Towards a mechanical description of Steelpushing

[Arcanist Lupus he/him]

It could be that burning speed, and thus power derived from metal, depends on the mass of the person. This doesn't really make sense, but I could see the argument being made for some weird subconscious limitation.

Again, I'm not saying this is plausible, I'm just throwing it out there so that someone can maybe turn it into a plausible theory.

[Triasmus]

true.

That's why when Vin had an anchor she was able to hold her own against kelsier.

People will start to be ranked on the power of their pushes and pulls when they're able to put scales on the wall (or on the other side of the wall) and push or pull against them.

[Eric]

@lil_literalist: He seems to be explicitly talking about physical strength in the second paragraph, with the reference solely to strength tapping.

If I remember correctly, Ham is also the one who later put forth the theory that she is stronger than other Allomancers because she uses the same amount of power throughout less mass during their training in Luthadel in the Well of Ascension.

Kelsier also warned Vin to not get into pushing matches with people who weigh more, after she nearly beat him despite *both* of them having anchors. (She lost because her anchor gave out first, if you recall. His wall lasted longer than her tree.)

As of yet, I do not believe it to be conclusively shown that there is no relationship between mass and the force of a Steelpush, or even Allomancy in general.

[lil_literalist he/him]

Newton's third law: For every action, there is an equal and opposite reaction. If nothing is accelerating, then there are equal forces being applied to both anchors. It is the simple fact that her anchor gave out first.

[Eric]

That was more directed at Lantern13 commenting that she could hold her own against Kelsier when she had an anchor. If he hadn't had one as well, he would have lost. I was posting from my phone, sorry.

---

However, I found that passage I was looking for. It happened to be the very next few paragraphs after what you quoted:

"Now, most Thugs -- myself included -- figure that making their bodies strong will only add to their power. After all, a muscular man burning pewter will be that much stronger than a regular man of the same Allomantic power."

Ham rubbed his chin, eyeing the passage Vin had left through. "But... well, I'm beginning to think that there might be another way. Vin's a thin little thing, but when she burns pewter, she grows several times stronger than any normal warrior. She packs all that strength into a small body, and doesn't have to bother with the weight of massive muscles. She's like... an insect. Far stronger than her mass or body would indicate. So when she jumps, she jumps."

"But you're still stronger than she is," Spook said.

Ham nodded. "And I can make use of that -- assuming I can ever hit her. And that's getting harder and harder to do."

He is very clearly talking about pewter Allomancy throughout the whole thing, and saying that mass is related to strength. She gets greater returns, but he's still stronger overall. To make this perfectly clear, the exchange that started this was:

"How'd she do that, Ham?" Elend asked. "The jump, I mean. That leap seemed inhuman, even for an Allomancer."

"Used steel, didn't she?" Spook said.

Ham shook his head. "No, I doubt it."

"Then how?"

He's explicitly clarifying how strength normally works for Thugs, and theorizing that Vin has a workaround because of her build.

---

Now, as to whether mass affects steelpushing, if we assume that with a given Innate Ability, Effort, and Purity, then the Distance and Mass are the only two remaining variables. Let's make the starting Distance 1 m to eliminate it at first. With equal mass and traction, the anchor and the Allomancer will be forced apart at the same rate of speed. For the moment, allow me to assign a value of 1 m/s to that initial Push speed. So they start 1 m away at 0 s, and are at 3 m away at 1 s. We could plug in these new numbers to get the Force of a sustained Push as it happens, right?

If one is too massive or well-anchored to move (relatively speaking, as the force is still imparted and some motion will occur), the other will be the only one moving. This means that they start at 1 m away, and the lighter object is only 2 m away at 1 sec, right? But since the Distance hasn't increased as much as when they were the same mass, won't the Force imparted be greater at this point? Meaning you'll get greater Force with sustained pushes.

Is this accurate, or am I mistaken somewhere? If it is accurate, is it something that gets taken into consideration with the formula, or is it something that has to be accounted for separately?

[Triasmus]

When I said that she held her own against Kelsier I was meaning that if neither of them had an anchor she would have been pushed farther than him, because she's lighter. but with anchors she was able to hold her own against him. Mass doesn't have anything to do with the power allomancy gives you, it only has do do with how much you're pushed.

