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The Movement of Bicycles

The Movement of Bicycles

There are many physics stories in the bicycle. For example, the motion of a bicycle can be easily understood using Sir Isaac Newton’s laws. A bicycle moves because its rear wheels are turned. As the rider exerts pedal force F, which creates a torque, the chain wheel or chainring rotates with angular velocity ω0, but the front sprocket and rear sprocket. Connected by a chain is like a pulley system.

Torque is created on the front disc, so it can be transmitted to the rear wheel. This causes the rear wheel to spin with angular velocity ω and angular acceleration α, which results in the bicycle having linear acceleration a according to the following equation.

a = FpR
IG

From this equation it is clear that the acceleration of bicycle a is directly proportional to the rider’s recoil F. The greater the pedal force, the greater the acceleration. This can be seen from the fact that some cyclists as they are starting or about to cross the finish line will get out of the saddle. in order to exert a lot of kicking force It is also directly proportional to the length of the crank arm p, which is generally limited to about 16 – 17.75 centimeters, because it has to match the rider’s leg length. Can sit comfortably on the saddle. And finally, it is directly proportional to the radius of the R wheels. As you can see, racing bikes have larger wheels with a diameter of 29 inches, while mountain bikes have larger wheels. It will have smaller wheels, typically 26 inches in diameter (because mobility is more important).

In addition, it is inversely proportional to the moment of inertia I of the bicycle wheel. which is approximately equal between the front wheel and the rear wheel It can be seen that the wheels of a flat race car have a slimmer shape than normal bicycle wheels. and will be made with lightweight materials such as carbon fiber. This is because I want to reduce the I value as much as possible. In addition to reducing the friction between the wheels and the road surface and reducing air resistance. This is because the I value of any object depends on its mass. It is also inversely proportional to the gear ratio (G), which is the ratio d1/d2, where d1 and d2 are the diameters of the front and rear sprockets, respectively.

The smaller the gear ratio, the less d1 or d2 increases, or both. Two cases at the same time, the higher the acceleration value, the gear ratio may also be calculated from the ratio of the number of teeth on the front crank to the number of teeth on the rear sprocket. because the size of the teeth are all the same and the circumference of any circle is equal to (Diameter X π) A gear with a longer circumference has a greater number of teeth. is a straightforward proportion.

If you look at the academic facts just mentioned here. Commonly used bicycles tend to have a small gear ratio, but why in practice this is not the case?

This is because there is another fact according to the equation that must be taken into account, namely

v = RGω0

Here v is the (linear) speed of the bicycle (in m/s), more or less depends on the wheel radius (R) corresponding to the gear ratio (G), which This can be seen as the opposite of the linear acceleration of the bicycle (Equation 1) and to the angular velocity of the front crank (ω0), which is measured in radians/s, or rev/s, because 2π radians is equal to One complete rotation But the front crank rotation is directly related to the rider’s “cadence”. If you want to achieve the desired speed which is used around the legs to be comfortable for himself You must know how to adjust the gear ratio that is suitable for yourself and the road conditions.

By considering both performance and riding comfort. Therefore, the bicycle must be able to adjust the gear ratio.

The answer to this is the use of gears. Professional cyclists train not only on muscle strength, but also on the strength of their muscles. But will have to practice how to adjust the gear to suit the terrain as well. so that the circumference of the legs is the most suitable for themselves On average, long-distance riders use a cadence of 80 – 120 revs/minute (Lance Armstrong uses a cadence of 120 revs/minute).

If a cyclist using a bicycle with a transmission consisting of a front 3 crankset and an 8 rear sprocket [2] is riding on a flat road, With the desired speed and a certain cadence that was comfortable for him, assuming (extremely to make the numbers clear) that at that time he was using 3/8 gears, using the largest front crank. (with a total of 42 teeth) coupled with the smallest rear sprocket (There are 11 teeth in total), so gear ratio = 42 / 11 = 3.8, which is the most valuable for this car’s transmission. (Consistent with Equation 2). The cyclist will immediately recognize that it is increasingly difficult to try to turn the front crank each lap. Because while riding uphill, there is an increase in gravity as a counterweight. (Unlike when riding horizontally where the gravitational force of the earth is perpendicular to the direction of movement of the car Therefore, it is not a counterweight or an extra body) The more steep, the more difficult it causes the legs to fall by default.

Let’s evaluate how difficult it is for a cyclist to continue riding uphill in 3/8 gears. A gear ratio = 3.8 means that for one revolution of the front crank, the rear wheel will spin approximately 4 laps, that is, if a bicycle wheel has a diameter of 29 inches, 4 turns of the rear wheel will move the bicycle around 9 meters, which if going uphill means that the rider has to work very hard to pedal the discs. The front turns 1 turn in order to propel the car up a hill for a distance of 9 meters. The knees won’t be able to fight.

The solution is to move to a lower gear. Using lower gears means lowering the gear ratio, for example, assuming a 1/1 gear shift, that is, using the smallest front crank. (total 22 teeth) with the largest rear sprocket (There are 34 teeth in total), so the gear ratio = 22 / 34 = 0.65, which means that with one revolution of the front crank, the rear wheel will only turn a little more than half a turn. That is, for a wheel with a diameter of 29 inches, 2/3 turns of the rear wheel will allow the bike to travel only 1.5 meters, and the rider has to do much less work since the effort is required to propel the bike only uphill. Only 1.5 meters (per 1 lap of cycling) is said to be much more comfortable.