Steelpush Physics

[DrPhysics]

This started as a discussion with @idanstark42 about quantum mechanics and investiture, then changed enough that we thought we should start a new thread. 

Also, I wrote up a lot of my notes for this in a reddit post, but with the way things are going over there I don't want to leave that as a primary source, so I'm copying the relevant bits over here.

I also want to acknowledge this thread where the topic has been discussed before. Much of my model came about by addressing the oddities brought up there.

Copied content:

Physical Rules of a Steelpush
This section is formatted so that the general rule is the high-level bullet point and any lower-level bullet points are an attempt to briefly explain the relevant physics.

• While steelpushes are related to electromagnetic forces, they can't simply be caused by an allomancer creating and manipulating electromagnetic fields with their bodies.
  • Generally speaking, metals are attracted to anything that creates electric or magnetic fields, so it would be impossible to push on metals. There are some metals (called diamagnetic metals, like silver and copper) that they could push on, but the forces involved would be much smaller than anything we see in the books.
  • An allomancer couldn't target specific metals to push/pull on. Manipulating your charge, for example, would make the allomancer pull on all metals surrounding them.
• The "Strength" of a push is limited by two factors: a maximum pushing force and the Power (energy per time) that an allomancer can produce by burning metals.
  • The books do not give enough details to quantify (turn into equations) the relationship between these two limits.
  • Allomancers (at least those that have described pushing/pulling on metals) either only feel the power of their push OR can't tell the difference between pushing with maximum force or maximum power. My best guess is that they can feel how quickly they are burning the metal and rely on the third law push-back to feel how hard they are actually pushing.
  • The maximum force behaves similarly to how gravity and electrostatic forces do in our universe. They both depend on how much force causing stuff (mass for gravity, charge for electromagnetism) the interacting objects have as well as the distance between the objects. In the case of a steelpush, that limit is the allomatic strength of the individual and how much metal they are pushing on.
  • The power delivered to an object is equal to the force applied to an object multiplied by its velocity in the direction of the force (e.g. if an object is moving north-west and being pushed to the north, only the northward part of its velocity counts). If you "push" two objects using the same amount of power but one is moving faster than the other, the force you apply to the fast one will be smaller than the force you apply to the slow one. Metals are still used up even if the push doesn't generate actual power (e.g. if the object doesn't move), similar to how our body would burn energy if we pushed on a wall without moving it. It takes energy to keep our muscles tense, but we don't deliver any power to the wall unless it starts moving.
• The direction of the force follows field lines like gravitational and electrostatic forces in our universe, but allomancers can manipulate how hard they push on each field line (sometimes without knowing it) and how much of their "self" they are using to push.
  • Field line example: every single piece of the earth pulls on every single piece of you, but when you add up all of those little pulls they act like one big force at your center of mass that points to the center of the earth. If the earth could decide to pull a little more with one side than the other (or completely stop pulling with one side of the planet), you'd get a gravity force that pulled you down and to the side instead of straight down.
  • That line from your center to the center of the earth would be like the blue lines that an allomancer sees. Skilled allomancers appear to be able to subdivide that further.
  • Once you were more than a few body lengths away from an allomancer you wouldn't be able to see a significant difference in force direction from say a pull towards an allomancers hand vs a pull towards their center, but it does allow for tricks like an allomancer pulling a coin from their belt directly to their hand.
• When two (or more) pushes occupy the same space, they add like pressure forces, not like field forces.
  • If you have two gravitational bodies pulling on you equally, every single part of your body (down to the atomic level) gets pulled on equally and the force is effectively zero everywhere in your body. You would feel weightless, rather than feeling like you had two people pulling you apart. (This ignores tidal forces where a tiny piece of your body that is closer to one planet will get pulled on very slightly harder than the other planet. You either have to be the size of a planet or near a black hole before you could feel a difference.)
  • When pressure is exerted on an object, the force changes gradually from one side of the object to the other, with the result that an object caught between two pushes would feel smashed. Likewise, an object caught between two pulls would be ripped apart.
  • These rules are based on what we see in the books. They operate much like how a push from our muscles operates. However, with how important perception (cognitive realm) is to magic in the Cosmere, a very skilled allomancer might be able to start perceiving the forces more like our electromagnetic forces and could do things like push/pull on non-metal objects or lift very heavy metal objects without being crushed, or even feeling any pressure at all (though they would still need an anchor).

Additional Rules Based on Discussion (Edits added later, for more details read the discussion)

• Investiture and/or connection (in both individuals and objects) acts like extra mass in how objects respond to allomatic pushes/pulls but not regular forces
  • The more mass you have, the more force it takes to accelerate you. The more investiture you have, the less you respond to allomatic pushes and pulls.
  • Examples:
    • Elend and a steel inquisitor (both about the same size) both push on the same piece of metal. The steel inquisitor expects them both to be pushed back about the same amount, but Elend (as a very powerful mistborn) hardly moves and the inquisitor goes flying off.
    • Wayne throws a charged "push" grenade into a group of armed people. The grenade rolls in just fine, but the weapons all go flying off. Since the grenade contains ettmetal/harmonium, it is very invested and acts like it has a very large mass in response to the pushes acting back on it (otherwise the grenade would just fly off). However, it is still easy for Wayne to pick up and throw, so it can't be that it suddenly gains lots of actual mass
• There is a minimum push strength which is hard to go below.
  • Vin and Kelsier both talk about how hard it is to fine-tune a push. For example, they both stop themselves from falling with a series of short pushes rather than one sustained weaker push.
  • It is unknown what limits this push (force or power). There just isn't enough detail to conclude which.
  • It may have something to do with what the allomancer expects will happen. Example: early in her training, Vin pushes up on a coin to see how high she can go. Eventually she slows to a stop, and then hangs there. If a strength of a push was only limited by distance (or power), her momentum would carry her much higher than where the force was equal to her weight, then continue to bob up and down centered on the point where her weight and push were equal, like a mass dangling from a spring. Since she slows to a stop and then hangs there, the slowing tells us that her push is actually less than her weight, then suddenly becomes equal to her weight at the stopping point. (There are a few posts discussing possible explanations for this.)

Examples that I've seen discussed and how this model explains them
How does the coin stay up when Vin and Kelsier are both pushing on it (I've also seen this as "does allomancy have friction").

