Physics of the Metallic Arts

[CosmereScholar]

A fan of Sanderson's work here! I thought I would create a thread with all of the conundrums in physics that occur in the Cosmere, and my theories. I hope these will be clarified eventually, as consistency seems very important to Sanderson's style.

Allomancy-Steelpushing/Ironpulling

Crushing/Ripping Effect- Several times in Mistborn it is mentioned that opposing forces can crush objects. In The Final Empire, Vin and Kelsier push on a coin, trapping it between them and flattening it. Additionally, at the end of Well of Ascension Vin opens a heavy door and anchors herself by pulling on sources of metal behind, and notes that the exertion nearly rips her apart. Several times it is mentioned Mistborn can burn pewter to strengthen their bodies and be able to push metal in opposite directions with being crushed.

If allomantic forces affected the object as a whole equally, or around the center of mass, then these effects should simply cancel.

Resistance to Lateral Motion- Though it is mentioned numerous times that allomancy can only exert forces directly towards or away from yourself, several times phenomena imply that pushes can cause an object to resist lateral motion as well. For instance, in mistborn, when Vin first studies allomancy, it is explained that a person can hover at the top of a steelpush off a single anchor, and allomancers do this throughout the series. However, it should not be possible without some sideways stabilizing force. One could argue that allomancers can exert a push off-center, as with an outstretched hand, or that they can push on their anchor off-center (shown to be possible in Kelsier's last fight scene in The Final Empire, where he pushes on different sides of a rod.) However, as coinshots are able to reach the hight of a city wall with this technique, and the anchor being so small the distance should be such that it would be impractial to balance oneself with this method, as the slightest deviation should send them toppling.

More conclusively, when Vin and Kelsier push on a coin and flatten it, as mentioned previously, it hangs in the air between them. If indeed allomancers could only push directly away from themselves the coin should fall immediately under the influence of gravity. One could argue their forces are directed slightly upward exactly enough to counteract the coin's weight, but the slightest deviation would push the coin to the side (as happens with other coins in the same scene).

 

Theory-Allomantic forces are not applied to the object as a whole. Instead, they are applied to the surfaces of anchor/allomancer exerting them which face each other. This would allow for a coin to be crushed, because the forces are applied each to only one side of the coin. It would allow for an allomancer to feel compression/stretching, as forces would be applied to different sides of their bodies. Additionally, there pushes exert some force perpendicular to their direction of action, acting a little like friction. The pushes on either side of a coin would hold it in place, because it would be like two walls pressing the coin together. It would also prevent Vin from falling at the edge of her push, as it would be as if she were standing on a virtual surface with friction.

There are problems with this, however. The most major one is that, if allomantic forces are not evenly distributed, then each time the allomancer pushes themselves into the sky, it would feel as if a car were crashing upward into them. Alternative explantions are that the effect is not strictly on the surface. They could penetrate inward into the body a bit, lessening the destructive effect.

Applications for the theory: If the effect resisting lateral force does act like friction, it would also reduce spin in objects affected by allomancy. So a spining rod heading towards an allomancer would slow its spin when pushed away. Whether or not the friction idea is correct, a mistborn should be able to suspend objects in midair, even at an angle, by pushing and pulling very strongly on the same object. Then, the object would be unable to move perpendicular to the push/pull (as Vin does not appear to slowly destablize on the top of a push, I postulate the force adjusts automatically to keep an object stationary, like static friction), and motion parallel to the beam could be adjusted by changing the power of the push (something like this might have helped Kelsier move objects back and forth towards the inquisitor at the end of his final fight with an Inquisitor, though I agree this could have just been done by adjusting his own position very carefully). One can imagine an ettmetal tractor-beam based on this phenomenon. Indeed, one might be able to create a trap for metallic organic molecules with enough power, though this would be several steps in power level above even the allomancy of the lord ruler, as a single molecule would be a poor anchor.

 

Feruchemy-Iron We have been told that weight storage actually changes your mass, but does so in a way that does not affect your density, using the Higgs Field in some way, and also has a strengthening effect, so the body can withstand small falls. Momentum is to be conserved in the iteration. It also shouldn't make a person's arm more massive, so they can punch someone with incredible effect, according to a WoB, nor make them so dense bullets can't affect them.

