PHYSICS OF MOUNTAIN BIKING
The purpose of this web page is to provide you, the reader, with a basic knowledge of the physics behind the sport of mountain biking. This sport is enjoyed by millions of people throughout the year, and is attracting more and more people everyday. Physics plays a vital role in this sport and without it; mountain biking would have no challenges and would cease to exist. The concept of mountain biking is simple. You take your bike riding skills that you gained when you were five years old, and ride trails found off the beaten path, away from pavement and the city, and ride until your heart is content. From this notion of riding a bike, an Olympic sport has evolved and many people have found meaning and joy in their lives.
GRAVITY
Gravity affects every aspect of our lives, and it plays a big role in mountain biking, especially when it come to hills. Whenever you pedal up a hill, you have to oppose the force of gravity that is working against you. The opposite is true however for riding down a hill, in this case gravity is working to your advantage and is pulling you down the hill. So when you bike down hills, you can accelerate due to your own power as well as accelerate due to the force of gravity.
Lets take a more in-depth look at this force called gravity! The force of gravity exerts a constant acceleration of 9.81 m/sec2 towards the center of the earth. While gravity is being exerted downward, a normal force is being exerted on the rider opposing gravity. This normal force acts perpendicular to the earth’s surface, and for our purposes the trail a biker is riding. So for example, if a biker were on a flat surface, both gravity and the normal force would be acting upon the biker, but in opposing directions, thereby canceling each other out and can be ignored. However, this combination of gravity and the normal force, is what makes climbing hills difficult and riding down hills a breeze.
FRICTION
In mountain biking, friction is encountered on the bike in a few very important areas. These are the wheel bearings, drivetrain, and brakes. The wheel bearings if properly maintained should produce a very inefficient amount of friction, and it usually goes unnoticed. The drivetrain on a mountain bike consists of the chain, gears, and shifting mechanisms, and it produces about a 1.5% efficiency drop. This performance from the drivetrain can only be achieved if the proper care is given to the different parts involved and it is regularly is lubricated. Finally we come to the biggest area of friction found on the mountain bike, and this is the brakes. In this case, friction is our friend, and actually prevents accidents and deaths when riding in the mountains. There are several types of brakes on the market for mountain bikes, but they all have one purpose, and that is to slow the bike down using friction.
Rolling Resistance
Rolling resistance is a result of the compression of the wheel, suspension system if you have it, and or the ground. Rolling resistance on a bicycle is determined by how much energy is required to move over the trail. A bike with no suspension is ‘unsprung’ and must be lifted over any imperfections found on the trail in order to move forward. These imperfections vary from rocks, tree roots, divots in the trail, and many more obstructions that are found on our path. On average, a bike and its rider weigh around 175 pounds, so all of this ‘unsprung’ weight must be lifted over these imperfections. With suspension however, the majority of the weight is ‘sprung’ and imperfections are absorbed by the suspension. So in this case with suspension, only the unsuspended portion of the bike (wheel and lower frame) and a small portion the riders weight needs to be lifted, which amounts to a mere 35 pounds. Common sense tells you that it would take a lot less energy to lift 35 pounds versus trying to lift 175 pounds. This helps to explain why most all high-end mountain bikes feature full suspension and why full suspension bikes are easier to ride. And all this time you thought full suspension was just for comfort!
AIR Resistance
Air resistance is a big factor when bike riding, but not so much for mountain biking as it for road biking, therefore I will spend little time describing what it is, but I still feel it is important enough to include on this page. Air resistance is self explanatory in the fact that can be defined for our purposes as the bike and riders resistance to air. To give an example of air resistance, think about driving in your car and placing your hand out the window (this is not advised, but I’m sure we’ve all done it at one time). If you turn the palm of your hand towards the direction your driving, you will fill a much greater force than if you turn your hand palm down towards the ground. What you feel is the affect of air resistance. Wind Resistance can add to air resistance if traveling against the wind, but it can also aid a biker in fighting air resistance, if we happen to be traveling in the direction of the wind, which seems to never happen!
Acceleration & Deceleration
In the sport of mountain biking you experience both acceleration and deceleration. This is what makes this sport so exciting, but it also the reason why you should wear a helmet! Acceleration is defined as a change in velocity divided by a given amount of time. A rider accelerates as he or she exerts energy and starts to pedal, but can also accelerate as he or she rides down a hill, and this acceleration is due to the force of gravity mentioned earlier. During the process of accelerating, the weight of the wheels affects the acceleration process three times as much as the weight of the bike and its rider. So one pound in a wheel feels and behaves more like three bounds. Once the rider eventually coasts to a stop or applies the brakes, he or she experiences a deceleration. This deceleration is what causes the bumps and bruises a mountain biker is bound to get as they ride and eventually crash.
Energy
In the sport of mountain biking, a cyclist possesses two forms of potential energy, potential energy stored in muscles from food and potential energy attained from sitting at the top of a hill. Both of which get transferred into kinetic energy. First lets look at the energy stored in the legs. This energy is transferred to the pedals, which turn the rear wheel, and causes the bike to move. The potential energy stored in the legs is what gets us to the top of inclines, which allow us to experience the second form of potential energy. At the top of an incline, a mountain biker if at rest, possesses only potential energy, and if he is in motion then he also possesses mechanical energy. As the biker rides down the hill his potential energy from the incline is depleting and becoming kinetic energy. At the bottom of the incline his kinetic energy is at its maximum, and the only energy left is the energy stored in his legs.
Forces
m = mass of bike and rider
g = gravitational force
A= acceleration
mu = kinetic friction coefficient
- Inertial Forces = m x A
- Frictional Force = mu x m x g * cos
- Graviational Force = m x g x sin
Gravity is the force that holds the bike to the ground and causes riding up hills challenging and riding down them easy. While gravity is acting straight down on the mountain biker, a normal force is exerted on the biker that opposes gravity. While a bicyclist pedals or rides down a hill, he or she encounters an acceleration, and this is due to either gravity or the potential energy stored in the biker’s muscles. When accelerating from rest, inertia is the biggest force encountered. But once the bike rider gains momentum, this force is no longer the main opposing force. The mass of a mountain biker is dependent upon the weight of the bike and of the individual, and can be easily calculated by multiplying the combined weight of the bike and its rider in kilograms by the gravitational force exerted by the earth. These forces and more are discussed throughout this of this web page.
Bibliography
The Boyertown Institute of Science. Bikeway, 1999. Retrieved April 2, 2003 from World Wide Web:
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Kyle Heenk, The Physics of Cycling, 1998. Retrieved April 2, 2003 from World Wide Web:
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The Physics of Bicycling, Date Unknown. Retrieved March 28, 2003 from World
Wide Web:
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Rolling Resistance, Date Unknown. Retrieved March 28, 2003 from World
Wide Web:
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