Anti-shardplate weaponry

[Aspren]

In the interest of finding mundane weapons capable of adequately damaging shardplate I thought I might do some calculations. From what we know so far there are two weapons capable of cracking shardplate with one blow and possibly destroying shattering shardplate in subsequent blow. Namely a Warhammer and a massive rock-sling.

In Chapter 65 of The Way of Kings we see some Parshendi slinging head-size rocks at Dalinar, which slightly crack Dalinar's shardplate.

 

In order to do these calculations I'm going to have to make quite a few assumptions:

1. I'm going to assume that the Parshendi slingers are stronger than us humans (I'm sure they are, I just can't remember where this was stated). 

2. The method of propelling the head-size rock is via a 2-handed sling, so the action should be similar to a hammer-throw (the kind you see in the Olympics).

3. As a result I'm to assume the rock has a mass of 6 kilograms (a weight of 41.2 N or 9.26 pounds). It's unlikely that it's more than 7 kilograms or less than 4 kilograms. The mass of an Olypmic hammer is 9 kg at most, but I chose 6 kg because any more and the effective range would be too low and I also can't imagine any sling would be able to take such strain. It is also worth remembering that Roshar's gravity is roughly 7/10 of Earth's gravity. So 6 kg isn't too excessive, I hope.

4. The effective range (range at which the rock can be thrown with sufficient accuracy) of this sling is 80m (263 feet) or so. 

 

okay, now for some calculations:

 

For the most part I'm measuring the ability to damage shardplate by determining the kinetic energy (E_k) of the projectile. That's mass times velocity squared and all divided by two.

 

E_k = (1/2)(mv^2)

 

I've already determined that the final velocity of the projectile would be roughly 23 meters per second when reaching the target that is in the effective range, while the initial velocity (its velocity when it is released from the sling) is roughly 30 meters per second (or 100 feet per second). It's lost quite a bit of it's kinetic energy to friction, but due to gravitational acceleration it has regained some by the time it reaches the target.

 

    = (1/2)(6 kg)(23m/s)^2

E_k = 1587 Joules

 

So now we've got a baseline. I'm going to assume that 1580 or so Joules is close to the minimum amount of energy required to crack shardplate.

 

Long story short, here is a table of some other weapons with their approximate E_k calculated:

 

                                                     Mass                  Velocity    E_k (at initial velocity)     Effective E_k (66% of E_k , the E_k at the effective range)

Rock-sling                                              6 kg (rock)            30 m/s      2700 J                       1587 J

Throwing club                                          1.5 kg                  40 m/s      1200 J                       1067 J

Javelin                                                    1.5 kg                  45 m/s      1518 J                       1012 J

150 lb draw bow                                      0.2 kg (arrow)        63 m/s       397 J                        265 J

175 lb draw crossbow                              0.2 kg (bolt)           97 m/s      941 J                         638 J

3300 lb draw siege-crossbow                   0.94 kg (bolt)          70 m/s      2043 J                      1536 J

Mace                                                     2 kg (head)            30 m/s      900 J                         900 J 

Warhammer                                           4 kg (head)            30 m/s      1800 J                       1800 J

Shardbearer's warhammer                       8 kg (head)            35 m/s      4900 J                       4900 J

5500 lb draw Ballista                               1.14 kg                  84.m/s      4022 J                       2681 J

 

 

As you can see, the two heaviest warhammers, the (3300lb draw-weight) siege-crossbow and the 5500 lb draw-weight ballista all have an effective E_k exceeding or near to 1587 Joules. The shardbearer's warhammer shown is probably capable of shattering shardplate in a single blow (if it's a direct hit, and not say, a glancing blow).

 

The bows and crosbows have their draw weight indicated (the weight, in pounds, required to draw the bowstring/crossbowstring back). The 3300 lb draw weight siege-crossbow treads the line between a ballista and a crossbow, being that it is barely portable (up to 25 kg).

 

There are probably quite a few other heavy weapons capable of adequately damaging shardplate, which I can't think of at the moment. If you can think of any, please point them out.

 

It's also interesting to consider the possibilities of fabrial enhancements in improving these weapons anti-shardplate capabilities. What sort of enhancements do you think they could be given?

 

 

EDIT: Added a ballista in the table.

Edited January 25, 2014 by Aspren

[Pinpoint]

This is pretty awesome I'm not going to lie. However, what about the time when the chasm fiend is trying to crush Dalinar? Is the Chasm fiend weaker than a warhammer? 

 

I still think this is really cool though. Upvote for you.

Edited January 25, 2014 by Pinpoint

[bartbug]

Remember, if it had been any other shardbearer, they probably would have died.

[Mysty]

Stormfather but you like to figure out the mechanics of WoK. First the model of the bridge and now this? Upvote for sheer nerdiness!

