In 2011, "Science" magazine published a paper titled "A bicycle can maintain balance without the help of gyroscopic or caster effects." In the article, researchers from the University of Dalford in the Netherlands denied the possibility of maintaining balance. The gyroscopic effect and caster effect of bicycle stability are absolutely correct. (All stabilizing measures qualify as destabilizing measures under the right conditions).

In the past 200 years, physicists and mathematicians have published hundreds of relevant documents. When physicists and mathematicians were studying why bicycles did not fly, two particularly important influencing factors were identified. Neglecting what is not discussed is the actual role of friction and conservation of momentum. The external force that really makes cars and bicycles (human-powered unicycles) accelerate is the friction generated by contact with the ground, not the output force of the engine and pedal force.

On a completely frictionless surface, there will be no circular motion when the bicycle tilts to the ground, because on a completely frictionless surface, there is no horizontal external force acting when the bicycle falls. , the momentum of the bicycle in the horizontal direction is conserved, but the momentum of the bicycle in the vertical direction can change due to the effects of gravity and ground support forces. In the case of ignoring the gyroscopic effect of the front and rear wheels of the bicycle (the front and rear wheels of the bicycle account for a small proportion of the total mass of the rider and the bicycle, and the speed is low, the gyroscopic effect is actually present and has a very small impact. It is different if it is a high-speed rotating gyro. ), no matter how fast the bicycle is, on a completely frictionless surface, the time it takes for the bicycle to tilt to the ground is the same as the time it takes for the bicycle to fall to the ground when the speed is zero.

Pedestrians, bicycles or human-powered unicycles on a completely frictionless surface, regardless of whether they have initial speed or not, cannot change the overall horizontal momentum value by relying solely on their own actions. This is shown in the process of falling to the ground ( Because the vertical momentum value can be changed due to the action of gravity and ground support force), it cannot change the vertical point position of the center of gravity on the horizontal plane. That is, when it is stationary, it cannot change the vertical point position of the center of gravity on the horizontal plane just by relying on any action of its own (the gravity and the ground support force cannot change the vertical point position of the center of gravity on the horizontal plane). Under the simultaneous action of the supporting force, it can tilt and fall to the ground, but it will not change the vertical point of the center of gravity on the horizontal plane).

On a surface with a large friction coefficient, when the bicycle tilts in a circular motion under the control of the caster effect, and the rotational moment generated by the centrifugal force component is less than the opposite rotational moment generated by the gravity component, the bicycle continues to tilt. The rotational moment generated by the centrifugal force component will prolong the tilt time and partially offset the opposite rotational moment generated by the gravity component. If the rotational moment produced by the centrifugal force component (no centrifugal force component produces a rotational moment when traveling straight) is greater than the opposite rotational moment produced by the gravity component, the bicycle is righted. When the bicycle is righted by the rotational moment generated by the centrifugal force component, it cannot continue to turn in the tilt direction. At this time, if the riding goal requires that the bicycle continue to turn in the tilt direction, (when actually riding a motorcycle, the speed is 8 kilometers per hour. Turning is a common action at and above speeds) The rider must subjectively and actively control the external force (actually the amount of friction) to achieve continued steering movement (only when the horizontal external force is not zero can the horizontal momentum be changed) (at this time self-balancing is necessary It is good for maintaining balance, but it is not conducive to the realization of the riding goal. In order to achieve the riding goal, you must break the self-balance). If the bicycle speed is very high, directly turn the handlebar to make a steering movement (you will do this before learning to ride a bicycle) , the centrifugal force is also very large, and the rider may be thrown out by the centrifugal force. This phenomenon can be seen when a motor vehicle turns at high speed. Through observation and mechanical analysis, in actual riding, when the bicycle speed is very high and the centrifugal force is also very large when the bicycle is turning, the cyclist takes advantage of the fact that the speed cannot make a sudden change and tilts the body in the turning direction in advance to increase the component of gravity to produce a greater rotation. The torque offsets the opposite rotational moment generated by the centrifugal force component during subsequent turns (reducing the circumferential radius), in which the cyclist's subjective initiative plays a key role (the psychological process is implicit and is the focus of psychological research). If the offset fails, the cyclist may fall or be thrown out by centrifugal force.

