Shardplate Math!

[Dunkum]

3 hours ago, hwiles said:

True, I can't prove that the arrows aren't hollow, however, for projectiles as large as these, the amount of air-resistance would be tremendous.  Without access to both an aviation and well-stocked material science lab it's difficult to say, but I'm pretty confident that, if they wanted to reduce the weight of the shafts, shaving the outside down, rather than hollowing them out would result in much better accuracy and range, and a solid shaft of that size probably wouldn't rip apart at those speeds and forces.  I feel like I may have glazed over these points before, so thanks for the opportunity to clarify!

A quick look at the coppermind couldn't confirm, but do we know the intended use of grandbows?  if they are intended for hunting chasmfiends or killing men in armor, then they would need stronger shafts, and hollow ones might not be sufficient.  if they were just meant for range against reguar soldiers, then they could maybe be weaker.

[+hwiles]

16 hours ago, Dunkum said:

A quick look at the coppermind couldn't confirm, but do we know the intended use of grandbows?  if they are intended for hunting chasmfiends or killing men in armor, then they would need stronger shafts, and hollow ones might not be sufficient.  if they were just meant for range against reguar soldiers, then they could maybe be weaker.

The Fun Part:  If the arrows were solid (and made of wood) and shattered on contact (worst case scenario in terms of doing damage to the target), they'd still be delivering almost 4x the impact of a professional athlete swinging a baseball bat, which, just off the top of my head, ought to be enough to ruin a person's day if they aren't wearing some kind of magical inertia-dampening armor (shardplate).

If the intended targets are people, the Grandbows are, simply put, wildly over-engineered, as crossbows made centuries ago could punch through plate armor.  I assume then that the Grandbows were designed as a kind of portable (ie: high-mobility) siege weapon.  For the purpose of wounding/killing soldiers from a distance, a shardbearer could probably do more damage at a faster rate by carrying around and throwing fist-sized rocks than by aiming and shooting a bow.  With that in mind, I'd think it would make the most sense to maximize the destructive force of the arrow as greatly as possible, which is accomplished by optimizing both velocity and mass.  Velocity is more important and can be increased by decreasing the projectile's mass, however (due to air-resistance), after a certain point (which is generally estimated using differential equations and then more clearly identified through repeated experimentation) reducing the mass further results in a net-loss in the destructive force of the projectile.  The mass of the arrow can be reduced by either removing material from its outside or hollowing it out.  Reducing the outside diameter of the shaft reduces the amount of air-resistance it will be subjected to (thereby increasing velocity) by making it more aerodynamic.  Although it may seem somewhat counter-intuitive, a hollow tube is usually going to be more structurally stable than a solid cylinder of the same mass; the wider the hollow tube, the greater its stability to mass ratio, but this too is a delicate maximization problem.  If the stability to mass ratio isn't high enough the arrow will shatter on impact, which reduces how effectively it transfer energy to the target.  These design considerations are why modern aluminum/carbon fiber arrows are relatively thin (to minimize their profile without becoming flimsy), thick-walled (to optimize weight), and hollow (to maximize their stability-to-weight ratio).  If Grandbow arrows were made of metal, they would have to be hollow otherwise they would be too heavy to be effective projectiles, however, in terms of maximizing the destructive capacity of metal arrows, it would make more sense to make the arrows thinner than they are described in the book if a reduction in mass was desired, which is why I've concluded that the arrows must be made of wood.  I'm not aware of any instance of hollow wooden arrows being used in real-life (except by very dedicated hobbyists) as its hard enough to keep a wooden arrow's weight balanced without trying to drill a hole straight through its center (lengths of wood usually aren't uniformly dense) and while the stability-to-weight ratio increases, there's actually an overall loss of stability due to the loss in mass.  I'm starting to think I've put too much thought into this at this point...but still, always happy to contribute to a dialog!

TLDR;

Grandbows = Good at damaging/wounding individual high-value impact-resistant targets like Greatshells and possibly shardbearers and castle walls as well.

Grandbows = Suck at killing soldiers compared to what a shardbearer is, generally-speaking, otherwise capable of.

[Rasarr]

@hwiles - this is a fascinating analysis (and this entire threat is amazing and awesome, as an aside), but referring to grandbows being less-than-useful as an anti-personnel weapon, we know Sadeas was carrying a grandbow with him and Parshmen don't possess castles. Could warform, with its armour and increased toughness, be a valid target for a weapon as overpowered as this?