Firstly, if indeed Higgs Field interactions were changing a person's mass, then Feruchemist's density should certainly be increased. Let us say however, that the person's increased mass is instead attached to them abstractly, perhaps around their center of mass. Then we could have punches be light, though one could still injure someone by jumping on top of them, and we do see Wax do this a bit in Mistborn Era 2, both jumping onto someone and knocking open a door like this, though not to its maximum effectiveness in my opinion.

However, Wax should definately be impervious to bullets if he chooses to based on what we have seen, regardless whether the above theory is correct. Even if he is not becoming denser, we know he can strenghten his body enough to withstand pressures which break paving stones and crush floors (though he should really be pulverising his clothing on landings). He should also be able to then withstand the pressure of a bullet, or possibly even a knife. Also, if he is strong enough to stand at such weights, he should be strong enough to kill with a single punch, though it could be he just prefers his flying at low weight tactic.

Also, using the strengthening effect, he ought to be able to withstand large falls without pushing off an anchor. He could fall at normal weight, then increase his weight dramatically at the last moment, so as to become impervious to a speed which would have been generated by a very small fall at that weight. Possibly he has had no need of this tactic, though it seems unusual he has not mentioned it.

There are also distinct problems in Wax's conservation of momentum. He mentions several times that changing mass during a fall does not slow him, because acceleration due to gravity does not depend on mass. While this is true, he should definitely slow down temporarily if he increases his mass, otherwise, he would be gaining momentum. Also, he mentions that he speeds up slightly if he reduces his mass midflight. This is unusual, as if he halves his weight, his speed should actually double, hardly a slight effect, though he could just be misjudging both of these cases.

There is one scene specifically in which Wax does not conserve momentum. At the finale of Alloy of Law, he reduces mass, Pushes off the floor, increases mass, then pushes up at a building, annihilating it. He does this presumably so pushing the building doesn't send him down through the floor. However, since he became lighter, he almost certainly did not have much upward momentum before his massive push. If he conserved momentum, this would not have slowed his descent much at all. Possibly, he was so massive he did not appear to accelerate and was mistaken that his strategy would have helped, though he ought to have noticed massive downward acceleration when he lightened again.

Feruchemy-Crashing(F-Iron+A-Steel) There is an additional effect of Wax's powers that appears unusual. He mentions that he can gain an advantage by lightening himself mid-jump, to gain a slight boost of speed. This would indeed make him faster. But, would it not be even faster for him to stay light as much as possible while flying, so he could accelerate more rapidly? Perhaps this is just him being unfamiliar with his powers, but I find it strange to have someone as experienced as Wax make wrong analyses.

Feruchemy-Steelrunning This is by far the most unusual physics-wise, as has already been observed in the forums. It is supposed to make someone faster without really increasing the force they can exert. In Shadows of Self, we see Bleeder run down steps and jump a window ledge at high speed. However, using conventional propulsion would have destroyed the steps, and indeed the ground whenever she tried to run. Also, she would have had to pull herself down the steps, not run as was described (though it might not have been visible at speed) for her to move down faster than she could have fallen. Also, I doubt ground could support static friction necessary for walking at such conditions. Also, Marasi strangely doesn't seem to notice any inertial effects as she moves around.

The only explanation I can think of is that Steelrunning actually manipulates time, creating a bendalloy bubble just around your person. Then, gravity would function normally from your perspective, allowing Bleeder to go down steps with no trouble, and forces you exert would be the same as normal movement, and would only interact with the surroundings briefly from their point of view, causing no damage, and also keeping you from punching someone with unusual strenght.

However, there are problems with this theory. The inertia of objects would make them very difficult to move from your perspective, making it so you could only open doors and wield guns at normal speeds, contradicting what we know from Shadows of Self. More seriously, your clothing and the air would resist your passage, and Marasi did not appear to notice the effect of her clothing in Bands of Morning, though she could have been unconsciously tapping strength to move it, though this would likely have damaged it. The most likely explaination is that the Bendalloy field also encompases objects you're touching, but not other people if you punch them, because their investiture rejects it. I would expect that someone very powerful would then be able to overcome this effect however. Sanderson has stated that it would be possible to "burn up" by using too much speed though, and this fits with this theory.

