Mistborn vs Full Radiant

[8bitBob]

7 minutes ago, Rob Lucci said:

Kaladin could dodge arrows as a proto-Radiant when he hadn't even sworn his Second Ideal yet. Doesn't seem like a stretch to me to assume that a full Radiant can dodge coins, especially with the mobility they have.

Arrows would be nowhere near as fast as coins. Like, not even in the same ball park. Even in shorter distances, where they're at their weakest. Imagine you had a 600 ish pound crossbow (lowball estimate for max weight a Coinshot could lift) with a draw length of twenty feet, as opposed to twelve inches. Pewterarms gain increased speed and reflexes, but it didn't seem to help them to dodge either.

[Vissy]

A full Radiant is on a completely another league compared to a storming Pewterarm.

[8bitBob]

Based on what exactly? The descriptions between Kaladin's abilities (speed, dexterity, reaction times, etc) have always been described pretty similar to the effects of pewter. Extraordinary, but not completely inhuman, which is what it would take to dodge a bullet. Are you sure you're not just overestimating the capabilities of Knights? I'm open to examples otherwise if you disagree.

Edited May 26, 2017 by 8bitBob

[Steeldancer]

All I know is that it would be storming amazing. 

[The One Who Connects]

16 hours ago, Andy92 said:

Eh, not really. Force equals mass x acceleration. A Mistborn shooting a coin using a duralumin steel push is going to have such a high acceleration that the overall force of the coin would probably exceed that of an arrow shot from a bow.

I was more commenting on the fact that coins lack sharp edges (did TFE era coins have an official shape to them? I forget) so an Arrow would have more potential to be deadly, as opposed to the physics of the matter.

[Andy92]

24 minutes ago, The One Who Connects said:

I was more commenting on the fact that coins lack sharp edges (did TFE era coins have an official shape to them? I forget) so an Arrow would have more potential to be deadly, as opposed to the physics of the matter.

Good point to that. Not sure about their shapes in that era. I always imagined them as similar currency to what you see around the word here, just circular coins made from some sort of metal. 

[Calderis]

2 minutes ago, Andy92 said:

Good point to that. Not sure about their shapes in that era. I always imagined them as similar currency to what you see around the word here, just circular coins made from some sort of metal. 

I know it actually has no bearing on the the shape of the coin, but the word "boxing" always made me picture them as square coins. 

[cometaryorbit]

20 hours ago, 8bitBob said:

If Adolin had the strength of twenty to thirty men in Plate, he would have thrown Kelsier clean across the training pit and probably pushed his rib cage out his back.

Not necessarily, it would depend on exactly how the force was applied, positioning etc.

People have survived getting hit by very large bears, and the larger ones probably have something like twenty times the strength of the average man (at least upper body strength - human musculature is more endurance running focused, which is why bulky burst-strength creatures like apes and bears seem so ridiculously strong relative to us).

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I think you're overestimating the durability of Plate and underestimating the strength of Steelpushes. We've often seen Plate be cracked by mundane things such as hammers wielded by regular troops, sling stones from regular troops and enhanced punches

Mundane weapons can do it, but with lots of time and losses among the regular troops. The sling stones were human-head-sized rocks from Warform Parshendi; that's well beyond baseline human strength.

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Imagine trying to kill someone with a forty five pound bow (or sling shot, if that's easier to picture) and all you have to fire is a coin. It's barely going to penetrate even the softest flesh, let alone go clean through as Coinshots have been known to do. If anything else we've seen break Plate can, a Coinshot with a decent anchor most certainly can.

Possibly, but not necessarily. There are two difficulties with determining how effective coins would be against Shardplate:

1) Shardplate doesn't seem to quite work like a better version of conventional armor - it seems like massive blunt force is used against it rather than concentrated force (pointed/edged weapons).  This doesn't line up with the kinds of weapons (flanged maces, estocs, real warhammers which were more like a modern claw hammer than a maul) invented to fight highly developed plate armor in our world.

From what we've seen, it's quite possible that a big slow hammer/stone is a lot more effective vs Shardplate than a small fast coin.

2) Coinshot coins seem to cheat physics a bit. While getting hit with a fast-moving coin would be dangerous, in the real world I don't think it could be made into a reliably lethal/incapacitating weapon against even unarmored normal humans. Against armor, even fairly poor armor, they'd be pretty much useless.

Coins are probably subsonic, due to the lack of sonic booms/bullwhip crack sounds. At 250 meters per second, a 5 gram US nickel would have 156.25 joules of kinetic energy [ from 1/2mv^2: 0.5 * 0.005 kg * (250 m/s)^2 ]. That's very close to a .22 bullet according to this:

That's dangerous, although it's not the kind of bullet one would use against armored enemies. However... the center-of-mass nature of Iron/Steel allomancy means that the coin is almost guaranteed to hit side-on - air resistance will flip it side-on unless the starting alignment is completely perfectly edge-on. So the impact will be spread out over a much larger area - the nickel is 21.2 mm wide, while the bullet is 5.7 mm wide. That's 3.7 times the diameter, but 13.7 times the area. And the bullet is somewhat pointed at the end...