If allomatic pushes were only center to center, when Vin and Kelsier both push on the same coin directly between them it would drop straight to the ground (there is no force holding it up). I've also seen this scene explained with an "if the coin was slightly higher then their centers, then they could hold it up", but that position would be very unstable and any small twitches would send it shooting off in any direction as long as it stayed equidistant from Vin and Kelsier.

The coin would stay easily if they subconsciously pushed more on the top than the bottom. This is something we do all the time with our feet to keep from falling over when standing. We just make tiny adjustments in how we are pushing. To explain it in the Vin and Kelsier case, you could just imagine the coin being replaced by four lumps of metal held together by sticks to form a plus sign. If it starts to fall, the allomancers can push harder on the top than they do on the bottom and it will start to rise slightly. Whenever it starts drifting to the left, pushing a little bit harder on the right would recenter it.

Having the forces add like pressure also explains why the coin was flattened in the push.

Other scenes explained by this differential pushing: Any time an allomancer balances on a single coin (especially Zane's ability to re-orient himself in the air) and Kelsier's ability to start an object rotating during one of his fights with an inquisitor.

**Lost metal spoiler -**

Spoiler

Marsh crushes a gun between his hands.

The above examples only demonstrate allomancers changing how they push on metal while still pushing with their whole selves. When Marsh crushes a gun to get Wax out of jail, he could do that by limiting the push as coming from his hands rather than from his whole self.

 

Vin recoiling when her coin hits a building, also why allomancers don't leap by pushing on coins in the air.

These scenes can both be explained with a power-limited push and by the fact that allomancers can't feel the difference between the force of a push and the power it uses.

In the first Mistborn Vin gently pushes a coin out of Kelsier's fingers and is later thrown back when the coin hits a building. If she was controlling the force of her push, she wouldn't have felt any different when the coin hit the building. According to Newton's third law, the coin pushes on Vin just as hard as she pushes on it regardless of whether or not it has hit a building.

But, if Vin was pushing so that the force felt the same, the coin would continue requiring more and more power to maintain the same force as it sped up. When the coin rapidly stopped by hitting the building, that power would go very quickly from pushing the coin to pushing Vin, whose much smaller velocity would result in a much bigger force.

Technically, an allomancer could jump off a ten-story building and push on a coin with enough force to stay at the same height (they would just need to push with a force equal to their weight). But, that coin would hit the ground in a few hundredths of a second (ten times faster than human reaction time), and the sudden acceleration that would come from them maintaining the power needed to hover would kill them instantly. They wouldn't have time to pull back the power.

It's something that would be possible, but allomancers would very quickly learn not to do it.

For fun, I ran the numbers on what would happen if you dropped a coin from the top of the empire state building and used it to hold yourself up. The time it would take to get from the top of the building to the ground would still be significantly less than even world-record human reaction times and the accelerations due to the coin impacting the ground would be large enough to completely liquefy the allomancer. They wouldn't just break bones. Their bones would be crushed into dust.

Edited November 29, 2023 by DrPhysics
Adding summary points based on the discussion

[therunner]

Good set of notes!

One thing, where does this assertion come from?

Quote

The power delivered to an object is equal to the force applied to an object multiplied by its velocity in the direction of the force (e.g. if an object is moving north-west and being pushed to the north, only the northward part of its velocity counts). If you "push" two objects using the same amount of power but one is moving faster than the other, the force you apply to the fast one will be smaller than the force you apply to the slow one.

I don't recall anything in the books mentioning that or hinting at this, so I am curious what motivated it.

[DrPhysics]

2 minutes ago, therunner said:

One thing, where does this assertion come from?

That is real-world physics. It doesn't come from the books.

[DrPhysics]

Other fun tidbit:

The scene where Kelsier and Vin both push on a coin and flatten it gives us one place where we can quantify the forces involved. The coin is made out of copper (2.7 grams of it if the collectible version can be considered canon, but the weight doesn't come into play when calculating the forces). 

The force is strong enough to flatten the coin and break the small aspen tree that Vin was pushing against. Using the compressive strength of copper and combining that with the shear strength of aspen, Both Vin and Kelsier would have been exerting a force of 12 tons (24,000 lbs or 105,000 N), which a human could easily survive without negative long-term consequences (though it would be impossible to breath in).

 

Edit: Made a math mistake (squared a diameter instead of a radius) The force should be 3 tons, 6,000lbs, or 26,000 N

Edited October 26, 2023 by DrPhysics

[therunner]

2 hours ago, DrPhysics said:

That is real-world physics. It doesn't come from the books.

Oh, I misunderstood then.

Though specifically only velocity due to push would count for the purpose of power, not velocity of the object in general. The way you phrased it it sounded like if I throw a coin and then push it, vs. pushing a stationary coin, one would take more work to accelerate than the other (which yes, due to wind resistance, but that is a different conversation).

EDIT:

Quote

The force is strong enough to flatten the coin and break the small aspen tree that Vin was pushing against. Using the compressive strength of copper and combining that with the shear strength of aspen, Both Vin and Kelsier would have been exerting a force of 12 tons (24,000 lbs or 105,000 N), which a human could easily survive without negative long-term consequences (though it would be impossible to breath in).

Oh, interesting. Would you mind sharing the calculation details?

I will say that this is one of the situations which raises an issue (i.e. is internally inconsistant). If Vin weight ~50 Kg, then such force applied to her would give her acceleration of astonishing 2100 m/s^2, i.e. 210 G's. That would kill her on the spot, if she tried to launch herself with this strength (i.e. when flaring). And this is without A-Duralumin.

Additionally, it would let her accelerate to far higher speeds than what we see A-Steel can do. e.g. 0.01s would lead to velocity of 21 m/s, which is already an upper edge of what Mistborn can do period.

Edited October 26, 2023 by therunner

[DrPhysics]

3 hours ago, therunner said:

The way you phrased it it sounded like if I throw a coin and then push it, vs. pushing a stationary coin, one would take more work to accelerate than the other

It does take more work, even ignoring air resistance.

3 hours ago, therunner said:

I will say that this is one of the situations which raises an issue (i.e. is internally inconsistant). If Vin weight ~50 Kg, then such force applied to her would give her acceleration of astonishing 2100 m/s^2, i.e. 210 G's. That would kill her on the spot, if she tried to launch herself with this strength (i.e. when flaring). And this is without A-Duralumin.

