You start your trip with a perfectly packed suitcase, and when it is time to go home and cram all your clothes in there, all the exact same stuff seems to have magically expanded.

旅行開始時，你的行李箱收拾得整整齊齊，可當你回家把所有衣服都塞進去時，所有一模一樣的東西似乎都神奇地膨脹了。

It is always harder to get the bag closed on the return trip.

回程時，要把包合上總是比較困難。

And that is because physics is working against you.

這是因為物理學對你不利。

As it always seems to be, especially during physics class.

似乎總是這樣，尤其是在物理課上。

So naturally, physicists have studied this to figure out the ideal way to fold your clothes and absolutely stuff that carry-on.

是以，物理學家們自然而然地對此進行了研究，以找出摺疊衣服的理想方式，並將其完全塞進隨身攜帶的行李中。

They didn't actually specifically research carry-ons, but we can apply their findings to packing clothes.

實際上，他們並沒有專門研究隨身行李，但我們可以把他們的研究結果應用到衣物包裝上。

And we've squeezed it all into this video on how science says you should pack a suitcase.

我們把這一切都濃縮到了這段視頻中，告訴你科學告訴你應該如何打包行李箱。

[♪ INTRO ♪)]

[♪ INTRO ♪)]

In the masterpiece that is a well-packed suitcase, each folded t-shirt acts like a single LEGO brick.

在包裝完好的行李箱這個傑作中，每件摺疊好的 T 恤衫就像一塊塊樂高積木。

They all fit together because of their shape.

由於形狀的原因，它們都能組合在一起。

But there is, of course, variety among LEGOs, and just like a LEGO's shape determines where you can put it, the way you fold a particular piece of clothing determines where it fits in your bag.

但是，樂高當然也有多樣性，就像樂高的形狀決定了你可以把它放在哪裡一樣，你摺疊某件衣服的方式也決定了它在你包裡的位置。

And we can use math to figure out what the ideal clothing brick looks like.

我們可以用數學來計算出理想的服裝磚是什麼樣的。

Starting with a thing called the volume fraction.

從一個叫做體積分數的東西開始。

That's the volume of your shirt divided by the space it occupies after folding or crumpling.

這就是襯衫的體積除以摺疊或揉皺後所佔的空間。

And that number gives you an idea of how condensed the shirt is.

通過這個數字，你就能瞭解襯衫有多厚實。

For example, a flat piece of paper doesn't take up much space.

例如，一張平整的紙張不會佔用太多空間。

It's just the volume of its fibers.

這只是纖維的體積。

Its volume fraction is 1.

其體積分數為 1。

But of course, if you crumple up that same piece of paper, it would take up much more space without having any additional material.

當然，如果把同一張紙揉成一團，在不增加任何材料的情況下，它所佔的空間會更大。

So its volume fraction is much less than 1.

是以，它的體積分數遠小於 1。

And that is not what you want.

這不是你想要的。

So on a scale from 0, you're wasting a lot of space in your bag, to 1, you've perfectly solved the packing puzzle.

是以，從 "0 "到 "1"，您的包浪費了很多空間，而您則完美地解決了打包難題。

Here is how different packing techniques measure up.

以下是不同包裝技術的衡量標準。

Starting out with the it'll definitely fit crumpling strategy.

從 "一定能裝下 "開始。

This is where you just throw all your clothes into the suitcase and smush with all your might.

這時候，你只需把所有衣服扔進行李箱，然後使出渾身解數。

Does this save you time?

這能節省您的時間嗎？

Absolutely.

當然。

But I gotta break this to you.

但我必須告訴你

You are definitely paying for that second bag fee.

你肯定要支付第二個行李箱的費用。

See, if you crumple your shirt into a ball, it takes up a deceptively large amount of space.

你看，如果把襯衫揉成一團，它所佔的空間就大得驚人。

We know this from experiments on crumpled aluminum sheets.

我們通過對皺巴巴的鋁片進行實驗得知了這一點。

The outer section of the crumpled ball might pack in relatively well, forming flat-ish layers that stack on top of each other.

