Steelpush Physics

therunner · November 12, 2023

1 hour ago, IlstrawberrySeed said:

I brought it up since you say it's the same for a single practitioner, which it's not if their a savant, since they can turn their efficiency up beyond typical levels, which means they can return to regular levels and change it throughout the push. I agree it's best to make the assumption that it's the same throughout the push for the model, especially since we're basing it on "normal" misborn & mistings, but was rather saying it's not necessarily all of the variables at play.

I don't think savants can 'turn up' their efficiency. Rather their efficiency is always turned up because they are savants, and their spiritweb is changed because of that.
If it something they can tune, it could be included in the burn/flare scale as that describes how much effort is the Allomancer exerting.

It is possible I am forgetting something however.

IlstrawberrySeed · November 13, 2023

19 hours ago, therunner said:

I don't think savants can 'turn up' their efficiency. Rather their efficiency is always turned up because they are savants, and their spiritweb is changed because of that.
If it something they can tune, it could be included in the burn/flare scale as that describes how much effort is the Allomancer exerting.

It is possible I am forgetting something however.

It's possible I'm reading into the way Brandon words it, but I specifically remember "can" which implies "but not necessarily."

therunner · November 13, 2023

1 hour ago, IlstrawberrySeed said:

It's possible I'm reading into the way Brandon words it, but I specifically remember "can" which implies "but not necessarily."

Fair enough!

DrPhysics · November 14, 2023

On 11/11/2023 at 8:56 AM, therunner said:

So moderating burn rate (and hence push force) below burn rate it difficult, i.e. using it to explain away issues of your model is ignoring parts of the worldbuilding.

Well, that makes it much harder for the physics to make sense, possibly to the level that we can't consider a push a force. I'll have to chew on this one for a while.

On 11/11/2023 at 8:56 AM, therunner said:

The discontinuity in applied force when coin hits wall/ground is also something unexplained by your model.

Controlling power instead of directly controlling the force of the push would still explain the discontinuity, just not quite how I described it in the example.

DrPhysics · November 14, 2023

I just realized another hole in my model when answering a question on another thread.

While metal seems to follow F=ma, there are several instances where powerful objects (like an allomatic grenade) or people behave as if their mass is much larger than it actually is.

Well, back to the drawing board.

therunner · November 16, 2023

On 11/14/2023 at 11:42 PM, DrPhysics said:

Controlling power instead of directly controlling the force of the push would still explain the discontinuity, just not quite how I described it in the example.

How is that?

Also, I hope I don't come across as 'combative', I just happen to be stronger at hole-poking as it is, than at proposing in-depth explanations myself.

On 11/15/2023 at 12:21 AM, DrPhysics said:

I just realized another hole in my model when answering a question on another thread.

While metal seems to follow F=ma, there are several instances where powerful objects (like an allomatic grenade) or people behave as if their mass is much larger than it actually is.

Well, back to the drawing board.

You could possibly address that by modifying the equation to account for 'Invested-ness' of the object?
I.e. we know that heavily Invested objects are more difficult to affect by Pushes/Pulls (e.g. Shardblades being unpushuble by anyone seen on-screen per WoBs).
If the acceleration goes more like a = F/(m+I), where I is investiture, that would work in broad strokes. (or it could be that the Force applied is reduced by Investiture, F_final = F - I*constant)

Shardblade is light (m small), but gigantically Invested (I huge). Hence, no movement.
Elend is more Invested than Inquisitor (as he is Lerasium Mistborn), hence he is pushed less than Inquisitor.

DrPhysics · November 16, 2023

1 hour ago, therunner said:

On 11/14/2023 at 3:42 PM, DrPhysics said:

Controlling power instead of directly controlling the force of the push would still explain the discontinuity, just not quite how I described it in the example.

How is that?

See the Vin/door example in the very first post of this thread.

idanstark42 · November 25, 2023

Hi!
I wanted to write here for a while now, but got busy with other things.