IE, subsonic coins will have basically zero penetration. A jacket or significant fat would probably block them.

And if you increase the speed, you get into "impact depth" issues - basically, you can't make low-mass-per-frontal-area projectiles very penetrating by making them very fast (because of conservation of momentum - to make a hole, the projectile has to push the mass of the armor/flesh/whatever out of the way).

The only way to make side-on coin impacts effective weapons would be to get the speeds so high they start acting like explosives: shooting it out of a railgun at Mach 8 would probably work.

Edited May 27, 2017 by cometaryorbit
force applied

[cometaryorbit]

19 hours ago, Rob Lucci said:

I still think you're overhyping Mistborn. What kind of a Mistborn are we talking about? A prodigy like Kelsier, or your run-of-the-mill TFE-era assassin?

Kelsier isn't that exceptional: he has top-level skill with iron/steel, but Vin is way better. (That comes up in the attack on Cett's tower in WOA: Vin takes out ten hazekillers easily and realizes that Kelsier had a lot of trouble with six.)

And that's before she turns on the duralumin, so it is a fair comparison.

Kelsier is better with iron/steel, but he was only a Mistborn for a couple of years: I wouldn't assume he was all-around better than your average well-trained Noble House Mistborn. Others might be better with pewter, better at processing tin-senses, etc.

(Yes, he killed an Inquisitor, but that was more a matter of knowing its weakness. With that known and the Feruchemical Gold healing advantage therefore mostly taken out of the picture, an Inquisitor -- one that didn't start as a Mistborn anyway -- is going to be weaker in all metals but one than a natural Mistborn.)

[Yata]

19 minutes ago, cometaryorbit said:

Kelsier isn't that exceptional: he has top-level skill with iron/steel, but Vin is way better. (That comes up in the attack on Cett's tower in WOA: Vin takes out ten hazekillers easily and realizes that Kelsier had a lot of trouble with six.)

Actually Kelsier was really strong as raw power compared to TFE's Mistborn. He was actually more powerful (by raw power) of Vin. But she was litherally a genius and her skill fast surpass Kelsier's one.

Ah just a thing regard the Coin (and again "coin" here would mean "little metal object" not leterally coins) VS Gun's bullet. The bullets lose momentum very faster than "coin" as the coin is keep pushed (in the end for it keep to going faster) while the bullet after the first (huge) push has only friction on itself

Another couple of points I considerated over the night:

- As we took the Radiants at their fullnest, could we include savantism or some other bonus from the Mistborn's side ?

- How the hell could Nicrosil interact with Stormlight ? (Because if it's force the Stormlight to go out in a great burst...could be a relevant move from the Mistborn's side.

[8bitBob]

2 hours ago, cometaryorbit said:

From what we've seen, it's quite possible that a big slow hammer/stone is a lot more effective vs Shardplate than a small fast coin.

This is basically why I've always said you'd probably need a better anchor than a coin, and is one of the reasons I said Mistborn would be at a disadvantage if they didn't understand the opponent. WoB says that Plate would stand up pretty well against small arms fire, and that's pretty much what coins are.

You're also right about all of the points about penetration, but I think it's important to remember that this in no way prevents allomancers from killing with them. Steelpushing is that powerful. It's also versatile, so there's no reason they can't just use a better projectile for the job against an armored target.

2 hours ago, cometaryorbit said:

The sling stones were human-head-sized rocks from Warform Parshendi; that's well beyond baseline human strength.

Parshendi are indeed stronger, but they're not Koloss tier or anything. Remember that Roshar is 0.7g, which is going to make things easier than we expect. They were also two handed slings, which I've yet to see in real life, but I imagine makes it easier.

2 hours ago, cometaryorbit said:

From what we've seen, it's quite possible that a big slow hammer/stone is a lot more effective vs Shardplate than a small fast coin.

So yeah, still agree here. I just don't think a Mistborn would find it challenging if they had a heavier projectile. A rock the size of your head is still just a rock, and a hammer is still just a hammer, yet these still managed to crack Plate. The phrase has been used in this thread before, but Steelpushing truly is in another league compared to traditional medieval weaponry. The best comparison we've actually seen is when Szeth drops a many times Lashed large brick from a wall on a Shardbearer, which instantly shatters the breastplate and kills them.