 

 

Any thoughts?

Edited March 17, 2019 by CosmereScholar

[+Artemos]

15 hours ago, CosmereScholar said:

Allomancy-Steelpushing/Ironpulling

An explanation that's been thrown around is that Pushing and Pulling is similar to forces like gravity and magnetism in that you're Pushing on all the particles of metal in an object at once. This appears equivalent to Pushing on the center of mass on the object. Then, skilled allomancers can slightly control how they distribute their Push throughout their own body (in the case of Zane's balancing act) or the target (for Kelsier and the rod).

This would explain the 'crushing' effect because there's two opposing, slightly uneven opposing  forces acting on each particles of the coin/Vin, kind of like a spaceship trying to fly between two strong sources of gravity in a sci-fi movie.

There's also the matter of the blue lines pointing to metals connect to the chest/heart in the books, not the center of mass. Still, there's no torque acting on the allomancer (because mistborn in flight are not like beyblades), so Pushes must usually be acting on the center of mass.

16 hours ago, CosmereScholar said:

One could argue their forces are directed slightly upward exactly enough to counteract the coin's weight, but the slightest deviation would push the coin to the side (as happens with other coins in the same scene).

Yeah, this is the only possible explanation. Brandon is a writer first and a physicist... third? fourth? This scene definitely adheres to the "rule of cool."

16 hours ago, CosmereScholar said:

So a spining rod heading towards an allomancer would slow its spin when pushed away.

I'm not sure if this the case. For a uniformly shaped rod spinning like a spoke in a wheel, uniformly pushing on the surface of the rod from any direction won't apply a torque. If the center of mass is in the center of the rod, the half of the rod facing you and moving towards you is the same size as the half the rod facing you and moving away from you.

16 hours ago, CosmereScholar said:

Whether or not the friction idea is correct, a mistborn should be able to suspend objects in midair, even at an angle

We've never seen a mistborn suspend an object in the air at an angle and I doubt we will. The books often say that you can only apply a Push and Pull directly towards or away from you, so suspending at an angle would make that statement a lie. Sanderson has always said that limitations are more interesting than powers, and the limitation of the direction of a Push is fundamental to Allomancy. Still, an ettmetal tractor beam would be cool.

[CosmereScholar]

Quote

This would explain the 'crushing' effect because there's two opposing, slightly uneven opposing  forces acting on each particles of the coin/Vin, kind of like a spaceship trying to fly between two strong sources of gravity in a sci-fi movie.

But, in reality, a spaceship would not be affected by flying between two strong sources of gravity. They would just cancel. Unless they were strong enough for the distribution of force to be skewed significantly from one side of the ship to the other, in which case a tidal force would cause the ship to stretch, even if there is only one source of gravity, not two competing ones (just as the moon causes the tide.)

What do you mean though by uneven opposing forces? Because if they weaken across the coin with distance from the allomancer, that would cause the coin to turn so it was in-plane with Vin and Kelsier, as occurs with tidal effects. However, if this were generally true, we would indeed see a slow in the rotation of objects as they were pushed as they become tidally locked, though to clarify, I doubt this rotation would actually happen. This is merely a test I would like to conduct to test this frictional theory.

I agree the forces must be unevenly distributed to some degree, at least when the allomancer chooses, in order for the crushing to happen, though I would prefer for them to be evenly distributed, as I like the smooth acceleration theory. But, why do allomancers then not damage their bodies? Unless...this only happens when two pushes act on an object, and they affect each other's distributions. I did not think of this! That would actually explain crushing perfectly, and I hope it becomes cannon someday (though I realize it almost certainly wasn't Sanderson's original intention).

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We've never seen a mistborn suspend an object in the air at an angle and I doubt we will.

Unfortunately, there does definately  need to be some perpendicular force on pushed objects for allomancy to be consistent. But, I agree with you : (

[Scion of the Mists]

Nice theories.  One thing to add is that we know that as an Allomancer becomes more skilled, they are able to relax the "center of mass" restriction on both the target object and themselves.  This can (kind of) explain things like hovering and Zane twisting in mid-air.  

