User blog:Pythonraptor/Science of the Shinobi, Issue 1 – Why ninja can walk up vertical surfaces

"Science is to see what everyone else has seen but think what no one else has thought"

- Albert Szent-Gyorgyi

Introduction
Hey everyone! In this issue of Science of the Shinobi, I’ll be addressing the topic of ninja walking up trees, walls, and the like. Why exactly can ? Keep your eyes glued to your monitors and your thinking caps screwed on, and you’ll soon find out.

Tree Climbing Practice
Just what is it that keeps the feet of a ninja firmly rooted to that tree bark? The answer, really, is quite simple: air pressure. Yes, air pressure. Let’s talk about the Earth’s atmosphere briefly. As I’m sure most of you know, the earth’s atmosphere extends hundreds of kilometers in space, yet the bulk of it lies within about ten kilometers above sea level, and thus the air pressure is greatest in this region. Now, let’s talk about pressure; pressure is defined as force per unit area, and is measured in Newtons per meter squared (Nm^-2). A Newton is a unit of force (named after the 17th century physicist Isaac Newton) which is defined as the force required to accelerate a mass of one kilogram at a rate of one meter per second squared. Now, saying “Newtons per meter squared” as the unit of pressure can become verbally cumbersome, so another name for the unit of pressure was coined, the Pascal (named after the French mathematician Blaise Pascal). So, one Pascal of pressure is a force of one Newton acting on an area of one square meter. If 100 Newtons of force acted on one meter squared, the pressure would be 100 Pascals, and so on and so forth.

At sea level, the pressure exerted by the atmosphere is a little more than 100,000 Pascals – this is equivalent to the weight of ten cars pressing down on one square meter. Living things aren’t crushed by this enormous pressure because of the pressure in their blood, which acts oppositely to the atmospheric pressure. The true effects of atmospheric pressure were demonstrated by a German physicist, Otto von Guericke, when he fashioned a pair of hemispheres from which air was evacuated. As a result, the steel hemispheres were held together solely by the force of the molecules of the atmosphere acting on them. Two teams of eight horses, harnessed to the hemispheres and ordered to run in opposite directions, could not provide enough force to separate them. Impressive, isn’t it? In contrast, a human being would be torn limb from limb if subjected to the same conditions, a fact which was taken advantage of by opportunistic executioners in the punishment known as quartering.

Do you think that you don’t witness the effects of atmospheric pressure in everyday life? If you do, you’d be wrong. When you drink through a straw, you’re not really “sucking” the liquid up. The liquid is “pushed” through the straw by atmospheric pressure. Air is evacuated from the straw by the action of your lungs, which creates a pressure difference between the straw and the liquid; air is pushing down on the liquid strongly in the container, but not as strongly in the straw. Due to the difference in pressure, air is forced up the straw. For those of you who like to watch juice boxes collapse when you suck the air out of them, you’re not really sucking the walls of the box in. Since the air is removed from the interior of the box when you inhale through the straw, the external air pressure is greater than the internal air pressure, and the box gets crushed by the atmosphere.

Anyone who has flown on a commercial airliner knows that the aircraft cabins are pressurized. The earth’s atmosphere becomes progressively thinner the further from the surface you rise, which is why it becomes more and more difficult to breathe the higher up you go. Most jet aircraft fly above 10,000 meters while cruising – at this height, it would be impossible to breathe normally. The systems of the aircraft are designed such that air pressure is the same in the cabin as it is around sea level, so that the passengers aren’t asphyxiated. In this case, the internal air pressure is much greater than the external air pressure. This is why aircraft must be built with sturdy materials such as aluminium, to prevent the airframe from bursting like a balloon. Now, when a door is (rarely, if ever) opened during flight, or when we’re in one of those awesome movies when a hole gets ripped in the plane, such as Iron Man 3 (if you haven’t watched it, you know not what you have missed), an explosive decompression occurs. The pressure inside the plane wants to balance with the pressure outside the plane, and thus everything appears to be “sucked” out of the hole in the airframe. In reality, the excess pressure is forcing everything outside.

But how does all of this apply to the Tree Climbing Practice? From what Kishimoto has stated, we know that ninja must expel a steady stream of chakra from their feet to keep themselves attached to the tree, wall or what have you. Too little chakra, and the ninja will fall to the ground and land unceremoniously on his ass. Too much chakra, and the ninja will be propelled off the tree. That’s not very scientific, but here’s where I come in:

In the diagram at right, the shape of the chakra used in the Tree Climbing Practice is shown. ‘A’ represents the ninja’s foot, ‘B’ represents the region underneath the arch of his foot, and C represents the region underneath his chakra. The chakra is in blue, the air outside the chakra is represented by green arrows, and the air inside his chakra is represented by red arrows. Note that the green arrows are larger than the red ones. Now, to attach himself to a tree, a ninja would have to maintain the general shape of that chakra I have drawn. When he steps down, air is forced out from under his chakra. This means that there would be less air inside the region encompassed by his chakra than outside his chakra, and less air pressure inside than outside. As you should expect, the ninja’s feet remain on stuck to whatever surface he’s on. To remain strongly attached to the surface, the ninja shapes his chakra such that there is less space underneath it. To remain less strongly attached to the surface, a ninja shapes his chakra such that there is more space underneath it. To remove his foot from the surface, the ninja stops expelling chakra. The real-world equivalent to the Tree Climbing Practice is, of course, suction cups.

This clearly corroborates everything that Kishimoto has said thus far about the Tree Climbing Practice. If a ninja expels too little chakra from his feet, the pressure difference will not be enough to hold him in place. If he expels too much chakra, the chakra will lose its arched shape and exert a force on the tree, and the tree, being stationary, will exert an equal and opposite force on the ninja (Newton’s third law of motion).

Whether or not you accept this scientific basis for the Tree Climbing Practice, there is one principle of physics which applies to it, regardless of what Kishimoto says: center of gravity. The center of gravity of an object is the point through which the weight of the object can be said to act.

The center of gravity of a human, when standing, is located approximately at the torso. This would be quite problematic for a ninja when he walks up a near-vertical surface; with feet firmly anchored to the surface, the ninja’s body would want to flop downwards, bending at the knee joints, unless the ninja used his abdominal muscles to keep his upper body parallel with his calves. This, of course, would require much energy. In order to circumvent this problem, a ninja would most likely have to vitalize his abdominal muscles with chakra, in order to focus his attentions on running. Center of gravity also provides an interesting training exercise; a ninja could anchor himself to a vertical surface, and do abdominal crunches, thus giving himself a six-pack in a rather short time compared to traditional exercises.

Calculations
Okay, here’s the fun part, the calculations: What pressure would be required to keep Kakashi stuck to the tree when he first demonstrated the Tree Climbing Practice to Team 7? Assuming that the radius of the chakra shape (and that it’s a perfect circle) is 4 cm, that acceleration due to gravity is 9.8 ms^-1, that atmospheric pressure is 101325 Pascals, and knowing that he weighs 67.5 kilograms, then:

Pressure required to keep Kakashi stuck to the tree = Force/Area

Force = Mass * Acceleration due to gravity = 33.75 * 9.8 (each suction cup has to support half of Kakashi’s weight)

Area of suction cup= π*r^2 = π*4^2 = 50.3 *10^-4 meters (1 cm = 10^-4 meters)

Therefore, pressure difference (33.75*9.8)/(50.3 * 10^-4) = 65755.5 Pascals The pressure inside the cup is then 101325-65755.5= 35569.5 Pascals