Shulou(Shulou.com)11/24 Report--

On this day, my colleague sent a video to the editor, saying that he would take an examination of the editor.

Source: bilibili @ TheQ handmade "how can the wheel not be balanced when it is taken apart?"

Can the problem of bicycles baffle my 12-year-old cyclist?

If we want to know why this kind of bicycle cannot be balanced, we only need to analyze why ordinary bicycles can be balanced.

Ordinary bicycles can keep balance, not because.

Because of what?

If we say how to control the balance of bicycles, the editor knows this problem so well that it is no problem to write a paper.

But why are bicycles balanced?

Did the editor ride a fake bike all these years?

With the question, the editor tried to look up the information to find the answer. This check is also startled. It turns out that the problem of bicycle balance has plagued the scientific community for hundreds of years, which is really not easy.

Bike: I bet you don't understand my balance

It is said that the earliest bicycle was in 1790, when a Frenchman thought that a horse-drawn carriage took up too much space, so he slapped his head and removed half of it, leaving only two wheels, thus giving rise to the prototype of a bicycle.

Wooden draisine, an early bicycle that appeared around 1820, is powered entirely by the pedals, but can control the front wheel steering. Source: reference 4 after hundreds of years of development, bicycles have gone through a variety of strange designs and finally become the common shape today.

It is such a means of transportation that everyone is very familiar with, but it makes scientists difficult.

If you ask how air conditioners regulate temperature, scientists can tell you about the Carnot cycle.

Reverse Carnot cycle cooling diagram | Source: benchmark-id.com if you ask the principle of the remote control, scientists can tell it in terms of infrared and coding sequences.

Infrared detector | Source: Baidu pictures but the bicycle, as a product of life experience, did not consider why it could be balanced when it was invented, but found one problem after another when later generations tried to analyze it.

Why can it be maintained only after riding? what kind of role does speed play in it? Push the bike out so that it can be balanced without being controlled. Why is that?

Mature bicycles should learn to drive by themselves. Source: 3 A hundred years after the invention of the bicycle, the British mathematician Francis Whipple (Francis Whipple) deduced the Whipple model, which uses four rigid bodies to represent the bicycle and introduces 25 parameters such as mass and wheel radius to describe the motion state of the bike. it is one of the earliest and most enduring bicycle models in the world.

Whipple model, the bicycle motion is described by R, B, H, F four rigid body motion | Source: reference 1 it is a pity that this model only provides us with a simulation method, but does not point out the principle behind it.

02, Sommerfeld et al.: in the 20th century, the unsolved problem of bicycle balance has attracted the attention of a large number of scientists, including one of our old acquaintances in physics, Arnold Sommerfeld (Arnold Sommerfeld).

Arnold Sommerfeld, a famous physicist and one of the pioneers of quantum mechanics and atomic physics, discovered fine structure constants. | Source: Baidu Picture he and two other scientists, Felix Klein (Felix Klein) and Fritz Noether, jointly proposed an explanation-the gyro effect.

What is the gyro effect?

The gyro effect is actually the expression of the angular momentum theorem. Under the action of the external moment, the angular momentum of the rotating object changes, resulting in precession angular momentum. In other words, under the action of the gyro effect, the rotating object will not fall directly, but will change the direction of rotation.

You should have played with the top when you were a child. When the gyro rotates, it rotates around a rotation axis, and at the same time, this rotation axis rotates around a vertical axis. The phenomenon that the rotation axis of a rotating object rotates at the same time is called precession.

Source: bilibili's "Inception" gyroscope's precession state is very stable, even if a certain external force can be applied to maintain balance, this is the gyro effect. Gyroscopes, for example, make use of the gyro effect to keep objects of great mass from falling down.

The wheel maintains its stability under the action of the gyro effect | Source: bilibili @ NASA Chinese synchronization actually the above dynamic picture has already explained very clearly. Under the action of the gyro effect, the wheel overcomes gravity, forms precession, and maintains its balance by changing direction.

This balance state is related to the speed of the wheel. The faster the speed is, the smaller the inclination angle of the wheel is, and the more stable the body is. So when we ride a bike, we will find that the faster we ride, the easier it is to keep balance.

Now looking back at the initial problem, why can't this kind of car be balanced?

After the front wheel is taken apart, only 1/3 of the parts can contact the ground at the same time, the other parts have no direct external torque, can not form precession, and there is no gyro effect to keep it stable.

03. Jones: we have to look at "steering wheel tilt". In fact, so far, the gyro effect has explained the initial problem and has persuaded the editor very well.

You think it's over? NO!

Sixty years after Sommerfeld and others put forward the explanation of the gyro effect, a chemist named David Jones published an article that overturned the explanation of the gyro effect.

Doesn't it say that the gyro effect is suitable for common models? 'then I'll design a bike that doesn't work, 'Mr. Jones said. So you have the car in the picture below.