揉成一團的球的外層可能會相對較好地包裹起來，形成一層層疊加的扁平層。

And based on all the wrinkles you will find upon unpacking, you might assume that this method is pretty efficient at condensing the shirt into a small volume.

根據你拆開包裝時發現的所有褶皺，你可能會認為這種方法能非常有效地將襯衫壓縮到很小的體積裡。

But an x-ray view of that crumpled ball reveals that the inside part is 30% less dense.

但通過 X 射線觀察這個皺巴巴的球，可以發現內部的密度要低 30%。

And there's no stackable order to the chaos in there.

裡面一片混亂，沒有任何可疊加的秩序。

Several experiments have shown that crumpled sheets, even those compressed with very strong forces, only have a volume fraction of about one quarter.

一些實驗表明，即使是被強力壓縮的皺巴巴的薄片，其體積分數也只有四分之一左右。

So even if you got your strongest friend to smush your suitcase, you are leaving three quarters of the space empty.

是以，即使你讓你最強壯的朋友把你的行李箱壓扁，你也會留下四分之三的空間。

Which explains why your clothes don't fit as well on the way back if you're packing them this way because you just gotta get out of the hotel.

這也就解釋了為什麼你這樣打包，衣服在回來的路上就不那麼合身了，因為你必須離開酒店。

Thank you for supporting SciShow by watching, commenting, and telling people about us.

感謝您通過觀看、評論和向他人介紹我們來支持科學秀。

And if you got yourself a 2025 Complexly calendar, thanks for supporting SciShow that way too!

如果您購買了 2025 Complexly 日曆，也感謝您對科學秀的支持！

Complexly calendars are all about bringing together Complexly shows in one piece of merch.

Complexly 日曆是將 Complexly 演出彙集在一起的商品。

They showcase Crash Course, Eons, Bizarre Beasts, Study Hall, and SciShow.

它們展示了 Crash Course、Eons、Bizarre Beasts、Study Hall 和 SciShow。

The 2025 theme is a quarter-century of progress, so each month celebrates something from the last 25 years that gives us hope about how far we've come and just how many possibilities lay ahead.

2025 年的主題是 "四分之一世紀的進步"，是以每個月都會慶祝過去 25 年中的一些事情，這些事情讓我們對我們已經走過的路以及未來的可能性充滿希望。

From mRNA vaccines to expeditions aboard the International Space Station, there's a lot to celebrate.

從 mRNA 疫苗到國際空間站探險，有很多值得慶祝的事情。

But we're only making a limited number, so get them while you can at complexly.store slash calendar or the link in the description.

但我們的數量有限，請在 complexly.store slash calendar 或描述中的鏈接購買。

Much to the chagrin of laundry haters everywhere, wrinkles take up a shocking amount of space.

褶皺佔據的空間之大令人震驚，這讓所有討厭洗衣服的人感到懊惱。

All that air between fabric folds really adds up.

布料褶皺之間的空氣會不斷增加。

So it might be worth it to take notes from the next person.

是以，向下一個人做筆記也許是值得的。

The neat-as-a-pin folder.

整潔如針的文件夾。

This person precisely folds each piece of clothing into the same dimensions, ensuring identical packing bricks.

這個人將每件衣服精確地摺疊成相同的尺寸，確保包裝磚完全相同。

As boring as it is, neatly folding your clothes does significantly increase your volume fraction.

儘管枯燥乏味，但整齊地疊放衣服確實能顯著提高你的體積分數。

This is because those layers of clothes are mostly flat on top of each other, eliminating the low-density spaces that plague the crumpling method.

這是因為這幾層衣服大多是平放在一起的，消除了皺褶法所帶來的低密度空間。

In theory, by folding carefully, your volume fraction could be very close to 1.

理論上，只要仔細摺疊，您的體積分數可以非常接近 1。

But of course, clothes can't be folded perfectly flat.

當然，衣服不可能完全疊平。

There will always be bends that leave empty space along the crease.

