The quintessential Summer Olympic event has yet again come and gone, and as was the case in Beijing in 2008, Usain Bolt of Jamaica has captured the gold medal in the 100 m dash in convincing style. True, fellow countryman Yohan Blake has the ability to run with Bolt, and a few others in the field can compete with him on their best day, but for half a decade, Usain Bolt has held the coveted title of 'world's fastest man'. The question I would like to address is "Why?"
Let us begin with a quick kinematic assessment of the 100 m dash, using Bolt's 2009 World Record setting run in Berlin as an example. Starting from rest, Bolt ran 100 m in 9.58 seconds - a feat that will likely not be matched for a long while. Bolt's average speed (distance over time) on this occasion was 10.44 m/s. He reached his top speed at around the 65 m mark of about 12.27 m/s. That is 44 km/hr, which carries a hefty fine for a car in a school zone.
The race can be separated into two kinematic phases, which follow a brief reaction time (time between the start of race and the start of motion) of about 0.15 seconds. The first phase of acceleration is when the runners go from rest to their coasting speed; this is usually accomplished in the first 30 m. Bolt reaches his 12 m/s stride at about the 30 meter mark, though his acceleration in doing so is not constant.
The second phase is one of approximately uniform motion. This is where Bolt excels the most. He can just about maintain his top speed for the remaining 70 m. Typically, sprinters begin to slow somewhat over the last 30 m.
To determine what allows Bolt to achieve such incredible kinematics, we need to examine the kinetics involved in this situation. We first need to address the surprisingly complex question, "What is running?"
In engineering terms, a human being is a machine - that is, an interconnected system of rigid bodies and joints. Running is a particular sequence of motion of these joints that allows the body to lunge from one foot to the next. From a mechanics standpoint, it is helpful to think of sprinting as a series of jumps. The body accelerates based on the contact force between each shoe sole and the ground. The ground exerts a horizontal static friction force as well as a vertical reaction force, which conspire to propel the body diagonally with each stride.
Running is a method of transport unlike any man-made system. A car has wheels that are fastened to an axle, which is turned by a motor. A car accelerates quickest if its motor has a high power output and the total mass of the car is low. For a sprinter, power to mass ratio is also the key parameter. Power means the ability to exert a high force at a high velocity. This is where the analogies to a car end. The physics of rolling is nothing like that of running. Running is more like kayaking: though the medium is different, it is simply a series of impulses between a body and a medium.
If you watch the 100 m final at the London Games, you will notice that Bolt's reaction time is not the greatest, and that his acceleration phase is only average. Blake has an advantage over Bolt in the acceleration portion as he is highly muscled, leading to greater power. It is Bolt's lean muscle and long legs (he is 6'5") that give him a decided edge in the cruising portion of the race.
One other key though subtle feature when it comes to running is the angle of attack. What is the first thing you do when you want to go from standing to running? Try it. Before your legs do anything, you use your hips to bow your head. That's right, you lean forward in order to run. Let us treat this as a rigid body motion problem.
We have established that when running, the ground exerts forward thrusts onto the bottoms of our feet. If we were standing entirely upright, such a force would cause us to lean back (positive angular acceleration due to positive applied torque). To avoid this, we tilt our body forward slightly. By shifting our center of mass slightly ahead of our contact with the surface, the gravitational force causes a negative torque that counteracts the positive one due to our propulsion. As a result, we can maintain our angle of attack.
A simple free body diagram of a sprinter shows that the greater the contact force, the greater the necessary gravitational torque. This means, essentially, that faster runners can maintain a greater angle of attack. Bolt's inclination when running is ever so slightly greater than that of his competitors, and that is why his cruise phase is so unbelievable.
Usain Bolt is a remarkable athlete who for years has left fellow sprinters in the dust. It is easy to forget that his success is owed not so much to Gatorade, but rather to his superior rigid body motion.
Learning science is one of the hardest things a person can do. It often forces us to shift the way in which we see the world. The process is demanding, but is ultimately rewarding, because it allows us to interact with nature in a deeper, more meaningful way. If we continue down this road, we become empowered with the means to shape our environment - we become engineers.
Tuesday, August 7, 2012
What Makes Usain Bolt so Fast?
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