Hopefully, you'll see my edit. The force is 1/4 the size of my original calculation. However, 210 g's actually is survivable, especially if it is distributed all over the body and only lasts a short time (as Vin starts moving, the force will decrease very rapidly and she stops pushing a moment later). Toss in that she was flaring pewter and that she was accelerated backward (the best direction for large g-forces) and the situation becomes even more survivable (Especially when you use the right force and she only feels around 50 g's).

 

To calculate the force, I just took copper's compressive strength (70 MPa) and multiplied it by the surface area of the coin, which according to the replica is 2.2 cm in diameter (NOT radius, like I did the first time, oops). To check the reasonability, I found the shear strength of ash ( 6.0 MPa) and found the diameter of the tree it would need to take that force (6 in. or 15 cm diameter on the bad calculation, 3 inches or about 8 cm on the one I did the right way), and found that it was a plausible situation based on the tree type and the flattening of the coin.

 

[therunner]

10 hours ago, DrPhysics said:

To calculate the force, I just took copper's compressive strength (70 MPa) and multiplied it by the surface area of the coin, which according to the replica is 2.2 cm in diameter (NOT radius, like I did the first time, oops). To check the reasonability, I found the shear strength of ash ( 6.0 MPa) and found the diameter of the tree it would need to take that force (6 in. or 15 cm diameter on the bad calculation, 3 inches or about 8 cm on the one I did the right way), and found that it was a plausible situation based on the tree type and the flattening of the coin.

Thank you!

10 hours ago, DrPhysics said:

It does take more work, even ignoring air resistance.

Ah yes, you are correct. I was thinking of increase in momentum, not energy.

10 hours ago, DrPhysics said:

Hopefully, you'll see my edit. The force is 1/4 the size of my original calculation. However, 210 g's actually is survivable, especially if it is distributed all over the body and only lasts a short time (as Vin starts moving, the force will decrease very rapidly and she stops pushing a moment later). Toss in that she was flaring pewter and that she was accelerated backward (the best direction for large g-forces) and the situation becomes even more survivable (Especially when you use the right force and she only feels around 50 g's).

210g's is barely survivable. In the single confirmed survival the incident led to victim needing 18 months for recovery. That is beyond what Pewter would help with, it does not increase resilience that much.
And the G-force is not distributed all over the body, that is what makes it a g-force and why it's dangerous.

52G's is more reasonable, and certainly survivable, though it would/should knock them out.
However the acceleration is still too high with what we see in other instances (e.g. taking few moments to jump ~30 meter wall when pushing off a coin). If we assume she was not flaring, and that the A-pewter rule (flare about doubles your output) holds, then she would have pushed off with 26 g's.

At that point she is certainly untrained person. Untrained person can experience G-LOC (loss of consciousness due to g-forces) between 4-6 g's if they are sudden. Even if she is flaring pewter (which is not said) and pewter doubles all physical attributes (which is apparently not the case), she should still lose consciousness at ~18g's. But instead she does not describe any symptoms whatsoever.

Combined with her description of flight up, I don't think she was pushing off with more than low G's.

Alternative explanation is that the force of the push decreases exponentially with the distance, for F=F_0 * exp(-x/7.59) you get that (x is distance in meters) at 30 meters, 26 000 N is reduced to about ~1g so she would be balanced (as we see).


One additional note, in the scene in TFE where Vin first jumps using a coin (chapter 8), she mentions that she decelerates as the line grows sufficiently weak. But at the same time she simply stops eventually, left hanging over the line.

That deceleration (despite pushing) implies that the force of the Push is less then gravitational force, but at the same time the force of push must be equal to gravitational force once Vin reaches peak. So the force would have to decrease with distance, and then increase again. Or we can say she was unconsciously modulating strength of her push.

[DrPhysics]

11 hours ago, therunner said:

And the G-force is not distributed all over the body, that is what makes it a g-force and why it's dangerous.

Looks like what I said didn't match up with what I meant. When I said G-Force was distributed all over the body, I meant that the force causing her acceleration should be distributed all over her body. When that happens, you don't get the same negative effects of G-Force (Though she would have felt it when pressed against the tree, and the book does talk about the pressure increasing). 

We feel the negative effects of G-Force when something is pushing against us on the outside (like in a cockpit). That creates a pressure differential, which then makes it hard to pump blood, get oxygen to the brain, etc.

With field forces (and pushes seem to act like field forces unless there are multiple pushes in the same space), we don't get a pressure differential unless something is keeping us from accelerating with the field force. Example: Get a water bottle, poke a hole in the side, then unscrew the lid. You should get a stream of water coming out because the pressure inside the bottle at the bottom is higher than the air pressure outside of the bottle. Now drop the bottle. As it falls, the stream will stop because the pressure equalizes everywhere.

So, If an Allomancer isn't bracing against an object (like a tree), they shouldn't feel a g-force. They would be limited by air resistance, but as long as the air resistance stays below 4 g's, they could have any acceleration and not experience G-LOC. (And if they are going face first, they could push until air resistance hits 40-50 g's (80 with pewter), though that might be fast enough you have to worry about heating). G-LOC and the negative effects of G-Forces are very dependent on both duration and direction. The 4-6 g's figure only applies vertical accelerations that last for a few seconds. You can withstand much higher g's for shorter times, and other directions. Here's a good graph, if you're curious.

And I found the passage you are talking about:

Quote

VIN SHOT INTO THE AIR. She suppressed a scream, remembering to continue Pushing despite her fear. The stone wall was a blur of motion just a few feet away from her. The ground disappeared below, and the line of blue pointing toward the ingot grew fainter and fainter.

What happens if it disappears?

She began to slow. The fainter the line grew, the more her speed decreased. After just a few moments of flight, she crept to a halt—and was left hanging in the air above a nearly invisible blue line.

I can see two interpretations of that (and the exponential wouldn't fix either)

1) Brandon just got the science wrong. In the early books, he made a lot of mistakes with Newton's first law, and Peter didn't catch them. There are some pretty egregious examples all the way up through Starsight. They are better at it now.

2) Vin panics a bit when she asks herself "What happens if it disappears?" and either consciously or unconsciously backs off with her push.

The reason why the exponential won't work is that it doesn't consider her inertia. With the exponential, she'd be at equilibrium at 30 m, but wouldn't come to a stop. She'd overshoot, fall, overshoot, fall, then repeat until she either changes how she is pushing or wind resistance lows her down over hours.

Personally, I think #1 is boring, so I like explanation #2 better. We do similar things with our muscles all the time. We don't choose a force and go, instead, we make tiny adjustments to match the motion we want without thinking about it. 

