Arrows in the Ballpark


The following is a quick-and-dirty estimate of the energy, force, and pressure of the arrow penetration event in RoTJ. I'll update this in the not-too-distant future, but wanted to go ahead and post an estimate, if even a terribly rough one. Again, I reiterate . . . this is just a rough estimate. The margin of error may be huge, but I'm going to aim for a reasonably conservative (i.e. high-end) estimate.

For example (and I don't have the movie in front of me, I'm just playing): Let's say that the arrows are two feet long. That's 61 centimeters. For the purpose of determining mass, let's give them a diameter of 5 centimeters.

Total volume = 1197.7cm, or 0.001198m.

Let's break out the uber-dense 1,750kg/m wood from the AT-ST example. Total mass = 2.1 kilograms. Let's make it 2.5 to account for the arrow-head, and because I like integers and half-integers.

Now, we need speed. I don't have the slightest clue offhand what the speed was. Let's say it was two meters per frame, which (at 25fps) would be 50 m/s.

KE = .5 (2.5kg) (50m/s)
KE = 1.25 (2500)
KE = 3125 joules.

Interesting . . . the 7.62mm NATO round rates at 3,318 joules. As calculated previously, the .44 Magnum comes out to over 1,410 joules.

Without knowing the thickness of the armor or the diameter of the arrow, the rest of this is just gross guesswork. Let's say the arrows were a centimeter wide. As for the arrow's penetration, that's hard to say. It was lodged in there far enough that the arrow stayed in, even when dude brushed a branch. One Warsie has argued that, since the guy was injured, it must have penetrated about six inches. Let's say four inches . . . that's 10.16 centimeters, which brings it down to 30758 N of force. With the arrow area of 1.57cm, we have 19591.1 N/cm, or 195 megaPascals.

As previously calculated, a .44 Magnum would blast a 1cm target with a pressure of 1,512 megaPascals.

In other words, unless trooper armor is way thicker than a centimeter (which it doesn't appear to be, judging by the cracked armor footage and other scenes), then Stormies aren't bulletproof. Further, the cracked armor footage may imply that these figures are way too high anyway.

 

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