Artemos

Welcome to the Shard! To be directly influenced by Ruin, I believe that you have to be spiked. I don't remember any record of Yeden being pierced by metal, so I don't think Ruin was the reason for his attack. Also, it would devalue the explanation that's already there. Because Kelsier made himself into such an almighty figurehead, Yeden believed that it was impossible for the rebellion to fail. Kell's message of survival and hope made them overconfident. Yeden was a victim of hubris - both his own and Kelsier's.

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.

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. 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." 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. 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.

"Allomancers Pushing on air" definitely fits into the realm of "It's possible! but you need a couple infinities of Investiture to do it!"

I agree with RShara's WoB from above for burning a spike that was taken from someone else. I have a little pet theory that probably isn't true that if someone spikes an aspect out of you and you somehow don't die, you could take that spike back, spike yourself with it, and burn it up to return your spirit to how it was before. It's a bit too clean for Hemalurgy, but... eh. It would be cool.

Yes. You need a group of players as well as a game master (GM). The GM either writes their own narrative or uses a pre-written story that presumable comes with the game you buy (which is probably a set of rulebooks and character sheets). The players then play through this narrative. Depending on the GM, this narrative may be very linear, and the players follow a story that the GM wants them to follow. Better GMs will learn to improvise and let the players make plot-bending decisions and write their own narrative, to a degree. The best GMs often write their own settings and stories, personally tailored for their players. For specifics, I found a preview of the rulebook from Crafty Game's website, so it should be legal. Page 47 shows what sorts of things a Coinshot could do in-game.

How familiar are you with other tabletop RPGs, like dungeons & dragons, pathfinder, and shadowrun? We can get you better advice if we know that specific detail. I've never played MAG myself but I've had my fair share of other tabletop games and it looks very interesting to me.

Yes, as indicated in the bottom-right corner for each one. Yeah. Tweaking constants involved would make everything happen quicker. This had just enough tuning of parameters to compare the different models in a reasonably short enough time. There will never be a model more elegant than this one. There's no "extra boost" from pushing on a target, simply pushing on a coin that stays relatively close to you will provide more force over time than a coin that flies beyond pushing range in milliseconds. It doesn't not work in the game. I always liked that one, but it just doesn't give the same "impact" or "feel" as getting a boost from an anchored target that the narrative suggests. The velocity "drag" force helps to stabilize an Allomancer when they near their maximum height; however, that would be unnecessary if the Allomancer simply pulses their Pushes on/off when nearing their maximum height. They'll stabilize easily in that case, too. Of course, Pushing duels work best with the velocity factor. I guess the next thing on my to-do list is to go back to experimenting with anchors having no direct affect on the force calculation. Keep things simple. At least it'll help to see if we've been running in circles for the past few weeks.

Fiddling with the constant V makes arctan and 6/7 pretty close. I'd say its a valid option. And it's a definitely a lot prettier than the exponential relationship. Yes and yes. The "gif at the end" is has no differences, it's just returning the coin and the right wall to their original positions as the simulation partially restarted. I kind of threw that one together as I started working on the new simulation. Speaking of... Coin/Ground Simulations The "Relationship" mentioned in each simulation corresponds to the relationships listed in this graph. The Allomancer-coin pair on the left begins stationary in the air. The pair on the right begin stationary on the ground. In the center is a coin in free-fall that shows how gravity is affecting the scene. The time scale is set to 5% until the left coin hits the ground, at which point the time scale is set to 100% (real-time). Simulation 1 - Symmetrical (velocity constant V = 16, distance constant D = 16) The velocity factor both adds and subtracts from the force to dampen the oscillations, allowing the Allomancer to eventually balance at around 10m. Simulation 2 - Only Moving Away Decreases The velocity factor no longer adds to the force; it only subtracts from it. The dampening is less effective, so the Allomancer takes longer to stabilize. Simulation 3 - Both Directions Decrease The velocity factor subtracts from the force both ways. After the Allomancer reaches their maximum height, they begin falling downwards due to gravity - and that downwards velocity decreases the force more and more. The force just isn't strong enough to beat that - with this constant V, at least. Simulation 4 - Linear distance relationship Changing to a linear distance relationship didn't actually change much. In this case, the "maximum range" (the big R constant) of the Push is 20m, and they stabilize a little closer to the ground. Simulation 5 - Setting V = 1, Symmetrical This might be my favorite. Reducing V makes the velocity factor have a greater impact. Using the same parameters as Simulation 1, the Allomancers can reach their maximum height with no oscillations. It does do that! Simulation 6 - V = 1, Both Directions Decrease I don't know what really to gleam from this, other than It Feels Good To Look At. Let me know if there's any other parameters you want me to test this with.