I have a model I want to suggest, which is a submodel of @DrPhysics's model, with a few specificities that are meant to solve the issues brought up here. But before that, I have a few thoughts about specific topics brought up here:

1. Modulation of force: It seems from all accounts that modulation of the force is probably impossible, and what is possible is using PWM to control the average force over time. This made sense to me because of Kelsier's quote where he says to turn the poewr on and off. I thought that better control of the "strength" would be to learn to turn the power on and off quickly enoguh to have better control over the final result.

2. Mass of Invested objects: Invested objects are known to have some wierd things happening with them and mass. I always assumed this to be a non-classical effect, either reletavistic or quantum, and so I don't think we need to regard it in this model, since allomancers and the metals they control are usually not that invested.

3. Steelpushing/Ironpulling & Electromagnetic forces: I think there is a WoB that says those are definity not electromagnetic forces. They of course cannot be directly electric or magnetic forces, since they work on all metal and not just on those that are electrically charged or have some specific form of magnetism (ferromagnetic/paramagnetic). This brings up the question: what about transition metals? I mean, steel is technically a metal-nonmetal compund (iron & carbon in the books). What makes a material "metal"? I think, since we are talking about the cosmere here, and I will justify this in my model, that this "metal" a spiritual/cognitive idea defined into the connection that Preservation created when he created Allomancy.

Finishing here because this is getting long, and I'll add the model in another comment.

alder24 · November 25, 2023

17 minutes ago, idanstark42 said:

1. Modulation of force: It seems from all accounts that modulation of the force is probably impossible, and what is possible is using PWM to control the average force over time. This made sense to me because of Kelsier's quote where he says to turn the poewr on and off. I thought that better control of the "strength" would be to learn to turn the power on and off quickly enoguh to have better control over the final result.

You can do that:

Spoiler

Seonid

Is the level of burning a continuous distribution, can I burn 0.1 level of steel all the way up to flaring? Or is it just I burn or I flare?

Brandon Sanderson

The more skilled you are, the more you have the ability to moderate that. For most people it is burn or flare. But you can kind of burn up to a flare, does that make sense? Going below is really hard.

Seonid

Can you push a flare?

Brandon Sanderson

Yes.

Salt Lake City Comic-Con 2014 (Sept. 4, 2014)

21 minutes ago, idanstark42 said:

What makes a material "metal"? I think, since we are talking about the cosmere here, and I will justify this in my model, that this "metal" a spiritual/cognitive idea

Yes, kind of. Metals in the periodic table count in Allomancy, but in its most powerful application, Allomancy can affect even fundamental forces. WoBs:

Spoiler

Questioner

What's the chemical definition of a metal in Mistborn? Is it the entire chunk of the periodic table defined as a metal, or...?

Brandon Sanderson

A: It is technically that [...], but many of them are Allomantically inert. But things like cesium still count.

Shadows of Self Chicago signing (Oct. 12, 2015)

24 minutes ago, idanstark42 said:

defined into the connection that Preservation created when he created Allomancy.

Preservation didn't create Allomancy, Allomancy (and invested arts) just happened on its own based on the interactions between Shards of Ruin and Preservation and the world they've created. Invested arts aren't created by Shards, they just appear. Invested arts are manifestations of Shardic powers of creation.

Spoiler

Kaimipono

Allomancy is fueled by Preservation's body? How exactly does that work? And how does that interact with Atium—it's fueled by both gods' bodies?

Brandon Sanderson

The powers of Ruin and Preservation are Shards of Adonalsium, pieces of the power of creation itself. Allomancy, Hemalurgy, Feruchemy are manifestations of this power in mortal form, the ability to touch the powers of creation and use them. These metallic powers are how people's physical forms interpret the use of the Shard, though it's not the only possible way they could be interpreted or used. It's what the genetics and Realmatic interactions of Scadrial allow for, and has to do with the Spiritual, the Cognitive, and the Physical Realms.

[...]

