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How many slopes a bicycle can climb, physicists still have a few
How many slopes can you climb?
This is a topic that is particularly prone to enthusiasm for cows, coupled with the fact that people commonly confuse two different types of slope units, all of which make this topic controversial.
Today, we're working with Rhett Allen, a professor of physics at the University of Louisiana at Southeastern United States, to find out what the maximum number of steps a bicycle can climb.
The first is to look at the definition of slope, which is the degree of steepness of surface units. Usually, the ratio of vertical height h to horizontal distance l is called slope i. Percentages and degrees are expressions of slopes. The calculation formula of percentage is Vertical height/horizontal distance* 100%, degrees are tanα=vertical height/horizontal distance.
For example,
The maximum slope of the highway is 5%, 3°;
The maximum slope of parking garage is 15%, 8°;
The climbing ability of a car is 36% and 20°. Some off-road vehicles can climb up to 60% of the slope, which is almost 30°. This is also the gradient of stairs in ordinary buildings;
The 100% slope is 45°, which is almost the feeling of a cliff. Feel the picture of a car.
How steep the slope can climb does not depend on power
"If you don't care about the speed of climbing, such as a few tenths of a second, then you can climb constantly with very little friction. It's like if you use a pulley to lift a heavy object, you really only need a small electric motor. â€
Rhett Allain is a professor of physics at the University of Louisiana in the Southeast, and he has his own physics science column in the Wired magazine.
In theory, as long as a suitable gear ratio is found, a small amount of power is enough to maintain the climb.
However, the reality is relentless. A small gear ratio means that the driver must turn his legs franticly and maintain a very high cadence. If he is not careful, he will crash because it is too slow.
Combined with the actual situation, the speed of climbing can not be too slow, so Professor Alan set the minimum speed of climbing as the walking speed, 2 meters per second. He then used extremely professional physics to perform extremely complex calculations. He concluded that the 40% slope is the maximum slope that the bike can challenge. At this time, 422 watts of work must be done. The power that a professional cyclist can almost reach. value.
If you also want to drill a horn like me, you want to see if the slope reaches, no matter how much power we output, and how the bike's transmission ratio is, we can no longer go up one meter. A keyword.
The only thing you can't pass is the center of gravity
One common sense is that when the slope is steep to a certain degree, we will regress.
Specifically, when the intersection of the cyclist's vertical center line of gravity with the ground is not between the contact points of the two wheels and the ground, we will regress.
Where is the cyclist's center of gravity?
Keith Bontrager, an elite Bikefitting technician, said that this is a very difficult concept to explain, but he usually sets the center of gravity when the side crank is at 9 o'clock, 3 to 4 cm behind the pedal.
Now, in order to understand the point where the cyclist regresses, we must do a trigonometric calculation: Tilt angle = 90° - [Tan-1 (the height of the center of gravity 水平 the horizontal distance from the location of the rear wheel to the center of gravity)].
According to this formula, we obtained a critical point of 25.8°, that is, a 48% slope. Of course, this is the case where the rider has been sitting in the seat during the climb.
When the angle becomes steep, we all leave the cushion and shake two steps.
If the center of gravity of the cradles is recalculated in this standing position, a new critical point of 41 degrees, or 86.9%, will be obtained. It seems that the cyclist can even conquer every cliff that makes the off-road jeep shame.
However, in this group of calculations, one factor is significantly less considered, the friction between the tire and the ground. Those who often drive know that when the slope is too steep, the tires can slip, and the bicycle is no exception.
The first disappointment is always tire friction
Hristian Wurmbäck is the product manager of the company's brand tires. When he bluntly climbed the steep slope, the tire's friction was the first to fail.
"The friction coefficient of this complex compound like rubber, you really can't tell forever, it's dry, it's wet, how dry it is, how moist it is...you'll never get that exact can be used for All scene data."
“If you have to say it, from the asphalt floor to the wet concrete road surface, the tire's friction coefficient ranges from 0.3 to 0.9.â€
Prof. Alan optimistically set the coefficient of friction to 0.8. After putting in his complicated formula, the tire's friction can only support climbing to 38.7°, that is, about 80% of the gradient.
However, the estimate of 0.8 is always too optimistic. Considering that 30% of the ramps are constructed of concrete instead of tarmac roads, the friction coefficient of rubber during exercise will drop to 0.6. The slope obtained is about 60%.
When you are confident that you have enough power, a proper size ratio, and an extraordinary center of gravity control, you will still be defeated by a 60% steep slope because your tyres will sell you unless you have a bottle of 502 in your cycling suit.
The good news is that the UCI International Self-Association defines the HC Grade Climb (short for French hors catégorie, meaning "outside the grade", indicating the most difficult climb) and just over 10 kilometers of climbing with an average slope of 7.5%. .
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