[Eric Meulemans]

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.

[Jim Mearkle]

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.

[Jared Smith]

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.

[Dan Howard]

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

[Robert Subiaga Jr.]

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.)

[Joel Minturn]

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.

[Glen A Cleeton]

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

[Dan Howard]

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.

[Jared Smith]

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.

[Jeff Demetrick]

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.

[Joel Minturn]

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.

[Jeff Demetrick]

[Nat Lamb]

[Joel Minturn]

[Jared Smith]

[Eric Meulemans]

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?

[Lukasz Papaj]

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.

[Lafayette C Curtis]

[Lafayette C Curtis]

[Lafayette C Curtis]