[IlstrawberrySeed]

On 10/27/2023 at 2:33 AM, therunner said:

One additional note, in the scene in TFE where Vin first jumps using a coin (chapter 8), she mentions that she decelerates as the line grows sufficiently weak. But at the same time she simply stops eventually, left hanging over the line.

That deceleration (despite pushing) implies that the force of the Push is less then gravitational force, but at the same time the force of push must be equal to gravitational force once Vin reaches peak. So the force would have to decrease with distance, and then increase again. Or we can say she was unconsciously modulating strength of her push.

On 10/27/2023 at 2:37 PM, DrPhysics said:

I can see two interpretations of that (and the exponential wouldn't fix either)

1) Brandon just got the science wrong. In the early books, he made a lot of mistakes with Newton's first law, and Peter didn't catch them. There are some pretty egregious examples all the way up through Starsight. They are better at it now.

2) Vin panics a bit when she asks herself "What happens if it disappears?" and either consciously or unconsciously backs off with her push.

The reason why the exponential won't work is that it doesn't consider her inertia. With the exponential, she'd be at equilibrium at 30 m, but wouldn't come to a stop. She'd overshoot, fall, overshoot, fall, then repeat until she either changes how she is pushing or wind resistance lows her down over hours.

Personally, I think #1 is boring, so I like explanation #2 better. We do similar things with our muscles all the time. We don't choose a force and go, instead, we make tiny adjustments to match the motion we want without thinking about it. 

Please correct me if I'm wrong, but wouldn't either of these work:

As V->0, if Push=G, then stationary would be acheived. So one would only need solve for Push modulation based on distance. Personally, it seems that if it decreases tetratively, then some factor would allow it to equal Gravity at the same point velocity roughly hits 0. And crept to a halt doesn't imply single direction either, I envisioned her bobbing slightly for a second.

Alternatively, push strength is also based on velocity, such that it decreases as you speed up, which is why it seems like constant acceleration for longer than a point, and so f(distance) increase and g(velocity) increase would be roughly equal at the start, but at a point f(distance) gets larger than g(velocity), and then G(velocity) starts to decrease as well, causing the g(v)/f(d) approach G. That means that g(0) != 0, but we have the value of both g(0)/f(~0) and g(0)/f(~30), which should let us get some approximate points to play with.

[DrPhysics]

23 hours ago, IlstrawberrySeed said:

then some factor would allow it to equal Gravity at the same point velocity roughly hits 0.

In order for the velocity to reach zero, the push must already be less than gravity in order forher to slow down. Therefore, she has to push with less force, and then increase it. 

23 hours ago, IlstrawberrySeed said:

Alternatively, push strength is also based on velocity, such that it decreases as you speed up, which is why it seems like constant acceleration for longer than a point, and so f(distance) increase and g(velocity) increase would be roughly equal at the start, but at a point f(distance) gets larger than g(velocity), and then G(velocity) starts to decrease as well, causing the g(v)/f(d) approach G. That means that g(0) != 0, but we have the value of both g(0)/f(~0) and g(0)/f(~30), which should let us get some approximate points to play with.

I'm have a hard time following your notation here does f(distance) mean force as a function of distance? or does it mean force times distance? And how is g different from G?

[therunner]

On 10/27/2023 at 11:37 PM, DrPhysics said:

Looks like what I said didn't match up with what I meant. When I said G-Force was distributed all over the body, I meant that the force causing her acceleration should be distributed all over her body. When that happens, you don't get the same negative effects of G-Force (Though she would have felt it when pressed against the tree, and the book does talk about the pressure increasing). 

...

So, If an Allomancer isn't bracing against an object (like a tree), they shouldn't feel a g-force.

I got what you meant, I just don't think that is what is happening.
Allomancers are specifically pushing from the center of self (typically middle of chest) to center of self to object. So based on that force should not be distributed.

Second, if literal Surge of Gravitation causes g-forces despite literally having no reason to, I doubt that steelpushing/ironpulling won't.

Perhaps eventually he will change his mind, but so far it does not seem to be the case.

But at the end of the day, rule of cool will win over physics any day. So if Allomancer needs to push with gigantic force, they will.
And if Surgebinder has to greatly accelerate over short distance, they will do so and won't faint, despite smaller accelerations having impact on them.

On 10/27/2023 at 11:37 PM, DrPhysics said:

G-LOC and the negative effects of G-Forces are very dependent on both duration and direction. The 4-6 g's figure only applies vertical accelerations that last for a few seconds. You can withstand much higher g's for shorter times, and other directions. Here's a good graph, if you're curious.

Thanks for the graph, I did not notice it before.

However, if anything the graph shows that Mistborn cannot accelerate as fast as your calculation estimated (i.e. ~52 G's when flared). If Vin jumped off with 26 G's (since she was pushing as hard as she could, but it was not explicitly said she was flaring), then she would experience over 20 G's for over 0.2 seconds, which is beyond human tolerance in perfect conditions per the graph. And this is with assuming exponential decay of the force, not just 1/r^2.

The graph (and the original book) state that human in perfect conditions can withstand 20 G's for about 0.1 second of vertical acceleration, and even than there is risk of injury. Vin is decidedly not in ideal conditions, and even if A-Pewter doubles resilience to injury, she would be over the time limit and over the acceleration for that time limit.

Flared steeljump would be vastly beyond what is survivable for human based on your calculations,  as 52G's is not even on the graph.

Edit: Second line of argument against even the revised strength, is the very simple fact that if flared Steel can apply 26000 N to a small coin, that coin would have giant acceleration.
Even if we assume it is very heavy (e.g. 100 grams), then the acceleration applied to it will be 260 000 m/s^2), which is definitely far beyond what Mistborn do with the coins.
They don't push coins to supersonic speeds, and these speeds would be far beyond that, since 0.0015 seconds of that force would accelerate the coin to ~360 m/s, beyond sound barrier. And drag forces prior to sound barrier would be far too small to reduce the strength of the push, even with large coin with radius of 2 cm).

So I don't think even the revised calculation is realistic for strength of steelpush, as the force 26000 Newton is simply far too large for everything else we see Steelpushes do.

On 10/27/2023 at 11:37 PM, DrPhysics said:

I can see two interpretations of that (and the exponential wouldn't fix either)

1) Brandon just got the science wrong. In the early books, he made a lot of mistakes with Newton's first law, and Peter didn't catch them. There are some pretty egregious examples all the way up through Starsight. They are better at it now.