When Ham was talking about pewter strength he was saying "a person has a given amount of strength. If they build up their muscles then their given amount will be more. Pewter gives say... 10 units of strength on top of what you have. I, being awesome, have 4 units of strength without pewter, while Vin only has 1/2 a unit. Since I'm sooo much stronger than Vin, I weigh a lot more. When we both burn pewter, I'm still stronger than her. I'll have 14 units of strength while she only has 10.5 units. If I can hit her, she'll be hurt. But she's sooo stinkin' fast (she doesn't have to move (limbs) as much to go the same distance as someone who's heavier. She can start moving (her body) quicker than most [since reaction times are still close to the same].) And you saw her her jump!! All that strength pushing up on that tiny body makes for supersuperhuman jumps."

[ulyssessword he/him]

I'm fairly certain that having a greater mass greatly increases your ability to exert force through Allomantic steel (and, presumably, iron). Every time that Wax needed to push on something strongly in AofL, he increased his mass. I don't believe that every single time it was only so that he would not be pushed as far. (also, IIRC, he does some stunts that Vin would have been envious of while increasing his mass).

By keeping the comparison to a single person, we can eliminate the variation between strengths of different people.

[Triasmus]

I'm fairly certain that having a greater mass greatly increases your ability to exert force through Allomantic steel (and, presumably, iron). Every time that Wax needed to push on something strongly in AofL, he increased his mass. I don't believe that every single time it was only so that he would not be pushed as far. (also, IIRC, he does some stunts that Vin would have been envious of while increasing his mass).

By keeping the comparison to a single person, we can eliminate the variation between strengths of different people.

Well of course. Force = Mass x Velocity^2 (I think) Force = mass x acceleration (I didn't do good in physics. Thanks ulysses). But the power from steel is the same. In those cases it's mass of person vs mass of object (with friction included)(the only thing I can actually think of from the book is when he crushed the building. In that case, because he was soooo heavy, instead of the building pushing him up, he pushed it down. but the steel was still only giving him the same amount of power as normal. I also have snippets of memory telling me that wax regularly made himself lighter so he could push himself around easier/faster, which has the same explanation as Vin being faster than normal pewterarms)

Edited May 3, 2012 by Lantern13

[Aradel he/him]

The crux of it is that mass does not affect the energy output of burning steel. Allomantic strength is determined by the user's spiritual connection to Preservation.

Mass does affect steelpushes (and Ironpulls) because of inertia. Larger mass objects have more inertia than objects with smaller mass. That means that they're harder to put into motion, and harder to bring to a stop.

Higher mass characters like Kel can appear to put more force behind their pushes because they have the mass to toss around larger bits of metal without bracing or anchoring themselves.

Lower mass characters like Vin are more easily pushed away because they have to brace themselves to push against objects that higher mass characters can push easily.

On the other hand, because Vin has lower mass than Kel she can push herself around more easily. This makes her steeljumps more effective.

Edited May 2, 2012 by Goradel's Nephew

[Eric]

So, correct me if I'm wrong, but wouldn't the mechanical description of Steelpushing necessarily include that information?

[ulyssessword he/him]

(the only thing I can actually think of from the book is when he crushed the building. In that case, because he was soooo heavy, instead of the building pushing him up, he pushed it down. but the steel was still only giving him the same amount of power as normal...)

So Wax (who is, presumably, an average powered Allomancer) can flatten buildings, just like anyone else (the only difference being that he does not go flying)? I find it hard to believe that any other Coinshot could do the same, especially since it is remarkable in-world.

Another example was in the beginning fight when he pushed the tables (etc.) away from himself while at increased mass.

P.S.: Force = Mass x Acceleration

[Triasmus]

he increased his mass to reduce the effect of a bunch of tables "squeezing" him (since a side effect of increasing mass is making your body stronger to handle it).

other coinshots can't store weight. Wax used up years of going 75% mass in seconds. He was immensely heavy (as in, very very very very very very very very very very heavy) when he pushed down on all the metal parts of the building. There was a force pushing Wax and the metal apart and since wax was soooo stinkin' heavy, the metal got pushed from him instead of him getting pushed from the metal.

