Feruchemy WoB on Iron question + math

[Boondokz]

Can anyone find when Brandon talked about how iron feruchemy works? I was discussing the Sazed falling scene and how wrong it was and I know Brandon has commented on this before. 

My theory on how iron works based on how Sazed falls is that Iron changes the way acceleration due to gravity effects an individual. Others have said it is a change in density but   p=M/V . So if Sazed's body does not change shape his volume does not change therefore a change in density is equal to a change is mass. Weight is Fg=M*Ag . So a change in mass would cause a change in weight. However this will not alter the acceleration due to gravity. Fnet=Fg-Fd  (Fd is the force of drag from air friction) Fd=1/2 Cd*p*A*u^2         Cd= coefficient of drag        p=air density            A= area of falling object         u=flow speed of the air relative to the object. 

As can be seen mass is not accounted for in the equation. However terminal velocity can effect the maximum velocity you can reach and is based of off mass. The average human has a mass of 62kg and terminal velocity is about 53 m/s. That is equal to 119 mph. To find terminal velocity the equation is Vt=sqrt((2*m*Ag) / (p*A*Cd)         A= area (average human is less than .5m^2 however we will go to .5 because of Sazed's clothes)  p=air density we can say equal to 1    Cd= drag coefficient equal to about 1      Ag= acceleration due to gravity on earth is 9.8 m/s^2 (I know it is not Earth but still close enough)      

Lets make Sazed reduce his mass to 1kg or 1/60th of his normal mass (weight) Vt= sqrt((2*9.8*1) / (1*.5*1) = 6.26 m/s  This is equal to 14 mph. The average human runs at 8mph so this fall would have felt like Sazed was sprinting not casually falling.

Of course the air density may be different and the acceleration will 100% be different, but the differences would have to be drastic. My math could of course be full of errors and I made many assumptions. If anyone wants to run their own equations I welcome the findings. All I am saying is if Iron magically changed how gravitational acceleration effected the user the explanation would be very simple.

[The One Who Connects he/him]

I'm no math expert, but the concept seems sound

Sazed did mention putting his metalminds on his ankles to keep him pointed down... Short of Zero G, what else screws with up/down balance?

[Pagerunner he/him]

First of all, welcome to the Shard!

Here's a post that talks about Iron Feruchemy. Someone asked Brandon at a signing for Bands of Mourning, and he confirmed that it is actually changing the mass by altering the Higgs field.

I think I know the scene you're talking about (Sazed slowing his fall in the Conventical of Seran), but I don't remember too many details. I did see a couple of issues with the calculation, though:

• Density of Air is 1.225 kg/m3 [source]
• Drag Coefficient of a long cylinder (rough approximation of a human slowly falling feet-down) is 0.82 [source]
• Surface area of an adult male is ~1.9 m2 [source]
• Also, you forgot to close a set of parenthesis in your terminal velocity equation [source]

The different density and drag coefficient basically offset each other, but the change in surface area will have a significant effect, since you're using a value that's almost 75% smaller. If we backtrack the math, then to fall at 8 mph (3.6 m/s), I calculate 1.26 kg as Sazed's target mass. The record speed for a human is 12.4 m/s, and Sazed would achieve that terminal velocity at 15 kg.

So, it's a good analysis you've performed, but I'd check a couple of your assumptions. Why did you limit Sazed to 1 kg? Is based on the weight of his clothing and equipment? And where did you get your value of 8 mph for the target speed and 0.5 m2 as the surface area of a human body?