Mathematical Exploration
Calculus in Climbing
I have decided this mathematical exploration will center around rock climbing. As I read the list of sample topics handed to me by my teacher, I instantly gravitated to rock climbing. It is a topic I have substantial interest in and a sport I routinely participate in. However the crag is a long away from the classroom, does math really have its place in rock climbing? I needed to decide where math applies in the vertical world. The solution to this question is the Spring Loaded Camming Device (SLCD). Used in rock climbing, this removable piece of protection is placed into a crack and has a unique self-locking property that prevents the “Cam” from being pulled out, especially when holding a fall. SLCD’s are so successful because of the logarithmic spiral or golden ratio they were designed from. The SLCD’s logarithmic shape, allows the device to have the same ratio of pulling force to frictional force. This ratio is completely independent of the size of the crack the cam is placed in or the amount the lobes are extended or retracted. The optimal camming angle is found between 13.5º and 14º.
Before learning why an SLCD works I must first know how it works by asking questions why were they invented? How do they stop a climber from falling? The sport of rock climbing was revolutionized by the invention of the SLCD by Ray Jardine. In the three decades since their invention, they have radically transformed the idea of what climbs can be led safely. As seen above in Figure 1 part A, nothing protects the climber from falling to the ground. In Figure 1 part B, cams placed in the wall as protection will prevent the climber from hitting the ground in the event of a fall.
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...ell and hurricanes allows the cam to keep the same “camming angle” no matter how contracted or expanded it becomes. The outward force distributed by the cam lobes become twice the downward force applied to the cam allowing it to stay locked in place even when climbers falls apply forces ten times their own weight. The SLCD allows me to conclude that there is an extraordinary amount of math in rock climbing.
It would be interesting to compare the SLCD’s created by different companies with varying camming angles. There are many different cam companies that produce a variety of different products. A further exploration could be done to see how the camming angle of a certain device affects its holding power. Are cams with a 13-degree camming angle safer than a 14-degree angle cam as proven in this exploration, or is the difference so slight that it would not matter?
Enhanced Basal Creep - Stress concentrations around the upstream side of an obstacle result in locally high strain rates which causes ice to accelerate around the obstacle. The basal ice continually modifies its shape to allow a continued sliding. This process works best when the obstacle is over 1m in size.
He judged the distance to be about a mile from the lodge to the waterfall, and crept slowly past the spiders. Careful not to make a sound, he trudged only on the dry land whenever he could and had to take off his shoes sometimes to avoid a squelching sound. He almost reached the water when suddenly a spider changed direction and came for him. Losing all sense of sneakiness, he ran to the waterfall and hid behind it. Although he lost the spider, his clothes were drenched and he had lost his shoes during the run. Now that he’s made it to the actual waterfall, it's time to climb. Now as a child Jerry’s dad always made him practice climbing, in case he got trapped somewhere in the mountain and had to climb out. Those punishing practices left blisters and limbs that ached for days, and Jerry hated them. But now, faced with an life-or-death moment he was glad for having them. The only problem was the shoes being missing. The distance vertically from the bottom to the top of the waterfall was about a hundred feet, easily accessible for someone without a fear of heights and good climbing skills. But Jerry had two major liabilities; the absence of shoes and the mossy slippery stones. Then Jerry realized that his strength was waning as the cold of the water seeped into his bones. And so without a second thought, he began to climb. The toes and hands fighting for whatever room they had on the smooth rocks and moss. Jerry was about half way up when disaster struck. It was a particularly smooth section of the rock and when his right foot tried to gain purchase, the left foot slipped, causing Jerry to plummet. The sensation of falling was almost relieving to the exhausting climb, during which he was shivering. Right as he began wondering when the fall was going to end, he landed back first into the bog and slammed his left arm into a small piece of sharp rock. The pain
Skiing is a sport enjoyed by millions of people around the world. The adrenaline rush that skiers get from flying down the slopes is unmatched, but all too often the cause for this rush is overlooked. Physics plays a crucial role in skiing and without it, there would definitely be no skiing. The concept of skiing is simple. You attach a ski to each foot, go to the top of a hill or incline, and slide down, turning side to side. From this basic concept of sliding down an inclined plane, a worldwide sport has evolved. In this paper, I hope you gain a useful knowledge of the vitally important role that physics plays in the sport of downhill skiing.
Fortunately the rider can produce a few forces of their own. Mainly, the rider only has a combination or leg strength and arm strength to counter with. But, there is a lot that a rider can do to overcome these forces through body positioning.
So Abrams introduced me to an article about a man who changed the film world forever. This man’s name is Garrett Brown and he invented the Steadicam, the Skycam, Flycam, and the Divecam. Now you maybe wondering what are these things? Well, let me give you a little history lesson. Back then, cameras were attached to a chair and the chair would travel on a rail or the camera would move around on a dollie where it was attached to a platform. However, this would take a very long time to build and of course, cost a lot. At the same time, handheld cameras would be all over the place. Garrett thought there has to be a better way to be able to film and move at the same time, so he invented the Steadicam. The Steadicam allows cameramen to follow
In the making of the film “Gattaca”, the director Andrew Niccole has used the film technique: camera angles to represent the theme of the film. The definition of camera angles is the position of the camera to allow the viewer to understand the relationships between the characters. I found this definition by searching on the internet and comparing the definition in the dictionary.