Hero of Ages Q&A - Time Waster's Guide (Oct. 15, 2008)

Spoiler

Questioner

From what I understand, Ruin and Preservation create the world together, and they created humanity as copies of the original humankind. So how did they give Allomancy to Scadrial?

Brandon Sanderson

Yes. So the magic systems are kind of built into the setting and the world. And there are certain natural pathways that exist, in the same way there are certain natural pathways for them to create life. Which is my explanation for why life is so similar on all the different planets, is that they're following natural pathways, and these magics are kind of the same way. For instance, Lightweaving predates the Shattering of Adonalsium. A lot of these other things are suggestive of magics that existed before that were built around Adonalsium. They weren't 100% created by the Shards, but they also do have the Shards' influence on them.

Skyward San Diego signing (Nov. 7, 2018)

idanstark42 · November 25, 2023

Ok, so here is the model. There are two ideas here:
1. The force is an inverse squared force (sort of)
2. The force is based on Connection.
Let's start with the first. Given that the force is a simple inverse sqaured force with a constant nominator

F = k/r^2

When one pushes on a coin (we'll get to the third law in a minute, assume for now that the push is strong enough to push the person upwards), there will be a point of equillibrium in the middle of the air:

mg = k/r^2

r = sqrt(k/mg)

Pretty basic stuff so far. This will be true of course for any force reducing with distance, so the only reason to hang on to the inverse sqaure model is that we are working in 3d, and this is just the rule for field forces in 3d. However, this idea solves, I think, our 1st law problem: depending on the strength of air resistance and friction, the initial position, and the constant k, there will be an oscillation period or there will not be (depending on the total damping ratio). This could be a tool to calculate possible values of k, since we know that for the most part there were'nt oscillations in the book, or if there were they were very small.

Now for the second idea. This, I think, is the more far-fetched, but the one that solves our 3rd law problem. The idea is that the blue line, which is a visualization of the Spiritual Connection between the metal and the allomancer, dictates the distance between them directly, yet it has some form of elasticity. This means, that the actual force applied follows:

F = k * (R - r)

Where r is the current distance and R is the distance spelled by the connection. In this idea, Steelpushing allows the allomanct to add length to that Connection, and Ironpulling allows them to remove length from that Connection. This does not follow the inverse square that I talked about above, but I'll merge the two ideas in a minute.

Let's assume the rate of adding length is constant R = r0 + αt Where r0 is the initial distance, and therefore the initial length of the connection, and α is the speed of the connection. For simplicity let's define r0 = 0. The force is then:
F = k * (αt - r) = mr''

This simple equation is solved into

r = αt + c1*sin(ωt)+ c2*cos(ωt), ω = sqrt(k/m)

Which shouldn't be a surprise. I don't know yet what the right rate of change is for the length of the Connection, but something tells me it won't really be constant. What this does promise is that we have the position of the person which is directly connected with the position of the pushed object. Solving for the two body problem, first when they are both free and then when one is non-moving, we get the result of pushing on a coin: When the coin is in the air, the allomancer would be only slightly pushed, depending on the relation to the total mass of the system, and when it's on the ground, it will be pushed with the entirety of the force.

So we have two seperate solutions, one for the 1st law problem and one for the 3rd law problem. Now we need to combine them.

The combination I thought about is simply to put the second solution into the nominator of the inverse sqaure law. This made sense to me since in this model the strength of the power comes from adding the length to the Connection, but it can the constant k can still be modified using the inverse square law. We would get something like:

F = k * (R - r) / r^2

Putting R = αt and solving is not so simple this time (I didn't have time to fight over this equation, but if you find a solution I'd love to see ), but what we can do is see what the potential is. The potential for force for any specific R is
φ = k(2R/r + ln(r))
Which has a minimum point at, of course, r = R. Add mgh to the potential (or in this case mgr) and you get a slightly lower point of equillibrium. The interesting thing is that the force itself has a maxima in 2R, after which it becomes weaker until it reachs 0 at infinity.
So, we got a model that follows the 1st and 3rd law requirements and work with WoBs and things we know about the world. The things that this model does not take into account and are very interesting:
- What affects the constant k? We talked about mass of the allomancer, mass of the object maybe? metalic compund? what else?
- What about the coin bending, breaking, flattenning or staying in the air? This model doesn't explain those issues.

