The Physics of Alagaesia, Part 1
Welcome to my new column, The Physics of Alagaesia, inspired by The Physics of Superheroes. In this column I will be analyzing the feats of power and endurance that characters in the Inheritance cycle perform. I’m choosing them randomly, and without many picked out yet, so if there is a particular scene you would like to see me discuss, please feel free to mention it.
We are going to start out with a small fragment of the battle that takes place in Brisingr between Eragon and Arya against however many hapless Imperial Fodder Pawns. I’ll probably be coming back to this scene a couple of times, because it has a lot of hilarious, but I’ll focus on a single segment for the moment.
Trapped, he did the one thing he could: he struck the man in the chest with all his might. A fount of blood and sweat erupted as his fist connected. The blow staved in the man’s ribs and propelled him more than a dozen feet over the grass, where he fetched up against another corpse. (p. 114)1
Calculations
Now, there are some things to note. This man is dressed in maille, and is a soldier besides. Let’s estimate the soldier at 200 pounds, or about 91 kg.2 The maille would be around another 10kg.3 So let’s call the total weight a nice even 100kg. Let’s call more than a dozen feet thirteen feet, although this might be low, because that will come out nicely to four meters. We’ll want to account for the force of friction here, and we’ll assume the grass isn’t already slick with blood, in which case mu = .35 should serve as a reasonable guide.4 Let’s draw the free-body diagram now.

We want to know just how strong Eragon’s arms are, so we are solving for Fpunch. Our first task is to determine what kind of initial velocity would be necessary to propel the soldier four meters. The deceleration due to friction is
g * mu = 3.5 m/s2
So we can solve the equation for initial velocity, v0.
v0 – 3.5t = 0
???
Here we encounter a problem. We need to know how long the man travelled before collapsing to the ground. The best we can do at this point is do some armchair calculations. We set up a second equation, describing the distance travelled.
4 = v0 t – 3.5 t2
If we attempt to solve this for t using the quadratic formula, we’ll notice something. We only have real results when

sqrt(v02 – 56) >= 0
Since I’m trying to favor Paolini at every single turn here, we’ll try and take the very lowest bound value. So, v 0 = sqrt(56) = 7.5 m/s. Now then, let’s determine what kind of force Eragon needs to exert to accelerate a man to that speed.
Guesstimating that the impact time of a punch is a tenth of a second, although a much shorter duration is possible (in which case Eragon would be even stronger), then Eragon is exerting a force of
(7.5)/(.1)*100 = 7500 Newtons
Interpretation
So Eragon can lift 750 kg, at minimum, since our calculations assumed the lowest possible numbers everywhere we could. 750 kg is close to 1650 lbs, and this is with one arm. This isn’t the full extent of the our favorite Gary Stu’s power, of course. By adjusting numbers in our estimation, we could easily have him lifting 12,000 lbs, but we wouldn’t do that, would we?
Next time around, we will calculate how far Arya can jump, and why she should have been able to escape from Durza.
1 Brisingr
2 http://pediatrics.about.com/cs/growthcharts2/f/avg_wt_male.htm
3 http://homepage.ntlworld.com/trevor.barker/farisles/guilds/armour/mail.htm
4 http://hypertextbook.com/physics/mechanics/friction/

By Kitty
on Feb 16, 10:05 PM