Saturday, September 13, 2014

Anatomy

Super powered cybernetics


               The term cybernetics is commonly used to refer to the replacement of a person’s body parts with a technological replacement of some kind.  These replacements can run the gamut from a replacement organ to a replacement limb.  In the medical profession the term prosthetic is used when referring to a replacement limb, and artificial organ when referring to an internal body part.  At the current time modern medical science has created a wide range of prosthesis to replace missing body parts do to disease or injury.  Some of these include artificial arms, hands, legs, or feet, depending on the needs of the patient.  Despite the success of recently disgraced South African runner Oscar Pistorius, these replacement limbs have to completely match a normally functioning limb let alone exceed it.

Above the knee artificial leg


Below the elbow artificial arm


               In the world of anime and manga however the story is a bit different, with many characters gaining increased strength and ability from a replacement body part.  Some examples are shown below.

Edward Elric Full Metal Alchemist


Motoko Kusanagi


               As any fan of anime can probably tell me right now is that the Edward only has an artificial arm and leg, while the Major has an entirely cybernetic body.  This distinction is important and will be covered later on in the blog.  For now I will be looking at cybernetics where only part of the body is replaced such at Edward Elric.

Limits of the human body

               The human body is capable of performing many feats of strength and agility some of which are listed below.
Clean and Jerk Olympic record 411 lbs.
Squat world record 1268 lbs.
Bench press world record 722 lbs.

               Sadly to have any chance of being a real life superman you need to look something like this.


               Edward Elric he isn’t, but his size is needed in order to be able to lift such impressive amounts.  You will notice in the world’s strongest man competitor in the picture below the man’s entire body is quite large despite using his legs to lift the weight.


               The reason for this actually quite simple if the man’s back and arms were not strong, the act of lifting the weight would cause them to tear from their sockets.   Now this is not happening on a regular basis because most people lack the ability to lift a weight heavy enough to cause their own arms to tear from their sockets.


Partial Cybernetic Replacement

               This of course would be different for a person who was fitted with a super powered artificial limb if such a device could be built.  Now let’s take for instance Ross Syllabus shown below from Armitage the Third.


               Due to events in the movie his right arm is replaced up to the shoulder.  This enhanced limb allows him to operate heavy equipment with ease as shown above.  Now let’s examine his potential for greater than human ability.  If Ross uses his limb to crush a can or other object in his hand, then he will not run into any problems.  However should he try to use that arm to perform any action that required the support of the rest of his squishy body then the following will occur.


Conclusion

                Sadly our bodies are squishy and cannot support the extreme force of super powered cybernetics.  As such super powered cybernetic limbs are



Full Body Cybernetics

               There is however a caveat to the above rule and that is full body cybernetics.  In anime a full body cybernetics is used to refer to a person that has had their entire body except for the brain and or spinal cord replaced with a mechanical body.  Some of the more famous examples include the previously shown Motoko Kusanagi, Briareos (Appleseed), or Gally (Battle Angel Alita).

Briareous


Gally


               A completely cybernetic body removes the problem of the squishy human body.  This is due to the artificial body supporting the weight removing any biological components from the equation.  As such super powered could be used up to the limit of the artificial body.  Thus, a completely cybernetic body has the potential to give a person super powered abilities, provided it can be built in the future.


               Thanks again for reading and I hope you learned something.  List any comments, questions, concerns, or recommendations below.

Saturday, September 6, 2014

Physics


Black Lagoon


               Welcome class and please get out your physics books as this week’s lesson is on trajectory and Black Lagoon.  No we will not be examining bullet trajectories from the numerous shootouts found in the show, but the infamous boat scene.  For those of you who are not familiar with it, the clip can be found below.


Considerations


               Now just at first glance, there are several factors that need to be examined, to determine if this stunt is possible in real life.  The speed of the boat, angle of the ramp, height of the helicopter, not to mention the strength of the ramp, and the strength of the boat’s hull.  For the purposes of this examination I will not be including the strength of the ramp or the strength boat’s hull.  The reason for this exclusion is because a PT boats hull is made out of wood, specifically mahogany, which while strong, does have its limits.  This is also the reason for excluding the strength of the sunken boat that is used as a ramp.  From the few shots that are shown of the boat it sports a fair amount of rust, and has been sitting there for an undetermined length of time.  Given the amount of force needed to launch a boat into the air, it is entirely possible that the PT boats hull or the ramp could give out as soon as they collide ending the myth right there.  Now given that the ramp is successfully used in the clip, we will assume that both the hull of the boat and the ramp are strong enough.