Although the self-balancing function of a human-powered unicycle or bicycle (such as the gyroscopic effect) is sometimes beneficial to maintaining balance, cyclists ride a human-powered unicycle or bicycle to achieve subjective riding goals. The self-balancing function of a human-powered unicycle or bicycle The maintenance result is rarely the same as the cyclist's subjective riding goal. When the balance maintenance result conflicts with the cyclist's subjective riding goal, it is necessary to break the self-balancing function of the human unicycle or bicycle. At this time, it is necessary to rely on the cyclist (or AI The active control role of the intelligent system), so the active control role of the rider (or AI intelligent system) is very important in human unicycle or bicycle riding.

Understand the basic physical laws that must be followed when an object changes its state of motion:

1. External force is the fundamental reason for changing the state of motion of an object.

2. The change in the state of an object (generating acceleration) must be affected by one or several external forces whose resultant force is not zero.

3. An object remains at rest or moves in a straight line at a constant speed when there is no external force or the resultant force of all external forces is zero.

In order to study why bicycle riding does not occur backwards, the cycling process is divided into the following states:

State 1. The cyclist and the bicycle are standing upright and traveling at a constant speed of 10 kilometers per hour. linear motion.

State 2. The cyclist and the bicycle are standing upright and moving in a straight line at a constant speed of 20 kilometers per hour.

State 3. The cyclist and the bicycle are tilted to perform uniform circular motion with a radius of R1 and a speed of 10 kilometers per hour (the tilt angle cannot be specified during equilibrium. Only two of the three quantities can be specified. Specify the first two quantities. The third quantity is the only one that is determined during post-balance. If the third quantity cannot be determined or the determined starting time or size fails to be determined, the riding control of the bicycle must fail (no proof is required based on the basic knowledge in the textbook) , if the third quantity cannot be determined or the determination of the starting time or size fails and the cycling control of the bicycle is successful, the result that the knowledge of physics and cybernetics is wrong will be obtained). Generating the correct tilt angle based on the status results and combining it with your own knowledge is a necessary condition to control the tilt during riding. In the automatic driving system, the sensor collects information and the control computer accurately calculates the tilt angle and executes it. The rider controls the behavior process. The psychological activities in it are implicitly verifiable and repeatable, and strictly abide by the laws of physics (the probability of success is 100%).

State 4. The cyclist and the bicycle are tilted to perform uniform circular motion with a radius of R1 and a speed of 20 kilometers per hour.

State 5. The cyclist and the bicycle are tilted to perform uniform circular motion with a radius of R2 and a speed of 10 kilometers per hour (R2>R1).

State 6. The cyclist straps 50 kilograms of cargo to the right side of the back seat of the bicycle and moves at a constant speed in a straight line at a speed of 10 kilometers per hour.

Refer to the process of satellite launch and orbit change, the rocket transporting the satellite is ignited on the ground and accelerates upward (the acceleration is a1). It accelerates to the predetermined speed V1 and runs for a period of time. When it reaches the predetermined height, the satellite and the rocket separate. The satellite enters an orbit with a radius of r1 (state a), and then changes to an orbit with a radius of r2 through orbit change control. During the orbit change process, the attitude must be controlled to keep the front of the solar cell facing the sun. The satellite must perform precise calculations before changing its orbit. At the beginning of the orbit change, an external force F must be ignited (the size and direction must be continuously controlled). The balance of state a must be broken first, and the satellite continues to be affected by the external force (the size and direction must be controlled). The acceleration is generated to change to state b. When reaching state b, the external force must be removed or the resultant external force should be kept at zero, and the operation of state b must be maintained. Breaking the balance of state a is a prerequisite for changing trajectory to state b.

