How fast could a steel pushed bullet go...

[Colors]

We've seen Wax amplify the speed and power of his shots in the past.

How fast do you think a Fullborn sniper with a spike for abrasion could push a bullet?

Imagine, they can increase their weight in the same manner as Wax, they could use a duralumin assisted steel push, and they could negate the friction imposed on the bullet completely.

Any way to calculate roughly how fast they might be able to push a standard rifle bullet?

[therunner he/him]

Well, physics of Pushes is wildly inconsistent (if you Push with constant force coins should be handily supersonic, which they are not), so sadly no proper calculation can be done.

Theoretical maximum with Abrasion applied (and assuming Abrasion won't interfere with pushing), is of course speed of light, however they won't reach that.

I'd wager something along the lines of several dozens of Machs.

[Quantus he/him]

2 hours ago, therunner said:

Well, physics of Pushes is wildly inconsistent (if you Push with constant force coins should be handily supersonic, which they are not), so sadly no proper calculation can be done.

Theoretical maximum with Abrasion applied (and assuming Abrasion won't interfere with pushing), is of course speed of light, however they won't reach that.

I'd wager something along the lines of several dozens of Machs.

That's actually not true, friction is not the only source of drag.  Even with zero surface friction there is inertial drag from the mass of air that is getting compressed and/or shoved out of the way, and these forces become far more significant when you reach the speed of sounds of whatever atmosphere you are in. 

For the math, it will be fundamentally different and more complicated on Roshar where gravity and the atmosphere are both non-standard for earth, so assume Scadrial for ease.  It's not an easy calculation without a lot of assumptions because the math all starts at the chemical energy released by the gunpowder mix, and then it will depend on the bullet size and shape.  Also, a frictionless bullet is not going to react to barrel rifling, so you'll have to find some other way to impart spin on the bullet, or it might prove no more effective than a musket-ball.  

[therunner he/him]

1 hour ago, Quantus said:

That's actually not true, friction is not the only source of drag.  Even with zero surface friction there is inertial drag from the mass of air that is getting compressed and/or shoved out of the way, and these forces become far more significant when you reach the speed of sounds of whatever atmosphere you are in.

Good call, forgot all about that.

Quote

For the math, it will be fundamentally different and more complicated on Roshar where gravity and the atmosphere are both non-standard for earth, so assume Scadrial for ease. 

Not fundamentally different or more complicated. Gravity won't play a role at all (at most in range, but that is not part of question), and atmosphere mix will change how reactive atmosphere is. However, acceleration would be dominated by the Duralumin Push, not by the gunpowder explosion, so atmosphere will play only a minor role.

 

[Colors]

1 hour ago, Quantus said:

That's actually not true, friction is not the only source of drag.  Even with zero surface friction there is inertial drag from the mass of air that is getting compressed and/or shoved out of the way, and these forces become far more significant when you reach the speed of sounds of whatever atmosphere you are in. 

For the math, it will be fundamentally different and more complicated on Roshar where gravity and the atmosphere are both non-standard for earth, so assume Scadrial for ease.  It's not an easy calculation without a lot of assumptions because the math all starts at the chemical energy released by the gunpowder mix, and then it will depend on the bullet size and shape.  Also, a frictionless bullet is not going to react to barrel rifling, so you'll have to find some other way to impart spin on the bullet, or it might prove no more effective than a musket-ball.  

Great point, I had not considered about the rifling. 

As far as abrasion, that's fascinating. So even with abrasion applied the bullet would not travel as if in a vaccuum, in theory the the compression of the air in it's path would add some degree of drag even without friction? 

[Duxredux he/him]

Well... let's do a bit of loose math with some internet calculators to get a rough idea of how much force we're talking here. In TLM Wax was able to launch himself while carrying Wayne on his back in a single impulse to a boat traveling from Bilming to Elendel. The distance between Bilming and Elendel is about 100 miles based on the in book map. To aim low, let's assume to boat was only 30 miles away from Bilming and as they were at an elevated position on a tower probably near the coast, I'll say they were about 500 feet in the air. Reeeaaally loose numbers. For context, the fastest bullet according to Wikipedia has a muzzle velocity of 1422 m/s.

Using this calculator, assuming a 45 degree angle launch, starting 500 feet above the target, taking into account gravity, and to hit a target 30 miles away, Wax and Wayne would need to be moving about 1550 mph. Let's assume that Wax shed all of his weight prior to launch and is only carrying himself, Wayne, and their weapons, so... let's say Wax launched 250 pounds of mass. That's what, 27,000,000 joules of kinetic energy? Toss that into this calculator for bullet kinetic energy, assume a 140 grain round, and if you apply 27,000,000 joules of force you'll need... a velocity of 254,000 feet per second, or 173,000 mph which... makes me question my math. That's almost 7 times faster than what you would need for escape velocity. That's probably fast enough that if you fired it horizontally it still wouldn't land on the planet, and that's just Wax with a Duralumin spike. If we add in air resistance, Wax retaining some weight, or assuming the ship is farther out then that force just gets higher.