[Erunion]

3 hours ago, Rasarr said:

@hwiles - this is a fascinating analysis (and this entire threat is amazing and awesome, as an aside), but referring to grandbows being less-than-useful as an anti-personnel weapon, we know Sadeas was carrying a grandbow with him and Parshmen don't possess castles. Could warform, with its armour and increased toughness, be a valid target for a weapon as overpowered as this?

Depending on the user, EVERYTHING is a valid target for a weapon as overpowered as this...
 

Shardbows are likely favoured by 2nd line generals - officers who want to engage in the fight but not get stuck in. Wielding a shardbow, a shardbearer could do damage while directing a battle or while acting as a reserve (holding back until a weak point opened up, either in the enemies line to be exploited or in your own line to be shored up). 
Furthermore, you may well be able to take out multiple opponents with a shardbow - it's so overpowered that it might simply pulverize the target area and move through, hitting another target behind (or dragging the first body with it). 

[+hwiles]

2 hours ago, Rasarr said:

@hwiles - this is a fascinating analysis (and this entire threat is amazing and awesome, as an aside), but referring to grandbows being less-than-useful as an anti-personnel weapon, we know Sadeas was carrying a grandbow with him and Parshmen don't possess castles. Could warform, with its armour and increased toughness, be a valid target for a weapon as overpowered as this?

In general, no, I don't think a shardbow would be particularly useful for sniping individual soldiers or parshendi.  That's not to say it couldn't be used that way; a person or pashendi hit by a Grandbow would probably resemble a cake being hit with a baseball, armor/carapace or no armor/carapace.  But it comes down to a question of battlefield tactics and combat effectiveness.  In general, I would think that a shardbearer, whether they have a shardblade or are completely unarmed, is going to be most effective in close quarters combat, specifically, at the head of a charge where they can either cut through, smash, or otherwise maim multiple targets with sweeping strikes, while using their incredible weight and momentum to tear open holes in enemy lines.  I believe Dalinar and Adolin make use of this type of maneuver several times to open holes in parshendi lines, allowing their normal infantry soldiers to outflank and rout the enemy.

A Grandbow might be good for taking potshots at an enemy shardbearer whom you didn't want to face in close quarters...But even at the very start of a battle, even an unarmed shardbearer is almost always going to be more useful leading a charge than sniping individual targets.  It's difficult to imagine realistic scenarios where such a weapon would be of strategic use except for hunting greatshells, where mobility is key, or taking potshots at enemy shardbearers during lulls in a battle, since traditional siege weapons (which can be operated with just a handful of normal soldiers) would still outstrip them in terms of range and destructive force, and normal arrows (which can be shot in huge numbers by normal soldiers) are a pretty effective anti-infantry tool already.

[+hwiles]

14 minutes ago, Erunion said:

Depending on the user, EVERYTHING is a valid target for a weapon as overpowered as this...
 

Shardbows are likely favoured by 2nd line generals - officers who want to engage in the fight but not get stuck in. Wielding a shardbow, a shardbearer could do damage while directing a battle or while acting as a reserve (holding back until a weak point opened up, either in the enemies line to be exploited or in your own line to be shored up). 
Furthermore, you may well be able to take out multiple opponents with a shardbow - it's so overpowered that it might simply pulverize the target area and move through, hitting another target behind (or dragging the first body with it). 

I hadn't considered the fact that you really could conceivably damage multiple targets with a single Grandbow arrow, so props on that point.

But 2nd line generals in Altheti forces generally loan or give their shardplates and blades to their more combat-skilled underlings as I understand it.  A reserve shardbearer strikes me as a little odd.  The parshendi do it to try and kill Dalinar...but not deploying their shardbearer early also needlessly cost them hundreds, maybe thousands, of additional lives as part of a gamble that didn't pay out...I'd think a shardbearer would be more useful for creating weakspots in enemy lines, rather than taking advantage of them.  Who knows though, Sanderson is a tricky one, I can't say I'd be completely dumbfounded if he found a way to make good use of Grandbows later in the series.

Edit: Sorry for the double-post...I didn't realize @Erunion responded before my last one posted...