Also, have you checked out this thread?

[CosmereScholar]

Thank you!

Indeed, I have read that thread. Unless I missed something, it appeared to mainly address the strength of pushes and pulls. These are issues which I believe have not yet been discussed. The discussion on Steelrunning I mentioned comes from

https://www.17thshard.com/forum/topic/79017-allomancy-physics/#comment-762438

 

[Calderis]

@CosmereScholar

I am extremely frustrated by Feruchemical steel, and have had the opportunity to ask Brandon about it... And as much as I want it to be it is not a temporal effect. 

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Calderis [PENDING REVIEW]

In Shadows of Self, in the scene where Paalm is speaking to Wax from a floor above, she rushes out the window and down past him. The window isn't damaged, the earth that she runs on isn't damaged, and she runs down a flight of stairs at speed. Being as "speed" affects gravity, and physics apply to Paalm as if she were moving at normal speed, is Feruchemical steel a temporal effect?

Brandon Sanderson [PENDING REVIEW]

*laughs* Nice. I'm going to ask for more definition. What do you mean by temporal effect. What exactly do you mean by that? Are you reaching into magic system definitions, or are you trying to use our definitions? Give me more.

Footnote: A follow-up for this question was asked here.
Skype Q&A (Oct. 8, 2018)

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Calderis

I recently got the opportunity to ask you a question about Feruchemical steel and if it was a temporal effect and you told me to define that better. When tapping steel, the mind of the Feruchemist is sped up and physics affects their actions normally. When storing, their mind is not slowed and the effect seems tortuously difficult to amass. Storing generally seems to be the more dangerous/difficult option in Feruchemy, so does [Feruchemical steel] alter a person's personal relationship to the flow of time, with the disconnect between the Physical and Cognitive as a drawback of storing?

Brandon Sanderson

I see what you're asking. The mind-altering effects of [Feruchemical steel] are similar to the slight strength you gain from [Feruchemical iron]--it is your Spiritual nature adapting to the new influx of an attribute that it's not really expecting, and siphoning some of that investiture to make you capable of actually using it. So there is a slight temporal effect here, but nothing as big as I think you're looking for.

Footnote: This question is a follow-up to this question.
Skyward Pre-Release AMA (Oct. 31, 2018)

So at this this point, all I can say is that Steel just breaks physics, because you shouldn't be able to do half of the things Paalm does at this speeds without being a wrecking ball and flying through the air on accident. 

[CosmereScholar]

Indeed, I have seen both of your WoBs. They did not seem to me to specifically say that speed does not create a personal speed bubble, though perhaps I was mistaken. But, this is definitely inconsistent if the effect is not temporal. I hope that Sanderson will not canonize how it works yet.

Any thoughts on the other physical conundrums?

Edited March 17, 2019 by CosmereScholar

[Calderis]

The whole crushing/ripping thing is just inconsistent in my opinion. 

The lateral force problem is... Actually not a problem in my opinion, it's just not understood well in world at all. As you said, we know that you can redirect where you are able to push on a metal from Kelsier and the bar. I also believe that you can alter where the push originates on your own body, both from Zane's hovering flip in the air, and this

Quote

Questioner

So my quick question: Can you use Identity (I love the speed bubbles!) to anchor speed bubbles to yourself?

Brandon Sanderson

Uh, this is possible. That's less a matter of Identity. What’s gonna happen there, like, the more someone uses the powers, the more familiar and intermingled with their soul the powers become, and they are able to accomplish things that others can't. This would be like a Mistborn learning to hover a coin, right, which they can do, but most think you can't. That's the sort of level we're going with.

Necarion

So a savant could?

Brandon Sanderson

A savant could totally do that. The problem is, things moving in and out of a speed bubble, there's a transference of energy. This is how we keep speed bubbles from irradiating people when light moves through them, right, red shift. And so there's a transfer of energy directly from the Spiritual Realm, which means that moving with a speed bubble, you're gonna run into that, and it's gonna be, it's gonna cause all kinds of problems, but it would be possible.