2) Vin panics a bit when she asks herself "What happens if it disappears?" and either consciously or unconsciously backs off with her push.

The reason why the exponential won't work is that it doesn't consider her inertia. With the exponential, she'd be at equilibrium at 30 m, but wouldn't come to a stop. She'd overshoot, fall, overshoot, fall, then repeat until she either changes how she is pushing or wind resistance lows her down over hours.

Oh I know exponential won't fix the issue of her reaching equilibrium, the point was that if we take your calculation of strength of steelpush as max output, then the only way that scene could even begin to make sense is if steelpushes weaken exponentially. Additional modifications would be required, or we have to headcannon Vin as unconsciously backing off.

However, since we know that Steelpushes have finite range (i.e. you can push only on objects that are so far from you) than modeling that with exponential decay is reasonable, as we model forces with such behavior that way IRL.

Even assuming that flared Steelpush applies circa ~3000 Newton on coin is way too much. Coin weighing 100 grams would be accelerated with 30 000 m/s^2. Under such force, even assuming exponential decay in strength (exp(-x/8)), the coin would reach sound barrier in about 0.015 second. And that is assuming heavy coin of 100 grams.

You could make argument that typically Mistborn push on multiple coins, so the strength get divided over them. In that case, if they were typically pushing on ~50 coins at once, those coins would achieve speeds of about ~85 m/s in circa 0.04 second, at distance of ~20 meters.

Edited November 1, 2023 by therunner

[IlstrawberrySeed]

On 11/1/2023 at 11:44 AM, DrPhysics said:

In order for the velocity to reach zero, the push must already be less than gravity in order forher to slow down. Therefore, she has to push with less force, and then increase it. 

I'm have a hard time following your notation here does f(distance) mean force as a function of distance? or does it mean force times distance? And how is g different from G?

I guess I don't understand why Air resistance cannot bring it to 0 at the right time, for the first model.

For the second, f() and g() are functions, G is gravity. Sorry for the confusion. I'm sure there is a model that works based on these, it just might not be the simplest (and therefore the one that works based on actual principles). For example, a cubic that spikes at velocity=0, and then slowly increases again as a function of velocity (Or perhaps distance') over a function of distance would allow it to decrease as she approaches the top, then land on the constant |G|.

Edit: I just spent a while trying to figure out a set of functions that worked, but It's hard since I'm having trouble finding a calculator OK with recessive integrals. However, I realized that if it's force oscillates about V=0, then bobbing would be cut to neigh even with a linear or quadratic decrease based on distance.

Edited November 2, 2023 by IlstrawberrySeed

[DrPhysics]

On 11/2/2023 at 10:23 AM, IlstrawberrySeed said:

I guess I don't understand why Air resistance cannot bring it to 0 at the right time, for the first model.

Air resistance is proportional to speed, and while you can have big forces at high speeds, as you slow down they get weaker and will take a very long time to slow you to a "stop" (technically, air drag can never truly stop you).

Also, your model seems to be relying on a "force of motion" (i.e. when force is zero, you stop). That isn't the case.

On 11/1/2023 at 4:27 PM, therunner said:

I got what you meant, I just don't think that is what is happening.
Allomancers are specifically pushing from the center of self (typically middle of chest) to center of self to object. So based on that force should not be distributed.

We also treat gravity as if it pulls on the center of mass, but in reality, it pulls on every single piece of us. The behavior of steelpushes suggests that they follow similar rules (see rule #3 in the original post).

On 11/1/2023 at 4:27 PM, therunner said:

Second, if literal Surge of Gravitation causes g-forces despite literally having no reason to, I doubt that steelpushing/ironpulling won't.

I went looking for examples, and I couldn't find where it's talked about. Do you remember where this happens?

On 11/1/2023 at 4:27 PM, therunner said:

Second line of argument against even the revised strength, is the very simple fact that if flared Steel can apply 26000 N to a small coin, that coin would have giant acceleration.
Even if we assume it is very heavy (e.g. 100 grams), then the acceleration applied to it will be 260 000 m/s^2), which is definitely far beyond what Mistborn do with the coins.

They could for a very short time, but wouldn't be able to maintain the acceleration (see rule #2, the push is limited by both a maximum strength and power delivered).

[therunner]

10 hours ago, DrPhysics said:

We also treat gravity as if it pulls on the center of mass, but in reality, it pulls on every single piece of us. The behavior of steelpushes suggests that they follow similar rules (see rule #3 in the original post).

I went looking for examples, and I couldn't find where it's talked about. Do you remember where this happens?

I think Oathbringer, it is discussed in this WoB (https://wob.coppermind.net/events/315/#e10357). We have to treat entire Cosmere consistently, so for this reason I don't think pushing and pulling can behave like that.

Since Brandon felt it necessary to consider the impact of acceleration on human body in Windrunners, but not in Mistborn, I think we can easily say that Mistborn are nowhere near those accelerations.

Quote

They could for a very short time, but wouldn't be able to maintain the acceleration (see rule #2, the push is limited by both a maximum strength and power delivered).

But what is the limiting power then?
You argue that maximum force is somewhere around 26 000 N, however if the force has to decrease to account for limited power, this fact alone is meaningless.

Vin and Kelsier in their pushing match are clearly struggling, but why would they if they expand same amount of power either way? The force won't magically increase just because there is something stopping the acceleration, if it acts as field as you say per point 3# then force is just gradient of potential.

Additional problem is that the force would go down proportionally to increase in speed, which is too slow, e.g.  if maximum output of Mistborn is ~1 MW, then the coin would feel acceleration of 130 000 m/s^2 when moving at ~80 m/s. When the coin is nearing sonic speed (~300 m/s), the acceleration would still be ~33000 m/s^2, and the force would be still larger than air drag (that being ~80 N ).

We could set maximum power output lower, but we would still run into issues that in some situations the equations match what is in the books, but at others don't.

Final problem is the simple fact that Wax pushes on bullets to considerably increase their speed. If there is maximum power output that stops Mistborn from launching sonic coins, then Wax could not feasibly accelerate his bullets with pushes, because they are already moving at those speeds.
So the 'maximum power output' hypothesis does not match what is shown, as AoL directly contradicts it.

Edited November 7, 2023 by therunner

[DrPhysics]

7 hours ago, therunner said:

You argue that maximum force is somewhere around 26 000 N, however if the force

I've never made that argument.  Only that that was a scene where we could approximate a force.