(I had some confusion earlier because I hadn't refreshed the page after Jofwu's edit.) I agree that it is elegant in its simplicity, but it doesn't provide the desired effect. Relationships 4/5 and 6/7 are the ones that work well with Pushing duels, which have asymmetry in the velocity relationship. Relationship 4/5 is asymmetric, but 6/7 does have rotational symmetry. In-game, I refer to it as the "Symmetrical" option, since it both adds to and subtracts from the force. Here's an updated version of the simulation of a coin being pushed into a wall with a couple more options: Based on this comment and your graph, I'm working on something that should show an Allomancer throwing a coin to the ground and Pushing on it, showing how they rise into the air with different models.

Regardless of how velocity enters the equation, if the force on the Allomancer and target is equal, whichever one is lighter will accelerate more. That's just Newton's second law. I might be misunderstanding you, though. (Also, is that last quote field supposed to say "4 hours ago, Jofwu said" ? I'm a bit confused, since I can't find a post of him saying that anywhere) Regardless, for that final point, we have tried leaving out the velocity factor and have tried tweaking the distance factor. Changing the distance factor won't increase the Push on an anchored target, as seen in the books. Over time, perhaps, but it doesn't account for the discontinuity/sudden increase in force when the coin hits the ground. Edit: I hadn't refreshed the page, so I hadn't seen Jofwu's edit - hence the confusion.

I missed this on my first read-though of your post. As someone who's done a lot of work with PID control, Harmony bless this comment. Pushing and Pulling darn better not use PID loops because I'm the idiot who would have to program it. I think a lot of the confusion came from how I worded things somewhat badly in my simulations/replies on the game thread. Here are clarifications of my interpretation and implementation of the "Exponential with Velocity" model. Click here to see the formula I used for this model. Let's start simple and work our way up. Click the circles to the left of each relationship to toggle each one. Feel free to experiment with the numbers. Relationship 1: N is the Net Force acting on the Allomancer. It is equal and opposite to the Net Force acting on the target. F is the Allomantic Force. In this graph, it's a constant, set to 1. In practice, it's a jumble of other factors including distance, strength, masses, and burn rate. |v| is the magnitude of the velocity of the target relative to the Allomancer, projected onto the line pointing from the Allomancer to the target. The reason this is the relative velocity projected on to the line between the Allomancer and target is to keep everything acting on the single axis between the Allomancer and target. If the target is standing on top of a train moving parallel to the line between the Allomancer and target, I don't think that velocity would affect the Push. If the Allomancer is the camera, compare this image to this one. The velocity in the first image won't affect the force as much as the second. Note that this the magnitude of the velocity. It is not affected by sign. V is an arbitrary constant. This shows the relationship between the Net Force and velocity in its most basic form. The higher the |v|, the lower the Net Force. This was Simulation 2 in the above post. Relationship 2 and 3: (toggle both circles) This relationship defines bounds where the Net Force is equal to the Allomantic Force when v is less than 0, but Relationship 1 when v is above zero. But, what is v? In this context, v is the dot product of the relative velocity (same as above) on the direction of the Allomantic Force acting on the Allomancer. Essentially, if the relative velocity is in the same direction as the Push, v will be positive. If the relative velocity is in the opposite direction of the Push, v will be negative. Using a well-known example, let's say the Allomancer throws a coin downwards and Pushes it towards the ground. The relative velocity will be pointing towards the ground, but the Allomancer's Push points upwards. The dot product is negative, so the Net Force will be equal to the Allomantic Force. This isn't what we're looking for, of course. This was Simulation 4 above, which is Hot Garbage. Let's swap the bounds. Relationship 4 and 5: This is the opposite of the above relationship. When the dot product is negative, the Net Force will be decreased by the velocity factor. When the Allomancer Pushes the coin towards the ground, the Net Force is weak until the coin lands. At this point, the relative velocity suddenly swaps sign, as the coin and Allomancer are getting closer. v is positive, so the Net Force equals the Allomantic Force, much higher than before. This was Simulation 5. Relationship 6 and 7: This is my personal favorite, but I didn't include it in the simulations post because it was too similar to Simulation 5. It has the same effect as Relationship 4, where the Net Force decreases for a negative v. However, when v is positive, the Net Force increases as well. Not only will the Allomancer's Push against a falling coin be weaker, but the Push will also be stronger while the Allomancer is falling towards towards the anchored coin. In the latter case, the relative velocity is pointing in the same direction as the Push on the Allomancer, so v will be positive. This "improved" Net Force will asymptotically approach twice the Allomantic force as the relative velocity approaches infinity. The result of this is something that feels intuitive to play with. If you Push on a metal block, you'll get some force. But if you Push on that block while digging your feet into the ground and charging towards it, that force will increase. I will leave it as an exercise to the reader's brain to figure out the vectors in that one. I'm starting to like the velocity factor idea more now, if only for the fact that I've been drafting a theory based off of Pagerunner's Model 3 that has been Rust to program and Ruin to work in Pushing duels.