Arcanum Unbounded San Francisco signing (Nov. 30, 2016)

I don't see how either of those feats would be possible other than by altering where the push effects the body. So I think that to some extent that is done subconsciously by all of them and it's just written off as "balance."

There's also this WoB showing that it's more complicated than Brandon ever intended. 

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Questioner

Do Allomantic Pushes and Pulls generate friction?

Brandon Sanderson

Do they generate friction. So... *sighs* I've had to ask myself this because if they didn't generate friction certain things that I do in the books wouldn't happen. I assume if you've seen the physics of it you've noticed. I have to go with yes. But the physics of it I'm a little wishy-washy on. I mean it's pretty obvious from the way I do things that they do.

Questioner

Yes! I have won the argument on the 17th Shard.

Brandon Sanderson

I mean, you've seen the science of it, right? You Push things up and they stay there. And so if they didn't generate friction, two people couldn't both Push on a coin to hold it in place, but it does get held in place.

Questioner

I just won a 17 page argument.

Brandon Sanderson

But I have to tell you... Peter is going to have to break his brain making the physics of that work. But I mean, it's canon. I put it in the books so it’s not like we can just ignore the fact.

Firefight Seattle Public Library signing (Jan. 7, 2015)

For Iron... Man, Iron is just broken.

Brandon does a great job of things, but there's definitely some points that things get... Fudged. 

Edited March 17, 2019 by Calderis

[CosmereScholar]

Wow! So indeed there is a frictional force perpendicular to the pushes/pulls. Thank you! You have just confirmed that part of my theory. I cannot believe I had never seen that. This by itself explains the coin situation and the balancing on the top of beams (assuming friction also affects the allomancer, which I hold is very likely).

This implies that it would indeed be possible to build a tractor beam using allomancy, as speculated! Also, if this behaves similarly to normal friction, it would slow the rotation of objects affected by allomancy, and allomancers themselves, as they push. I wonder if in future novels this effect might be discovered.

Though it is merely speculation, I do think that different pushes/pulls repelling to be centered in different parts of the body would explain all of the crushing/ripping phenomena, though I agree that it appears inconsistent at this point.

You're talking about Feruchemical Iron I assume. Yes, there are severe problems with it.

[+Invocation]

4 hours ago, Calderis said:

Brandon does a great job of things, but there's definitely some points that things get... Fudged. 

Worth it just because of the Rule of Cool.

[CosmereScholar]

Foolishness. : )

Edited March 17, 2019 by CosmereScholar

[+Oltux72]

On 3/16/2019 at 8:45 PM, CosmereScholar said:

If allomantic forces affected the object as a whole equally, or around the center of mass, then these effects should simply cancel.

Actually no, they should not. They should only if they act on the whole object equally. That forces can be treated as if they were acting on the center of gravity of an object to compute its trajectory is a mathematical simplification. We actually know that it is false. If it were absolutely correct, tides could not exist. And most people living on a coast will tell you that tides absolutely exist. And don't let them tell you that tides require three objects (Earth, Sun and Moon). That is a misconception . The Earth would still have purely solar tides without the Moon.

So it does not take two Allomancers to generate tidal forces. The tides generated by gravity go by the inverse of distance cubed. To exactly answer this we are back at the allomantic force by distance question.

 

So yes, a space ship between two objects would be stretched. But this is because we are talking about ab attractive force  If you have a repulsive force, the objects would indeed be crushed instead.

Edited April 6, 2019 by Oltux72
Overlooked important component by Artemos

[Karger]

On 3/16/2019 at 3:45 PM, CosmereScholar said:

Crushing/Ripping Effect- Several times in Mistborn it is mentioned that opposing forces can crush objects. In The Final Empire, Vin and Kelsier push on a coin, trapping it between them and flattening it. Additionally, at the end of Well of Ascension Vin opens a heavy door and anchors herself by pulling on sources of metal behind, and notes that the exertion nearly rips her apart. Several times it is mentioned Mistborn can burn pewter to strengthen their bodies and be able to push metal in opposite directions with being crushed.

If allomantic forces affected the object as a whole equally, or around the center of mass, then these effects should simply cancel.

