Steelrunner

There's been a fair amount of discussion about steel compounding on these forums as one of the most exciting forms of Twinborn. The general consensus (with support from Word of Brandon: wob.coppermind.net/events/93-odysseycon-2016/#e2695 ) is that a steel compounder could feasibly run at incredible speeds while being magically protected from many of the consequences for an extended period of time. So I decided to do the math on what it would look like for a steel compounder running at 10x normal speed (well within what Bleeder does in Shadows of Self, I think). Here's what I found: Imagine our Steelborn throwing a ball. Now, an ordinary person throwing a ball has their arm swing through a distance (call it 1 m) in a certain time and releases with a certain final velocity (call it 25 m/s for fairly ordinary humans - thats ~50 mph). Now, our Steelborn is moving 10x as fast, which I take to mean he takes 1/10 the time from start of throw to release. That implies he has 10x the release velocity (also what we expected). But he accelerated a ball to 10x the speed in 1/10 of the time of an ordinary human and acceleration = velocity/time (for constant acceleration of an object from rest, a decent approximation here), which means the Steelborn's ball has 100x the acceleration. F = ma, so either the ball had 1/100th of the mass, or our Steelborn applied 100x the force. Option 1: Changing strength Let's assume the ball's mass didn't change for now. Our Steelborn needs to apply 100x the force, which means our Steelborn needs to be 100x as strong as normal. It gets better. Our Steelborn has 100x the strength of an ordinary man and can run 10x as fast. Power = Force x Velocity, which means our Steelborn has 1000x the power output. If an ordinary human can output 300 Watts, our Steelborn can output 300 kW, or 400 horsepower. Of course, with 100x the strength, our Steelborn will need his tendons, ligaments, bones, etc. reinforced by 100x to avoid his enhanced strength tearing himself apart (see WoB above). Human skin normally has about 20MPa tensile strength, so a 100x increase puts us close to Kevlar's 3000 MPa tensile strength. His maneuverability with A-steel remains unaffected, though. There's no reason to assume his Steelpushes have enhanced strength, so he can't Push a coin any faster or Push himself off a skyscraper any quicker. (F = ma.) But the truth is, he hardly needs this. With 10x throwing speed, an ordinary 25 m/s pitch turns into a 250 m/s projectile (9mm pistol rounds travel at ~300 m/s, or ~1000 fps). With 20 bullets a throw and assuming he can get off 5 throws/sec, that means he is putting out the equivalent of 100 pistol rounds/second. (World War II machine guns fired ~10 rounds/sec.) He'd have to be aware of the recoil, though: he's not any heavier to absorb it! It's not all upside, though. Even with 10x the top speed and 100x the strength, our Steelborn is limited by the friction between his feet and the ground, which hasn't changed. Unless he can push off of something, he can't accelerate (or turn) at anything more than about 10 m/s^2. If he's moving at 10x an ordinary run speed of 4 m/s, and remembering that turning radius = velocity^2/acceleration on turns, we have turning radius = (40 m/s)^2/10 m/s^2 = 16 m. No hurtling around tables for him. Actually, I don't think he would run at all. With 100x the strength, each footfall would propel our Steelborn high into the air. I suspect he would move like astronauts walking on the moon instead. Option 2: Changing mass + gravity But all that doesn't match up with what Bleeder does in Shadows of Self. So instead of assuming that our Steelborn gets stronger, let's assume that our Steelborn's mass decreases to 1/100th of normal instead. 