongols, Turkish tribes, Samurai, others? I don't study any of them.)

I would expect this kind of horse speed and accuracy of straight line shots to be useful within a range of roughly 50 yards. At the kind of speeds we have been discussing (~ 41 mph or 66 km/hr horse) some room is needed to turn unless the tactic was to charge completely through an enemy line. I would want at least 20 yards to perform a right angle turn at this kind of speed. It does seem plausible for hit and run tactics on reasonable terrain, or for raids passing straight through scattered enemy lines.


Shooting ahead seems to have been perfectly practicable, and--as Jared said--it appears to have been predominantly used by heavy cavalry formation whose archery was meant to disrupt and disorganize the target formation along the approach to a charge. It's also a handy skill to have for pursuing enemy horsemen (i.e. shooting them in the back) once they had been routed.
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Lafayette C Curtis




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PostPosted: Sat 16 May, 2009 7:29 am    Post subject:         Reply with quote

Lukasz Papaj wrote:
One thing that comes to mind that in the beginning of XVc in Poland, when there were a horse - banners, and part of the tactics (supposedly) was a shower of bolts in direction of charge - it was crossbow that was used, not the bow.


Not just in Poland. At least in Germany, and probably just about everywhere else, shooting ahead once and then drawing swords, maces, or axes to charge without reloading seems to have been a very common tactical method for mounted crossbowmen, at least when they're not going head-to-head against proper men-at-arms.
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