Perhaps they do not actually effect just the object's center of mass.  Sanderson has revealed that it is theoretically possible to hover a coin above your hand just by pushing on it.  So it is theoretically possible to effect an object on just one part of it. 

[Scion of the Mists]

On 4/6/2019 at 4:46 AM, Oltux72 said:

That forces can be treated as if they were acting on the center of gravity of an object to compute its trajectory is a mathematical simplification. We actually know that it is false. If it were absolutely correct, tides could not exist.

It's true most of the time, though.  The only real exceptions are fluids/non-rigid bodies (like the tides) and spaghettification (which only comes about with really large forces, like black hole large).  In general though, the whole point of a center of gravity (or the center of mass, which is virtually identical) is that it's what you get if you were to integrate all of the forces across the whole object

 

On 4/6/2019 at 4:46 AM, Oltux72 said:

So yes, a space ship between two objects would be stretched. But this is because we are talking about ab attractive force  If you have a repulsive force, the objects would indeed be crushed instead.

While each object would apply a tidal (uneven) force to the spaceship, why wouldn't the two opposing tidal forces cancel?  

 

17 hours ago, Karger said:

Perhaps they do not actually effect just the object's center of mass.  Sanderson has revealed that it is theoretically possible to hover a coin above your hand just by pushing on it.  So it is theoretically possible to effect an object on just one part of it. 

It's actually directly in the books that you can affect parts of objects (Kelsier did it with the bar).  The coin hovering thing isn't about affecting part of the coin, it's about pushing from a different point in your body.  

Edited April 8, 2019 by Scion of the Mists

[CosmereScholar]

On 4/6/2019 at 4:46 AM, Oltux72 said:

So yes, a space ship between two objects would be stretched. But this is because we are talking about ab attractive force  If you have a repulsive force, the objects would indeed be crushed instead.

I’m afraid you are mistaken. A repulsive force would also cause stretching tidal forces. The effect is caused by a difference in force from one side to another, if the effect could reverse like this, it would reverse if you circled to the other side of a gravity source, which would not make sense.

41 minutes ago, Scion of the Mists said:

While each object would apply a tidal (uneven) force to the spaceship, why wouldn't the two opposing tidal forces cancel? 

This would not happen completely, but you are correct, the effect would be reduced.

On 4/6/2019 at 4:46 AM, Oltux72 said:

Actually no, they should not. They should only if they act on the whole object equally

Allomantic forces must act on an object almost equally, as Allomancers do not appear to experience tidal forces from a single push, and are able to tolerate large forces on their bodies with little effect. Note, that they do experience the crushing and ripping effects mentioned in the first post whenever they are subject to multiple pushes. This could only be explained if they interfere with each other in some way, not through Newtonian mechanics.

 

However, there is one scene with a Duralamin push in WoA that contradicts this, where Vin blacks out. This seems to suggest there are indeed tidal forces but which are very small under ordinary pushes. But, more likely this is mistake. There is a similar blacking out scene in Oathbringer while freefallling under gravity, which should never happen.

[+Oltux72]

2 hours ago, Scion of the Mists said:

It's true most of the time, though.  The only real exceptions are fluids/non-rigid bodies (like the tides) and spaghettification (which only comes about with really large forces, like black hole large).  In general though, the whole point of a center of gravity (or the center of mass, which is virtually identical) is that it's what you get if you were to integrate all of the forces across the whole object

But that is exactly the case we are talking about. If an object is deformed, it is clearly not rigid.

2 hours ago, Scion of the Mists said:

While each object would apply a tidal (uneven) force to the spaceship, why wouldn't the two opposing tidal forces cancel?

Because the forces depend on the distance to the source, hence they are not equal on both sides and do not fully cancel.

2 hours ago, Scion of the Mists said:

It's actually directly in the books that you can affect parts of objects (Kelsier did it with the axes).  The coin hovering thing isn't about affecting part of the coin, it's about pushing from a different point in your body.  

Yes, but what happens if he pushes on an object? Does he really push on everything equally, or do the pushes depend on distance, hence there will be tides?
 

 

1 hour ago, CosmereScholar said:

I’m afraid you are mistaken. A repulsive force would also cause stretching tidal forces. The effect is caused by a difference in force from one side to another, if the effect could reverse like this, it would reverse if you circled to the other side of a gravity source, which would not make sense.