Edited July 5, 2016 by hwiles

[Erunion]

8 hours ago, hwiles said:

I hadn't considered the fact that you really could conceivably damage multiple targets with a single Grandbow arrow, so props on that point.

But 2nd line generals in Altheti forces generally loan or give their shardplates and blades to their more combat-skilled underlings as I understand it.  A reserve shardbearer strikes me as a little odd.  The parshendi do it to try and kill Dalinar...but not deploying their shardbearer early also needlessly cost them hundreds, maybe thousands, of additional lives as part of a gamble that didn't pay out...I'd think a shardbearer would be more useful for creating weakspots in enemy lines, rather than taking advantage of them.  Who knows though, Sanderson is a tricky one, I can't say I'd be completely dumbfounded if he found a way to make good use of Grandbows later in the series.

Edit: Sorry for the double-post...I didn't realize @Erunion responded before my last one posted...

And here we strike another of Erunion's geek points - military history and tactics. Last time I geeked out on this on these forums I wrote a 2000+ word essay. By accident. You have been warned (it's in the first couple pages of 'Roshar vs. Scadrial', if you're interested....).

Shardbearers are unique. They're much akin to super heavy cavalry, or even tanks in more modern combat. Strong, mobile, deadly, almost unkillable in a direct confrontation, but vulnerable to being swarmed and overwhelmed. 

As such, I see them being used much like I would use kataphractoi, or late medieval knights, or other units of super heavy cavalry. You have a plethora of deployment options.

You can treat them as classic medieval Knights - charge the enemy head on, pull back, reform, then charge again. Repeat until the enemy breaks and runs. 

You can use them as a flanking force - tie down the enemy with your main line, then sweep your shardbearers (likely with cavalry) around the flanks and hit the enemy in the sides or the rear (much akin to the Zulu 'horns of the buffalo' tactic). 

You can use them as Dalinar does, as the vanguard of your force - striking deep into the enemy lines, shattering them, and then holding the gap open for your footsoldiers to exploit. This exposes the shardbearers to great risk, but protects those self-same footsoldiers. Greatest risk to the bearer, least risk to the infantry. The main disadvantage, however, is flexibility. Once stuck in; it's hard to get out. Having your shardbearer engaged in a brutal front line conflict 

You can use them as your second attack - hold them in reserve, and then send them to deal with problems or exploit gaps. This is, by far, the safest and most sensible usage of a shardbearer, if not always the most effective. 

 

The tactics used would inevitably vary with the situation. Every battle is different, every army you bring in is slightly different, every enemy you face is different, every battlefield you fight over is different. Somedays, you would NEED to use your shardbearers as Dalinar does on the shattered plains - use them to hold a beachhead while a bridge is lowered behind, or to hold a breach in a cities walls. Somedays you would face an army in an open field, not holding close formation. Then you would sweep in with shards, cavalry and heavy infantry, and with luck sweep the enemy off the field (like Theoden's Eored before the walls of Minas Tirith). Other times you would face down against a strong wall of infantry. Then it would be wisest to send the shards around the flanks while engaging the main body of the foe, so that they would take the enemy from the side and disturb their lines the whole way down. 

Most often, were I to have shardbearers, I would hold them in reserve. Not for long - but just long enough to see how the battle was going, what the enemy was doing. The shardbearers could be used to blunt any spearhead as my foe tried to pierce my lines, or foul a flanking attack. More often, once the battle was engaged, I might see a chance to break the enemies lines and win the day, and to that task I would set my shardbearers and the cream of my forces in their tow. 
And so my shardbearers would have bows. Not to make a huge difference, but to give them something to do, some useful task they can accomplish while I hold them back, waiting for the opportune moment to strike. 

[+hwiles]

8 hours ago, Erunion said:

....

The tactics used would inevitably vary with the situation. Every battle is different, every army you bring in is slightly different, every enemy you face is different, every battlefield you fight over is different. Somedays, you would NEED to use your shardbearers as Dalinar does on the shattered plains - use them to hold a beachhead while a bridge is lowered behind, or to hold a breach in a cities walls. Somedays you would face an army in an open field, not holding close formation.

....
And so my shardbearers would have bows. Not to make a huge difference, but to give them something to do, some useful task they can accomplish while I hold them back, waiting for the opportune moment to strike. 