[cometaryorbit]

16 hours ago, 8bitBob said:

So yeah, still agree here. I just don't think a Mistborn would find it challenging if they had a heavier projectile. A rock the size of your head is still just a rock, and a hammer is still just a hammer, yet these still managed to crack Plate. The phrase has been used in this thread before, but Steelpushing truly is in another league compared to traditional medieval weaponry.

Well, depends on what they had available... if there was a large dense metal object available that would be a lot better than a coin. I don't think Steelpushing swords or spears into a Shardbearer would be terribly effective, but if they had something like an ingot or a hammer that would work fine. IIRC it takes a bunch of hits for normal hammers to break Plate though, depends on how much kinetic energy you actually get on a Steelpush of an object that size.

But if Shardplate is resistant to modern small arms, I don't think it would be terribly easy for a Mistborn or Coinshot to break. The Mistborn could keep out of Shardblade reach if they knew about Shardplate's jumping ability, so they could probably wear them down eventually if the Shardbearer was insistent enough on going after them.

[cometaryorbit]

19 hours ago, Yata said:

Actually Kelsier was really strong as raw power compared to TFE's Mistborn. He was actually more powerful (by raw power) of Vin. But she was litherally a genius and her skill fast surpass Kelsier's one.

Vin was definitely super-intuitive about how to use Allomancy, probably better at that than anybody ever.

But given what Kelsier says about Vin being stronger than she should be in the Push contest when they're training in TFE, and the comments about Vin being abnormally strong in the training scene at the beginning of WOA, I think Vin was stronger in raw power than Kelsier.

Kelsier's advantage was his skill/precision specifically in iron and steel, which was very high - there's a WOB that he and Zane were about at the maximum possible degree of control. Given that Kelsier got there without Zane's Hemalurgic boost, that's quite impressive.

[8bitBob]

1 hour ago, cometaryorbit said:

But if Shardplate is resistant to modern small arms, I don't think it would be terribly easy for a Mistborn or Coinshot to break. The Mistborn could keep out of Shardblade reach if they knew about Shardplate's jumping ability, so they could probably wear them down eventually if the Shardbearer was insistent enough on going after them.

Think about the forces involved here. We have seen a Coinshot is capable of lifting at least their self and another person while pushing off a coin, which is a weak anchor. That's easily 300 pounds with gear and clothing just to counteract the effects of gravity, which means it's likely far in excess of this. While some very strong people can lift this kind of weight, their range of force projection is paltry compared to even a short range Steelpush, which is where the real power comes from. With more than a few yards of travel distance, the Kinetic Energy imparted on the projectile is going to immediately dwarf anything the human body could generate.

The easiest way to think about this is in terms of jumping vs Steelpushing. In book one, Vin suspends herself one hundred feet in the air by pushing on a single ingot on the ground, which means she's currently generating enough force to counteract the effects of gravity for a roughly 100lbs person (she's pretty small). I don't think I need to explain how, even with a pewter flare, Vin could have never jumped even close to this height. That is because Steelpushing is practically a cheat mode for generating absurd forces over a distance, and all that kinetic energy can be used as a weapon. Just getting to that height means Vin has a Potential Energy of 13k joules, never mind how much Kinetic Energy that would translate to on the horizontal. That is far, far in excess of the energy that small arms fire generates.

Comparing this to hammers, slings or small arms simply doesn't make sense to me. It really is on a whole other level.

Edited May 28, 2017 by 8bitBob

[cometaryorbit]

1 hour ago, 8bitBob said:

Think about the forces involved here. We have seen a Coinshot is capable of lifting at least their self and another person while pushing off a coin, which is a weak anchor. That's easily 300 pounds with gear and clothing just to counteract the effects of gravity, which means it's likely far in excess of this.

Well, yeah, but I doubt you could break Shardplate just by having someone jump on it. That's an equivalent force.

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While some very strong people can lift this kind of weight, their range of force projection is paltry compared to even a short range Steelpush, which is where the real power comes from. With more than a few yards of travel distance, the Kinetic Energy imparted on the projectile is going to immediately dwarf anything the human body could generate.

No, kinetic energy is just 1/2 * mass * velocity squared. The travel distance isn't going to affect it (bullets, arrows, etc. lose energy as they travel since they lose velocity, but coins are continuously pushed).

And things propelled by Coinshots/Mistborn just aren't moving that fast.

However, they do seem to be able to impart more energy to larger objects. Vin flying has way more kinetic energy than a coin pushed at any subsonic speed. If Vin is 45kg, she'd have 9000 joules of kinetic energy flying at 20 m/s -- which is like 45mph/72kph, they seem to go really fast so that doesn't seem too much. Even at 10 m/s (22.5mph, 36kph), that would be 2250 joules.

Even if my previous coin estimate was low, a 10 gram coin (which is very large coin, US quarter is 5.7 grams, US half dollar is 11.3 grams) moving at 300 m/s would have only 450 joules.