摺痕處總會有彎曲，留下空隙。

So in practice, the volume fraction is a little less than 1.

是以，實際上體積分數略小於 1。

And the more times you fold something, the more empty space you introduce.

摺疊的次數越多，空隙就越大。

This is especially true for very thick or stiff materials.

對於非常厚或堅硬的材料來說，尤其如此。

So if you're packing bulky sweaters or jeans, you're better off just folding those once.

是以，如果您要打包大件毛衣或牛仔褲，最好只摺疊一次。

Finally, we have what I call the I-saw-this-on-clean-talk roller.

最後，我們還有一個我稱之為 "我在清潔談話中看到的滾筒"。

This person carefully rolls their clothes into cylinders.

這個人小心翼翼地把衣服捲成圓筒狀。

These cylinders have similar volume fractions to neat folding, but with the added benefit of a convenient shape if you're packing a duffel bag or some other container that doesn't have perfect 90-degree corners.

這些圓柱體的體積分數與整齊摺疊的相似，但如果您要打包旅行袋或其他沒有完美 90 度角的容器，它們的形狀會給您帶來更多方便。

When you're filling a rectangle, you want the stuff you're putting inside to also be rectangles, so you don't lose a bunch of space in the corners.

當你填充一個矩形時，你希望放在裡面的東西也是矩形，這樣你就不會在邊角損失大量空間。

But if your bag has flexible sides or odd corners of any kind, the math officially recommends that you roll as many of your clothes as possible.

但是，如果您的包有彈性邊或任何奇怪的邊角，數學官方建議您儘可能多地捲起衣服。

The cylindrical bricks can line curved surfaces or fit into those weird crevices made by the suitcase handle, but it matters how tight you roll the cylinders.

圓柱形磚塊可以鋪滿彎曲的表面，也可以塞進行李箱把手造成的奇怪縫隙中，但關鍵是你要把圓柱滾得多緊。

If you've got super strength and you roll your shirts really tightly, you'll end up with cylinders that are hard to deform.

如果你有超強的力量，把襯衫卷得非常緊，你最終會得到很難變形的圓柱體。

Since its cross-section is a circle, you then are basically left packing circles into a box, which is a surprisingly difficult thing to optimize.

由於它的橫截面是一個圓，所以基本上只能把圓裝進一個盒子裡，而這是一件很難優化的事情。

In a 2D assessment of circles crammed into a square, the very best-case scenario ends up covering about three-quarters of the space, which, applied to packing, leaves one-quarter of your bag totally empty.

在二維評估中，圓圈擠在一個正方形中，最好的情況最終會佔去大約四分之三的空間。

Luckily, your shirt's probably squishier than just circles in geometry.

幸運的是，你的襯衫可能比幾何圖形中的圓形更柔軟。

Alternatively, you can roll your shirts into less rigid cylinders, leaving a little bit of slack.

或者，你也可以把襯衫捲成不那麼硬的圓筒，留出一點鬆弛的空間。

This allows them to squish together until your bag's cross-section looks more like a honeycomb.

這樣可以讓它們擠在一起，直到袋子的橫截面看起來更像蜂巢。

In fact, bees build hexagonal honeycombs precisely because of their optimal packing properties.

事實上，蜜蜂建造六角形蜂窩正是因為它們具有最佳的包裝特性。

If the cylinders are squishy enough, you can get a volume fraction of nine-tenths, meaning that clean talk has successfully life-hacked once again.

如果圓柱體足夠鬆軟，就能得到十分之九的體積分數，這意味著 "清談 "又一次成功地 "破解 "了生活。

So physics has spoken!

是以，物理學已經給出了答案！

Depending on what you're packing and what you're putting in, your best strategy is either neatly folding or rolling.

根據您打包的物品和放入的物品，最佳策略是整齊地摺疊或滾動。

See?

看到了嗎？

You never know when you need to fold a little bit of physics into your everyday life.

你永遠不知道什麼時候需要在日常生活中融入一點物理知識。

[♪ OUTRO ♪, thanks for watching!]

[OUTRO，感謝您的收看！]