It does reverse. Consider the case of standing on a planet which does not rotate. You experience high tide at midsummer, which is also noon. And again at midwinter. By which time you are at midnight, so you are facing away from the sun. The same force now pushes the water away from the sun, because you are at the opposite point of your orbit.

Hence a repulsive force does create a compresssing effect.

1 hour ago, CosmereScholar said:

Allomantic forces must act on an object almost equally, as Allomancers do not appear to experience tidal forces from a single push,

Then what is this force they are feeling when they are between two heavy objects they push on? Clearly the force is not acting on every part of their body equally. Now we could assume that they are acting differently on the metals they push on, but why? Unfortunately we have never seen an Allomancer push on liquid metal.

1 hour ago, CosmereScholar said:

and are able to tolerate large forces on their bodies with little effect. Note, that they do experience the crushing and ripping effects mentioned in the first post whenever they are subject to multiple pushes. This could only be explained if they interfere with each other in some way, not through Newtonian mechanics.

Why? In fact why do they feel anything at all when they push? If the acceleration were uniform across their bodies, they should feel nothing.

 

[CosmereScholar]

1 hour ago, Oltux72 said:

It does reverse. Consider the case of standing on a planet which does not rotate. You experience high tide at midsummer, which is also noon. And again at midwinter. By which time you are at midnight, so you are facing away from the sun. The same force now pushes the water away from the sun, because you are at the opposite point of your orbit.

Hence a repulsive force does create a compresssing effect.

This is not exactly what I meant. I meant that the effect would reverse from streching to compression, which does not happen. Though the apparent direction of the tidal effect changes, never would negative tides, compression parallel to the field, be experienced.

[+Oltux72]

24 minutes ago, CosmereScholar said:

This is not exactly what I meant. I meant that the effect would reverse from streching to compression, which does not happen. Though the apparent direction of the tidal effect changes, never would negative tides, compression parallel to the field, be experienced.

Sorry for misunderstanding.

Why would it reverse? In case of a repulsive force the parts of a pushed object closer to source of the effect than its center of gravity will experience a stronger push. And the parts of the object beyond the center of gravity will experience a weaker push. If you put your frame of reference into the center of gravity of the pushed object, the parts of the object beyond the center of gravity would indeed see a force towards the center of gravity.
Is that the reversal you were refering to?

[CosmereScholar]

No, it was not. But, you are right. I was mistaken. If the repulsive force decreases in magnitude with distance to the source, there will indeed be compressive tides.

[bacontime]

Quote

Whether or not the friction idea is correct, a mistborn should be able to suspend objects in midair, even at an angle, by pushing and pulling very strongly on the same object.

This is entirely possible without allomantic friction, but would take extreme finesse.

Please refer to the following doodle technical diagram:

Suppose you have an mistborn skilled enough to apply forces to parts of objects rather than the entirety of an object. He wants to pick up a brass idol from a pedestal without getting close (scary spiders are at the base of the pedestal). The idol has a mass of 25 kg and its height is 1/6 of the distance between the allomancer and the idol. The bottom of the idol is level with the allomancer's center of mass. For simplicity, assume that gravity on Scadrial creates a downwards acceleration of 10 m/s.

In order to overcome gravity, the allomancer needs to exert more than 250 N of upwards force on the ball. Let's double it and say that they want to produce 500 Newtons upward. In order to apply that much vertical force by pushing on the top of the ball, the total force of the push must be (500/sin(9.824°) = 3041.38) N. But this push also results in a perpendicular force of 3000 N away from the allomancer. If he pulls on the bottom of the idol to counteract this force, then the net forces will lift the idol straight upwards.

(Also, the idol will start spinning like mad, so if the allomancer wants to keep applying the force, he needs to be very good at juggling his target points.)

 

A corollary to this is that a mistborn can theoretically hover in midair using multiple anchors which are neither above nor below her. The closer the anchors are together, the more power and finesse are required to pull this off.