 

7 hours ago, therunner said:

if maximum output of Mistborn is ~1 MW,

Then it must be much less than 1 MW.

 

7 hours ago, therunner said:

Wax pushes on bullets to considerably increase their speed.

Why isn't that possible? We can use the colt single action army revolver for a stand in. Those would fire a .45 caliber, 16 gram bullet at about 300 m/s.

At that speed, drag alone is about 1 kw. 10 kW of a push would have the bullet moving at 350 m/s at 10 meters from the gun, 400 m/s at 25 meters. That's a big increase without much power. (And the push averages to about 30 N)

Pushing a coin at that constant power does get it up to 500 m/s, but that involves very large initial forces that would knock an allomancer down.

An average person (70 kg, 1.7m) in a good stance could take a 140 N force without being knocked over. If you run the numbers limiting a maximum force to 140 N and a maximum power to 10 kW, you get coins that hit fast but still subsonic speeds (260 m/s) at 10 meters, which fits what we see in Era 1.

 

Also, thanks for finding that WOB. Now I know what my next deep dive topic will be: what flying with lashings would really feel like.

[IlstrawberrySeed]

23 hours ago, DrPhysics said:

Air resistance is proportional to speed, and while you can have big forces at high speeds, as you slow down they get weaker and will take a very long time to slow you to a "stop" (technically, air drag can never truly stop you).

So it's mostly about timeframe?

23 hours ago, DrPhysics said:

Also, your model seems to be relying on a "force of motion" (i.e. when force is zero, you stop). That isn't the case.

No, I was setting up the requirements. When V=0, A must = 0 for there to be a stop. Since V=0, push must equal gravity for A=0.

Alternitively, you may have been seeing my Air resistence or push forces, which both factor in velocity/delta distance (Which I noted as the same thing since we're working in 1D)

Basically, I postulate that the Force of a 1d push with a mounted object is based on 2 variable, Velocity and Distance. The exact relation in my head is changeing as I try to make more accurate models in my head, currently I'm wondering in inverse proportionality works for them both. That would imply (for the mistborn)

A= 1/(PV)-g-rV     (g gravity, r air resistance)
V=∫ (0, t) 1/(PV) dx -gt - rP
P=∫ (0, t) ∫ (0, x) 1/(PV) dy dx - .5gt - r∫ (0, t) P dx
(This general format works for any push strength function by replacing 1x/(PV) with whichever formula you use)

Anything with recursive integrals is annoying to calculate. I typically end up using a script or chatbot, and having it linearly and quadratically estimate values of V and P and then plug them into the formula for A. Is there a better way to do it?

 

Edited November 7, 2023 by IlstrawberrySeed

[therunner]

17 hours ago, DrPhysics said:

I've never made that argument.  Only that that was a scene where we could approximate a force.

If you don't argue that is a maximum that is even worse, because the force is far too large.

17 hours ago, DrPhysics said:

Then it must be much less than 1 MW.

Yes.

17 hours ago, DrPhysics said:

Why isn't that possible? We can use the colt single action army revolver for a stand in. Those would fire a .45 caliber, 16 gram bullet at about 300 m/s.

At that speed, drag alone is about 1 kw. 10 kW of a push would have the bullet moving at 350 m/s at 10 meters from the gun, 400 m/s at 25 meters. That's a big increase without much power. (And the push averages to about 30 N)

Ah, true, I forget bullet are quite lighter.
However, how did you get those numbers? Running them, the bullet should be moving at ~480 m/s at 10 meters from a gun, and at ~600 m/s at 25 meters. Far larger increase.

Quote

Pushing a coin at that constant power does get it up to 500 m/s, but that involves very large initial forces that would knock an allomancer down.

Initial force does not matter, Allomancer could start with lower force (to avoid being knocked down) and then continue pushing as hard as they can.
Even if the coin weight 50 grams, and the constant force of push is ~30 Newtons, at 10 meters the coin would be moving at ~108 m/s, quite fast already.

17 hours ago, DrPhysics said:

An average person (70 kg, 1.7m) in a good stance could take a 140 N force without being knocked over. If you run the numbers limiting a maximum force to 140 N and a maximum power to 10 kW, you get coins that hit fast but still subsonic speeds (260 m/s) at 10 meters, which fits what we see in Era 1.

Why are you now arbitrarily limiting maximum force to 140N? Your prior calculation claims that Mistborn can push at coin with ~26kN.

In books it is stated that modulating strength of push/pull is very difficult (e.g. Kelsier struggles with it, despite his proficiency), basically the only variation they can do unless they have decades of experience is burn vs flare strength (or possible Hemalurgic enhancements).

So if flare is 26kN, regular push would be at very least ~10 kN as well, since Vin quite explicitly is not able to do such fine control of her Pushes/Pulls even well into WoA, so after all the scenes we are discussing so far.

Edited November 8, 2023 by therunner

[DrPhysics]

6 hours ago, therunner said:

Ah, true, I forget bullet are quite lighter.
However, how did you get those numbers? Running them, the bullet should be moving at ~480 m/s at 10 meters from a gun, and at ~600 m/s at 25 meters. Far larger increase.

I set up a simple Euler's method code in Python. There isn't an analytical solution that can include both power delivered and drag force.

6 hours ago, therunner said:

Why are you now arbitrarily limiting maximum force to 140N? Your prior calculation claims that Mistborn can push at coin with ~26kN.

Newton's third law and statics. If I push with 140 N, 140 N pushes back on me. An average (70 kg, 1.7m tall, chest height at 1.3m, 0.5 m stance) person, without bracing, will fall over if pushed by a force larger than 140 N at chest height. Most of the time that we see coinshots pushing coins, they are pushing multiple coins and aren't bracing. 140 N gives the net force they could exert without bracing against something behind them.

6 hours ago, therunner said:

In books it is stated that modulating strength of push/pull is very difficult (e.g. Kelsier struggles with it, despite his proficiency)

 

Kelsier says that is it hard, (Exact quote, while training Vin early on: “Varying the strength with which you Push or Pull is difficult, but possible. It’s better to just fall a bit, then Push to slow yourself. Let go and fall some more, then Push again. If you get the rhythm right, you’ll reach the ground just fine.”), but we have to remember that he is not a physicist, and "strength" does not necessarily mean the same thing as force. Also, when he does say it, he's talking to a brand new Mistborn just starting with her powers. My best guess is that conscious control is hard, but we modulate our strength all the time in unconscious ways. Therefore, any model that tries to describe pushing as an allomancer simply setting some "force of push" is bound to fail.  That would be like trying to model our muscles based on tension in our biceps. We don't think about how hard we are flexing our bicep to move our arm or lift a thing, we're thinking about what kind of path our arm takes as we lift (or fail to lift) the thing that we are trying to move. We can find some limits (human bicep will tear if it exceeds a certain tension), but those limits don't let us model every single motion.