Quote

In book one, Vin suspends herself one hundred feet in the air by pushing on a single ingot on the ground, which means she's currently generating enough force to counteract the effects of gravity for a roughly 100lbs person (she's pretty small). I don't think I need to explain how, even with a pewter flare, Vin could have never jumped even close to this height.

Well, sure, but that doesn't mean Steelpushing generates more force or more power than pewter. A pewter jump is much more limited because the force stops being applied as soon as the Allomancer's feet lose contact with the ground.

Vin floating there is using much less force than she's using to jump (since she's not moving upwards - she's only matching the force of gravity, not exceeding it) but applied for a longer time. But to break stuff, you need bursts of force, so that doesn't make a Coinshot better at getting through Shardplate than a Thug throwing rocks.

1 hour ago, 8bitBob said:

 Just getting to that height means Vin has a Potential Energy of 13k joules, never mind how much Kinetic Energy that would translate to on the horizontal.

Sure, but it can't be applied very usefully as a weapon. That energy was accumulated over time; it's not necessarily comparable to what Vin could achieve in a brief horizontal push.

Now, there's the possibility of lifting a heavy object that would make a useful weapon and dropping it on a Shardbearer... that could be very effective and deadly, but awkward to set up.

[8bitBob]

2 minutes ago, cometaryorbit said:

Well, yeah, but I doubt you could break Shardplate just by having someone jump on it. That's an equivalent force.

No, it's the equivalent of having multiple people jumping on a concentrated point with a far more rigid structure that isn't losing energy to the natural shock absorbing qualities of the human body. It's not the same at all.

Amusingly though, Kaladin actually does almost exactly what you say in the multiple opponent duel by Lashing himself horizontally many times, falling a very short distance and kicking them, and it actually cracks the breastplate, so that would undermine this counter point even if I agreed.

7 minutes ago, cometaryorbit said:

The travel distance isn't going to affect it (bullets, arrows, etc. lose energy as they travel since they lose velocity, but coins are continuously pushed).

What? Yes it does. Maybe this is where we're having issues. Steelpushing applies a continuous force. This means that a longer distance between the target and the starting point provides more time for the force to act upon the projectile, which increases the velocity until it hits a theoretical limit where the force of air friction is equal to the applied force and it stops accelerating, which is going to be significantly higher than terminal velocity for falling objects due to the greater force.

This is the entire reason why Coinshots are deadly. We even have concrete proof of this concept in book one when Kelsier is fighting in a cramped room and, due to the very short distances, it fails to penetrate and just pushes the target back.

19 minutes ago, cometaryorbit said:

And things propelled by Coinshots/Mistborn just aren't moving that fast.

While pushing herself above the wall in book one, Vin describes it as "blurring past" her. It's pretty fast even for people sized objects.

14 minutes ago, cometaryorbit said:

Vin flying has way more kinetic energy than a coin pushed at any subsonic speed.

If Vin were to push on a coin in a vacuum in space, they would both have equal kinetic energy in opposite directions (but different velocities). Actions and reactions and all that. It's only due to air resistance that heavier objects are imparted with more kinetic energy. This is why you need a heavier projectile, as you're going to be able to impart far greater energy into it before it hits the theoretical limit.

So yes, you're probably right about coins, but that is not what we're discussing here.

28 minutes ago, cometaryorbit said:

Well, sure, but that doesn't mean Steelpushing generates more force or more power than pewter. A pewter jump is much more limited because the force stops being applied as soon as the Allomancer's feet lose contact with the ground.

Vin floating there is using much less force than she's using to jump (since she's not moving upwards - she's only matching the force of gravity, not exceeding it) but applied for a longer time. But to break stuff, you need bursts of force, so that doesn't make a Coinshot better at getting through Shardplate than a Thug throwing rocks.

Sure, but it can't be applied very usefully as a weapon. That energy was accumulated over time; it's not necessarily comparable to what Vin could achieve in a brief horizontal push.

Yes, I think this is indeed where we're having issues. If it helps, don't think of it as force, but work. Due to the ability to project force at a distance, a Coinshot can do more more work on a projectile than is humanly possible, and thus impart more kinetic energy. If a five pound object is moving five hundred miles an hour when it hits you, it doesn't matter if it gained that energy instantly or over time, so long as it strikes you at the same velocity.

So yes, Vin's legs apply greater force when jumping, but Steelpushing does more work, and that's more important here.

[Voidus]

Few points, on Pewter vs. Shardplate, a Koloss blade can be up to ten feet long that creatures with the strength of 5 people use and Vin wields one as easily as Dalinar wields his giant hammer that took 2 people to carry and this is an environment with increased gravity.
Now anyone who cared to emulate Vin vs. Straff could hurl themselves and that giant heavy sword from outside of visibility to behind you holding your decapitated head in approximately too fast to react seconds.