I always providing better education to the patients and their families to help reduce the incidence of fall in the hospitals and in home also. We had a nursing meeting in our facility there we discussed about video monitoring, it allows us to keep patients safe than ever before. And we can watch six patients at a time on the monitor, we were able to provide close supervision to patients. We will locate our video monitoring station close to our patients’ rooms, so that we could react to any sudden movements or behavior changes in an instant. But I am still searching more solution to prevent future fall for my patient
People who work at the site highlight Niagara Falls in variety of colours at night for visitors, and make it more gorgeous and better to see at night. Niagara Falls is not only for people to look at. People can also take part in various forms of recreation such as boating, bird-watching, swimming, and fishing. Some people have even tried to walk on a tight-rope across Niagara Falls from Canada to the United States, or climb the frozen Niagara Falls in winter. Nik Wallenda and Will Gadd were two people who have done that. Nik Wallenda was a brave man who crossed Niagara Falls with just a tight-rope and a balancing bar. Will Gadd was a ice climber whose been climbing for 30 years. He was the first person to scale the ice wall at Horseshoe Falls. He trained 6-8 months just to climb this huge waterfall. Niagara Falls once again came to the consciousness of people around the world due to these
Athletes can use a measuring tape, pigeon step or run from the board in the opposite direction. The reason behind these steps is that athletes will to develop and maintain maximum speed toward the board. The athlete’s first 4-6 step should be powerful while driving and acceleration with the same momentum into the transition phase where athletes are ready for the second stage. According to a presentation in Atlantic City 2002, Jim Giroux who has a USATF Level II Certified in Jumps, who also coaches at the UMASS for 12 years said ‘’The slower your athletes are, the faster they will get to top speed. Your faster athletes will take longer to achieve maximum speed’’. The remaining numbers of steps are executed at maximum controllable speed. Maintenance of this rate and the upright posture at the end of the approach is crucial to
Anchor systems are vital for a climber and whether or not an anchor is secure can mean the difference between life or death for the climber. Good anchors are not difficult to set up and all they require is a little experience in setting up and some common sense. We will anaylze the forces generated in two different types of anchor systems. Another factor in the forces generated in an anchor system that can be applied to both systems is that of the angles involved in the system. The greater the angle at the bottom of the anchor system, where the rope attaches to the anchor, the greater the force that is exerted on each anchor point. The table below reflects this.
Francois Dussenne from Belgium introduced the Machard Tresse, an unusual climbing hitch, to all those present at the first European Tree Climbing Competition. He had used the climbing hitch in 1992 to help him win his second French Championship. Everyone who had a chance to try the Machard tresse agreed that it was more complex than the other climbing hitches. There was an equal sense of intrigue and caution among us.
One personal challenge that I have faced is overcoming my fear of lead climbing. One of my many hobbies is rock climbing. When I got on the intermediate team “Dragons” I had to learn how to lead climb. Lead climbing is when a lead climber climbs while clipping into quickdraws every 5 feet. Quick draws are a type of protection for falling. Since the climber is only protected from falling about every 5 feet, falls can be as much as 15 feet. Like most people, free-falling 15 feet and hitting a wall, made me terrified, so I had to practice. The first time I lead, I took a practice fall, only a few feet above my quick draw. I fell about 5 feet and had my belayer lower me to the ground. When I got off I was shaking from fear. I did this a few more
The Gecko effect- when strong adhesion is needed (e.g., adhesive tapes) or for reversible adhesion (e.g., climbing robot);
There are four different descriptions of an angle of a camera based on the frame image: a bird's eye angle, a high angle, an eye level angle, and a slanted angle. The bird's eye camera angle and the slanted angle will most likely be the most common camera angle descriptions for each frame shot. A birds eye camera angle is an angle of the action directly overhead and looks down slightly upon the objects/subjects and the action. An eye level camera angle is a camera angle by which the film camera is located high above the objects/subjects and the action. It differs from the bird's eye camera angle in the fact that in a high angle, the camera is pointed directly down upon the actions and objects. An eye level camera angle, most commonly known as the most basic camera angle, is a camera angle in which the film camera is positioned at the same height as if a human were observing the action in person. The shot is taken five to six feet above ground level, which is approximately the average height of a human. The last camera angle is the slanted, or oblique, angle. This angle refers to an angle in which the film camera is not placed at a 90 degree angle horizontal to the ground and looks tilted. Although this angle can look unique and awkward at times, this angle more often than not creates a better perspective for
Indoor rock climbing gyms offer a range of wall angles and artificial holds to simulate outdoor rock climbing. Most of the gyms have rock-like textured walls and holds as varied and unique as natural rock. The majority of the climbs are top-rope routes where the rope is already attached to the top of the route before you climb. They are the safest, most controlled way to ascend. Many gyms also include lead routes which are similar to "sport climbs" because the leader puts the rope through attached protection points as they climb. Lead climbs suit more advanced climbers who have passed a lead test at the gym. Most indoor rock climbing gyms also offer bouldering walls and caves. These are short routes, often very steep, that are low enough to the ground that a harness and rope aren't required. Bouldering moves require good strength and power. Many climbers use them to train difficult moves, and to develop skill and strength.