Terminology


               In order to determine if the Black Lagoon can attack the helicopter with torpedoes, the trajectory of the Black Lagoon must be determined.  Trajectory is the path a projectile takes through space.  While the Black Lagoon is a PT and not a true projectile, once it leaves the water and can no longer propel itself, it can be considered one.  The type of trajectory that we are interested in is a ballistic trajectory.  In this type of motion the object moves both vertically and horizontally near the earth’s surface.  The force of gravity is the main force acting on the projectile so other forces like air resistance are excluded as their influence in this case would be negligible at best.

Basic Facts of the scene


               Before we begin diving into the math let’s consider the facts that will be used to consider if this particular scene is in fact possible.  In the picture below we can see that at the peak of its trajectory the Black Lagoon reaches a height greater than that of the helicopter.


               We can use a second picture to estimate the approximate altitude of the helicopter.


               In this picture we are concerned about the trees shown in the background as a way to determine the approximate altitude.  We can assume at this point in the show that the Black Lagoon is in an estuary close to Ronanapur, a fictional city in Thailand.  Mangrove trees are a common tree found in estuaries in Thailand.  There are several different species mangroves with a range of heights from 6 meters on the shorter side to species that can grow up to 35 meters on the larger side.  Now let’s assume that trees beneath the helicopter are of the shorter variety at 6 meters.  An examination of the image shows that the helicopter is two tree lengths from the water at a height of 12 meters.  Given the first image the Black Lagoon must reach a height of at least 12 meters for the scene to be possible.

The Math


               Projectile motion is motion in two directions and the equations for each are shown below.

Glossary
x- Horizontal position
y- Vertical position
v- velocity- speed
t- Time
a- acceleration- change in speed= to the force of gravity at 9.8m/s2
f- Final
i- Initial

Determining horizontal position

               Xf = vt + Xi

Determining vertical position

               Yf = Yi +viti +atf2
               Vf2 = Vi2 +2a(Yf – Yi)

               The above equations work in situations where the object is not projected at an angle like a plate sliding off the edge of a table.  If the projectile is launched at an angle another wrinkle needs to be added in order to complete the calculations for a parabolic trajectory shown below.


               As shown in the diagram the angle of the launch determines the height and distance the projectile travels assuming each one is launched with the same initial speed.  For the purposes of this evaluation only the vertical component of the Black Lagoons trajectory will be considered as it does fly past the helicopter in the scene, and they can be considered close enough for the torpedoes to hit the target.  The maximum height will be determined for each of the three angles shown above

Calculating the vertical component of the initial velocity
                Vyi = Vxi(sin angle)

               The maximum speed of a PT boat is 76 kmph and it can be assumed that Dutch keeps the Black Lagoon in top form.  To make the math easier 76 kmph converts to 21.1 meters per second.

Vertical speed at 30 degrees

               Vyi = 21.1m/s x sin30
               Vyi = 21.1 x 0.5
               Initial vertical velocity at 30 degrees = 10.6 m/s

Vertical speed at 45 degrees

               Vyi = 21.1m/s x sin45
               Vyi = 21.1m/s x 0.71
               Initial vertical velocity at 45 degrees = 14.9 m/s

Vertical speed at 60 degrees

               Vyi = 21.1m/s x sin60
               Vyi = 21.1m/s x 0.87
               Initial vertical velocity at 60 degrees = 18.4 m/s

Calculating the maximum height of the Black Lagoon

Maximum height = (Vyi2) / (2a)

At 30 degrees

               X= (10.6)2 / 2 x 9.8
               X = 112.4 / 19.6
               Max height = 5.7 meters

At 45 degrees

               X= (14.9)2 / 2 x 9.8
               X = 222 / 19.6
               Max height = 11.32 meters

At 60 degrees

               X= (18.4)2 / 2 x 9.8
               X = 338.6 / 19.6
               Max height = 17.3 meters

Conclusion


               Well the numbers don’t lie guys, and to be honest I was surprised by this one.  If the angle of the sunken boat the Black Lagoon uses as a ramp is more than 45 degrees then the boat clears the 12 meter mark and the stunt works.  I did not expect to be able to call this one confirmed but here it is



               The infamous PT boat vs helicopter scene can actually work if we assume the hull of the boat and the ramp can survive the stress.  Plus Dutch has to be able to aim the torpedoes to hit the helicopter.

Note


               For anyone who is reading, if you could let me know what you think on this one since I am mainly a biology and chemistry teacher.  Plus it’s been a while since I've done any physics.  Any suggestions you guys have are welcome.  I am always looking for new ideas.