Iron feruchemy and conservation of momentum

[DoomslugTD]

So, I havn't found anything on this, so if there is already an answer out there please tell me. I was wondering about storing weight and the whole conservation of momentum thing. For example according to science, if you let yourself fall while being 200kg you would be falling with an incredible amount of energy (at terminal velocity (66m/s) it would be about 435600 joules), if you then suddenly stored your weight untill for example you were 10kg you would suddenly accelerate to 20 times your previous velocity (about 1320m/s) untill air resistance slowed you back down, but it does not really seem like the books emphasize this that much and I was wondering if anyone has an explenation? also as a fun thought, if that is how it works, an iron compounder+lashings could effectivly become a rocket, all they would have to do is make themselves like 10000kg then triple lash themselves in a direction and let themselves get to terminal velocity, they could then store weight until they weighed 1kg and go 10000 times faster (around 198000 m/s), and they can just heal from the damage casused by this with stormlight.

[alder24]

44 minutes ago, DoomslugTD said:

So, I havn't found anything on this, so if there is already an answer out there please tell me. I was wondering about storing weight and the whole conservation of momentum thing. For example according to science, if you let yourself fall while being 200kg you would be falling with an incredible amount of energy (at terminal velocity (66m/s) it would be about 435600 joules), if you then suddenly stored your weight untill for example you were 10kg you would suddenly accelerate to 20 times your previous velocity (about 1320m/s) untill air resistance slowed you back down, but it does not really seem like the books emphasize this that much and I was wondering if anyone has an explenation? also as a fun thought, if that is how it works, an iron compounder+lashings could effectivly become a rocket, all they would have to do is make themselves like 10000kg then triple lash themselves in a direction and let themselves get to terminal velocity, they could then store weight until they weighed 1kg and go 10000 times faster (around 198000 m/s), and they can just heal from the damage casused by this with stormlight.

Conservation of momentum is applied in F-iron and A-steel/A-Iron maneuvers. What you describe is happening in the books, but not on that scale. Wax in BoM in conversation with Khriss confirmed that conservation of momentum is, well, coserved. And multiple times he did store/tap iron to gain/lose velocity. But again, not even close to the speed of sound, with far smaller speeds involved. But going extreme speeds like you propose at the end would cause them to be immediately dead, as they would just burn in the atmosphere (stormlight healing takes time). 

Spoiler

Questioner

So during the chase scene in Shadows of Self, it seems to imply that conservation of momentum is...

Brandon Sanderson

Yeah, yeah, yeah, Allomancy follows the law of conservation of momentum, yes. 

Questioner

So that is intentional?

Brandon Sanderson

It is, it does follow the laws of conservation of momentum. That was very intentional.

Shadows of Self Lansing signing (Oct. 13, 2015)

 

Spoiler

Questioner

So, Metalminds: if you store weight, how does that work, do you decrease your mass or...?

Brandon Sanderson

So, storing weight actually plays with your mass, because if you look at how we do the physics of it… This one is really screwy, because we are changing mass and playing with it. You watch, like with Wax decreases his weight while he's in motion he'll speed up, and if he increases it, he'll slow down. The conservation of momentum and things like that, but we'll doing really weird stuff. It's like, how can you store your mass… Well, in the magic system it works, but it’s one of the weirdest things we do. *pauses to sign book* We kind of play loose and free with the physics sometimes. Like the example that I often use is Wayne doing a speed bubble, the light that is trapped in the speed bubble...like if he turns on a flashlight would actually radiate because of the redshift, and you could just kill everybody by flashing that. So, we make the speed bubbles not cause a redshift for that reason. We kind of work with what is good storytelling first, and then work the physics around it, but we have to put in all these little breaks and things like that in there regularity in order to actually have the story.