When riding a bicycle, first press the pedals hard to accelerate forward with the help of the friction generated, and continue riding for a certain distance when reaching the predetermined speed V1 (midway 28 people sitting on the back seat of the large bicycle get off The bicycle) then performs the movement of state 3 around a center point w, and then changes from state 3 to state 5. During the riding process, the rider and the bicycle cannot tip over. The entire control process and control conditions are the same as those for satellite launch and orbit change (the support force of the ground against the bicycle and the pressure of the bicycle on the ground are equal in magnitude and opposite in direction, and the resultant force is zero, no acceleration and torque are generated, and are ignored). The calculation formulas and data are also Universal. The difference is that the centripetal acceleration of the circular motion when riding a bicycle is generated by a component of gravity by tilting the cyclist's body and forming an angle between the bicycle and the ground plane. It is ultimately controlled subjectively by the cyclist (it can be reasoned, observed and observable). Repeated verification), the change process of the angle between the cyclist's body and the bicycle and the ground plane as the radius and speed changes meets the requirements of cybernetics (if it does not meet the requirements, it will fall, or it will fail to change the track). It is absolutely correct to refer to satellite launch technology and combine it with basic science to conduct in-depth research on human behavior and psychological activity patterns during cycling.

Cycling behavior can be defined as the cyclist controlling body movements through subjective consciousness, and then indirectly controlling the friction force on the speed, balance, and direction of the bicycle through body movements to ensure that the bicycle does not tip over at a certain level while riding. The controlled behavioral process of taking a cyclist to the destination at a speed.

High school physics question, when the bus accelerates forward at 9.8 meters/second^2, use a 50 cm long rope to hang a small iron ball on the roof of the bus (can be regarded as a simple acceleration When balancing, each angle between the rope backward and the roof corresponds to a certain acceleration, and the rope can never reach an absolute level. The rope will break when the acceleration increases to a certain level. These are all based on basic knowledge of physics. You can refer to physics textbooks to decide). At what angle can the small iron ball remain stable when the rope is held backwards and the roof of the car? The answer is an angle of 45 degrees. The small iron ball is a stable balance system that can automatically restore its balance when disturbed by external forces. At the same time, passengers standing in the carriage without holding on to the handrails or relying on any support still need to lean forward 45 It is an unstable balance. When it deviates from the balance, it cannot automatically restore the equilibrium state. It must rely on external force to restore the equilibrium state. In life, when riding a human and riding a unicycle, it accelerates forward at 9.8 meters/second^2. When driving, at what angle must the cyclist and the human-powered unicycle keep forward and to the ground so that the cyclist and the human-powered unicycle can remain stable? The answer is also an angle of 45 degrees (corresponding to the operating instructions and actual operation of the electric unicycle. The answer is derived from the basic knowledge of the physics textbook. If verified by experiments, it is 100% consistent).