18 hours ago, IlstrawberrySeed said:

No, I was setting up the requirements. When V=0, A must = 0 for there to be a stop. Since V=0, push must equal gravity for A=0.

I misunderstood your notation. It makes sense now. Sorry.

18 hours ago, IlstrawberrySeed said:

I postulate that the Force of a 1d push with a mounted object is based on 2 variable, Velocity and Distance

I agree, but I think it makes more physical sense to model the force based on Power (which is proportional to Velocity (P=FV)) and Distance. Power would reflect how quickly the allomancer can convert Investiture into kinetic energy. The faster they can make that conversion, the more powerful they are. Whereas, there is no good physical model that would suggest why velocity alone would matter.

 

Edited November 8, 2023 by DrPhysics

[IlstrawberrySeed]

4 hours ago, DrPhysics said:

I misunderstood your notation. It makes sense now. Sorry.

I agree, but I think it makes more physical sense to model the force based on Power (which is proportional to Velocity (P=FV)) and Distance. Power would reflect how quickly the allomancer can convert Investiture into kinetic energy. The faster they can make that conversion, the more powerful they are. Whereas, there is no good physical model that would suggest why velocity alone would matter.

 

It's fine.

I don't understand. You want to model F(P,D), which means that F(FV,D)? I don't understand that idea.
As for no physical model, I thought of this from reference frames/vector addition. However, it would make it similar to air resistance, which is why I thought it made sence physically. I push away from me at 3 m/s, but I'm moving at -2m/s, so what I'm pushing only moves at 1m/s.

[therunner]

23 hours ago, DrPhysics said:

I set up a simple Euler's method code in Python. There isn't an analytical solution that can include both power delivered and drag force.

Thanks!

Quote

Kelsier says that is it hard, (Exact quote, while training Vin early on: “Varying the strength with which you Push or Pull is difficult, but possible. It’s better to just fall a bit, then Push to slow yourself. Let go and fall some more, then Push again. If you get the rhythm right, you’ll reach the ground just fine.”), but we have to remember that he is not a physicist, and "strength" does not necessarily mean the same thing as force. Also, when he does say it, he's talking to a brand new Mistborn just starting with her powers. My best guess is that conscious control is hard, but we modulate our strength all the time in unconscious ways. Therefore, any model that tries to describe pushing as an allomancer simply setting some "force of push" is bound to fail. 

Not just Kelsier, Vin also marvels at precision Zane has. And it took Wax over 2 decades to learn to set up his steel bubble. 
Even when using it to move Vin calls Pushes/Pulls 'blunt' things that lack subtlety, which is after ~2 years of experience. There is no reason why she would subconsciously control her pushes when doing it with coins, but not when doing it to move around.

However, claiming that at every point where the theory does not match what is in the book, Allomancer was unconsciously doing something that is explicitly stated to be difficult feels like a cop out.

Also, even if Allomancers subconsciously limit themselves, that does not explain why Vin can push a coin, and is then suddenly thrown backwards once the coin hits the wall.
Or when Kelsier throws coin down in the air and Pushes on it, he feels back reaction only once it hits ground.
Both of those examples show that they are pushing hard enough to grant considerable acceleration to themselves (in Kelsiers case the force is ~700N at minimum).

Quote

That would be like trying to model our muscles based on tension in our biceps. We don't think about how hard we are flexing our bicep to move our arm or lift a thing, we're thinking about what kind of path our arm takes as we lift (or fail to lift) the thing that we are trying to move. We can find some limits (human bicep will tear if it exceeds a certain tension), but those limits don't let us model every single motion.

You can model muscles like that, modeling entire limbs like that is hard.
However, Allomancers only push outwards or pull inwards. The only variables are:

• 'Strength' of Allomancy (always the same for single user)
• Mass/weight of user (typically the same for single user)
• weight of pushed object
• burn vs flare (unless you claim subconscious control)
• distance between allomancer and object
   

When allomancer pushes on a coin they have on their person, all variables are basically accounted for.

Edited November 9, 2023 by therunner

[DrPhysics]

19 hours ago, IlstrawberrySeed said:

I don't understand. You want to model F(P,D), which means that F(FV,D)? I don't understand that idea.

When constructing a physical model, you need a justification for each piece. So, we could talk about relative velocity and show that the bigger the relative velocity, the harder it is to push the thing, but that doesn't give us a reason.

Saying that an allomancer is limited by the power they can produce (the rate they can convert investiture into energy), however, tells me that I'd expect the force to be proportional to 1/v, rather than 1/v^2 or exp(-v), all of which get weaker when you have a larger velocity. Those kinds of justifications are especially important if you don't have solid data to put a fit to. If we had a graph of Vin's speed over time and we saw that the fit was actually 1/v^2, then we'd have to figure out why that is, but until then, it's better to find physical, direct cause reasons for any models that you build.

As another example, since the pushing applies to metals, we'd have to guess that it is at least somewhat related to electromagnetism, so I'd guess that we follow Coulomb-like forces and we'd expect the push to be proportional to 1/D^2.

So what I was really trying to say is that any model I'd use would have the force proportional to 1/V and 1/D^2, unless I had a really good reason not to.

1 hour ago, therunner said:

However, claiming that at every point where the theory does not match what is in the book, Allomancer was unconsciously doing something that is explicitly stated to be difficult feels like a cop out.

Part of the problem is that pushes/pulls aren't as consistent over Era 1 as they are through Era 2. I think Sanderson was still developing his model, so we see lots of oddities in Era 1 that don't pop up as much in Era 2. For example, this scene from TFE:

Quote

Kelsier spun and flew amid a maelstrom of metal. Every time something hit the ground, he flicked it back up. The items always flew in straight lines, but he kept moving, Pushing himself around, keeping them in the air, periodically shooting them at the Inquisitor.

That wouldn't happen if we could describe pushes and pulls as a force exerted on the object that points directly at the allomancer. Instead, we'd see them curve and arc like we do when Vin travels with horseshoes in the next book.