The way I implemented e^-v, a "positive v" didn't make the -v term positive; it made the entire e^-v term positive. It added something to the force rather than subtracting, but it wasn't a positive exponential relationship (e^x) relationship. It looks something like this, where N is the net force, V is an arbitrary constant, and F is the original Allomantic Force. A "positive v" or "negative v" is determined by the dot product of velocity and the Allomantic Force.

Velocity is a vector, so I meant that to be the magnitude of velocity - the velocity term e^-v should be reworded as e^-|v|, and it will never be greater than 1. I can talk about the math later. Thinking about it, you're right. Still, I don't believe anything is backwards in my code. I'll review some things and come back later.

This reminds me of my biggest gripe with force as a function of velocity: how it handles high-speed projectiles in scenarios other than the ones we've previously discussed. Wax's steel bubble would be useless due to the high negative relative velocity between Wax and the bullets. I also feel like Vin's Horshoe Wheel would be much more difficult (if not impossible) to execute. That could just come down to skill, though. Keep in mind that in Simulation 3 (the good one), the velocity factor is only applied if the Allomancer and target are moving towards each other. If the factor is applied for velocity regardless of its sign, you get (2), which is not the desired effect. Should velocity be applied regardless of the sign? It is another arbitrary decision to make it only apply when the relative velocity is negative.

This is definitely the case. When I was rereading The Final Empire, I noted that Kelsier instructed Vin to land by pulsing her pushes on the coin.

I'm not sure if @Pagerunner ever adhered to the theory that the normal force is transmitted to the Allomancer. That's something that I believed, but I'm changing my mind from the discussion here. I'm thinking of another idea inspired by Model 3 that I think I'll make a separate topic about at some point. Yeah, quantifying "effective mass" seems very sketchy, especially regarding partially anchored metals. Let's say you're an Allomancer standing next to a a metal block sitting on a high-friction surface. You Push on the block, which grinds against the ground, but does still move. It's not perfectly unanchored, since the block is resisted by friction, nor is it perfectly anchored, since it's still moving a bit. The strength of this particular Push would be higher than that on an unanchored target but smaller than that on a perfectly anchored target. The effective mass of the target would have to be somewhere between the mass of the target and the mass of the target + planet, which really doesn't sit right with me. I can't imagining calculating it without using the normal force, as you said.