So what do you think?

idanstark42 · November 25, 2023

6 hours ago, alder24 said:

Preservation didn't create Allomancy, Allomancy (and invested arts) just happened on its own based on the interactions between Shards of Ruin and Preservation and the world they've created. Invested arts aren't created by Shards, they just appear. Invested arts are manifestations of Shardic powers of creation.

You're right of course. I forgot about this.

I see two interesting things in this part: the one where he said he went with his gut, and the part where he talks about fundamental forces.
Fundamental forces mean that this is something behind metals per se, and we could look at a Connection at the fermionic scale, I would love to connect this to soemthing like the orbitals and the solutions to the Spherical Laplace's Equation, but for now I don't see if that's possible.

Edited November 25, 2023 by idanstark42
Forgot to add one line.

DrPhysics · November 27, 2023

On 11/25/2023 at 3:55 PM, idanstark42 said:

Let's assume the rate of adding length is constant R = r0 + αt Where r0 is the initial distance, and therefore the initial length of the connection, and α is the speed of the connection. For simplicity let's define r0 = 0. The force is then:
F = k * (αt - r) = mr''

This simple equation is solved into

r = αt + c1*sin(ωt)+ c2*cos(ωt), ω = sqrt(k/m)

You didn't factor in how alpha depends on r. Unless you are assuming that alpha is constant. That would explain the sudden increase in force when the object being pushed hits something solid, but doesn't describe regular leaping through the air.

On 11/25/2023 at 3:55 PM, idanstark42 said:

Putting R = αt and solving is not so simple this time (I didn't have time to fight over this equation, but if you find a solution I'd love to see )

I couldn't find an analytical solution, but I only fed it into Mathematica. If it has one, it isn't easy to find.

On 11/25/2023 at 3:55 PM, idanstark42 said:

The potential for force for any specific R is
φ = k(2R/r + ln(r))

Combining the forces to create this potential doesn't fix the first law problem, it just shifts the equilibrium point. To fix it, you'd need some sort of very strong damping, (proportional to the velocity) so that you have an overdamped system. But, that damping would also have to make sense with Wax speeding up bullets and Duralumin-enhanced jumping.

Or we can use the copout that Vin pushing up on a coin to stop at the top has some cognitive realm-based damping because she was expecting to stop which isn't present in other examples of steelpushing.

idanstark42 · November 28, 2023

15 hours ago, DrPhysics said:

You didn't factor in how alpha depends on r. Unless you are assuming that alpha is constant. That would explain the sudden increase in force when the object being pushed hits something solid, but doesn't describe regular leaping through the air.

Yes, in this model, all dependency on r is direct. If alpha is not constant, I don't see it as related to the distance. Perhaps to the power, as energy is drawn from the body of Preservation.

Can you explain the percise situation this doesn't explain? Because I'm not sure I understand what you're referring.

15 hours ago, DrPhysics said:

Combining the forces to create this potential doesn't fix the first law problem, it just shifts the equilibrium point. To fix it, you'd need some sort of very strong damping, (proportional to the velocity) so that you have an overdamped system. But, that damping would also have to make sense with Wax speeding up bullets and Duralumin-enhanced jumping.

Do we see actual damping in the book? Or do we just not see oscilations? I think that without knowing that for certain we could say that it is very close to critically damped. We could add a damping force to the Connection itself, if neccesary. I did not run the numbers themselves (I don't think we have actualy numebrs, do we? If we did it would make it much easier to check)

Edited November 28, 2023 by idanstark42
pressed enter preemptively

DrPhysics · November 29, 2023

On 11/28/2023 at 4:58 AM, idanstark42 said:

Can you explain the percise situation this doesn't explain? Because I'm not sure I understand what you're referring.