You don't always have to go for brute force, kaladin proved a spearhead to the eyeslit works. The trouble is getting close enought to the eyeslit without getting sliced by the shardblade, or loosing your whole spearman squad. Are there any projectile weapons accurate enough to slip through, especially with fabrial enhancement?

[Pinpoint]

Yes, but the shardplate didn't crack

[Aspren]

This is pretty awesome I'm not going to lie. However, what about the time when the chasm fiend is trying to crush Dalinar? Is the Chasm fiend weaker than a warhammer? 

 

I still think this is really cool though. Upvote for you.

 

Good point. I think the rate of change in momentum in the case of  Dalinar catching the Chasmfiends claw is less than the rate of change in momentum when a warhammer strikes shardplate that is motionless. When Dalinar caught the claw he bent with the blow till he was down on one knee. That increased the time over which the force of the Chasmfiends blow would be divided. Similar to how withdrawing your hands while catching a fast moving ball seems to lessen the impact. I'm not sure by how much the blow would be lessened by that though. So you're probably right.

 

That, or he was doing some surgebinding that we don't know about.

 

Or, the Chasmfiend was being friendly and never intended to hurt anyone.

 

Or it was a fake chasmfiend. An illusion made by...   uh, uhm, Taravangian and stuff. 

I'm getting a bit desperate here.

Edited January 25, 2014 by Aspren

[Aspren]

You don't always have to go for brute force, kaladin proved a spearhead to the eyeslit works. The trouble is getting close enought to the eyeslit without getting sliced by the shardblade, or loosing your whole spearman squad. Are there any projectile weapons accurate enough to slip through, especially with fabrial enhancement?

 

It's probably quite hard to have a projectile weapon that is both accurate and fast enough to go through an eyeslit. What could work is maybe a fast firing crossbow, or rather a whole squad of crossbowmen with fast firing crossbows. Something like a chukounu or a polybolos. Just bombard the shardbearers face with crossbow bolts. One of them is bound to eventually go through the eyeslit.

Edited January 25, 2014 by Aspren

[PorridgeBrick]

Ooh, awesome! By any chance, would you be able to find out how much damage a full on ballista would do? Obviously, it will crack, but will it crack it completely in one blow? If so, then that is probably the best option against a shard bearer. Move a giant ballista to the high ground right before an ambush of the enemy, and just snipe all the enemy shardbearers. Without time for fortifications, though, a giant hammer will work just fine too.

[Chlehrma]

Dalinar "caught" the claw and the weight of it drove him to his knees. That is not quite the same as a hammer hitting a person in shardplate. On the case of the chasmfiend, Dalinar basically displaced the force a bit by sinking with the blow, kind of like how a persons knees bend when they land after a jump--shock absorption. Granted, Dalinar is a special case and we do not know if the weblike cracks in his shard plate are because of him being slowly crushed like a nut in a nutcracker or if he was draining the stormlight from his armor for a strength boost or both. That is the only instance we see in the book where shardplate is being crushed with slow pressure rather than being hit by a rapid blow.

[Voidus]

Also keep in mind that the force from the Chasmfiend was a bit more spread out, wheras with a warhammer you're generally going to be aiming for just one of the plates.
But I think we all know that the best weapon for killing Shardbearers is...
The spanreed!
Throw a corresponding reed to the feet of the Shardbearer, then activate the pairing fabrial, pull yours up and jab them in the eye. 

[Kurkistan]

Finally! The ballista is vindicated, by SCIENCE!

[Chrono]

If Earth weapons were allowed on Roshar, then I'd suggest a high caliber sniper rifle in close range. If a good sniper rifle can be fired from over a mile away and still kill its target, at five hundred yards it might be able to puncture through Shardplate. The problem is (aside from Earth weapons not being allowed on Roshar, of course ), a sniper rifle of that kind of caliber is also dang heavy. You'd have to lug the thing over to a certain spot, then try and herd the Shardbearer towards the sniper. And then there's the problem of not dropping the Shardbearer right away, you have a PO'd man in Shardplate right on top of you. 

 

If we're playing by Roshar rules, Porridge Brick's idea is fantastic. 

[Mysty]

But I think we all know that the best weapon for killing Shardbearers is...

The spanreed!

Throw a corresponding reed to the feet of the Shardbearer, then activate the pairing fabrial, pull yours up and jab them in the eye.

That is a good idea. I wonder if you could put conjoined fabrials on a pair of daggers... might have better penetration than a reed.

[Two McMillion]

This would mean that, in terms of earth weapons, a Shardbarer is effectively invulnerable to small-arms fire. Even your .45 caliber pistol don't have the energy to crack shardplate. Conversely, however, quite a few rifles could crack it at a distance of 200 yards or more- just about anything larger than a .243.

[Voidus]

Actually if we're using conjoined fabrials I've always thought that pairing a ballista to just a random crossbow bolt would work well if you had good communication, you don't need to worry about portability then.

