we have yet devised.

但比人在單車上騎更神奇的是

But perhaps even more incredible than humans riding bicycles is the fact that bicycles

只要推出去的速度夠快，即使沒有人在騎

can ride themselves.

單車也能自行保持平衡前進

Yes, once they’re set in motion at a sufficient speed, bicycles can stay upright without any

很多人誤以為單車能保持平衡，是因為角動量守衡原理

human intervention.

即是說，由於車輪在轉動，當單車往一邊傾斜

A common misconception is that bikes stay up because of conservation of angular momentum

車輪就會生出某種反向力量，使車子保持直立

– that is, since the wheels are spinning, if the bike tips to one side there’ll be

這種說法很容易被推翻：只要把單車手把固定

some sort of countering force from the wheels that keeps the bike upright.

前進中的單車也跟靜止的一樣，馬上就會往一邊倒下

But there’s an easy way to see this explanation is wrong: simply lock the handlebars in place

另一常見誤解是，單車靠前進動量來保持平衡

and a moving bike will fall over just as easily as a stationary one.

但如果把自行前進中的單車往側推，它會改變方向

Another common misconception is that bikes stay upright because of their forward momentum.

然後繼續前進－只改變了動量，單車卻依然不倒

However, if you knock a ghost-riding bicycle sideways, it’ll change directions and then

那單車如何自行直立前進？我們知道的是

continue merrily on its way – plainly changing its momentum, but nevertheless staying upright.

當單車開始往一邊傾斜，車把會自動稍稍轉向同一邊

What we do know about how conventional bikes stay upright on their own is this: when a

使得車輪回到單車的重心下方，讓單車保持平衡

moving bike starts leaning to one side, it also automatically steers towards that side

這裡面包含了三種主要力學機制

a little bit.

第一，由於單車的轉向軸往後傾

The result is that the wheels come back underneath the center of mass, keeping the bike balanced.

前輪跟地面的接觸點位於轉向軸後面。當單車往左傾時

And there are three main mechanisms responsible:

地面向上的作用力會使前輪和車把轉向左

First, because of the backwards tilt of a bike’s steering axis, its front wheel actually

令單車車輪轉回重心下方位置

touches the ground slightly behind that axis.

第二，車把和前輪的重量分佈

This means that when the bike leans to the left, the upward force from the ground acts

一般在轉向軸的前方。當單車往左傾斜

to turn the wheel and handlebars to the left, helping the bike steer its wheels back underneath

重力會使前輪轉向左， 原理跟占卜棒 (divining rod) 或尋龍尺 (dowsing rod) 一樣

its center of mass.

你的手往哪邊傾斜，就會指向哪邊

Second, the weight of a bike’s front wheel and handlebars is generally distributed slightly

第三，車輪的確有陀螺效應，但不直接讓單車保持平衡

in front of the steering axis, so when the bike leans to the left, the downward pull

跟前兩點一樣，陀螺效應輔助車輪轉向，像 Destin 和 Carl 的清楚展示

of this mass also helps turn the front wheel to the left, the same way divining rods will

他們介紹直升機原理的影片展示，施力讓旋轉中的物件傾斜的話

turn towards whatever direction you tilt your hands.

會使物件向另一方向傾斜，轉向軸錯開了90度

Third, there is indeed a gyroscopic effect from the wheels, but it doesn’t keep the

這個古怪的現像，簡單地說，是因為你力矩的作用滯後於你施力的點

bike upright on its own.

現在想像單車上的情況，角度變成垂直，就能看到陀螺效應的作用

Instead, it helps steer: as Destin and Carl demonstrate excellently in this video about

陀螺效應讓左傾的前輪往左轉向，同樣地

how helicopters work, trying to tilt a spinning object makes the object tilt as if you pushed

也是讓車輪回到單車的重心下方

it at a point 90° away from where you did – it seems spooky, but basically the effect

簡而言之，一部普通單車的穩定性透過三者的組合達成

of your torque lags behind where you push.

前輪跟地面接觸面比轉向軸靠後

Now imagine this happening vertically on a bike, and you can see that the gyroscopic

前輪和車把重心位於轉向軸前方，和前輪的陀螺效應

precession from the bike’s leftward lean makes the front wheel turn to the left, again

三者都在傾斜時使輪轉向，令車輪回到重心下方

helping steer its wheels back underneath its center of mass.

起碼，當單車以正確速度前進時，情況就是這樣

In short, a normal bicycle is stable thanks to a combination of the front wheel touching

如果單車太慢，車輪的轉向速度就不足以把單車在車身太斜前拉起

the ground behind a backwards-tilted steering axis, the center of mass of the front wheel

另外如果把單車往後推，車輪的陀螺效應會反過來

and handlebars being located in front of the steering axis, and the gyroscopic precession

但另外兩種效應不會，於是車輪在車身傾斜時會轉向另一邊

of the front wheel, all of which help the bike automatically steer its wheels back underneath

離開重心下方

it when it leans.

要補充的是，這三種力單獨都不是單車保持平衡的關鍵

At least, when it’s moving forwards at the correct speed.

這台單車的車輪沒有陀螺效應，而且前輪跟地面接觸點

If the bike’s going too slow, it won’t turn quickly enough to keep from crashing

是在轉向轉前方，但也能自行平衡前進

into the ground.

這台車以後輪轉向，也能保持平衡； 而這張設計能做出一台穩定的單車

And if you push the same bike backwards, the gyro effect will reverse but the other two

但這車的轉向軸往前傾，而非往後

effects won’t, with the result that the wheels are steered out from under the bike

另一方面，我只是在我的單車的前叉後方加了點負重

when it leans.

就完全破壞了它的穩定性

What’s more, none of these three mechanisms is, on its own, the secret to bike stability:

很明顯，眾多不同的變量可以以各種各樣的方式組合

here’s a bicycle that has no gyroscopic effect and whose front wheel touches the ground

不同的組合決定單車的穩定性；加上一個人負責轉向、平衡

in FRONT of the steering axis yet which is stable without a rider.

有時，也能讓不穩定的單車變穩定

Here’s a stable rear-steering bike, and here’s a design for a stable bike where

你可能意想不到的是，針對沒有人在騎，單車自行平衡的情況

the steering axis tilts forward instead of back.

什麼變量、怎麼組合才是使車體穩定的公式，到現在科學家還沒有頭緒

On the other hand, I made my own bike totally unstable just by adding some extra weight

我們只知道，有些組合可以，另一些...不行

behind the front fork.

There are clearly a lot of different variables that can be combined in various and surprising

ways to make stable and unstable bicycles.

Adding a human to help with steering and balance can sometimes make unstable bikes stable,

and I imagine a rider would also make some stable bikes unstable.

But amazingly, even for a riderless bike, science currently doesn’t know what it IS

about the special combinations of variables that enables a bike to stay up on its own.

We just know that some combinations work, and others don’t.