Source: ref. 3 this bike has one big and one small front wheels, which rotate in opposite directions through the transmission between large and small front wheels. By controlling the proportion of the size, the angular momentum of the two front wheels is equal and the direction is opposite, that is, it is completely offset!

If the angular momentum is gone, where is the gyro effect? This proves that it is wrong to use the gyro effect to explain the bicycle balance problem.

Of course, Jones is not the one who just overthrew, regardless of reconstruction, he put forward a new theory-steering wheel tilt effect (the Caster Effects).

In this theory, there is an important concept: front wheel track (the trail). The front wheel track refers to the distance between the front wheel steering shaft extension line and the ground intersection and the front wheel contact point with the ground. If the steering shaft intersection is before the contact point, the front wheel track is positive; otherwise, it is negative.

The c marked by the red line is the front wheel track Jones pointed out that when the bike starts to dump, the positive front wheel track will cause the front wheel of the bike to tilt backward under the action of gravity, driving the front of the bike to turn, through this steering, the bike will return its center of gravity to the middle of the car body and return to balance.

The longer the front wheel track, the more stable the bike (although it will be more difficult to ride), while the negative front wheel track will make it impossible for the bike to maintain balance.

The blue line represents the extension line of the steering shaft, and the black line indicates that the ground will return to our starting problem at this time. After the wheel is split into three parts, the long front wheel makes the front wheel track negative most of the time, so it is impossible to maintain balance.

04, Schwab, etc.: you are all right, but. From this point of view, it is indeed very convenient to judge and explain the balance of bicycles through the "front wheel track".

Jones is also very proud of his theory. In his memoirs published 40 years later, he regarded the theory as one of his great achievements and declared: "I am now known as the father of modern bicycle theory."

I am now hailed as the father of modern bicycle theory.

-- David Jones

However, the most indispensable thing in the scientific community is reversal.

In the second year of Jones's memoir (2011), an article published in Science magazine entitled "A Bicycle Can Be Self-Stable Without Gyroscopic or Caster Effects" (bicycles can stabilize themselves without the effects of gyros and steering wheels).

The research team in this article did the same thing as Jones: design a bike that would remain stable after excluding the above effects.

In Jones's steering wheel tilt theory, the front wheel tilts under gravity, which redistributes the weight of the entire car body to counteract the negative front wheel trajectory. Then eliminate the gyro effect, and you will have the following bike.

Source: reference 1 the front and rear wheels are designed as upper and lower wheels, the two wheels turn opposite and the angular momentum counteracts each other; the steering shaft extension line intersects with the ground after the contact point between the wheel and the ground, the front wheel track is negative.

According to the two theories mentioned above, this kind of car can not maintain balance, but.

The car is not only balanced, but also very stable.

The author explained that by moving the car's center of gravity forward, the effect of the negative front wheel track can be offset, so that when the car is tipped, the front wheel will still tilt back to drive the car to turn, bringing the car's center of gravity back to the middle and restoring balance.

This is the third way for bicycles to maintain balance-- to change the mass distribution.

But this article does not negate the first two explanations.

This is also the breakthrough point of this article. It believes that the gyro effect, the steering wheel tilt effect and the changing mass distribution mentioned in this paper can all explain the balance of bicycles, which is a sufficient and necessary condition for bicycle balance.

Careful readers may have found that all three theories have one thing in common: turning a car's body into a steer. This is the fundamental reason why bicycles can maintain balance.

When any of the above three theories are satisfied, it can be inferred that the car can maintain balance; when all three are not satisfied, the car can also maintain balance as long as it can turn the body into a steering.

Rear wheel: does anyone remember me? So far, the problem of bicycle balance has been solved, but it has not been solved completely.

We know that the fundamental reason for bicycle balance is to turn dumping into steering, and we also know three theories that can achieve this transformation and the corresponding bicycle design.

But we still do not know whether there will be more theories to achieve this transformation, nor do we know whether there will be a theory that is sufficient and necessary to achieve bicycle balance. We still lack a "unified theory" of bicycle balance.

Oh, by the way, let me remind you not to forget the rear wheel. Although it has no sense of existence in all three theories (and it really has nothing to do with it), it is still an indispensable part of the bike. Can you ride a unicycle? That's all right.

Going back to the beginning question, has the problem of unbalanced bicycles been solved?

Solved, UP returned the front wheel to integrity.

Reference:

1.Borrell, B. The bicycle problem that nearly broke mathematics. Nature 535,338-341 (2016).

2.Kooijman JD, Meijaard JP, Papadopoulos JM, Ruina A, Schwab AL. A bicycle can be self-stable without gyroscopic or caster effects. Science. 2011 Apr 15: 332 (6027): 339-42.

3. Https://mp.weixin.qq.com/s/Z7c5lJJhnG_Hvq-aSnHxDw?scene=25#wechat_redirect

4. Https://encyclopedia.thefreedictionary.com/bicycle

This article comes from the official account of Wechat: Institute of Physics, Chinese Academy of Sciences (ID:cas-iop), author: happy Superman

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