For coin vs. Plate, even face side up a coin has an area of less than a 10th what Kaladins foot would have and he could only fall for a very short distance, maybe a couple of meters at most.
Now given that a Mistborn can apply that force for over a hundred meters, even if Kal lashed himself several hundred times it'd still only be equal.

[cometaryorbit]

On 5/27/2017 at 11:28 PM, 8bitBob said:

Amusingly though, Kaladin actually does almost exactly what you say in the multiple opponent duel by Lashing himself horizontally many times, falling a very short distance and kicking them, and it actually cracks the breastplate, so that would undermine this counter point even if I agreed.

The multiple lashings / kick mean a much more concentrated force than a person falling under normal gravity.

 

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What? Yes it does. Maybe this is where we're having issues. Steelpushing applies a continuous force. This means that a longer distance between the target and the starting point provides more time for the force to act upon the projectile, which increases the velocity until it hits a theoretical limit where the force of air friction is equal to the applied force and it stops accelerating, which is going to be significantly higher than terminal velocity for falling objects due to the greater force.

To a degree, yes... but we don't see the coins going supersonic (bullwhip crack/sonic boom effects) so that still limits the total energy.

Also, the force does drop off with distance, though not through anything like a classic inverse-square law. It has to, or Vin could levitate upward from a coin indefinitely rather than stopping at a hundred feet.

 

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While pushing herself above the wall in book one, Vin describes it as "blurring past" her. It's pretty fast even for people sized objects.

If Vin were to push on a coin in a vacuum in space, they would both have equal kinetic energy in opposite directions (but different velocities). Actions and reactions and all that. It's only due to air resistance that heavier objects are imparted with more kinetic energy. This is why you need a heavier projectile, as you're going to be able to impart far greater energy into it before it hits the theoretical limit.
So yes, you're probably right about coins, but that is not what we're discussing here.

Problem is, for a coin to have comparable kinetic energy to Vin travelling at "blurring" speed, it would have to be moving absurdly fast - well into hypersonic speeds.

Also, I think they'd have to have the same momentum - but not the same kinetic energy.  Which makes the problem even worse, since momentum is only linear with velocity, not exponential - so you're talking coins traveling at hundreds of kilometers per second to have the same momentum as Vin traveling at a few tens of meters per second (since Vin probably has something like 10,000 times the mass of a coin - say 45kg vs 2 to 10 grams for a coin).

I think anchor quality is the missing factor here. If Vin pushed on a coin in vacuum, Vin and the coin would get the same momentum in opposite directions - but it would be a tiny amount, since a free-floating coin is a terrible anchor. To fly, Vin has to put the coin on the ground, where it's anchored against the mass of the planet. However, it's still not as good of an anchor as a larger metal object on the ground would be.

A better anchor seems to allow more total force.

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Yes, I think this is indeed where we're having issues. If it helps, don't think of it as force, but work. Due to the ability to project force at a distance, a Coinshot can do more more work on a projectile than is humanly possible, and thus impart more kinetic energy.

True - but as coins still seem to be subsonic, the total work and energy can't be all that high.

[8bitBob]

7 hours ago, cometaryorbit said:

The multiple lashings / kick mean a much more concentrated force than a person falling under normal gravity.

Yes, but he only fell a few feet (had to make it not look suspicious), and Coinshots are also capable of generating more concentrated force than gravity too. Any additional force from the Lashings can easily be made up by a longer distance.

7 hours ago, cometaryorbit said:

To a degree, yes... but we don't see the coins going supersonic (bullwhip crack/sonic boom effects) so that still limits the total energy.

Just because we haven't seen it does not mean it's impossible. For one, a huge amount of the Coinshot combat we've seen involves other Coinshots, which means there are competing forces in opposite directions. For another, it's possible that, just like subsonic rounds, the killing power is enough that more energy and distance are not required. Remember, due to the nature of Allomancy, Mistborn have not had to deal with armor much as it's pretty much suicide.

7 hours ago, cometaryorbit said:

Also, the force does drop off with distance, though not through anything like a classic inverse-square law. It has to, or Vin could levitate upward from a coin indefinitely rather than stopping at a hundred feet.

Yes, the force drops off, but that doesn't mean the coin stops accelerating. It just stops accelerating as much. This will only happen when the Coinshot is incapable of generating a force greater than the force of air friction, which means going incredibly fast or flying very far.

7 hours ago, cometaryorbit said:

Also, I think they'd have to have the same momentum - but not the same kinetic energy.

You are entirely correct here. I blame it on a lack of sleep and having not been in a physics class in a few years.