[Eric]

I am very confused, because I think I understand what's being said, but not what we're disagreeing about.

As for making his body stronger to handle the tables, I think that's not quite correct. I think it was mostly the same trick he used on the building, making himself heavy enough to be the anchor. It wasn't a side effect he'd complain about, though.

Can an Allomancer push hard enough to injure himself from the force (not the impact, but the sudden acceleration)?

[Triasmus]

Well... if he's in the center of the room and he pushed out in all directions, it stands to reason that opposite directions will have approximately the same amount of tables, which mean approximately the same weight on either side, which means the tables will cancel each other out when pushing against both of them.

meh... he could have been increasing his weight for anchorage.

I'm saying that the allomancy gives a set amount of power on a normal burn (if it's flared it'll give more). Pewter gives 20 units of strength (maybe more if you're naturally a more powerful allomancer), steel gives 15 units of pushing. Changing your weight doesn't change the amount of power burning the metal gives. I thought people are saying that changing mass or strength or certain things will also change how much power burning a metal gives.

EDIT: oops.... failure to add the negative causes problems with arguments.

Edited May 4, 2012 by Lantern13

[lil_literalist he/him]

I can't believe that we didn't bring Wax into this discussion before this. I mean, this is the guy that would know whether or not weight affected the strength of steelpushes. I'd have to go back and look for specific instances of him changing his weight while pushing. I do recall him increasing his weight while pushing on the chandeliers, but that was only so that his flight trajectory wouldn't get thrown off. Also, when he climbed the Ironspine building, he decreased his weight. If doing so gave him less pushing power, he sure didn't mention it. Come to think of it, he doesn't mention that sort of thing at all during the book. The only use he seems to have for increasing his weight while pushing is when he wants to make other things move instead of himself. Of course, it's been a few weeks since I've read it, and I wasn't paying close attention to such things. Anyone have a book handy who wants to do a little searching?

[lil_literalist he/him]

Ok, so I've gone through the sample chapters online and found this:

He began to fill his metalminds—the iron bracers he wore on his upper arms—draining himself of more weight, making himself even lighter. That weight would be stored away for future use. Then, ignoring the more cautious part of his mind, he flared his steel and Pushed.

He shot upward. The wind became a roar, and the lamp was a good anchor—lots of metal, firmly attached to the ground—capable of pushing him quite high. He’d angled slightly, and the building’s stories became a blur in front of him. He landed about twenty stories up, just as his Push on the lamp was reaching its limit.

(Still at reduced weight)

He turned about on his perch. It was difficult to judge locations in the dark and the mists, but he did have the advantage of a youth spent in this section of the city. Things had changed, but not that much. He judged the direction, checked his steel reserves, then launched himself out into the darkness. He shot outward in a grand arc above the city, flying for a good half a minute on the Push off those enormous girders. The skyscraper became a shadowed silhouette behind him, then vanished. Eventually, his impetus ran out, and he dropped back through the mists. He let himself fall, quiet. When the lights grew close—and he could see that nobody was below him—he pointed his shotgun at the ground and pulled the trigger.

The jolt punched him upward for a moment, slowing his descent. He Pushed off the birdshot in the ground to slow him further; he landed easily in a soft crouch. He noticed with dissatisfaction that he’d all but ruined some good paving stones with the shot.

He leaped up onto the balcony railing. His way was mostly blocked by the chandeliers; he couldn’t make a direct jump to Wayne. He’d have to jump down, then up again, and bound to— No time. Wayne was dying.

Go!

Waxillium threw himself off the balcony. As soon as his feet were free, he tapped his metalmind and drew forth as much weight as he could. That didn’t tow him to the ground; an object fell at the same speed, no matter its weight. Only air resistance mattered.

However, weight did matter a great deal when Pushing—which Waxillium did, throwing everything he had against the chandeliers. They ripped apart in a line, the metal inside them twisting upon itself, crystal exploding outward in a shower. That gave him plenty of room along the upper portion of the room to jump in an arc toward Wayne.

