I was late to Firefly. Nearly ten years after the show first aired and then was subsequently cancelled, I holed up in my room, coffee and external hard drive in hand, aiming to blaze through one of the most beloved sci-fi series.

A mix of science fiction and “spaghetti-western” genres, Firefly was wonderful. It certainly awakened the fanboy in me, and I quickly understood why my girlfriend envied me for being able to watch the series for the first time.

It all ended abruptly, due to early cancellation, with the last episodes of Firefly barely answering any central questions or exploring the rich universe that had been so lovingly crafted by creator Joss Whedon. It was to my delight to learn that in 2005 there was a full-length movie in response to public (and private) outcries for more of Serenity and her crew.

Watching Serenity let me spend a bit more time in the ‘verse, and the film thankfully resolved a number of outstanding loops just craving to be closed. But the forced end of Firefly also forced Joss Whedon’s hand. He put in scenes that would only have appeared in a last hurrah like Serenity. One scene in particular shook me, like the unexpected sight of a Reaver ship. It’s a scene that drove me to NASA forums and technical reports, glass manufacturers, my calculator, and eventually to this post.

Needless to say, if you haven’t seen Firefly or Serenity, the ensuing discussion is spoiler-laden (and you should go watch them!).

You Can't Take This Guy From Me

Late in Serenity, after crash-landing at the mysterious base of “Mr. Universe,” pilot Hoban "Wash" Washburne meets his end at the tip of a Reaver spear. The immediacy of the violence, and his wife Zoe’s touching reaction, kept my mouth agape well into the next few minutes of the film. One of my favorite characters just died, as Firefly died. I couldn’t stand it. I had to be sure.

What if the Reaver spear couldn’t plausibly make it through the forward windows of Serenity? The movie may have been set in the future, but we too have built spacecraft with windows, and they are made to withstand impacts. If I could prove that a modern shuttle window (assuming that a future window would be even better) could withstand the impact that killed Wash, I could have the ultimate in fanboy closure: the movie is “wrong,” and my version of the story lives on.

Objects In Space

In terrestrial situations, a speck of paint is less than harmless. In space, it’s deadly. Travelling at a blistering 9,000 meters per second in orbit, the equations deem it lethal. It becomes a “hypervelocity” bullet.

Our spacecraft obviously must account for this deadly debris. Tens of thousands of pieces of extraterrestrial trash litter the orbit of Earth [PDF], meaning that a shuttle’s final impact could come from an errant hex nut. Shuttles today are outfitted with shielding to prevent such disasters, and feature two-and-a-half inch thick windows—the thickest pieces of glass ever produced in the optical quality for see-through viewing.

The largest impact to a shuttle window occurred when a fleck of paint struck STS-92—a flight to the International Space Station. A shuttle window has never been penetrated by a hypervelocity impact, but it doesn’t have to be. A deformation large enough could eventually cause window failure upon repeated take-offs and re-entries.

After engineers examined the crater in the window, the shape that best explained the damage was a sort of miniaturized plate. Based on the size and the speed (9 km/s!) of the fleck that hit STS-92, I calculated that the window weathered an approximately 5,000 pounds per square inch impact, creating more than enough damage to warrant a window replacement. And such replacements from serious impacts are commonplace. Robert Lee Hotz notes in the Wall Street Journal that “NASA shuttle engineers have replaced the spacecraft's debris-pitted windows after almost every flight since 1981, at a cost of about $40,000 per window.”

That little fleck of paint was almost a catastrophe. Based on the thickness of the orbiter’s forward facing windows and the basic strength of the glass, made of fused silica, the windows of STS-92 could have resisted a pressure of 8,000 pounds per square inch—nearly three times that of a crocodile bite (amazing in two respects). Still, it was a close call.