 

Edited April 15, 2019 by bacontime

[+Artemos]

6 hours ago, bacontime said:

<snip>

That second situation makes perfect sense to me, thanks for the visual. Strong people can do that same thing in real life with just their arms. I imagine it would take a similar amount of mental effort (and physical stress) to push and pull in such a balanced way, but it's very doable.

The first situation feels a bit shakier to me. I feel like it should work. I can't find any physical problems with it, and it looks pretty straight-forward. The idol would experience a massive torque, so I doubt human would be able to keep concentration/perception of the "top" and "bottom" of the idol for very long. The skill necessary for that isn't seen in the first (or likely second) era, so I feel like it fits in with the allomantic motor that was mentioned a few months back.

[+Oltux72]

6 hours ago, Artemos said:

The first situation feels a bit shakier to me. I feel like it should work. I can't find any physical problems with it, and it looks pretty straight-forward. The idol would experience a massive torque,

The idol would also experience a lot of strain. At a certain point you would either fail or rip the idol in two.

[Truthless of Shinovar]

Ahh... Mistborn physics, this kind of stuff never gets old

[bacontime]

22 hours ago, Artemos said:

 The idol would experience a massive torque, so I doubt human would be able to keep concentration/perception of the "top" and "bottom" of the idol for very long. 

Oh absolutely. Someone commented on the image in the gallery that you'd probably need Feruchemical Zinc to switch target points quickly enough. And I'm inclined to agree. Instantaneous thrusts à la Kelsier's battle in the square are much more feasible than hovering.

 

15 hours ago, Oltux72 said:

The idol would also experience a lot of strain. At a certain point you would either fail or rip the idol in two.

Say the radius of the idol is 10cm. (That's actually a bit too large for 25kg of brass, but eh, round numbers.) The moment of inertia of a solid ball is (2/5)*m*r^2, which works out here to 0.1 kg m^2.

The depicted forces apply 600 Nm/rad of torque.

So the  angular acceleration is 6000 radians per second per second.

In other words, ignoring friction, it would take less than a second of constant hover juggling for the surface of the ball to accelerate past the speed of sound. I don't know enough about tensile strength to say exactly when the idol would explode, but yeah. It would heat up, start creating small sonic booms, and then rip in two.

(The second scenario avoids these problems by transferring all the force into the ground, which makes the system static.)

 

If you actually wanted to hover juggle something without Lord Ruler level skills, the ideal candidate would be something like a wide, lightweight hoop with a metal ring on the outside. (Cylinders have high moment of inertia for their mass.) It would also help to line the ring with some sort of structure to create plenty of drag and slow the spin. You could probably rig it up to make a musical sort of buzz. Spinning - that's a good trick!

Edited April 17, 2019 by bacontime

[Scion of the Mists]

@bacontime While theoretically possible, I think this would be very difficult to pull off.  In addition to the spinning/exploding issue already discussed, you'd have a terrible time adjusting your forces as the object raised in the air, which would be continuously changing the equations.  Maybe this could be overcome via the "instinctual" aspect of Allomancy (i.e. by a savant).  

I think an easier way to go about it is to push and pull from different points in your body.  This would allow both your forces to act on the center of mass of the object, which would eliminate the torque.  We know (or can assume) that this is possible from Zane's spinning in midair and from the "hovering a coin" WoB:

Quote

Questioner

So my quick question: Can you use Identity (I love the speed bubbles!) to anchor speed bubbles to yourself?

Brandon Sanderson

Uh, this is possible. That's less a matter of Identity. What’s gonna happen there, like, the more someone uses the powers, the more familiar and intermingled with their soul the powers become, and they are able to accomplish things that others can't. This would be like a Mistborn learning to hover a coin, right, which they can do, but most think you can't. That's the sort of level we're going with.

Necarion

So a savant could?

Brandon Sanderson

A savant could totally do that. The problem is, things moving in and out of a speed bubble, there's a transference of energy. This is how we keep speed bubbles from irradiating people when light moves through them, right, red shift. And so there's a transfer of energy directly from the Spiritual Realm, which means that moving with a speed bubble, you're gonna run into that, and it's gonna be, it's gonna cause all kinds of problems, but it would be possible.

Arcanum Unbounded San Francisco signing (Nov. 30, 2016)