I'll need ballistics people to tell me if I got that right or not, as well as how much force would actually be transferred to the target or if it would just leave a nice neat bullet hole going straight through with relatively little energy transferred to the rest of the target's body. So... I'll say that a Fullborn could fire a bullet faster than they would ever have a practical need to do so.

If I was a sniper Fullborn with a single surge, I might take Gravitation actually. I couldn't fire them out of a conventional gun, but Lashing the bullet towards my target before Pushing on them would let me ignore drop from Gravity entirely and that takes a significant variable out of the aiming equation.

[Tamriel Wolfsbaine]

2 hours ago, Duxredux said:

Well... let's do a bit of loose math with some internet calculators to get a rough idea of how much force we're talking here. In TLM Wax was able to launch himself while carrying Wayne on his back in a single impulse to a boat traveling from Bilming to Elendel. The distance between Bilming and Elendel is about 100 miles based on the in book map. To aim low, let's assume to boat was only 30 miles away from Bilming and as they were at an elevated position on a tower probably near the coast, I'll say they were about 500 feet in the air. Reeeaaally loose numbers. For context, the fastest bullet according to Wikipedia has a muzzle velocity of 1422 m/s.

Using this calculator, assuming a 45 degree angle launch, starting 500 feet above the target, taking into account gravity, and to hit a target 30 miles away, Wax and Wayne would need to be moving about 1550 mph. Let's assume that Wax shed all of his weight prior to launch and is only carrying himself, Wayne, and their weapons, so... let's say Wax launched 250 pounds of mass. That's what, 27,000,000 joules of kinetic energy? Toss that into this calculator for bullet kinetic energy, assume a 140 grain round, and if you apply 27,000,000 joules of force you'll need... a velocity of 254,000 feet per second, or 173,000 mph which... makes me question my math. That's almost 7 times faster than what you would need for escape velocity. That's probably fast enough that if you fired it horizontally it still wouldn't land on the planet, and that's just Wax with a Duralumin spike. If we add in air resistance, Wax retaining some weight, or assuming the ship is farther out then that force just gets higher.

I'll need ballistics people to tell me if I got that right or not, as well as how much force would actually be transferred to the target or if it would just leave a nice neat bullet hole going straight through with relatively little energy transferred to the rest of the target's body. So... I'll say that a Fullborn could fire a bullet faster than they would ever have a practical need to do so.

If I was a sniper Fullborn with a single surge, I might take Gravitation actually. I couldn't fire them out of a conventional gun, but Lashing the bullet towards my target before Pushing on them would let me ignore drop from Gravity entirely and that takes a significant variable out of the aiming equation.

Your case for Wax and Wayne jump is interesting but I think Iron screws with it a lot more. Momentum is conserved thus tapping a massive weight and duralumin pushing would build a TON of momentum... then shedding that weight would actually cause you to accelerate as well while flying. 

If I remember correctly the support beams bent in as well. Any crumple in the structure being pushed off means there was even more initial energy that was lost in that push as well.

The only reason I want to blame Iron for the feat instead of duralumin steel is because it seems more consistent with what we have seen outside of Vin running on the mists and ascending. 

The conservation of momentum seems more viable as in theory every time you half the weight you double the speed. We know Wax can store millions of pounds worth of his own weight to use.  In fact if Wax is 180lbs and stores 33% of that all the time then he is storing 59lbs all the time. Lets round it out to 60lbs.

If Wax stores 60lbs per second for 18 hours a day he stores 3,888,000 lbs for use later. Tapping that much... if you have the anchors to make a push and get airborne (which duralumin with steel could do) you would take off with so much momentum and it would carry you further than a high velocity alone.  

That thought is just to say that I don't think Wax's jump accurately shows what could happen to a bullet. Wax can hack and gain speed after the push is over with thanks to his iron feruchemy. The bullet can't. And there is only so much of a push that you can do on a bullet before it is beyond your ability to push it more. Where Wax could still be manipulating his jump well outside of steel pushing range. 

[Clockwork King he/him]

also consider the type of gunpowder used and the metal and casings of the bullet as both of those can greatly change the math involved 

[ScadrianTank he/him]

If the fabrial tech progressed quickly enough in Era 3, it wouldn't surprise me if all modern military rifles were hypersonic. Maybe something similar to AAI's flechette rifle prototype.