It's the method I've been using for the game because I believe it to be true, it uses fairly intuitive physics concepts, and it gives satisfying gameplay. It conserves momentum and the like because it makes Pushes work like physically grabbing and pushing on something and experiencing a resistance (a normal force) from that object. From the original post: If you held a long vertical pole and pushed down on the ground, the ground would push back on you and the pole. If you tried to push the pole into the ground, the ground would resist, and you could climb upwards relative to the ground. Allomancy mimics this effect. When pushing on the coin, it is like you are physically connected to the coin. If something resists your push, you experience that resistance. It's just like you're literally pushing against the coin with your fists. If the coin's in the air, hardly anything happens. If the coin's on the ground, the ground resists. By this theory, there's two components to the Net Forces that the target and the Allomancer experience - the Allomantic Force and the Allomantic Normal Force (ANF). The Allomantic Force is calculated from all the factors you'd expect, such as Allomantic strength, burn rate, and distance from target. It's definitely equal for both the Allomancer and target. If both the Allomancer and the target are completely unanchored, the ANF term will be 0 and the Net Force is going to equal the Allomantic Force. When either the Allomancer or target are anchored or partially anchored, the ANF will be nonzero and the Net Force will be equal to the portion of the Allomantic Force that is resisted. It behaves similar to normal force due to gravity; a feather, a brick, and a safe can sit on a table, which provides normal forces of different strengths depending on how much the objects are pushing down on it. I made these pictures with my original post last year. I'm not sure if the scale of the vectors are right, but the pictures still illustrate it pretty well. Indeed, if the target is perfectly anchored, the ANF would be equal to the Allomantic Force, and the Net Force experienced by the Allomancer would be twice the Allomantic Force. Whether that's strong enough is subjective, and sometimes I agree that a factor of 2 is not enough to account for the difference in anchored/unanchored Pushes. My interpretation is that you cannot be resisted more than you can push. The ANF is calculated from the Allomantic Force (your "actual" pushing strength), not the Net Force experienced by the Allomancer or target. If both you and your target are anchored, you'll experience a Net Force twice of that against an unanchored target. There would be no feedback loop in much the same way that pushing a pole into a wall causes no feedback loop. Still, there are some flaws to it. Unless the Allomancer and target are both anchored in the exact same way, the ANF for the two won't be equal, and thus the Net Forces for the two won't be equal. I'm pretty sure this is how pushing on things works in real life, but I haven't yet taken the time to do a full mathematical analysis and see if everything perfectly cancels out. I'll have to write a math problem that asks and answers, "if I'm pushing on the coin, which is pushing on the wall, which is pushing on the earth, which moves the earth a little, does that conserve momentum in the closed system of the planet conserved..." etc. etc. At least this model explains the discontinuity in the force experienced by an Allomancer when the coin hits the ground. The second the Allomantic Force is resisted, a normal force begins being transferred to the Allomancer.

As promised, here's some more. Simulation 1 - Same physics as Simulation 3 in the above post. This performs exactly as @Pagerunner expected. As the coin is moving away from the Allomancer, the force is negligible. When it hits the wall and stops moving, the force increases dramatically. Simulation 2 - Instead of the velocity term, this simulation uses my Allomantic Normal Force strategy. Once the coin is anchored against the wall, the force that the wall exerts on the coin is applied to the Allomancer. Note that the time scales are different between the two simulations (20% and 4%) because Simulation 2 runs faster in real time than Simulation 1. Simulation 2 has significantly higher forces than those in Simulation 1. This is because the Allomantic Normal Force is something that is added to the original Force, whereas the velocity term is a factor between 0 and 1 that decreases the Force. Changing various constants could make them feel more equal, but that seemed unnecessary.

I knew I'd mess up somewhere. I put that in a text box on screen but I think it "fell off" at some point. Each target is 1kg. Most of the Allomancers are 60kg, as shown on the text boxes. This'll be interesting. Will do.