7 hours ago, cometaryorbit said:

I think anchor quality is the missing factor here. If Vin pushed on a coin in vacuum, Vin and the coin would get the same momentum in opposite directions - but it would be a tiny amount, since a free-floating coin is a terrible anchor. To fly, Vin has to put the coin on the ground, where it's anchored against the mass of the planet. However, it's still not as good of an anchor as a larger metal object on the ground would be.

I think you may be misunderstanding how anchors work, likely due to the use of it in physics. In Allomancy, anchor refers to the size of the object which you are pushing on, not how well it is fixed in place. This means that a coin pushing on the ground is just as bad an anchor as a coin flying through the air. We know it works this way because every time a Coinshot needs to jump really high and far, they use a more substantial anchor. A few examples:

• Vin and Kelsier use ingots to hover that high in the example scene we've been discussing
• To launch the Wilg, Wax pushes off of a large metal plate expressly built for this purpose
• To fly back up to the Wilg, Wax drops a whole gun to use as an anchor, rather than a coin

If simply placing the object on the ground were enough to make it a decent anchor, none of this would be needed.

edit:

Apologies, this is what I get for not rereading. I missed the last sentence here. The idea that anchors are stronger when braced is not crazy, as it could be chalked up to things Connection and Identity. That doesn't seem to be the case though. For example, WoB says that you can do goofy things like store your weight, Ironpull on an anchor you threw in the air to pull yourself up, increase your weight and Steelpush it farther, store your weight and Ironpull yourself even higher, etc etc, effectively allowing you to fly by throwing a rock and hitching a ride. Because magic. If flying anchors were significantly worse, then this sort of thing wouldn't really be possible.

Personally, I think that anchors aren't really a matter of weaker vs stronger forces, but short range vs long range. In my head canon, at two feet away, you could almost equally push on a coin as you could a giant metal block, but you'll more rapidly lose pushing power with the coin than you would the block. This would help reconcile why you can't push coins to completely absurd speeds, as you'll very rapidly hit a point where the force of air friction equals your pushing power.

7 hours ago, cometaryorbit said:

True - but as coins still seem to be subsonic, the total work and energy can't be all that high.

It's actually exceptionally high. Did some incredibly low ball calculations to illustrate it:

Assuming Vin weighs 100lbs, that means she's capable of generating at least 441N of force up to a distance of 100 feet (30.5m). In reality, the actual force she's capable of generating over this distance is far greater, since we know Coinshots generate more force the closer they are. Unfortunately, we have no way of knowing how to describe the distribution of force compared to distance, so I'm just ignoring it and use the lowest confirmed force we know, which is the force to counteract the effects of gravity. Just remember that, due to this, I am lowballing to a massive degree.

According to this random site I found, the weight of a small cast iron cannon shot was 4lbs, or 1.814kg. I think this is a pretty appropriate projectile to take down Plate, so I went with this.

With the force and the mass, we can calculate the acceleration that the projectile will experience if all of the force is placed on the projectile:

a = F/m

With distance, initial velocity and acceleration, we can find the final velocity that the projectile will be traveling at by the time it reaches 30.5m:

Vf^2 = Vi^2 +2ad

Vi is zero, so it can be cancelled out. Therefore:

Vf = (2ad)^0.5

Vf = (2(F/m)d)^0.5

Vf = (2(441/1.814)(30.5))^0.5

Vf = 121.78 m/s

With the final velocity, we can calculate the KE at point of impact after traveling 30.5 meters:

KE = 0.5mV^2

KE = 0.5(1.814)(121.78)^2

KE = 13,450 joules of energy

For reference, according to wikipedia, the muzzle energy (the kinetic energy with which a bullet leaves the barrel) of a 50 caliber rifle is 15,000 joules, while a 9mm pistol is about 520 joules and a major league fast ball is about 140 joules. That is an incredible amount of energy, and far more than the human body is capable of generating. A spherical cannon shot is going to have far less penetrating power, but you've said, and I agree, that it seems like breaking Plate has more to do with hitting hard rather than piercing it. Even if penetration is a factor, a Coinshot is perfectly capable of using a projectile shaped for such a purpose.

Keep in mind, it is guaranteed that Coinshots would actually generate more force than I have used, as discussed earlier.

 

Now, I know someone is going to question air resistance, so I'll just head that off now. For simple objects such as spheres, we can use the formula:

Fa = 0.5ARV^2

Where Fa is the force generated by air friction, A (pi r^2) is the cross section of the area of the sphere that is directional to the trajectory, R is the density of air at sea level (1.225 kg/m³ according to wikipedia) and V is the velocity at the instant of measurement. The force of friction will be greatest right before the point of impact, so I'll use that moment to illustrate how insubstantial it is:

Fa = 0.5(pi (0.0381)^2)(1.225)(121.78)^2

Fa =  41.42N of force due to friction at the moment of impact.