The same question is, when riding a bicycle in a circle with a centripetal acceleration of 9.8 meters/second^2, what angle must the cyclist and the bicycle maintain toward the center of the circle and the ground so that the cyclist and the bicycle can remain stable left and right without tipping over? , the answer is also an angle of 45 degrees. When the centripetal acceleration increases while riding, the angle between the rider and the bicycle and the ground in the center direction of the circle must simultaneously become smaller (such as Marquis' extreme bend when a motorcycle turns at high speed). As the centripetal acceleration in the line becomes smaller (that is, the radius becomes larger or the speed becomes smaller), the angle between the cyclist and the bicycle and the ground in the center direction of the circle must also become larger (a dynamic value). At equilibrium, the gravitational equivalent force generated by the accelerated motion and The direction of the resultant force of gravity passes through the fulcrum of the two wheels of the bicycle (the direction of the gravitational equivalent force and the resultant force of gravity generated by the accelerating motion of the human-powered unicycle when it is balanced passes through the fulcrum of the wheel of the human-powered unicycle on the ground, and the equivalent force of gravity and the resultant force of gravity generated by the accelerating motion of the human-powered tricycle When the direction passes through the plane formed by the fulcrum of the three wheels of the human-powered tricycle on the ground, it is balanced. When the direction of the gravitational equivalent force and the resultant force of gravity generated by the accelerated movement of the human-powered tricycle passes through the line connecting the rear left or rear right wheel of the human-powered tricycle and the front wheel. The tricycle becomes a two-wheeled bicycle (which often happens when the army is training on three wheels). The human-powered tricycle becomes a balance car when the direction of the gravitational equivalent force generated by the accelerated movement and the direction of the resultant force of gravity pass through the connection between the two wheels behind the human-powered tricycle. The human-powered tricycle When the direction of the gravitational equivalent force and the resultant force of gravity generated by the accelerated motion passes through the fulcrum of the rear left or rear right wheel of the human tricycle (the wheels must have braking and driving functions), the centripetal acceleration at equilibrium is related to the relationship between the rider and the bicycle. The angle between the ground and the center of the circle is the only corresponding relationship. The cyclist and bicycle system is an unstable balance system. If it is disturbed by an external force, it cannot automatically restore the equilibrium state. If the equilibrium state is lost, a strong force must be used to restore the balance (force is the only factor that changes the state of an object) (discussed in this article This is the case on a standard asphalt road. It is impossible to complete the turning, acceleration, and deceleration processes on a completely frictionless surface). If the angle is not maintained correctly, a moment will be generated and tilt will occur. It cannot be recovered unless it is corrected in time. equilibrium state. When actually turning a bicycle, the radius and centripetal acceleration change within a certain range. If the angle size or the start and end time of the angle tilt are incorrect for the rider, a moment will be generated and the bike will tilt (can be verified repeatedly). When riding a bicycle, the centripetal acceleration changes dynamically within a certain range. According to the principles of physics and cybernetics, during the entire successful riding process, the rider must correctly perceive, judge correctly, and complete the control behavior correctly (in the initial learning Control failures often occur when riding a bicycle, but the consequences are not serious and people do not pay attention to them).

First, the gyroscopic effect. When the front wheel of a bicycle rotates, inertia and centrifugal force will help it maintain balance, just like when a top is pumped, the top will maintain the inertia of the direction of rotation.

Theoretically, the gyroscopic effect can affect the maintenance of balance while riding a bicycle. The existence of gyroscopic effect when riding is theoretically only helpful for maintaining balance, but it is not conducive to breaking the balance, especially when turning. When turning, the direction of the rotation axis of the front and rear wheels will change, but in practice it has little effect.

Second, the centrifugal force effect. When the bicycle tilts to one side, the rider also turns the front wheel to the same side, and the bicycle moves along the circumference of the tilted side. At this time, the centrifugal force is directed toward the outside of the circle, and the bicycle will be righted. And the faster the bicycle is, the greater the centrifugal force and inertia are, making it easier to control. We sometimes see people letting go of their hands when riding a bicycle, which is based on this principle.

In actual bicycle riding, when the cyclist turns the front wheel to one side (novices will do this when learning), the bicycle will make a circular motion. At this time, the centrifugal force is directed toward the outside of the circle, which will break the balance of the bicycle and cause it to tip over (this phenomenon will occur when novices are learning). In order to keep the bicycle from tipping when turning, the cyclist needs to take measures in advance (without taking measures in advance, not tipping would violate the laws of physics).

Third, the caster effect. When a moving bicycle tilts, the front wheel will automatically deflect to the tilted side, and the bicycle will automatically right itself by the centrifugal force of the deflection.

