Overthinking It: the science of packing.

Like many travelers, we have discovered the truth of packing light; there’s something about travel or when the rubber hits the road (no pun intended whatsoever) that makes you prioritize about your luggage. No matter how little you pack, you end up making it work and what’s more, there will always be something you don’t end up using. When Steve and I were contemplating our choice of travel luggage, Erin, our BFF and dogmother to Stella, was the first to advise us not to purchase a large backpack, because we would simply fill it. So I got a 46 liter Osprey Porter,  and Steve got the 22″ Osprey Meridian, which have both been great!

Rolled up clothing in my Osprey Porter.

A few days, while we were getting ready to go to Shanghai, I was worried over the issue of how to fit my birthday presents (a beautiful green windbreaker/ raincoat and two new dresses) into my bag. Steve was also packing, albeit carefully rolling his pants and shirts into small cylinders. I knew he had a theory about this sort of thing, but wasn’t too clear on it, and as I watched him pile his clothing this way on compile all of his clothing this way, I couldn’t resist asking: why does rolling your clothing save more space?

Steve’s theory went that a circle was simply the most efficient way of minimizing surface area. A sphere, in fact, would be best, but in terms of clothing, the closest approximation was to roll things up into a cylinder. I was baffled; his theory seemed to make sense, but I just couldn’t believe that it would be that much better than the conventional method of folding clothing into piles and stacking them on top of the other — they’re layered so thin that way! So I asked Steve to prove it.

We worked this problem out by abstracting it down to 2D terms. Given a perimeter of 100 feet, you can create a number of shapes with varying areas; a long, thin rectangle with sides of 1 ft, 1 ft, 49 ft, and 49 ft would yield an area of 49 square feet. A more stocky rectangle of  10 ft, 10 ft, 40 ft, and 40 ft, would yield an area of 400 square feet, which is significantly better. A perfect square with 25 ft on each side would make 625 square feet. How do you improve on that? Well, you can make a shape with one side (or infinite sides, depending on who you’re talking to): a circle. The formula for a perimeter of a circle is diameter x π, so a circle with a perimeter of 100 ft would then have a diameter of 100/π. Its radius is then 50/π. Since the area of a circle is π r^2 (oh if I had LaTex), then we substitute in 50/π as r; to show our math, 50/π squared is 2500/π^2. When you multiply by π, it cancels out part of the π^2, leaving just π on the bottom, for a total area of 2500/π . Roughly, if you use 3.14159 for π, that works out to 795.78 (rounded) square feet. Tl;dr: we’ve proven that a circle with the same perimeter as a rectangle can contain more surface area.

This works the other way too; a circle is more efficient than a square, which is more efficient than a long skinny rectangle, when it comes to encompassing the same surface area. A perimeter of 100 feet can encircle 795.78 square feet. That same amount of area, arranged in a square, would require a perimeter of about 112.8 feet; again, in a long skinny rectangle with one side of 10, the other would need to be 79.58 (rounded) feet, making for a perimeter of nearly 180 feet. When it comes to packing, which is 3D, we think about volume = surface area times height, whether it’s a cylinder (analogous to a piece of clothing that has been rolled up) or a nearly-flat rectangular box (analogous to that same piece of clothing folded twice or three times) . If you assume that in the switch to volume or 3D that the height of the cylinder or length of the rectangular box is equal, then it just comes back to what shape is most efficient at containing the same amount of surface area. QED. (I think.)

All rolled up.

So of course, rather anti-climactically, everything fit in my bag with the rolling approach, even with my new outfits added in. Since starting to write this post, I’ve done a bit of research (okay, just Googling) online, and of course, many people have many opinions on the best way to pack clothing. There’s the die-hard traditional folders like the kind I used to be as well as those who have been converted to rolling clothes; there’s even a cult of bundle-wrappers who swear by wrapping clothes around each other. That sounds like a bit too much planning, IMHO, and impractical when you’re constantly packing and repacking your clothing on the run like we are. Many people agree that rolling is a better way of packing your clothes, but I feel reasonably certain that Steve and I have mathematically proven that it is most efficient. I however have no opinion on what packing method yields the least amount of wrinkles, though, mostly because we’re not on a business trip.

Okay, I know you all wanted to know more about what we’re up to, other than overthinking methods of packing. Other than that, we have spent time in the past four days running around the French Concession in search of Internet, watching the Bears getting beat by the Detroit Lions (Jay Cutler, why can’t you convert any third downs?), trying to sublease an apartment in Taipei for three months, hanging out with old college friends, eating xiao long bao, and watching both Looper (2012) and This Is The End (2013), which by the way, is a hilarious movie. It has been a good time, though Steve and I have become increasingly nostalgic for the States. Already, you say? Yeah, already. We even resorted to willingly ordering Domino’s, which was surprisingly good. I promise longer posts to come when we get settled on things we’ve learned in China, like how to cross the street and how to figure out who on the subway next to you is about to get off so you can take their seat. No lie; I think these are the most important things to figure out when you’re in China.

Tomorrow, we fly to Taipei for the beginning of a three month stay in Taiwan and hopefully, finally find our feet. We’re ready to start working — Steve on his app development and me on my grad school applications.

See you in Formosa!

2 thoughts on “Overthinking It: the science of packing.

  1. I can imagine! Steve and Rich seem to have a lot in common, and I’m really glad one of the two of us is good at paying attention to detail. Hope you’re enjoying the fall in Greenville!

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