This means that even at the worst point of drag in this scenario, the air resistance is going to account for a less than ten percent loss of efficiency. I think it's reasonable to discount this, as Vin's "real world" force generation is going to be far greater.

 

In conclusion, that is a crap tonne of kinetic energy, and far greater than anything a human could generate. I just cannot conceive of a situation where a bunch of strong guys slinging large rocks can compare to this level of energy.

Edited May 29, 2017 by 8bitBob

[Vissy]

That's of course assuming that they can prepare specifically for cracking Shardplate, accelerate the bit of metal for exactly as long as they need to and have the Surgebinder just stand there doing nothing as the big metal ball of death is speeding towards them. What's much more likely is that the Radiant is going to aim-dodge the cannonball easily and close in on the Coinshot, making his cannonballs (if we assume he can find one then we can assume he has an infinite stock of them, right?) useless or far too risky to use.

Oh and if we're giving Mistborn infinite equipment to choose from, then we should also give the Radiant as much Stormlight as they want.

Edited May 29, 2017 by Rob Lucci

[8bitBob]

54 minutes ago, Rob Lucci said:

That's of course assuming that they can prepare specifically for cracking Shardplate

Yep, as I've said before, Mistborn needs to have appropriate ammunition and understand the basics of Plate to do this. Knight wins resoundingly if it's a blind fight out of nowhere, in my opinion. Well, assuming the Knight happens to be wearing their Plate at the time, that is.

54 minutes ago, Rob Lucci said:

accelerate the bit of metal for exactly as long as they need to and have the Surgebinder just stand there doing nothing as the big metal ball of death is speeding towards him.

According to the same math I just posted, it would take exactly 0.4977 seconds to travel the full distance with it getting faster the closer it gets, making it harder to react to. Additionally, the projectile has a diameter of three inches, which isn't that big or easy to spot from range. Assuming the Knight can even see it coming at a distance of thirty meters, that's going to be pretty hard to dodge.

But let's say a Knight can indeed dodge it. I remain skeptical, but if they spotted it being fired, then they'd have a decent chance to with their increased reflexes and speed. Theoretically, the Mistborn could fire at a rate of 120 rounds per minute since they can immediately fire another projectile after the first. That doesn't mean they can keep firing for a whole minute, unless we say they're just sitting by a massive pile of ammo, but it does mean they can put a huge number of shots down range and then just collect their ammo with an Ironpull and try again, like Vin did with the horse shoes against the Koloss. Basically, this isn't just a one off thing that the Radiant only has to do once, but a constant threat that he will always need to be avoiding while trying to close the distance for a kill.

How many times can you avoid a projectile that's going to put you down? Even if the Knight had a 95% success rate in dodging these, statistics says they're going to get hit eventually, and it's going to be devastating. In addition, this ignores the versatility of Steelpushing. My math was simply meant to convey the sheer energy a Mistborn can generate, not provide a road map for taking down a Knight. Unlike a rifle, a Mistborn can simultaneously fire multiple projectiles at will for less power. It would be a much better idea to send multiple shots down range that are significantly harder to dodge, cracking the Plate and slowing the Knight down, before going in for a single heavy shot meant to end it.

Finally, the Mistborn can also just grab every scrap of metal nearby and Duralumin burst it all down range at completely absurd speeds. I'd like to see anyone dodge that (Okay Rashek, sit down. You could indeed dodge it. Stop showing off.)

Basically, the Knight is going to have to weather a non stop hail of "arrows" that actually present a threat, which is a nightmare for any melee combatant.

edit for your edit:

54 minutes ago, Rob Lucci said:

Oh and if we're giving Mistborn infinite equipment to choose from, then we should also give the Radiant as much Stormlight as they want.

As I mentioned, unlike a rifle, a Mistborn can just reuse ammunition, and they don't need a specific cannonball, but just a piece of metal the right size. Amusingly, Vin actually had the right idea, as horseshoes weigh about 2lbs, which would make a decent anchor for bludgeoning and are pretty common anywhere not Roshar.

So we're not giving the Mistborn infinite, perfectly suited equipment, just literally any metal of substantial size. Not exactly unreasonable when the Knight is bringing what amounts to powered armor.

Edited May 29, 2017 by 8bitBob

[Vissy]

If you want to give the Mistborn a single cannonball and claim it's more or less infinite ammo, that Mistborn would literally have to have Kelsier-levels of Iron and Steel manipulation skills. I guess it's fair to pit Kelsier against someone like Kaladin (when he's become a full Radiant that is), but so far we haven't even see what a full Radiant can do so I suppose it would still be a kind of a toss-up. If the power-ups are anything like First ideal to Second and Second to Third, though, it might be very significant indeed.