Shadows of Self San Jose signing (Oct. 9, 2015)

 

[DoomslugTD]

Thank you very much, that makes a lot of sense! as a follow up, would that mean that if wax for example, intentionally saved up a ridiculous amount of weight, he could push off an anchor while weighing an enormous amount, gaining an incredible amount of energy both because he is pushing stronger (cause of his increased weight) and his distance from the anchor is increasing slower (again cause of his weight) then rapidly make himself as light as possible to simulate a super powered duralimen push?

Edited April 18 by DoomslugTD

[Treamayne]

2 hours ago, DoomslugTD said:

Thank you very much, that makes a lot of sense! as a follow up, would that mean that if wax for example, intentionally saved up a ridiculous amount of weight, he could push off an anchor while weighing an enormous amount, gaining an incredible amount of energy both because he is pushing stronger (cause of his increased weight) and his distance from the anchor is increasing slower (again cause of his weight) then rapidly make himself as light as possible to simulate a super powered duralimen push?

From the Coppermind:

Spoiler

The Law of Conservation of Momentum holds when using iron Feruchemy. herefore, a Coinshot who has access to iron Feruchemy can alter their mass in order to increase or decrease their velocity. When one increases their mass, their velocity would decrease in order to equalize their momentum, and vice versa. When drag is put into the equation this creates, one gets an equation with explicit maxima; more simply, when one decreases their mass too much, the force of drag overcomes the increase in velocity via Conservation of Momentum, and therefore causes one to decrease in velocity; this also means there is a specific amount of stored mass where one's velocity hits its maximum.

When taking into account momentum and drag formulae, this should have two zeroes–that is to say, when one stores or draws upon too much mass, it would lead to their velocity falling to zero.

Also, keep in mind that Push Strength is less about weight than proximity:

Spoiler

The force of the Push upon an object is inversely proportional to the Coinshot's distance to said object. This continues until the Coinshot hits a zenith, or point of maximum altitude. This zenith is higher for more powerful Steelpushes, such as those burned in conjunction with duralumin, or with more massive steel anchors.

 

[DoomslugTD]

For the first part, im not saying that the forces of drag would not bring you back to equilibream after a little bit, but the change in weight would be a functionally instantanious change in speed that would let you go much faster for the short amount of time, meaning if you built up enough energy I think you should be able to still launch yourself quiet far. As for the second part, I know that your push does not scale entirly off the weight, though I remember reading somewhere that it does have an effect (for example when wax is super heavy it lets him push a little harder) but not only does the weight do that, it also means that when you steel push you move slower away from the object, meaning you have more time to build up energy from the push. 

[alder24]

12 hours ago, DoomslugTD said:

Thank you very much, that makes a lot of sense! as a follow up, would that mean that if wax for example, intentionally saved up a ridiculous amount of weight, he could push off an anchor while weighing an enormous amount, gaining an incredible amount of energy both because he is pushing stronger (cause of his increased weight) and his distance from the anchor is increasing slower (again cause of his weight) then rapidly make himself as light as possible to simulate a super powered duralimen push?

That would work the other way around. If Wax weighs 1 ton, and he is pushing a metal 100 kg in mass, Wax would not move at all, and metal would fly off into the unknown. Why? What is happening when a Coinshot is pushing on something with far lower mass than he has? The object is pushed away, he is not. What would happen if the object would hit a wall/ground? The object would stop moving, and a Coinshot would now be pushing against the mass of a wall/ground, which would cause him to fly. So the enormously massive Wax won't be able to push himself from many things, as there is no anchor massive enough for that, and most would deform because of force applied, and ground would also deform, which basically would make it very hard for Wax to do something like that. If he find one, he will be able to do it.

The closest he was to something like that was in BoM (I think) when the train car was disconnected, and Wax jumped out to push it back to the whole train.

But again, if he gained a ridiculous amount of speed, air drag would just kill him. So it's a very bad idea.

