Is there a physicist in the house?

[Oudeis]

Long story short, I'm in a roleplay forum, and someone just did something interesting in a combat scenario. I'm sure with a few hours of research I could figure it out on my own, but I could use some help.

A Mistborn is in mid-air about thirty feet off the ground. About ten feet above him is a coinshot (she weighs about 160). She's fired a coin at Jasun, hoping to get some height out of a push-contest. He turns the table on her. He's using steel to push against the coin between them, and finds solid anchors below him to also push against. He also burns pewter, and then burns duralumin.

Jasun's only got a little bit of steel left; about enough for 2 minutes. How much force would he put into that coin going upwards? Roughly how high would he shoot the girl, Fiusha?

(Please note; for brevity, I'm leaving out a lot of things not pertinent which explain why she doesn't just let the coin zip past her. I'm not interested in anyone's opinion of what she should do, or what he should do, or anything. I just want the answer to the physics question)

EDIT: For clarity

Edited January 18, 2013 by Darnam

[dj26792]

In short, high enough that short of having more metal and finding a good anchor on the way done death is not a possibility but a certainty. Beyond that I don't know, I think Chaos is the man to talk to for this, send him a PM to make sure he notices the thread.

[Oudeis]

short of having more metal and finding a good anchor on the way down

Well, Fiu, the coinshot being shot upwards, has plenty of steel left herself, and when she falls, she'll fall in a courtyard between a 15 story building and two 10 story buildings, both of which have plenty of anchors. Assuming 10ft per story, and using the Mistborn RPG to establish that a coinshot can push metal 100 ft away, that gives her 200 feet to decelerate herself. Anyone know what human terminal velocity is? Does that sound reasonable?

The real concern is, can the human body withstand such initial acceleration, or the heights that she'd get pushed to.

I think Chaos is the man, send him a PM to make sure he notices the thread.

Thank you, I will do this thing!

[name_here]

Terminal velocity is 120 mph.

Incidentally, the Mistborn falls thirty feet without pewter or steel and dies.

[dj26792]

I'm bored so I'm giving it a go, it will be a little rough and Chaos is much better at this sort of thing than me, I also haven't done this in 2 years or so.

I don't have the game so I don't know the rules, I found a preview of the steel sheet, which leads me to believe that they are accelerated to at least 100 mph almost instantly, if its only that fast that equates to about 45g shock load which is survivable (racing drivers have survived loads of up to 100g in similar scenarios.) They are launched upwards for approximately 4.5 seconds, resulting in being launched 101.8m (metres, can't be bothered to convert to miles) into the sky. Falling from this height is relatively easy for a coinshot in the environment you describe.

Also, I nearly screwed up my calculations and sent them 10km up, which would have been wrong, but much more exciting.

[Oudeis]

Incidentally, the Mistborn falls thirty feet without pewter or steel and dies.

Yeah, we'd figured that part out already. Technically, I think he'd get launch upwards himself (prolly not as much) before falling to his doom; the only other metals he has left are tin, bronze, and duralumin. He can see the ground coming at him VERY WELL before he's a mistpancake.

I don't have the game so I don't know the rules, I found a preview of the steel sheet, which leads me to believe that they are accelerated to at least 100 mph almost instantly

Trying to apply some physics to this... tell me if I'm wrong.

A Coinshot can, according to the full rules of the RPG and reference on this steel cheatsheet, shoot a coin at 100 mph in (here's where we're assuming) about a second. A coin generously masses at 5g. That's actually only .25 Newtons. If that's the maximum force that a steelpush can do, and factoring in duralumin letting him push with all of his (admittedly slim) reserves all at once, I figure he gets a whole 425 newtons of force, which if applied to a body approximately 75kg (more than 160lb) is only enough to shoot that body upwards at 6m/s^2. If the Mistborn is actually pushing himself upwards at the same time and transfers the force of THAT push, too, that would double it to 12m/s^2, which would have the girl fly a whopping 7.5m in less than two seconds before falling again. This... does not sound right.

Is the problem in my physics? With my math? Cuz there's no way a duralumin-fueled steelpush could be that weak. A normal steelpush should be stronger than that. If she herself were just pushing on an anchor, she'd go farther than that. Someone, please let me know where I'm making my mistake.

[dj26792]

You also have the force of the coinshots push, I assumed the duralumin does enough to get the person treated the same as the coin and also that the multiple pushes balance out and the mistborn is left wtih no metal 30ft off the ground which is easily survivable for a trained fighter like the mistborn is I assume.

Although he should take damage, but 50ft is considered borderline for the average person in terms of survivability fit people who know what they're doing can fall further without dying, a mistborn falls into this catagory.

[Oudeis]

I assumed the duralumin does enough to get the person treated the same as the coin

I'd prefer science to assumptions.

the mistborn is left wtih no metal 30ft off the ground which is easily survivable

But remember, he's Pushing himself up from the anchors on the ground, so with duralumin he'd send himself flying upwards, which force would be transfered through the coin to her. So when he finally peaks, he'll be left without useful metals a lot higher than 30 feet.