Of course you're right that Mistborn are far more versatile. Even a "regular" Mistborn would be able to recycle ammunition. This doesn't mean that they are capable of pushing cannonballs 30 meters in a span of half a second, though - and using Vin as a benchmark is, dare I say, a bit unfair.

Edited May 29, 2017 by Rob Lucci

[8bitBob]

38 minutes ago, Rob Lucci said:

Even a "regular" Mistborn would be able to recycle ammunition. This doesn't mean that they are capable of pushing cannonballs 30 meters in a span of half a second, though - and using Vin as a benchmark is, dare I say, a bit unfair.

To be clear, Vin's "strength" as an Allomancer wasn't because she was literally more powerful (aside from Bronze, due to Hemalurgy), like Elend was, but because she was better at using it with finesse and control. Pushing a bit of metal is easy, and any newbie Coinshot alive during her time should be able to push about as hard. She manages this on her very first night, and Kelsier remarks that, if she doesn't want to use steel to get back down, then she's going to have to explain to the guards why a Mistborn needs to use the stairs, implying any of them could have got up there this way. It would also make no sense for Kelsier to expect her to make it up if the average Coinshot couldn't, seeing as this was her very first use of steel and Kelsier has no idea of her capabilities.

So yeah, I do feel that, by this specific metric, it's entirely fair to use Vin as a benchmark. Especially considering the massive degree to which I lowballed things.

59 minutes ago, Rob Lucci said:

If you want to give the Mistborn a single cannonball and claim it's more or less infinite ammo, that Mistborn would literally have to have Kelsier-levels of Iron and Steel manipulation skills.

I don't really agree. Sure, Kelsier would use it better, but that doesn't mean that he's the only one that could keep track of a piece of metal. They kind of have lines pointing to them. Kelsier was amazing with Iron and Steel, no doubt. He was able to manage large numbers of objects and instantly drop his force when he felt the Inquisitor pull or push on them. In his fight with the Hazekiller's he was able to keep a single ingot of metal constantly flying through the air with expert pushes and pulls, without ever needing to directly handle it with his body. Vin was probably even better towards the end.

That is not what I'm proposing. It takes very little skill comparatively to pick up a piece of metal, hold it to your center of mass and push. Once you stop pushing, you grab another and hold it to your chest and fire. Once you run out, you burn iron and fetch them, manually catching them with your hand. Rinse and repeat. This is pretty much the most basic use of steel and iron, and shouldn't exactly require an expert to pull off. Like you say, even a regular Mistborn should be able to recycle ammo.

[Vissy]

Your calculations don't really match up to what is shown in the books, though. If what you say here is true, Mistborn would be able to rip apart koloss by the thousands with a single volley of coins.

[8bitBob]

1 hour ago, Rob Lucci said:

Your calculations don't really match up to what is shown in the books, though. If what you say here is true, Mistborn would be able to rip apart koloss by the thousands with a single volley of coins.

She does kill Koloss with coins. The issue there is a concept called stopping power, a common thread of discussion for gun enthusiast. It's also why arrows seemed to have little effect on them, according to Sazed. While Vin kills some with coins in Well of Ascension, their greater mass and density means it has to hit something vital to kill, which Sazed remarks upon. To reliably kill multiple Koloss per push, she would have to perfectly line up every coin being launched for, say, a head shot. To make things more complex, as coins pass through multiple Koloss (or get lodged in one) they're going to be robbed of their all important kinetic energy. If she keeps pushing, she'll just be thrown back. If she stops pushing, they'll stop on the first target. To kill with coins, you need to build up energy in travel, and there's just not enough distance in between targets for it to work reliably, from what it seems.

Personally, I think that steel is still the most efficient way to kill en masse, but we don't see a lot of that directly in the books. Mostly because it's reprehensible, but also because other Allomancers exist. In Well of Ascension, Vin specifically cites her low steel and iron reserves do to traveling across an entire dominance as the reason she doesn't use it to fight the army. In Hero of Ages, Vin and Elend fight hand to hand specifically so Koloss will see small people killing large Koloss so they'll feel fear and be open to control through Soothing, so no long range mass killing here either as that won't do the job they're aiming to do.

In situations where there is no Coinshot involved but against regular people, Vin can and has simply cut them down with coins. The one time we do see Vin kill en masse is when she attacks the Cett compound in Well of Acension, and she does indeed use steel to do most of the dirty work. She was also horrified by her actions and thought she was a monster for doing it, which is the real reason we don't see our heroes doing things like this against helpless rank and file soldiers, and why Allomancers weren't used in the Final Empire's army: it's complete overkill.

As for why my specific, large projectile example hasn't been seen, the last time we saw an Allomancer fight armored soldiers, she just threw them around like rag dolls. The need to penetrate armor simply hasn't come up yet. The math is perfectly sound though, and not even impressive compared to other things we've seen them do.

Edited May 29, 2017 by 8bitBob