[Chlehrma]

This would mean that, in terms of earth weapons, a Shardbarer is effectively invulnerable to small-arms fire. Even your .45 caliber pistol don't have the energy to crack shardplate. Conversely, however, quite a few rifles could crack it at a distance of 200 yards or more- just about anything larger than a .243.

The damage from Small arms fire depends on the cartridge. Also the energy released at the muzzle is not necessarily the same at impact. I will take a desert eagle up against a shard bearer any day...just give me a round in the chamber and a little warning. Edited January 25, 2014 by Chlehrma

[Aspren]

Ooh, awesome! By any chance, would you be able to find out how much damage a full on ballista would do? Obviously, it will crack, but will it crack it completely in one blow? If so, then that is probably the best option against a shard bearer. Move a giant ballista to the high ground right before an ambush of the enemy, and just snipe all the enemy shardbearers. Without time for fortifications, though, a giant hammer will work just fine too.

 

Okay, I added a ballista to table. I'm not too sure how accurate the data is but I think it'll do.

[The Count]

If we are considering other planet weaponry...

how hard can a coinshot fling a piece of steel? Or could they be accurate enough to hit the eye slit?

what about a twinborn (aka Wax)? He could make himself heavier and fling some pretty massive stuff at the shardbearer.

[Tarion]

Is there any way to work out the kinetic energy of the Grandbow?  I mean, theoretically, it's just a longbow with a particularly heavy draw.  You'd just need the approximate strength of a Shardbearer.  

 

The Count - A normal coinshot isn't going to do it - They're stopped by regular, wooden shields.  

 

Wax, on the other hand, would be able to smash them quite handily, if he had enough weight stored.  But that's true of more or less anything.  Give a Crasher enough time to store weight, and they're ridiculously powerful.  

[Aspren]

Is there any way to work out the kinetic energy of the Grandbow?  I mean, theoretically, it's just a longbow with a particularly heavy draw.  You'd just need the approximate strength of a Shardbearer.  

 

The highest draw weight of a bow that I've heard of is 150 lb, which I put in the table. I'd assume that a Grandbow would have a draw weight of maybe 5 times that amount. I won't be able to find any actual data to calculate that but I'd assume that it'd be somewhere between the 175 lb crossbow and the 3300 lb siege-crossbow. So probably an effective E_k of about 1100 J.

[carlucill]

According to wikepedia a dollar coin weights 8.1g, let’s just say a mist born coin is 10g (.01 kg). Let’s also assume we have a 160 pound (73kg/714N) allomancer. Finally let’s assume that a mist born push follows a distance squared law like gravity or magnetism. That means that the force pushing on the coin is 714N/xm^2. If we assume the allomancer is 50 meters away from the shardbearer, and the coin is held at arm’s length than the work done is the integral from .7m to 50m of 714N/x^2 dx which is 1005J. Work is equal to the change in kinetic energy and since the initial kinetic energy was 0, the coin has a kinetic energy of approximately 1000j. Working backwards we can see holding the coin closer or weighing more will increase the damage of the coin.

[Voidus]

The force of the push shouldn't be equal to the allomancer's weight, it would be a constant dependant on their allomantic strength, the weight just determines the acceleration of each I think. (Unless a downward push is used)
If it was equal to the weight then pushing off a coin on the ground (Which is effectively pushing off of the planet) would send you into orbit, not just soaring over buildings

[Cromptj]

Judging from descriptions in the book, it looks like impulse (change in momentum) is what is required to break shardplate quickly. So I would advocate using some kind of fabrial gun powered by a projectile linked to a missile on a siege ballista. If you set up three or four ballistae, you could have several bullets.

[Aspren]

Judging from descriptions in the book, it looks like impulse (change in momentum) is what is required to break shardplate quickly. So I would advocate using some kind of fabrial gun powered by a projectile linked to a missile on a siege ballista. If you set up three or four ballistae, you could have several bullets.

 

I used kinetic energy because it seems to be the standard when measuring the destructive potential of projectile weapons.

 

A fabrial powered projectile seems like a bit of a waste to me. Fabrials are relatively expensive, so making fabrial projectiles that are just going to be fired and then forgotten seems to be a waste of resources. Resources that would probably be better spent on making more weapons. 

[Moogle]

I used kinetic energy because it seems to be the standard when measuring the destructive potential of projectile weapons.

 

But that's not what determines what breaks something.  Momentum, surface area affected, and rigidity of the projectile is what determines whether or a projectile breaks though. A very thin arrow which is really heavy and strong and going very fast can punch through things that an equal kinetic energy blanket is going to do nothing on.

 

Kinetic energy is a really really rough measure. Bullets are not all that much more energetic than a mace (or so I see from a quick perusal of Wikipedia), but I think I'd prefer to be hit with a mace rather than a bullet when in Shardplate because the mace will spread the energy of impact around a larger area.

Edited January 26, 2014 by Moogle