Touche, it seems I have played the part of the Fool Eshu.  You're right of course, I was mainly only giving consideration to battles involving two sides of well prepared tight lines of soldiers...a silly mistake on my part, but still glad I made it considering the quality of the counter-argument it drew out.

[Erunion]

7 hours ago, hwiles said:

Touche, it seems I have played the part of the Fool Eshu.  You're right of course, I was mainly only giving consideration to battles involving two sides of well prepared tight lines of soldiers...a silly mistake on my part, but still glad I made it considering the quality of the counter-argument it drew out.

Ahahahah thanks! I have probably spent too much time thinking about historical/fantasy battles.... I blame a childhood spent strategy gaming with brothers. (Board games, video games, games we'd make up on paper - we did it all)

[+hwiles]

1 hour ago, Erunion said:

Ahahahah thanks! I have probably spent too much time thinking about historical/fantasy battles.... I blame a childhood spent strategy gaming with brothers. (Board games, video games, games we'd make up on paper - we did it all)

No worries, you won't find any judgement here.  I sort of gave up my right to critically evaluate how other people spend their free time when I decided to systematically identify and analyze specific scenes in fictional stories and attempt to apply mathematics to them in an attempt to establish a more-or-less concrete continuity between the abilities of magical heroes and artifacts.  I consider myself an intelligent person, so trust me when I say that I realize how...silly...that endeavor sounds.  That said, I have no plans on stopping.

To whomever might know or have an opinion:

I've thought of some holes in my first couple posts on this thread that are significant enough that I'd like to amend the numbers I put out, but I'm probably going to be too swamped with work to post for at least a week or two.  Would it be more appropriate to edit my earlier posts, reply to the bottom of this topic, or start a new topic?  I would only start a new topic if I could concisely outline all the "conclusions" I've developed in this topic (amended to reflect the additional information that's become available) as well as present significant new dialog.  If no one has any strong feelings I'll just decide arbitrarily once I'm free again 

TLDR;

Sometimes it's our hobbies that keep us happy enough, as well as sane enough, to be contributing members of society.  Even if those hobbies are a bit esoteric or don't conform with convention.

[asterion137]

Huh. Can anyone think of some kind of cannister shot for grandbows? Not just splinters, but actual balls of lead that sprayed everywhere on contact like a frag grenade. Might not be effective against heavy infantry like the parshendi but against badly armored troops they would be devastating. Something like that might also be effective against shardbearers if you got the shrapnel into their eye slits.

[Three1415]

52 minutes ago, asterion137 said:

Huh. Can anyone think of some kind of cannister shot for grandbows? Not just splinters, but actual balls of lead that sprayed everywhere on contact like a frag grenade. Might not be effective against heavy infantry like the parshendi but against badly armored troops they would be devastating. Something like that might also be effective against shardbearers if you got the shrapnel into their eye slits.

It's an interesting idea, but you must remember bows are much more velocity-limited weapons than modern rifles or grenades; it's unlikely such lead balls would be traveling fast enough to inflict more than minor wounds on those they impacted, unless one were to get a comparatively lucky hit (e.g., to the eyes or throat). More effective would probably be just launching a cluster of normal arrows in a single draw (though the practicality of this idea is up for debate) or perhaps a plethora of sharpened metal slivers, but neither would really replace more than a few standard archers. 

Personally, I see the greatest use for grandbows in attacking entrenched positions with siege weapons (and fairly heavy Shardbearer support) on each side: A Shardbearer, largely immune to the effects of said weapons, could use his superior assault power to briefly cleave a path through enemy lines, whip out a grandbow, loose a few shots at said siege weapons (probably destroying or crippling them), and pull out before the opposing force's Shardbearers could move to intercept. Thus, hit and run tactics against much heavier targets become a possibility. 

Writing this, I realize we really haven't seen Alethi battle strategy when it comes to engagements deploying a significant amount of Shardbearers on each side, or when attacking fortified positions for extended durations; indeed, I don't recall siege weapons of any kind being mentioned in SA at all, though I would be shocked if the Alethi didn't have at least something resembling trebuchets or catapults (this lack of reference is no doubt due to the fact that the Shattered Plains are not a typical combat environment, and the Parshendi are not typical foes). Hopefully we see more of this kind of thing in Dalinar's flashback chapters in OB.

Edited July 7, 2016 by Three1415