50 kg -> 0.5 kg. Additionally, the acceleration due to gravity must increase by 100x to leave the total force due to gravity unchanged to prevent him from bouncing high into the air with each step. Now, our Steelborn has the same strength and the same amount of traction (since he has the same weight as before) but 1/100th of the mass. F = ma, so that gives him 100x the acceleration. Hairpin turns are no problem: running at 40 m/s he has the same turning radius as an ordinary human running at 4 m/s (since turning radius = velocity^2/acceleration = 4^2/10 = (4x10)^2/(10x100)). Jumping is fine too: our Steelborn has 10x the takeoff velocity but 100x the downward acceleration. Jumping height = v^2/2g, so the effects cancel, leaving him able to **jump the same height as an ordinary human**. However, air time = 2*v/g, so he has 1/10th the air time, which is again what we expect. His maneuverability with A-steel is enhanced too. There's no reason to assume his Pushes have changed strength, so F = ma says with 1/100th the mass, his Pushes give him 100x the acceleration. The increased gravitational acceleration won't cause problems because the total gravitational force is unchanged. Additionally, he no longer needs Kevlar skin, as he hasn't gotten any stronger. Since his body has so little mass, his insane accelerations will result in the same forces on him as usual. He won't black out either. Clearly, the mass reduction and gravity enhancement must extend to the Steelborn's clothes, guns, coins, etc. Otherwise, carrying a 1 kg pistol when he himself has a mass of only 0.5 kg would reduce his maneuverability to 1/3 of expected, but we see Bleeder think nothing of Steelrunning with pistols. The problems begin, however, when we consider him throwing something. What happens when coins leave his hands and return to normal mass? I see three scenarios: 1. Coins return to normal mass but velocity unchanged. They increase in both momentum (p = m*v) and energy (KE = 1/2m*v^2). This gives him tremendous firepower: he can throw coins at 10x ordinary speed and 10x the rate, exactly as described above. His pistol rounds travel at 10x speed too: muzzle velocity = sqrt(2*d*a), so since 1/100th the mass -> 100x the acceleration by F = ma, bullets have 10x the muzzle velocity. To top it off, he's immune to bullets: incoming bullets are reduced to 1/100th of their mass upon hitting him. 2. Coins are reduced to 1/100th speed. This satisfies Conservation of Momentum: p = m*v, so if mass increases by 100x to return to normal, velocity decreases to 1/100th. Since KE = 1/2m*v^2, their energy decreases to 1/100th (losing energy is more permissible than gaining it at least!). His coins are reduced from 250 m/s on leaving his hand to 2.5 m/s - 1/10th of an ordinary throw speed. This affects bullets too: they have 10x the muzzle velocity initially, but as soon as they stop touching him, they are reduced to 1/100th of the speed. The net effect is to reduce a 300 m/s pistol bullet to a 30 m/s one. Our Steelborn's problems get even worse when we consider bullets striking him: they are suddenly accelerated to 100x their velocity, satisfying Conservation of Momentum, but resulting in a 100x increase in bullet energy since KE = 1/2m*v^2. 3. Coins are reduced to 1/10th speed. This satisfies Conservation of Energy: KE = 1/2m*v^2, so a 100x increase in mass is balanced by 1/10 velocity, but doesn't satisfy Conservation of Momentum. His throwing speed is unaffected, since coins leave his hands 10x faster than normal, but then are reduced to 1/10 speed, or normal throwing velocity. The same applies to pistol bullets. Bullets striking him are reduced to 1/100th mass but have 10x the velocity, leaving their energy again unchanged. Of all the options, I think 3 fits the best. Our Steelborn cannot throw or shoot at crazy speeds with F-steel - though he can still put out huge numbers of bullets and Push them to deadly speeds with the help of A-steel. Now that we have established how he (roughly) interacts with objects, much of his power depends on how far this field extends. Does it affect a bike he rides? A car he drives? A train? I suspect the explanation invokes his Connection to an object and the object's own Identity, but I see no evidence for how. The TL;DR The best match with Shadows of Self is that you can't change your strength with F-steel: you obtain crazy speeds by reducing mass and increasing gravity while permitting your muscles to operate at higher speeds. (This pairs well with F-Iron: both manipulate mass.) Anything you throw is reduced in speed and increased in mass when it leaves your hands. This gives enhanced maneuverability and speed without crazy firepower. Thoughts?