The shuttle windows are tough, to be sure, surviving nearly 1,400 impacts intact over 43 sampled missions, but are they strong enough to save Wash? Tiny particles are elevated to terrifying status because of their ridiculous speeds, not their mass. Conversely, the Reaver spear that killed Wash was larger, but moving much more slowly. A few assumptions and some physics equations would determine if I could save him.

I Am A Leaf on the Wind…

To get the general dimensions of the spear that killed Wash, I had to (unfortunately) go back to the scene in question, excruciatingly slowing down an emotional moment to be replayed over and over. Based on some general size comparisons with other objects in the scene, I’d put the tip of the spear no larger than a quarter.

Diving back into Serenity, I used an earlier Reaver chase scene to guesstimate the spear size and speed. If Reavers shoot spears slow enough to be dodged (which they do), the spear that kills Wash can’t be moving much faster than a Major League fast-ball, putting the upper limit on speed around 100 miles per hour (45 m/s). This is orders of magnitude slower than the hypervelocity impacts that a shuttle deals with, but the spear is thousands of times more massive than a fleck of paint. Assuming it’s fashioned out of a metal, and given its size, I’d guess it’s around 100-200 pounds (45-90 kg).

Kinetic energy is easy enough to calculate, as is pressure. The kinetic energy of a moving object is one-half of its mass multiplied by the square of its velocity. This equation gives the Reaver spear a frightening 101,250 newtons of force at the low end. The pressure exerted by the spear is then equal to the force divided by the area it is acting on. Making the tip of the spear the size of a US quarter, the resulting pressure is a ludicrous 31,800 psi—nearly three times the pressure at the bottom of the Mariana Trench. This is over six times the force of the largest recorded impact to a space shuttle window, and almost four times the maximum pressure a shuttle window can take before deforming and failing.

The math doesn’t lie—Wash didn’t stand a chance.

…Watch How I Soar

I thought I had found the perfect fanboy out. The windows in Serenity looked flimsy and thin, surely not something a space-faring craft would be outfitted with. If the windows were anything like what we use to traverse the ‘verse today, perhaps all that would have happened is a jolt of fright from a deflected Reaver spear, or so I hoped.

But even delving through a hundred page NASA technical report[PDF] on impact shielding couldn’t ease my psyche.

Now, this is at its core a fanboy rant. No matter what I found, Wash dies in the movie. It’s part of the larger story and serves as a plot point, not a meaningless killing-off. But I selfishly wanted closure; I needed to resolve the dissonance between a character’s death and the fact that we know he wouldn’t have died if the networks saw better numbers from Firefly.

Maybe this is a testament to the enduring qualities of the show. To create characters important enough, and in only fifteen short stories, to warrant hours of research and calculation that ultimately proves useless in the larger story is an outcome of a great narrative. It’s typical of a the fan base that will still pack a Comic-Con panel ten years after the airing of the show.

I fell headlong into a rich universe of content, only fleetingly illuminated. I guess my desperate attempt to change the story is a compliment to the creators. It’s a love that keeps the show alive, makes Firefly a home.

“Love. You can learn all the math in the 'Verse, but you take a boat in the air that you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps her in the air when she oughta fall down, tells you she's hurtin' 'fore she keens. Makes her a home.”--Capt. Malcolm Reynolds

-----

Featured drawings courtesy of award-winnings manga artist and TED fellow Sara E. Mayhew. You can purchase custom drawings at her Etsy shop here.

Update (1/11/13):

Based on the astute observations of readers, the original version of this post skipped a step when calculating impact forces (in Newtons). As such, I have stepped back and calculated impact energies of the Reaver spear and orbital debris instead (in Joules). In terms of energy, the fleck of paint that hit STS-92 struck the shuttle with 3,700 times less energy than a Reaver spear would. Based on the allowable damage to a shuttle window, a Reaver spear with this amount of energy could pierce the shuttle's crew cabin and thermal shielding, let alone its windows. This comparison is more aligned with how NASA characterizes impacts, has more empirical support based on reports, and still ends up at the same conclusion (unfortunately).