In a heartbeat, Waxillium stopped tapping his metalmind and started filling it instead, decreasing his weight to almost nothing. He Pushed on the broken harp behind, and a simultaneous quick Push against the nails in the floor kept him high.

The result was that he soared across the room in a graceful arc, passing through the space the large chandeliers had occupied. The glittering smaller chandeliers continued to shine on either side of him while crystal showered beneath, each tiny piece splintering the light into a spray of colors. His suit coat flapped, and he lowered the single revolver in his hand as he fell, pointing it at the bandit standing over Wayne.

Wayne ran forward and leaped onto a table in front of them. He dropped the speed bubble right as he launched himself off, and Waxillium braced himself by increasing his weight, then Pushed on Wayne’s metalminds, sending the man soaring through the air in an arc toward the bandits. Once Wayne was airborne, Waxillium flipped from tapping his metalmind to filling it, then Pushed on some nails, launching himself into the air in a slightly different trajectory.

Reducing his weight to ascend the Ironspine building supports the theory that the strength of a push does not depend upon mass. Otherwise, it wouldn't have mattered whether he was weightless or not. The part about the chandeliers does seem to imply that weight matters when pushing, but it seems to be talking about increasing his weight so as not to change his trajectory. The last quote also supports this line of thinking, since he increases his weight to give Wayne a shove (without doing the same to himself) and then decreases his weight so he can move quicker with his own push.

[Eric]

I think we've all been arguing in circles. Mass matters for force and acceleration (pretty much by definition), but not actual energy. Is this what everyone else has been trying to say as well? If so, I apologize, as the initial misunderstanding was mine.

[Aeshdan he/him]

The amount of force generated by Iron/Steel is not affected by your mass, but the acceleration created by that force is inversely proportionate to your mass, as per Newton's Second Law. Agree or disagree?

(I know this doesn't contribute much, but i'm just trying to make clear everyone's position. So please, no downvotes.)

[ulyssessword he/him]

The amount of force generated by Iron/Steel is not affected by your mass, but the acceleration created by that force is inversely proportionate to your mass, as per Newton's Second Law. Agree or disagree?

Disagree. (but well put, that is a clear statement of that position)

The amount of acceleration that a coinshot/lurcher can give themselves is not affected by their mass (assuming a sufficient anchor); the amount of force created is directly proportional to their mass.

As for the examples presented in support of force being constant: they can be read the opposite way as well, he becomes lighter to make full use of a weak anchor, and becomes heavier to increase the force he exerts.

Edited May 3, 2012 by ulyssessword

[lil_literalist he/him]

So some of you have just been arguing without knowing what we've been arguing about?

This goes back to the first few posts, when people were posting equations of what they thought the force exerted by a steelpush was. Many people thought that the force was directly related to the mass of the allomancer (meaning that the heavier the allomancer was, the more force would be behind his pushes).

I will now attempt to classify the two theories on this. Most of the discussion has been about the force between an allomancer and whatever he is pushing or pulling on, so that is what the theories will attempt to explain. If you don't have a good background in physics, just be sure to familiarize yourself with Newton's 2nd and 3rd laws of motion (F=ma and equal-and-opposite-reaction, respectively).

The first theory put forth is the "Mass-dependent" theory. This argues that an allomancer's pushes and pulls become stronger when the allomancer has more mass and less when the allomancer has no mass. If a coinshot was lying down and shot a coin up into the sky, the coin would go higher than it would if it were shot by an allomancer that was half his weight. On the other hand, those same two allomancers launching themselves upwards off of a coin anchored on the ground would experience similar forces on their bodies.

The second theory is the "Mass unrelated" theory. This argues that although an allomancer's mass affects the acceleration of the allomancer's body due to pushes or pulls, it does not affect the actual force between the allomancer and a metal object. If two coinshots of different masses were lying on the ground and both shot a coin up into the air, the coins would peak at roughly the same height. On the other hand, if those allomancers launched themselves into the air off of an anchor on the ground, the lighter allomancer wold have a higher acceleration and would have a higher peak than the heavier allomancer.