[Senor Feesh]

I probably don't have the math for this myself, but when this sort of situation arises in an RPG, I would resolve as follows:

As mentioned, Jasun becomes Mistcaek in short order without someone else intervening.

Fiusha moves at high velocity to a dramatically appropriate height, according to Narrative Determinism, and must now catch herself on the way down (or come up with some other creative solution to her problem).

Don't let physics bog things down when awesome drama is way more interesting and takes less time to resolve

That said, I'm still interested in the physics resolution from a purely academic standpoint.

[tecslicer]

"Fiusha pushes on the coin. Ballancing on a single anchor with all of her might. Suddenly she is hit by a huge force. The coin pushes her up farther then she could ever go by herself. The mists part in her path. As she reaches the top of her arc she turns her head to see the unveiled night sky. "Lord Ruler! It's full of stars!!!"

Edited January 18, 2013 by tecslicer

[Thought]

Unfortunately we don't have enough actual information to figure this out. The problem is, our hard numbers come from the RPG, but the RPG isn't reliable in this, so the best we can do is estimate. And if you want to estimate, why bother with math?

If we use the RPG to determine the force of a push, we get 0.2235 newtons. That isn't enough to let coinshots bound through the air, as we know that they can. But if we assume that a coinshot can push with a force of 2g (or 19.6 newtons), then they should be shooting coins at a rate of 3920 meters per second squared (or 1752.4 miles per hour per second), which is far too fast for how it's described in the books themselves.

The descriptions of duralumin can be taken two ways. One is that it it burns all the power that would have been released over time in an instant. So, with 2 minutes of reserve, a duralumin burn would increase power by a factor of 160. If a coinshot can produce 19.6 newtons, that translates into a force of 3136 newtons (or 320g's, enough to kill a person several times over). But if a coinshot can only produce 0.2235 newtons, then, duralumin gives 35.76 newtons. About 3.6 g's. That's too low for the duralumin pushes we see in the book.

However, we could assume a factor of 10 for a duralumin burn. So, 19.6 newtons of force would be 196 newtons (20 g's) survivable, but damnation fast (so this might actually be accurate if we compare it to Vin's launch from Luthadel in WoA). However, the 0.2235 newtons described in the RPG still don't overcome gravity itself.

So it is only if we assume what the force of a push is that we even get rational numbers. But, assuming the numbers aren't very scientific.

That said, assuming that a coinshot can push with 2gs, and that duralumin burns reserves for a max benefit of a factor of 10, then he'll push with a force of 196 newtons. I suspect my math is wrong, but I am getting a total upwards distance traveled of around 1960 meters. Add to that the original 40 feet (13 meters), and we get 1973. More than a mile.

EDIT: To note, clouds are around 2-6km above the ground. Assuming that Scadrial's ash layer is similar, that means that Vin might be able to push with around 3g's to get high enough to see clear sky, as she does in HoA.

Edited January 18, 2013 by Thought

[Oudeis]

I probably don't have the math for this myself, but when this sort of situation arises in an RPG, I would resolve as follows:

As mentioned, Jasun becomes Mistcaek in short order without someone else intervening.

Fiusha moves at high velocity to a dramatically appropriate height, according to Narrative Determinism, and must now catch herself on the way down (or come up with some other creative solution to her problem).

Don't let physics bog things down when awesome drama is way more interesting and takes less time to resolve ;)/>

That said, I'm still interested in the physics resolution from a purely academic standpoint.

This is basically what I ended up doing. I also decided that the shock of such rapid travel to such a great height, along with a few other factors, rendered her unconscious, and she was unable to catch herself. Again, it felt dramatically appropriate.

"Fiusha pushes on the coin. Ballancing on a single anchor with all of her might. Suddenly she is hit by a huge force. The coin pushes her up farther then she could ever go by herself. The mists part in her path. As she reaches the top of her arc she turns her head to see the unveiled night sky. "Lord Ruler! It's full of stars!!!"

TOTALLY DID THAT. If I was going to kill off my character due to traveling too high, she was gonna see stars, dammit. To preserve the uniqueness of Vin, she never technically breached the outer layer of mist, but she did technically get high enough that she could see a few of the brightest stars beyond that last scrap of misty veil.

Unfortunately we don't have enough actual information to figure this out. The problem is, our hard numbers come from the RPG, but the RPG isn't reliable in this, so the best we can do is estimate. And if you want to estimate, why bother with math?

If we use the RPG to determine the force of a push, we get 0.2235 newtons. That isn't enough to let coinshots bound through the air, as we know that they can. But if we assume that a coinshot can push with a force of 2g (or 19.6 newtons), then they should be shooting coins at a rate of 3920 meters per second squared (or 1752.4 miles per hour per second), which is far too fast for how it's described in the books themselves.