[DoomslugTD]

So for the point about air resistance, I am fully aware that there is a speed that is fast enough that it will hurt him, but mistborns are shown to not be hurt by things like duralimen pushes, so what im saying here is that he could experiment to get the exact right conditions to go as fast as safely possible. As for my thought experiment, I was more so thinking that wax would push off something anchored to the ground (such as a pole which is firmly planted) as long as he figured out the right weight for the right objects he wouldnt shatter them. If he does that, then when he pushes off the object while weighing a lot he would move away from it a lot slower then if he were a normal weight, meaning he spends more time closer to the object, therefore gaining greater amounts of energy, he could then reduce his weight to the point where he flies very fast, but not fast enough to kill him, thus simulating something around a duralimen push, or even a little bit stronger. 

[alder24]

17 minutes ago, DoomslugTD said:

but mistborns are shown to not be hurt by things like duralimen pushes,

That's mostly because they were duralumin burning pewter as well. In many cases they would get serious injuries without burning pewter with duralumin.

19 minutes ago, DoomslugTD said:

I was more so thinking that wax would push off something anchored to the ground (such as a pole which is firmly planted)

The pole would get crushed and nailed deep into the ground, absorbing a lot of energy.

 

But yes, Wax can do that, he can become heavier and push himself up, then store weight. I don't remember if he did that in books (he sometimes stores weight after normal push), but going unreasonably extreme like you are proposing is, well, unreasonable and dangerous.

You have to also consider landing. Coinshot can only push so far away (30 ft max? Vin pushing alongside Luthadel wall), he would gain a lot of energy, which he would have to lose in a very short period of time before safely landing. That's another reason why you don't want to go that fast. Becoming 10x as heavy would make you go 10x or more as fast later, that's more or less safe. Do that, don't go into extremes. 

[DoomslugTD]

Thank you, that makes a lot of sense. 

[Treamayne]

7 hours ago, alder24 said:

That's mostly because they were duralumin burning pewter as well. In many cases they would get serious injuries without burning pewter with duralumin.

1 hour ago, DoomslugTD said:

Thank you, that makes a lot of sense. 

You may want to check out this thread. Granted my original question was flawed (see the edit) - but it is where I collected all the references showing that strong/Duralumin steelpushes require Pewter to survive. 

Also, I may be misunderstanding, but it seems you think that a continual push would build up Potential Energy that is "released" when he drops his weight. I don;t think it works like that - the Steelpush is a vector (with direction and speed) and that speed adjusts with Mass because of the conservation of momentum - but any investiture spent by pushing while heavier is not likely to just "hang around" as potential energy. The investiture released by burning a metal creates an effect - then returns to the spiritual realm; it's already converted from IUs (investiture units - my generic term until we have a unit of measure) to kinetic energy to create/sustain the push and is gone as it is burned. Otherwise, a normal push would continue to accelerate after a push (if residual IUs were still converting to PE/KE after the "burn") rather than just using the remainnig momentum (as influenced by drag and gravity). 

 I can't think of a single example that creates Potential Energy from burning Steel. IUs convert to KE as long as they are burning and only momentum continues after they stop burning. 

[alder24]

19 minutes ago, Treamayne said:

You may want to check out this thread. Granted my original question was flawed (see the edit) - but it is where I collected all the references showing that strong/Duralumin steelpushes require Pewter to survive. 

He did have pewter? Wow, I didn't know. 

[Treamayne]

1 hour ago, alder24 said:

He did have pewter? Wow, I didn't know. 

Yeah, I missed it too (from the first DuraSteelPush I was dubious - but it was later in the thread when somebody found the reference - so I edited it into the first post)

Edited April 18 by Treamayne

[+Oltux72]

On 17.4.2023 at 9:50 PM, DoomslugTD said:

So, I havn't found anything on this, so if there is already an answer out there please tell me. I was wondering about storing weight and the whole conservation of momentum thing.

It isn't conserved. Let me quote from Bands of Mourning as Waxillium was dancing with who has to be Khrissalla: (chapter 11, page 190)

Quote

Tell me, have you ever tried increasing your weight while in midair

[..]