I might be misunderstanding what you mean by distance and how it relates to alpha. Is it cognitive distance or a physical one? The math makes it look like a physical distance. If it represents a physical change in distance, a push would always move you away from an object, so slowing yourself to a stop while moving toward metal would be impossible.

On 11/28/2023 at 4:58 AM, idanstark42 said:

Do we see actual damping in the book?

Only in the scene where Vin pushes herself as high as she can go then stops.

idanstark42 · December 1, 2023

On 11/29/2023 at 7:06 PM, DrPhysics said:

I might be misunderstanding what you mean by distance and how it relates to alpha. Is it cognitive distance or a physical one? The math makes it look like a physical distance. If it represents a physical change in distance, a push would always move you away from an object, so slowing yourself to a stop while moving toward metal would be impossible.

It is the physical distance dictated by the Connection, which is spiritual. The idea is that the spiritual connection creates a physical force that tries to get the distance to match it, that force is proportional to all the things we've seen so far (mass of metal, strength of allomancer, duraloumin, etc.), but also inversly proportional to the sqaure of the distance, like any field force.

I couldn't find the descending scene you talked about, but then again I had to search it online since I don't have the books here with me. In this model, you can slow down, when the force of the Connection is smaller then the force of gravity. Since the rigidity k of the Connection is finite. The equillibrium point would be somewhere in the middle of the air, so you cannot go all the way to the ground. You would have to switch your push on and off to calibrate your falling pace (similar to the PWM I mentioned earlier). Each time you turn off the pushing, the Connection length R resents to the new physical distance r, creating a new, lower, point of equillibrium. This will allow you to eventually, reach the ground.

Again, the scene is not in front of me, but if there is a way to slow my descend (creating an average force smaller then mg), and a way to push myself upwards (creating an average force greater then mg), then there must be a way to calibrate the force, regardless of the distance. This model was meant to show distance relation. Calibration of the force by the allomancer, in my opinion, is best explained by PWM or something similar, but there might be a source I'm unaware of that removes this option.

DrPhysics · December 1, 2023

9 hours ago, idanstark42 said:

Again, the scene is not in front of me, but if there is a way to slow my descend (creating an average force smaller then mg), and a way to push myself upwards (creating an average force greater then mg), then there must be a way to calibrate the force, regardless of the distance. This model was meant to show distance relation. Calibration of the force by the allomancer, in my opinion, is best explained by PWM or something similar, but there might be a source I'm unaware of that removes this option.

Yeah, many scenes don't work without some way for the allomancer to calibrate the strength of the push. I think I'm going to interpret the scenes where it talks about not controlling the strength to really mean that it's very difficult to go below some minimum strength, but then they can calibrate from that minimum up to flare (maximum).

Your model is an interesting one. I like it. Some of these fine details we won't ever be able to solve without concrete data. Until then, one guess is just as good (scientifically speaking) as another.

IlstrawberrySeed · December 4, 2023

On 12/1/2023 at 2:28 PM, DrPhysics said:

Yeah, many scenes don't work without some way for the allomancer to calibrate the strength of the push. I think I'm going to interpret the scenes where it talks about not controlling the strength to really mean that it's very difficult to go below some minimum strength, but then they can calibrate from that minimum up to flare (maximum).

Your model is an interesting one. I like it. Some of these fine details we won't ever be able to solve without concrete data. Until then, one guess is just as good (scientifically speaking) as another.

The way it's worded, I always assumed that variations in push strength given a set burn rate were difficult, and changing burn rate by small amounts is tough, and going below a burn is really tough.

idanstark42 · August 31, 2025

So, I had some thoughts about the pressure issue.

We this happen a few times. Vin and Kel smashing a coin, Wax smashing a gun.
For this to work we need the forces inside the metal to create stress. This means they enact different force on different parts of the metal.

What if the metal acts like a conductor for electric field, with very large Debye length? That would mean the force would get weaker and weaker in the material, and create a force gradient that could cause two oposing forces to collapse the coin.

Thoughts?

Steelpush Physics

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