Basic Concept Of Parkour

I am currently bored, so I'd thought that I'd take an hour of my time to write about two of my favorite hobbies.

Parkour’s idea is simply based on how efficient can you move around the obstacles in your path in order to get from point A to point B the quickest.
The basic movements in parkour will be analyzed with the laws of physics. The movements are the basic Passe muraille (pop vault), Saut de chat (Kong vault), and Atterrissage (landing) that goes hand in hand with roulade (roll).

If you are a beginner, the way of parkour starts with your posture. A right posture is necessary in order to prevent injuries. With a slumping posture, whether it be when standing running, or jumping, will tend to shift the center of gravity forward or backward causing a less stable equilibrium causing abnormal muscle strain.

A slumping posture will produce less stable balance, and the balls of the feet must exert more torque to maintain the balance, and more muscle tension is require, especially in the back muscle, to keep the unequal torques balanced.

Passe Muraille, commonly known as wall hop and it is a technique mainly used to overcome an obstacle such as a wall or a gate that is about 3/4th your height. In America, this move is commonly referred to as a vault, and vaults come in different techniques, however, the basic vault will be analyzed. In a basic vault, named speed vault, one jumps and kicks off last with the left leg and then kicking the right leg up in the air to give the whole body momentum when approaching a tall object. The jump must be made before the left hand touches the top of the object, both feet have left the ground. Then as soon as the hand touches on top of the object, the jump would give the body enough momentum to pass over the wall. The main purpose of the hand is to give stabilization; however, you can push of slightly with the hand for an extra boost of velocity. Then the question that comes to mind is: what is the vertical velocity required for an average human, say take my height 6.0 to jump a wall that is about 4/5th the person’s height, so h ~ 4.4 ft (to play it safe). Newton’s first, second, and third law comes in to play. F= ma, to every action there is a reaction, and an object at rest tend to remain at rest and vice versa. Now to calculate the trajectory, we start with a basic kinematic equations.

The third equation is used and Since v=0 at the peak of the jump, and, a = g =-9.81, so v^2=2|g|h. Using the kinematics, the y-component of the velocity to pass a 4.4 ft wall must be 16.8 ft/s or 11.5mph. A value that is short of the average sprint velocity, horizontally speaking, of 15 mph. This is asking too much from the body. However, the vertical velocity mustn’t be as that high when placing the hand on top of the obstacle after the initial jump to propel the lower leg portion of the body to the same level as the obstacle by the workings of the many abdomen muscles. This is a classic torque problem consisting of T=r*F, which tells that decrease the radius will decrease the toque. So when vaulting, remember to keep the knees slightly bent to decrease the radius from the pivot point of the center of mass.
The next to ask then is how much force must a leg provide for the vault? This concept is related with jumping, that is made possible by Newton’s third law which state that if a large force is exerted on the ground, the ground will push back with a similar force. So taking a mass, say 170 lb or 77.1 kg, then on earth, to find the acceleration, a=v/t, and say that the person spends ¼ second pushing on the ground using my leg muscles, then the acceleration is (16.8ft/s ÷ 1/4s) = 67.3ft/s^2 =20.5 m/s^2. That is an initial acceleration of 2.1*g. These values are reasonable to overcome for a healthy, fit body. Just as the left foot was used last to kick off, use the left foot as the first landing foot to keep the whole body upright when landing, and the direction of the entrance to the vault will not be shifted. Coming down at one foot at a time is beneficial if you want to keep the flow of the movement and continue running.
A little more challenging technique is the Saut de chat commonly referred to as the Kong vault, referring to the movement similar to that of an ape leaping. This move is commonly used to gain distances over relatively large barriers, such as a car, a picnic table, or a short gradient change faced as an obstacle. The Kong is similar to the pop vault, however when approaching an obstacle at full running speed, you begin to take large slides when nearing the obstacle, and then at close proximity of the obstacle is reached, one jumps with both feet at angle to make the body horizontal with the obstacle. In that split second of when gravity is bringing your body down, the hands must be placed without reaching too forward on to the end of the obstacle, and at that split second tuck in the knees to avoid clipping the foot on the obstacle. Then push of with the hands while extending the legs to land, and continue running. The hand technique will be hard for beginners because there will be less of a continued momentum if the velocity is abruptly changed by the slap of the hand on the obstacle, rather imagine grabbing the obstacle and heaving it underneath you. To pass greater distances, the experienced with upper core strength can ‘hop’ by a next ‘touch’ with the hand to a further distance, and ride the momentum on, and then end the technique as a normal Kong vault. This technique allows for a larger distance to be covered by projecting the body and using the arm sockets as pivots that bring the whole body forward, partially due to the angular momentum. After the pivot of the arm sockets, the horizontal body to its vertical landing position. The body is send over the obstacle like a projectile motion. Neglecting air resistance, the range of the body is by kinematics

The angle is relative to the angle the leg pushes the body. The projectile motion could be made simpler by imaging the obstacle’s height as negligent, yielding in a projectile motion with the same starting and ending points. The range, distance d = v^2*sin(2θ) / g. So then at θ of 45 degrees, sin(2θ) gets the largest value of 1. So, in relating with the real world, project yourself at an angle of say 45< θ <50 degrees for the greatest range.
Now say that you are at a relatively tall height and the only way to escape from a "pursuer" is to jump down from the height. But you want to do it in a way to reduce the chances of breaking your legs, or any other bone in your body. The solution is a landing with adding a roll. To begin with, the human body is highly flexible, yet fragile at the same time. The cortical bone – compact bone – is denser than the trabecular or cancellous bone which is less dense, softer, weaker, less stiff, and has more surface area than cortical bone. The tension that an average bone material can take is in table 1. And one must also keep in mind that ligaments, tendons, and muscles are much more fragile, and very susceptible to

easily snap my tibia and very well easily fracture or even break my femur as well. Now say that when I landed, I kept my angle between my knees a 90 degree angle and rolled properly at the instant that the floor was in contact with the ball of my foot, I could easily increase the impact time to a little more than 0.5 seconds. So with that in mind the new force is Ffloor = 77.1 kg (9.8m/s^2 + 9.9m/s/0.5s) = 2300 N, which is about 500 pounds of force. With a proper athletic body, and the sense that the force is spread over more surface area of the body when rolling than just on the leg, there is less compression forces on any specific part of the body, at least not enough to a point of breaking. However, it is not safe to jump from a height of more than 3 meters, unless you are a veteran parkour athlete with a few years of experience. Furthermore, the substance of impact is important as it determines the impact time. So it is not a good idea to jump from great heights to concrete. Grass, sand, or gravel is much safer as the impact times are made longer in such terrains, and generally a smart way for amateurs to start out, if they are interested in Parkour.
Check my math, and let me know if you catch a mistake.
Play Safe.