The descriptions of duralumin can be taken two ways. One is that it it burns all the power that would have been released over time in an instant. So, with 2 minutes of reserve, a duralumin burn would increase power by a factor of 160. If a coinshot can produce 19.6 newtons, that translates into a force of 3136 newtons (or 320g's, enough to kill a person several times over). But if a coinshot can only produce 0.2235 newtons, then, duralumin gives 35.76 newtons. About 3.6 g's. That's too low for the duralumin pushes we see in the book.

However, we could assume a factor of 10 for a duralumin burn. So, 19.6 newtons of force would be 196 newtons (20 g's) survivable, but damnation fast (so this might actually be accurate if we compare it to Vin's launch from Luthadel in WoA). However, the 0.2235 newtons described in the RPG still don't overcome gravity itself.

So it is only if we assume what the force of a push is that we even get rational numbers. But, assuming the numbers aren't very scientific.

That said, assuming that a coinshot can push with 2gs, and that duralumin burns reserves for a max benefit of a factor of 10, then he'll push with a force of 196 newtons. I suspect my math is wrong, but I am getting a total upwards distance traveled of around 1960 meters. Add to that the original 40 feet (13 meters), and we get 1973. More than a mile.

EDIT: To note, clouds are around 2-6km above the ground. Assuming that Scadrial's ash layer is similar, that means that Vin might be able to push with around 3g's to get high enough to see clear sky, as she does in HoA.

...Everything about this post is made of win. I agree with you, that we have to make so many estimations the entire thing becomes rather preposterous. That said, you've done far better math than I, and I think your guesses seem to be a reasonable approximation of what Sanderson intended, which is what's important. I plan to use your general outcome as the basis for the actual roleplay post; would you object if I link people directly to your work here as part of the combat?

[dj26792]

you've got to remember the reaction force from launching the coinshot up effects the mistborn as well, hence my suggestion that they stay essentially stationary. Also if they're balancing their output before they burn duralumin I think its reasonable to assume that their pushes stay balanced, mistborn lives or even that the duralumin only effects the upwards push in which case mistborn pancakes.

[Oudeis]

you've got to remember the reaction force from launching the coinshot up effects the mistborn as well, hence my suggestion that they stay essentially stationary.

...The push downward is against the earth, which will not give. The push upwards is against the coin and through it to the woman, who absolutely will give. He goes up.

Also if they're balancing their output before they burn duralumin

They hadn't been sitting there balanced. As she came into position over him, he pushed and burned.

the duralumin only effects the upwards push

That isn't how duralumin works. It's all or nothing.

[dj26792]

I thought that Duralumin would effect all pushes, hence my initial suggestion that the forces would be increased in the initial ratio of pushing thus, balancing out, I thought there was a scene where Vin anchored herself and duralumin pushed in a way that should have launched her if it was indeed all or nothing, but the ratio of balanced forces kept her still, but a quick search of the Ebook couldn't find it, so I'm now confused as to where I got that idea, regardless, I'm assuming that by now you've moved on in your rpg and this discussion is relatively pointless, and the mistborn is rather dead.

[Senor Feesh]

I thought that Duralumin would effect all pushes, hence my initial suggestion that the forces would be increased in the initial ratio of pushing thus, balancing out

If there was an immovable object above, then it would balance, however as she isn't able to offer the same resistance as the ground would, they're both heading skyward (her much faster and higher though).

[dj26792]

thats not even relevant to what I was saying Senor, what I meant was that if the mistborn was balanced hovering there, and then shoved upwards and burned duralumin, I thought the strength ratio of the pushes would stay the same, so all pushes become drastically stronger, but the ones holding it up wouldn't increase as much as the one throwing the coinshot up and therefore balance out the recoil, leaving it effectively stationary, in spite of the lack of solid anchors upwards, the more I have to explain myself the more I become confused as to why I assumed this, but regardless, I did.

[Inkthinker]

Terminal velocity is 120 mph.

Dang, beat me to it.

Skydiving?

"Fiusha pushes on the coin. Ballancing on a single anchor with all of her might. Suddenly she is hit by a huge force. The coin pushes her up farther then she could ever go by herself. The mists part in her path. As she reaches the top of her arc she turns her head to see the unveiled night sky. "Lord Ruler! It's full of stars!!!"

"Lights", maybe? A person who has never seen a starry sky would not know what a star was. Not that anyone on Scadrial would be consciously quoting Arthur Clarke. :)/>

It's about as cool a way for a character to go out as any I can think of. I like the visual.

Edited January 22, 2013 by Inkthinker

[tecslicer]

"Lights", maybe? A person who has never seen a starry sky would not know what a star was. Not that anyone on Scadrial would be consciously quoting Arthur Clarke. :)/>/>

Well if the mists followed the same progression as in the Alloy of Law then as short as 700 (or less) years after the Asscention, people would have been able see the stars at night. They would know that there are stars in the sky through myth, song, interpretative dance...

Like the word "Wine" Scadrial has no flowers after the asscention but they still call some alcoholic drinks "Wine".

As to quoting Arthur Clarke... I do. Why would they not have Arthur Clarke on Scadrial? Now you are just being silly...