Very true, I hadn't thought of that. No, the previous simulation used the "F is proportional to e^-distance" relationship that Jofwu thought of. I also don't like the inverse-square model because of it giving an infinite force at close ranges. I changed the simulation to use the relative velocity term, and, sure enough, it gave a pretty satisfying critically-damped effect to the system. Here's a couple more simulations, showing different combinations of velocity relationships, distance relationships, and Allomancers being anchored. None of the targets have gravity, nor is anything in the sims affected by the "Allomantic Normal Force" I've theorized about. This keeps it simpler. The targets all have a mass of 1kg. Simulations are spoilers rather than embeds to not bloat the page. Click the videos to see the HD versions. Simulation 1 All Allomancers are perfectly anchored Pair 4-Right and Pair 5-Left are Stronger Distance relationship: e^-r Velocity relationship: None A similar simulation as the one in the previous post. The target for Pair 5 collides with Allomancer Right. Simulation 2 - Same as previous, but with the velocity term All Allomancers are perfectly anchored Distance relationship: e^-r Velocity relationship: e^-v, where v = magnitude of the relative velocity between Allomancer and target. Because this factor is the magnitude of the relative velocity, it will be smaller (and thus, the force will be smaller) if the target is moving closer or further from the Allomancer. Not particularly interesting. Because the velocity term works in both directions, it just makes everything a bit slower. Simulation 3 - Same as previous, but with a modified velocity term All Allomancers are perfectly anchored Distance relationship: e^-r Velocity relationship: e^-v, where v = relative velocity between Allomancer and target if they are moving towards each other. If the Allomancer and target are getting closer, this term will be smaller. If they're getting further apart, this term will not affect the force (it'll equal 1) This is the interesting one. Using Pagerunner's analogy, the velocity term works like friction or a drag force, always resisting the target's forward movement. Simulation 4 - Same as previous, but with a modified velocity term All Allomancers are perfectly anchored Distance relationship: e^-r Velocity relationship: e^-v, where v = relative velocity between Allomancer and target if they are moving away from each other. The opposite of Simulation 3. Unsurprisingly, this system is extremely unstable with what I want to call "reverse friction" (even if that's not really correct...) Simulation 5 - Same as Simulation 3, but with a different distance term All Allomancers are perfectly anchored Distance relationship: 1/r^2 Velocity relationship: e^-v, where v = relative velocity between Allomancer and target if they are moving towards each other. Initially, the distance factor is extremely very high for Pair 1 because the target is so close to Allomancer Left. Most pairs are able to reach equilibrium quickly because both the velocity term and distance term help to balance out the forces when the target is closest to the center. In my mind, this is what Pushing duels between anchored targets feel like in the books. By this point, I'll say that I've been slightly deceptive regarding the distance relationship. The term is actually equal to e ^ -r/D, where r = the distance between the Allomancer and target, and D = an arbitrary constant. This constant significantly changes the behavior of the system. In the above examples, D = 16. Here's the same simulation as Simulation 3, but with D = 1: Simulation 6 This gives more of an under-damped system. and D = 32: Simulation 7 Like in Simulation 3, this one's critically damped, but the targets end closer to the Allomancers. Comparing between distance relationships is difficult, since e^-r/D is highly dependent on the constant factor. Simulation 8 - Simulation 3, but with unanchored Allomancers and modified Allomancers All Allomancers are not anchored All targets begin in the center Distance relationship: e^-r Velocity relationship: e^-v, where v = relative velocity between Allomancer and target if they are moving towards each other. Allomancer Pair 1: Equal masses, Right is Stronger Allomancer Pair 2: Equal Strengths, Left is slightly more massive Allomancer Pair 3: Equal Strengths, Left is significantly more massive Allomancer Pair 4: Left is more massive, Right is Stronger Allomancer Pair 5: Right is less massive but also Stronger (Looking at you, Vin) Alright, here's the fun one. In Pair 1, Right is stronger than Left. Right could push the target closer to Left, but both Right and Left lost their anchoring around the same time. Pairs 2 and 3 had Left being heavier, which let it stay anchored and "win" the duel around the same time for both Pairs. You can see that the formula I use for calculating Allomantic Force is slightly dependent on mass because Pair 3-Left pushes the target slightly further than Pair 2-Left. In Pair 4, Left was again heavier, but Right was stronger. The target got closer to Left, but Right was still pushed away As Kelsier always said, it's a bad idea to get into a pushing contest when your enemy weighs more than you. In Part 5, Right is lighter but stronger. Right's anchoring broke first, but its force did manage to push Left afterwords. I might come back here later to talk about this, but I should, uh, eat breakfast lunch.