"I've increased my weight while moving," he said slowly. "It doesn't do anything - all things fall at the same speed, regardless of how heavy they are"

[..]

What if you're soaring through the air on a Steelpush and you suddenly make yourself heavier. What happens?"
"I slow down -

 

On 17.4.2023 at 10:43 PM, alder24 said:

Conservation of momentum is applied in F-iron and A-steel/A-Iron maneuvers. What you describe is happening in the books, but not on that scale. Wax in BoM in conversation with Khriss confirmed that conservation of momentum is, well, coserved.

I am sorry, but no. Waxillium says that allomancy and feruchemy are different. And, yes, Brandon confirms that Allomancy conserves momentum. But that is allomancy specifically. Allomancy has the big advantage that pushing or pulling against something dictates the frame of reference.

With feruchemy you have a very big problem. Momentum in which frame of reference? Scadrial is spinning. You should experience considerable coriolis force each time you store or tap mass. Scadrial is moving around its star. You would experience forces due to that. And so on. Feruchemy on its own does not conserve momentum. Nor does it conserve energy. Every iron feruchemist is a perpetuum mobile. Just put him or her onto a spring.

And this is not just theoretical. We have seen Wax storing and tapping on a train. He was not flung towards the tip or tail of the train, as conservation of momentum would require.

[alder24]

1 hour ago, Oltux72 said:

It isn't conserved. Let me quote from Bands of Mourning as Waxillium was dancing with who has to be Khrissalla: (chapter 11, page 190)

Quote

Tell me, have you ever tried increasing your weight while in midair

[..]

"I've increased my weight while moving," he said slowly. "It doesn't do anything - all things fall at the same speed, regardless of how heavy they are"

[..]

What if you're soaring through the air on a Steelpush and you suddenly make yourself heavier. What happens?"
"I slow down -

 

WoB confirms this is an error. Momentum is always conserved (what Wax meant was that tapping mass doesn't change your gravitational acceleration).

Spoiler

Willbtsg

According to Wax's conversation with Khriss at the party in New Seran, changing weight while falling doesn't have any effect. However, storing/tapping weight while Pushing laterally through the air follows the conservation of momentum.

Peter Ahlstrom

Yeaahh…I will probably have to revise the first part of that discussion when we do the leatherbound for Bands of Mourning. It really isn’t consistent with the second part and how we’ve been accounting for it after it was determined that momentum is conserved. There is at least one scene in The Lost Metal where this comes into play.

MoriWillow

Is part of the issue that Wax is creating a false dichotomy between gravity and a Steelpush? (As both the force of gravity and the force of a Steelpush should change as he changes mass?)

Peter Ahlstrom

There does appear to be a false dichotomy, but it’s about velocity rather than force.

General Reddit 2022 (Oct. 19, 2022)

 

Spoiler

Phantine

I actually asked Peter Ahlstrom (who tends to handle math and magic system interactions with physics for Team Sanderson) about this a little while ago

A couple of friends and I are discussing if the iron feruchemy causing changes in speed is a retcon (since there's a mention in AoL that "increasing his weight manyfold would not affect his motion"), or if the effect is just more complicated (like only causing an instant change in speed if Wax changes weight while actively pushing on something).

Are you willing to weigh in on that, or is it just something we shouldn't be thinking too hard about?

Thanks

And his response was

I just don't know the answer to this question.

So I personally think the explanation is either 'Brandon thought it would be cooler for shifting your weight to change your velocity, and forgot he had mentioned it a couple times' or 'this is Wax's twinborn perk'. I'm leaning towards the latter, since the person who writes the magic system summaries at the end of the book specifically interrogated Wax about the effects, and mentioned she specifically was interested in his very unusual power combination.

As for the density thing, there is an explicit mention that you appear to get stronger when tapping, but only to the extent that you can still stand up and walk around - you still have more difficulty moving around overall. So (to pull out random numbers), if you're at 200% normal mass, you have 180% normal strength, and at 50% mass you have 60% normal strength. That means Wax habitually going around at 75% weight so he's 'light on his feet' makes sense - even if he's weaker overall, he's proportionally stronger.