[DrPhysics he/him]

Super late to this one, but it is a problem I've looked at before. Here's my answers in case someone stumbles onto it.

On 2/26/2024 at 9:11 AM, Quantus said:

Even with zero surface friction there is inertial drag from the mass of air that is getting compressed and/or shoved out of the way, and these forces become far more significant when you reach the speed of sounds of whatever atmosphere you are in. 

 

Yeah, with a bullet-shaped/sized object traveling at or above the speed of sound, skin drag will account for ~5% (at the absolute most) of the total drag. Most likely, it will be less than 1%.

 

On 2/26/2024 at 10:25 AM, Duxredux said:

Well... let's do a bit of loose math with some internet calculators to get a rough idea of how much force we're talking here. In TLM Wax was able to launch himself while carrying Wayne on his back in a single impulse to a boat traveling from Bilming to Elendel. The distance between Bilming and Elendel is about 100 miles based on the in book map. To aim low, let's assume to boat was only 30 miles away from Bilming and as they were at an elevated position on a tower probably near the coast, I'll say they were about 500 feet in the air. Reeeaaally loose numbers. For context, the fastest bullet according to Wikipedia has a muzzle velocity of 1422 m/s.

Using this calculator, assuming a 45 degree angle launch, starting 500 feet above the target, taking into account gravity, and to hit a target 30 miles away, Wax and Wayne would need to be moving about 1550 mph. Let's assume that Wax shed all of his weight prior to launch and is only carrying himself, Wayne, and their weapons, so... let's say Wax launched 250 pounds of mass. That's what, 27,000,000 joules of kinetic energy? Toss that into this calculator for bullet kinetic energy, assume a 140 grain round, and if you apply 27,000,000 joules of force you'll need... a velocity of 254,000 feet per second, or 173,000 mph which... makes me question my math. That's almost 7 times faster than what you would need for escape velocity. That's probably fast enough that if you fired it horizontally it still wouldn't land on the planet, and that's just Wax with a Duralumin spike. If we add in air resistance, Wax retaining some weight, or assuming the ship is farther out then that force just gets higher.

 

The problem with this math is that it assumes you deliver all the energy at once, so you can't translate the energy amount over to a bullet.

There's a lot of evidence in the books that suggests allomancers are limited by both the force of the push and the amount of power delivered through the push. For a moving object, the power delivered is calculated by the force times the velocity (P=Fv), so the faster something goes, the bigger the force you need to keep adding energy to it.  Also, as it gets faster it gets further away so the max pushing force also decreases.

I put together a simple simulation once to ball-park a coin's max speed (can't find it to run it again) using Vin's duralumin jump from Luthadel to scale it.

I found that we hit a max speed for coins somewhere around Mach 1 to 1.5. Starting a bullet at Mach 1 would let you get the speed up to about Mach 2. Starting at Mach 1.5 let us get up to about Mach 2.1 (The faster the object initially travels, the harder it is to add energy to it), so Mach 2 seems like a pretty reasonable limit. 

[JohnnyKaizen he/him]

On 2/26/2024 at 11:11 AM, Quantus said:

Also, a frictionless bullet is not going to react to barrel rifling, so you'll have to find some other way to impart spin on the bullet, or it might prove no more effective than a musket-ball.

I'm not saying I know how, but if the OP's scenario is possible in the first place, then I feel like there should be a way to connect the power of Abrasion to the end of the barrel, from the shooter's hand...so that, the bullet does not become frictionless until the exit and therefore has spin?

Edit: And if all this is possible, wouldn't the shooter basically have a portable rail gun? I don't think speed of light is possible, but some of the fastest bullets on the market today top out at Mach 4 (3067 mph) and if you search for "piece of plastic hits aluminum at 15,000 mph" (Mach 19.5ish) you'll see some serious damage. If a bullet could be pushed to between 10-20x Mach 4? I am assuming there's very few things (even in the Cosmere) that could withstand a hit like that.

Edited July 9 by JohnnyKaizen

[DrPhysics he/him]

On 7/9/2024 at 1:48 PM, JohnnyKaizen said:

If a bullet could be pushed to between 10-20x Mach 4?

Since the push gets weaker as the bullet gets farther away, at those speeds you can't push for very long before the bullet is too far away for the push to matter anymore. You max out at around Mach 2-3.

[JohnnyKaizen he/him]

17 hours ago, DrPhysics said:

You max out at around Mach 2-3.