I don't think Feruchemical gold helps you with aging. Would Bloodmaker Ferrings exist in this category as well? If not, what about someone compounding Gold? Brandon Sanderson Yes, you are correct. source

You couldn't use lead-free Pewter for Allomancy. There are specific percentages of components for each alloy that work with Allomancy. I can't find a WoB for it, but I assume that purity affects feruchemical storages in a similar way to how it affects Allomancy - the further the percentages from the "perfect" alloy, the less efficient the metalmind is.

Yeah, Bethesda... really isn't known for their physics. A professional Mistborn game definitely needs a studio with a reputation for programmers who won't let you walk through a wall by holding a bucket up to it. I get some pretty good vibes from Nintendo's Breath of the Wild engine. I can kind of see a Mistborn game in there, with the shrines' light-blue aesthetic & physics-based puzzles.

The precision necessary for this is not going to be found in Steelpushing. Allomancers don't have that much control over their push strengths, so they will almost always overshoot or undershoot the net acceleration needed to perfectly counter gravity. Especially in three dimensions. I modeled five different scenarios of a pushing duel. Gravity is disabled in all of these because the object will always immediately fly out of the perfectly straight line between two allomancers in real life. Simulation properties/definitions: Gravity is ignored. The cubes on the left and right are "allomancer Left" and "allomancer Right," respectively. They are both anchored. Both allomancers are pushing with their maximum possible force at every given time, calculated with the "F is proportional to e^-r" relationship mentioned earlier. The sphere at the center is the magnetic object that Left and Right are pushing on. The object begins with zero velocity. The "equilibrium point" is the position where the push from Left and Right on the sphere are equal. The Net Force there is 0. Scenario 1: Allomancer Left and Right are of equal strengths. The object begins touching allomancer Left. The equilibrium point is at the center. The object oscillates between the two allomancers, much like a spring. At first, Allomancer Left has a stronger push. As the object moves to the right, allomancer Right has a stronger push. This repeats indefinitely, as neither allomancer gains the upper hand. Scenario 2: Allomancer Left and Right are of equal strengths. The object begins halfway between allomancer Left and the center. The equilibrium point is at the center. The object again oscillates, but with a weaker amplitude than in Scenario 1. Again, this is very similar to a spring. Because the object started farther away from allomancer Left, Left's maximum push is weaker. Likewise for Right. Scenario 3: Allomancer Left and Right are of equal strengths. The object begins at the center. Both Left and Right exert equal forces on the object, and it is thus stuck perfectly at the center. This is caused by the object's initial position being at the equlibrium point. Scenario 4: Allomancer Right is stronger than Left. The object begins at the center. Right is stronger than Left, so the equilibrium point is to the left of the center. Again, the object oscillates around the equilibrium point. If the object began at the equilibrium point, it would not move, similar to Scenario 3. Scenario 5: Allomancer Left is stronger than Right. The object begins touching allomancer Left. The equilibrium point is to the right of the center. Left's sustained push is strong enough to push the object into Right. Overall, pushing duels are only effective in this simulation if one allomancer is stronger than another. Only when the object starts at the equilibrium point does is stay still. Duels will play out differently if: The object had some momentum to begin with The allomancers flare their metals or otherwise push "harder" A different force-distance relationship is used, or force is calculated differently elsewhere And, of course, this is all happening without gravity. With gravity, both allomancers quickly lose control of the object.