There is also another theory, which I will call the "Heavier burn rate" theory. It claims that allmoancers get the same amount of power from the same amount of metal, regardless of weight. However, allomancers who weigh more are able to burn metals at a quicker rate than lighter allomancers. This means that although mass is not directly responsible for differences in strength between allomancers, the effects are similar to those of the first theory.

[lil_literalist he/him]

The amount of acceleration that a coinshot/lurcher can give themselves is not affected by their mass (assuming a sufficient anchor); the amount of force created is directly proportional to their mass.

A well-put statement of your viewpoint, which I have labeled the mass-dependent theory.

As for the examples presented in support of force being constant: they can be read the opposite way as well, he becomes lighter to make full use of a weak anchor, and becomes heavier to increase the force he exerts.

I'll admit that becoming heavier to provide a stronger push does make sense, but not the other way around. Was makes himself lighter to push off of three things that I've mentioned:

1. A lamp post (the lamp was a good anchor—lots of metal, firmly attached to the ground).

2. The Ironspine building (those enormous girders)

3. Some floor nails and a broken harp.

Number 3 is debatable, but you cannot seriously believe that the first two are weak anchors that would move around with too much force. Why, earlier, he's pushing off of those very same lamp posts with ease, not concerned at all about how they're holding up. And as for the second one... It's a REDACTED skyscraper!

I want you to take a step back from the picture and reexamine all of the evidence. Don't go with what you feel, but actually look at what has been presented. Form an educated decision based on what you see. If you still believe that you are right, then tell me why. It is one thing to defend your viewpoint, but another thing altogether to prove it. Thus far, I haven't seen a single shred of proof.

Eric, sorry that it's taken me so long to get to this.

Now, as to whether mass affects steelpushing, if we assume that with a given Innate Ability, Effort, and Purity, then the Distance and Mass are the only two remaining variables. Let's make the starting Distance 1 m to eliminate it at first. With equal mass and traction, the anchor and the Allomancer will be forced apart at the same rate of speed. For the moment, allow me to assign a value of 1 m/s to that initial Push speed. So they start 1 m away at 0 s, and are at 3 m away at 1 s. We could plug in these new numbers to get the Force of a sustained Push as it happens, right?

If one is too massive or well-anchored to move (relatively speaking, as the force is still imparted and some motion will occur), the other will be the only one moving. This means that they start at 1 m away, and the lighter object is only 2 m away at 1 sec, right? But since the Distance hasn't increased as much as when they were the same mass, won't the Force imparted be greater at this point? Meaning you'll get greater Force with sustained pushes.

Is this accurate, or am I mistaken somewhere? If it is accurate, is it something that gets taken into consideration with the formula, or is it something that has to be accounted for separately?

Your physics is wonky. Also, it's more complicated because the forces that we're talking about aren't constant. Remember, the farther away you get from your anchor, the lesser the force.

[Triasmus]

I love for other people to do my work for me (as in, find proof for my arguments . It's so much more funner for me to argue than research)

[lil_literalist he/him]

Well so far, it seems like you and I are in agreement. And doing the research is no problem, as long as I have access to the text.

[Eric]

So some of you have just been arguing without knowing what we've been arguing about?

I had thought you were talking about removing mass from the equation you were working on, hence my confusion. I had forgotten about the mass-dependent theory, and apologize again. Please ignore my wonky physics.

[ulyssessword he/him]

I found a passage that supports the mass-dependant theory, without requiring any interpretation.

Wax drew every bit of weight he had left, draining his metalminds completely... with this incredible conflux of weight, his ability to Push grew incredible.

I find this to be much more solid evidence than any that has been presented so far, as it is a direct statement as opposed to an interpretation of someone's intent or a guess at someone's abilities.

Furthermore, I don't think that many of the "solid" anchors are sufficient to allow a full strength push at normal weight. Let's assume that Wax's maximum force exerted is normally 1000 lb (enough to accelerate his body at 5g, which is tolerable). That amount of force could easily tip over a lamppost, or punch nails through the floor. As for the skyscraper, I thought he was lighter to give himself more velocity from the shotgun blast, as well as making climbing easier, and just stayed light because there was no reason to switch back and forth.

Edited May 5, 2012 by ulyssessword