The way I personally think about things for bullets or whatever, anything 'inside' the body (where 'inside' is defined in the same way that pushing/pulling metal 'inside' the body uses it) interacts with your body as if it were normal. So tapping iron doesn't cause your ultra-massive blood to be impossible for your heart to pump, but it also doesn't prevent a bullet from passing through your flesh. That seems to be consistent with how it's portrayed in the books.

Brandon Sanderson

Just a note: in the quote of mine above, I was trying (I believe) to find a way for Wax to indicate that weight doesn't influence the rate at which he falls. IE, acceleration in regards to gravity. It's tough, and I made the call (perhaps incorrectly) not to use modern physics terminology in the W&W books. It has been very hard then to explain:

1). Wax changing his weight doesn't change the pull of gravity on him, or the rate at which he falls. 2) He DOES follow the laws of conservation of momentum.

My talking around these things has let me to tie a few paragraphs in knots.

General Reddit 2016 (Feb. 19, 2016)

 

1 hour ago, Oltux72 said:

With feruchemy you have a very big problem. Momentum in which frame of reference?

That thread was written 2 months ago...

Recently we've discussed F-iron behavior in different frames of reference which does indeed cause a problem with conservation of momentum. This might be an oversight from Brandon and Peter, or there is something we still don't know - or we're poking holes too deep and this won't ever matter in books. After all, those are fantasy books with fantasy physics which will never work in real life no matter how hard we try. We need Brandon and Peter's words on this one.

[Firesong]

On 4/17/2023 at 9:22 PM, Treamayne said:

From the Coppermind:

  Hide contents

The Law of Conservation of Momentum holds when using iron Feruchemy. herefore, a Coinshot who has access to iron Feruchemy can alter their mass in order to increase or decrease their velocity. When one increases their mass, their velocity would decrease in order to equalize their momentum, and vice versa. When drag is put into the equation this creates, one gets an equation with explicit maxima; more simply, when one decreases their mass too much, the force of drag overcomes the increase in velocity via Conservation of Momentum, and therefore causes one to decrease in velocity; this also means there is a specific amount of stored mass where one's velocity hits its maximum.

When taking into account momentum and drag formulae, this should have two zeroes–that is to say, when one stores or draws upon too much mass, it would lead to their velocity falling to zero.

 

 

Nice, some of the stuff I wrote! : )

Extra note on this, while this is what I got from putting in the formulae, it actually is supported in the books, as somewhere in The Lost Metal it does actually talk about when you reduce mass too much, drag starts to slow you down. Think it was when Wax was chasing someone in Chapter 25, but I may be wrong. 

And as what people said before, even if you could increase to absurd levels of velocity via this, they do still have to look at the effects wind resistance has on the body at very high velocities. Windrunners can go close to the speed of sound at their highest extent due to the fact their powers basically lessen the effect around them, but even this has its limits (Oathbringer Chapter 60, Rhythm of War Chapter 9, Rhythm of War Chapter 111). 

It is like what Brandon said about Steelrunners:

Quote

Questioner (paraphrased)

My friend wants to know how fast steel Compounders could possibly go, can they run up walls or over water like the Flash?

Blightsong (paraphrased)

*jokingly* Can they run through time?

Brandon Sanderson (paraphrased)

Steelrunners can resist a lot things due to the power, like they can withstand the Gs they are out through, but they can't ignore wind resistance and friction. They will burn up if they start running too quickly.

OdysseyCon 2016

https://wob.coppermind.net/events/93/#e2695

Addition: the "out through" is sic erat scriptum, not a typo on my part, somebody needs to fix it. 

So, while it is really good at increasing and decreasing ones velocity, and helping one do some pretty strong steelpushes, it does have limitations that prevent it from becoming as powerful as you (Original Poster) presume. 

Hope this helps. 

Edited July 10 by Firesong