There are bullets commercially available right now, (.220 Swift) that can come out of the barrel at mach 4, and there are experimental ammunitions that have been clocked at Mach 5.8 (Which in Wax's case, he was often shooting experimental rounds, because it seems like Ranette spent most of her time on just that). If we're talking about a full Mistborn and Feruchemist who can increase their weight to, say 2,000 pounds, and use a duralamin steel push on a round that's already going Mach 5.8 as it exits the barrel? 

I get that we don't have the math for an exact answer, AFIAK anway, when it comes to steel pushing, much less duralumin steel pushing, but it would have to have some considerable effect under the conditions the we (the OP and myself) are describing? Or am I missing something?

[DrPhysics he/him]

1 hour ago, JohnnyKaizen said:

I get that we don't have the math for an exact answer, AFIAK anway, when it comes to steel pushing, much less duralumin steel pushing, but it would have to have some considerable effect under the conditions the we (the OP and myself) are describing? Or am I missing something?

The part you are missing is just how incredibly fast Mach 5.8 is.

We know duralumin burns fast, but it still takes long enough that your body has time to perceive the effect. That means a push would take 0.1 to 1.0 seconds. Ignoring, reaction time (which averages around 0.1-0.2 seconds, but can be shorter if you know something is coming), our best-case scenario is that we can shorten our push into a 0.1-second burst. At Mach 1, a bullet will travel about 35 meters in that time. Mach 2 goes to about 70 meters. Mach 5.8? 200 m. At those distances, the bullet is just way too far away to give any significant push beyond those first few fractions of a second. Which is why you can get a Mach 1 up to Mach 2, but a Mach 2 bullet can only be sped up to about Mach 2.5

 

Reading through the books, you'll notice that Wax's push doesn't do much to the speed of bullets, but his pushes can add a lot to the stopping power. Hit a nearby target and add a full push as the bullet slows down inside the target: devastating.

Edited July 11 by DrPhysics

[JohnnyKaizen he/him]

2 hours ago, DrPhysics said:

The part you are missing is just how incredibly fast Mach 5.8 is.

We know duralumin burns fast, but it still takes long enough that your body has time to perceive the effect. That means a push would take 0.1 to 1.0 seconds. Ignoring, reaction time (which averages around 0.1-0.2 seconds, but can be shorter if you know something is coming), our best-case scenario is that we can shorten our push into a 0.1-second burst. At Mach 1, a bullet will travel about 35 meters in that time. Mach 2 goes to about 70 meters. Mach 5.8? 200 m. At those distances, the bullet is just way too far away to give any significant push beyond those first few fractions of a second. Which is why you can get a Mach 1 up to Mach 2, but a Mach 2 bullet can only be sped up to about Mach 2.5

 

Reading through the books, you'll notice that Wax's push doesn't do much to the speed of bullets, but his pushes can add a lot to the stopping power. Hit a nearby target and add a full push as the bullet slows down inside the target: devastating.

OK that makes sense. Unless there is some mechanism (biological, mechanical, and/or supernatural) that allows for a push within..say .001 seconds (or less) of the firing pin hitting the primer..there is just no way in the Cosmere to have any substantive effect on the speed of a bullet to any massive degree, especially when the bullet is already going so fast. The point on stopping power (damage increase) is a good one and makes sense.

[One of the Ten Fools he/him]

What if we change the set up, and have the person shooting the bullet inside of a small slow bubble and then have another person outside standing right behind them in speed bubble, so that they can react fast enough to push the bullet, and burn all of their metal. 

[JohnnyKaizen he/him]

9 minutes ago, One of the Ten Fools said:

What if we change the set up, and have the person shooting the bullet inside of a small slow bubble and then have another person outside standing right behind them in speed bubble, so that they can react fast enough to push the bullet, and burn all of their metal. 

If you're only going for a speed record and no accuracy...that seems like it would work? However, I thought one couldn't effect things with allomancy outside of a bubble?

[One of the Ten Fools he/him]

14 minutes ago, JohnnyKaizen said:

However, I thought one couldn't effect things with allomancy outside of a bubble?

I just checked that on the Coppermind, and it says that the speed bubble just interferes with most  investiture that goes through the bubble but that means that you might still be able to push on the bullet. 

[Mr. Misting he/him]

1 hour ago, JohnnyKaizen said:

OK that makes sense. Unless there is some mechanism (biological, mechanical, and/or supernatural) that allows for a push within..say .001 seconds (or less) of the firing pin hitting the primer...

Ah, but there is: zinc feruchemy. Assuming you've been in a near comatose state for years storing mental speed, or are able to compound, someone could store enough for some ridiculously fast computation. By duralumin flaring the compounded mental speed, firing the bullet, and then activating steel while the duralumin is still burning, you could get to the point where you could reasonably affect the bullet.

Edited July 11 by Mr. Misting