The inertial force of a moving bicycle (centrifugal force is also an inertial force) has the effect of maintaining the original state of the object, which is an inherent characteristic of the inertial force. The tendency of the inertial force to maintain the original state of motion during riding is related to the tendency of the bicycle to maintain its original state of motion. A Walker’s cycling goals cannot always be the same. The momentum of a system without external forces is conserved. To achieve the predetermined riding goal for a moving bicycle (human-powered unicycle), the rider (or AI intelligent system) can only respond to external forces (which cannot be random or fixed. It is actually calculated based on the imbalance or the riding goal). The dynamic value, the process follows the principles of cybernetics) and the riding goal can be achieved only if it is successfully controlled.

The analysis of the caster effect is better with the top view of the following figure. When the bicycle is running straight at a constant speed in a balanced state, the intersection point P of the extension line of the steering handle rotation axis and the ground, the front tire landing point Q, the rider and the bicycle*** The center of gravity G and the rear tire landing point W are on the same plane and are vertical. When driving to an intersection and it is necessary to turn left, assume that the front wheel turns 30 degrees to the left.

The intersection point P of the extension line of the steering handle rotation axis and the ground, the rider and the bicycle have the same center of gravity G, the rear tire landing point W is still on the same plane and is a vertical plane, the front tire landing point Q is on the right of the vertical plane, and the center of gravity G is on the ground The vertical point is on the left side of the line connecting the front tire landing point Q and the rear tire landing point W. At this time, the gravity component will produce a left rotation moment, which is recorded as M1, and the caster effect shows the effect of breaking the balance (in practice, breaking the balance is necessary to achieve the riding goal. If the goal of maintaining balance is always maintained, steering, acceleration, and deceleration cannot be achieved. It is impossible to complete the riding goal). At this time, if you want to maintain balance, you need to turn the front wheel to the left to return to 0 degrees, which is inconsistent with the actual steering demand (all changes in the motion state of an object need to start from breaking the previous state, and the subjective goals of movement are different. The breaking behavior must be different, such as turning left or right). This left rotation moment is a function of the height above the ground of the same center of gravity G between the rider and the bicycle, the length of the line connecting the front tire landing point Q and the rear tire landing point W, the total mass of the rider and the bicycle, and the change angle of the front wheel ( is not a function of speed, i.e. size is not affected by changes in speed). In actual riding, the center of gravity G, which is the same as the cyclist and the bicycle, will change slightly with the adjustment of the cyclist's posture, which is currently ignored. In actual normal riding (in practice, when you first learn to ride a bicycle, you will fall down due to the rotational moment generated by the gravity component when turning at a slow speed. If the speed is too fast, you will fall down due to the rotational moment generated by the centrifugal force component. Not noticed and ignored) When turning left, there is no left rotation moment M1 due to the gravity component and the vehicle falls down. It means that the left rotation moment M1 generated by the gravity component when turning left must be controlled or offset. Anyway, if the left rotation moment M1 generated by the gravity component when turning left is not controlled or offset and does not fall down, then Violates the laws of physics.

When turning left, the gravity component (less than the total gravity of the cyclist and the bicycle) produces a left rotation moment M1 (leaning the body further to the left can increase M1), which is caused by the centrifugal force component to produce a right rotation moment M2 Offset, but the centrifugal force is a function of the total mass of the rider and the bicycle, the angle at which the front wheel changes (i.e., the turning radius), and the square of the speed. The speed of bicycles and motorcycles can range from nearly 0 to 80 kilometers per hour, and the centrifugal force varies widely. Theoretically, the probability that M2 and M1 are in opposite directions and equal in size without control is very low. The successful riding process in practical riding is proof of the successful control process of M2 and M1. The analysis of the entire process requires the use of cybernetic principles. and physics mechanics. (Centrifugal force is an inertial force, a virtual force that does not actually exist. The force that actually generates the rightward rotation moment M2 is the result of the simultaneous action of the friction force on the ground and the ground support force.

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