 

Era 1 was pretty bad with Newton's first and third law problems (like the example above), but in era 2, they are much more consistently applied. Does that mean the first law applies or doesn't?  What about third law? At some point we need a little hand waving and justification, and it looks like we don't agree on which pieces to handwave away (and there's no reason that we should have to). For me, assuming those rules I posted above and that Allomancers have more unconscious control than they think that they do is how I'm able to justify most of the oddities that I run into. (Except for that Kelsier example. I can't think of any way to justify that other than Sanderson didn't understand inertia when he wrote it.)

[IlstrawberrySeed]

On 11/9/2023 at 8:26 AM, therunner said:

However, Allomancers only push outwards or pull inwards. The only variables are:

• 'Strength' of Allomancy (always the same for single user)
• Mass/weight of user (typically the same for single user)
• weight of pushed object
• burn vs flare (unless you claim subconscious control)
• distance between allomancer and object

Those are the only variables understood in world. However, we know for a Fact this isn't everything, since there is more control than Burn vs Flare in savants, and with hemalurgy. I see no reason why another variable couldn't be introduced to "fix" the model. However, we have to be careful we aren't pulling an epicyclical orbit style fallacy.

On 11/9/2023 at 10:14 AM, DrPhysics said:

When constructing a physical model, you need a justification for each piece. So, we could talk about relative velocity and show that the bigger the relative velocity, the harder it is to push the thing, but that doesn't give us a reason.

Saying that an allomancer is limited by the power they can produce (the rate they can convert investiture into energy), however, tells me that I'd expect the force to be proportional to 1/v, rather than 1/v^2 or exp(-v), all of which get weaker when you have a larger velocity. Those kinds of justifications are especially important if you don't have solid data to put a fit to. If we had a graph of Vin's speed over time and we saw that the fit was actually 1/v^2, then we'd have to figure out why that is, but until then, it's better to find physical, direct cause reasons for any models that you build.

OK, what's the justification for setting something equal to a non-calculous function of itself?

limiting an allomancer by the investiture they can produce is obviously neccessary, but since there is a level of control in the most powerful of cases (Savants/Hemalurgy), and there are no factors that influence the push and the investiture process, I see it as being a simple matter of proportionality: the force of a push of N investiture is equivalent to the force of a push of 1 investiture multiplied by f(N). (Likely a minor degradation, since I resists I)

On 11/9/2023 at 10:14 AM, DrPhysics said:

As another example, since the pushing applies to metals, we'd have to guess that it is at least somewhat related to electromagnetism, so I'd guess that we follow Coulomb-like forces and we'd expect the push to be proportional to 1/D^2.

That makes sense.

On 11/9/2023 at 10:14 AM, DrPhysics said:

So what I was really trying to say is that any model I'd use would have the force proportional to 1/V and 1/D^2, unless I had a really good reason not to.

It would model it more effectively given a static strength, which might be an incorrect assumption, but it is a reasonable assumption until we get a WoB. We need the strength of the push to decrease toward the middle and increase towards the end. And it needs a sharp increase, since it needs to be well below gravity. That sounds parabolic, though since V goes up then down, logarithmic function would look parabolic to an extent.

On 11/9/2023 at 10:14 AM, DrPhysics said:

Part of the problem is that pushes/pulls aren't as consistent over Era 1 as they are through Era 2. I think Sanderson was still developing his model, so we see lots of oddities in Era 1 that don't pop up as much in Era 2. For example, this scene from TFE:

That wouldn't happen if we could describe pushes and pulls as a force exerted on the object that points directly at the allomancer. Instead, we'd see them curve and arc like we do when Vin travels with horseshoes in the next book.

(Except for that Kelsier example. I can't think of any way to justify that other than Sanderson didn't understand inertia when he wrote it.)

He pushes on it and pulls on it only while opposite it? That doesn't sound too hard, and would explain how Kel was able to aim, since he had no practice hitting curves. It's certainly how I read it the first time.

[DrPhysics]

3 hours ago, IlstrawberrySeed said:

He pushes on it and pulls on it only while opposite it? That doesn't sound too hard, and would explain how Kel was able to aim, since he had no practice hitting curves. It's certainly how I read it the first time.

Either that or he does it in really short jerks so that by the time he is moving he isn't pulling anymore.

[therunner]

On 11/9/2023 at 7:14 PM, DrPhysics said:

That wouldn't happen if we could describe pushes and pulls as a force exerted on the object that points directly at the allomancer. Instead, we'd see them curve and arc like we do when Vin travels with horseshoes in the next book.

The quote itself provides explanation, Kelsier notes he 'flicked' the items, which implies he only pushed/pulled on them for a very short time. So he quickly pulls on an item, and gets it moving in a straight line.

On 11/9/2023 at 7:14 PM, DrPhysics said:

 At some point we need a little hand waving and justification, and it looks like we don't agree on which pieces to handwave away (and there's no reason that we should have to). For me, assuming those rules I posted above and that Allomancers have more unconscious control than they think that they do is how I'm able to justify most of the oddities that I run into.

Yes, some handwaving is necessary. However, it is not just Allomancers that think they lack control, Sanderson says that going below burn is very difficult, so this lack of control is part of the magic system

Quote

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)

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. Especially for e.g. Vin in TFE, or Elend in HoA, where both are certainly not skilled enough.
And pushing on coins is basically among the first things Mistborn/Coinshots do, so it should not require skill that per author they don't posses.

Quote

(Except for that Kelsier example. I can't think of any way to justify that other than Sanderson didn't understand inertia when he wrote it.)

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

21 hours ago, IlstrawberrySeed said:

Those are the only variables understood in world. However, we know for a Fact this isn't everything, since there is more control than Burn vs Flare in savants, and with hemalurgy. I see no reason why another variable couldn't be introduced to "fix" the model. However, we have to be careful we aren't pulling an epicyclical orbit style fallacy.

Savants 'quality' of burn can be included under the variable of 'strength' of Allomancy. Afterall, it just means they can do more with less, i.e. externally they will just appear as if they were stronger.

Edited November 11, 2023 by therunner

[IlstrawberrySeed]

On 11/11/2023 at 7:56 AM, therunner said:

Savants 'quality' of burn can be included under the variable of 'strength' of Allomancy. Afterall, it just means they can do more with less, i.e. externally they will just appear as if they were stronger.

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.