Animation of Vin's horseshoe journey.

[DrPhysics he/him]

I made these animations a while ago and posted them to reddit, but I felt like they had a place here (and I don't like where reddit is headed, so copying them over will preserve them). If there is a better place to put them outside of this discussion board, let me know.

 

These are physically accurate models of what it would look like when Vin pushes/pulls on those five horseshoes on her last minute run to Luthadel.

Vin in the animation is 5 feet tall.

Real-time Animation, as viewed by someone watching her pass.

 

Slow motion Animation, as viewed by someone watching her pass.

Real-time animation, view fixed on Vin

 

Slow Motion animation, fixed on Vin with lines showing when she pushes/pulls

Notice that there is a moment in every cycle where she isn't pushing. At that moment, she is pulling down hard enough on the horseshoe above her head that it holds her up.

A few fun facts:

• She would reach a cruising speed of ~80 mph, but could reach 120 mph if she took off her mistcloak and went into a Superman pose (i.e. face-first).

  • The major limiting factor is the sharpest angle where she could still push on the horseshoes. If they get more than 35 degrees behind her, the shoe would slip

• 1 horseshoe "orbit" takes about 1.5 seconds

• She gets the most efficient motion if she keeps pulling on the horseshoes as they whip around the top of her head and then lets it go when it is roughly even with her feet. That lets the horseshoe pull her forward a little bit while it is in the air.

• Once she gets everything going, she'd hover in a straight line roughly 10 meters above the ground. She'd be able to balance out the forces by feel, similar to how we do while running (there's not a lot of bouncing up and down if you are running the right way).

• The horseshoe is traveling at about 100 m/s (200 mph; 360 kph) when it hits the ground, which is comparable to the muzzle velocity of an early black powder musket (except the projectile is a horseshoe and not a small lead ball).

• The simulation is 2-d, but the system would stabilize side to side motion similar to how a bike works. If you start tipping to the right,  the horseshoe behind you would be slightly to the left, so when it flew up over your head it would land on your right side and your next push would send you back to the left, holding you up.

 

Model Details

The models assume that force strength is limited by the amount of power delivered to the object and the inverse square distance between Vin and the horseshoe (like how electromagnetic forces work on earth).

Orignially, I tried simulating her getting started, but the system was chaotic (tiny differences in initial conditions make for wild differences at the end) and I could find the right set of numbers (however, figuring out the timing would be pretty easy for a human who could feel the pushes/pulls).

So, instead, I held her fixed in place and calculated the path that one horseshoe would take that would maximize forward speed without accelerating Vin enough for her to black out while minimizing her up-and-down motion (practiced runners will do the same thing just by feel). I added the other five horseshoes and planned on letting Vin move in response to the horseshoes while they stayed on a fixed, then redo the horseshoe math while keeping Vin on the new path, then figure out Vin's new path, etc. until the paths stopped changing (we call that iterative convergence).  However, I got lucky. When I put Vin in the center of the five horseshoes, her relative position varied by only a few centimeters and she ended up exactly where she started (relative position) after every cycle (e.g. looks like I got it right the first time and iterating wouldn't change anything).

 

Edited 5 hours ago by DrPhysics
Fixing image location

[Argent he/him]

The idea that Vin is slamming chunks of metal into the ground with bullet speeds, and she does it to move, is lowkey terrifying; Allomancers are scary.

Love the animations and love the work put into it, visualizing Brandon's crazy book moments is some of my favorite stuff out there!

[DrPhysics he/him]

43 minutes ago, Argent said:

The idea that Vin is slamming chunks of metal into the ground with bullet speeds

Yeah, I like to imagine her coming into the valley. At first, you'd just see a cloud (think of all the ash that she would kick up) blazing towards you at 80 mph. Then you'd start to hear the thumping. Then finally, just in front of the billowing cloud, you would see Vin with her mistcloak streaming behind, centered in a wheel of metallic death.

 

I wish there were more scenes that were detailed enough that I could do the math and figure them out. However, then I'd be more likely to find inconsistencies, so maybe it's a good thing.