Theory
Aura
Aura is a form of energy unique to living things, with the exception of any species belonging to the Grimm family, who serve as the exception to this rule. It at its most basic function, creates a barrier of light around the living entity, providing a passive force which counteracts incoming forces. For most living things, the force generated by Aura is so minor as to hardly be noticed, but humans in particular have pushed this power source to incredible extremes. In order to determine if the Grimm can survive on this energy source, it is important to quantify this unique phenomenon.
In order to simplify the model, it is assumed that the output of Aura is constant across all the surface area of a living creature. There are slight variations based on height, diet, and a number of unquantifiable factors, but this is a good assumption for most cases. This Aura is felt as a pressure, which is defined in physics as the force acting on a body divided by the surface area the force acts upon.
P = F/S
The force can easily be solved with the data collected from Aurameters. The sensors are traditionally circular disks for a predetermined surface area that measure the pressure exuded by a person's Aura output.
F(aura) = P*S
This auric force propagates in all directions from the source as a series of various frequencies of light. This creates a field of energy called an "Aura Field". Unlike light which relies on ionized electric and magnetic fields, Aura is a radiation that produces a physical force. The term for the Aura field can be demonstrated thusly.
F(Aura) = A = ke*q/r^2
The term ke is a proportionality constant, and r represents the distance from the observer to the Aura source. The best way to describe "q" is to consider it as an "Aura potential" term. The larger the "q" value is, the more force a person's Aura is capable of generating. This potential can be solved with the data collected from Aurometers and knowledge of the distance.
q = F(aura)*r^2/ke
Most humans can be shown to have about the same value of Aura potential, which makes sense considering the forces at play. If two people, two Aura sources, stand close together, their Aura will clash with equal force, but in opposing directions. The two forces would cancel each other out, and any small forces that diverge are hardly noticeable.
This holds true for almost every living creature, with the exception of the Grimm, who possess no aura potential, and thus do not produce Aura force. This leaves the Grimm with a non-zero net Aura that bombards them from all directions. The intensity of this Auric radiation "I" is a term well known for traveling light waves, and since Aura is a form of light, the equation can be applied in this instance.
I = A^2/(2*muo*c)
This intensity is then collected by the surface layer of Chitin and transformed into an energy source that fulfills the Grimm's needs. Assuming a perfect transfer of power, the equation is simply the intensity of the Aura multiplied by the surface area of the Chitin plate.
P = I*S
Of course in reality a portion of the stored energy must be lost as waste heat in the conversion process. This inefficiency must be factored in as it affects how much power the Grimm needs to sustain itself by increasing the amount of power required.
P(required) = eta*P = eta*I*S
Grimm Power Demands
Now to determine how much power would be required for a Grimm to survive for a specific period of time. Because it is the simplest comparison, let's compare the Ursa to its similar cousin, the black bear. The black bear will normally consume about 5000-8000 calories a day. The calories here are misleading, as each food calorie is equivalent to 1000 standard calories. A standard calorie is in international units, 4.184 joules of energy. Because the Ursa requires carrying the heavy metal plate, and is much heavier than its black bear cousin, we will hold its calorie needs at the maximum value of this sliding scale.
8000 Cal = 8*10^6 cal = 3.3472 *10^7 Joules
This is how many Joules of energy an Ursa would need to survive per day. This in turn leads to the calculation of the power required.
P(required) = 387 Watts
In order for an Ursa to remain healthy, it must consume 387 Joules worth of power every second from the surrounding Aura. An efficiency of 10 percent would mean it must consume ten times that, or 3,870 Joules every second!
Is such a large amount of energy available in the wild? Hunters have been recorded to emit over 3000 newtons worth of force, which from our power calculations could satisfy a Grimm in just under 4 hours, even with a meager ten percent efficiency. Natural flora and fauna however, produce far smaller quantities of Aura, and usually output around 10 newtons of Aura for small animals, and 150 newtons for larger animals and trees. This means that even with a worst case scenario efficiency, a Grimm only needs around 60-70 large trees in an area to satisfy its base needs. This efficiency is only expected to go up once testing begins.
This section is simply to illustrate that the Grimm in question will be exposed to an ample supply of Aura by which to harvest. All this energy as well is simply excess power vented naturally off normal living creatures, so it's feasting is not harmful to other organisms around it. This would allow the creature to live safely without fear of reprisal from both predators and starvation.
Power Conversion
How does the Grimm harness this energy? Much of this field still needs to be fleshed out, and it is hoped that this project will help to refine the knowledge of this subject. A fellow student Gloria Hawthorne, has taken up the study of the cellular structure of the Chitin Plating, and has come up with an initial hypothesis (Hawthorne). The bone plating shares similar properties with conductive metals. When Aura strikes the bone plating, the base particles within the cells are excited, and ride across the deeper cells beneath the surface. Beneath the hard absorbent surface is a converter cell that transforms this pulse of energy into more useful forms. How this conversion works is still a mystery, as this sort of behavior is not replicated by any other strain of creature currently known.
For what this thesis will cover, the absorption properties can be calculated from the power term. In controlled environments, only one target will be expending Aura, and this Aura can be easily tracked through the Aura monitors mentioned in the proposal. This allows for the calculation of the Aura field, and the resulting power drawn. This power allows for the creation of a model, and this model is compared against the stress tests to determine if the Chitin Doped plating will stand up to large amounts of pressure.
Design of Experiments/ Response Surface Methodology
Design of Experiments and response surface methodologies are grounded in statistical foundations and aid an experimenter in gaining useful information from testing. The techniques founded by Montgomery (10) create a statistically robust picture of a design space, and allow for a higher clarity to results with less tests than the traditional One Factor At a Time (OFAT) tests.
Three principles are required to maintain an effective design; replication, randomization, and blocking. Replication is a repetition of the basic experiment, in order to compare responses. This allows for the estimation of pure error, and ensures that the results gathered in the test can be replicated by others in the scientific community.
To understand the importance of randomization, its important to know what "nuisance factors" are. Nuisance factors are elements that affect the response but are not easily controlled by the experimenter. Examples of these are humidity in the air, temperature, vibrations in the instruments, trace elements in gas compositions. These nuisance factors might generate a response that changes over time, and it is this problem that makes randomization important. By running the factors at random points, the possibility of a trend of nuisance factors shifting the response over time is drastically reduced, reducing noise and making the data more robust.
Blocking is a technique in which potential nuisance factors are placed into separate groups. A example of this would be a test on the performance of an aircraft. Two pilots help to conduct the tests, Pilot A and Pilot B. Pilot A has more experience that Pilot B, and that might show as better performance over his runs. To ensure that pilot experience doesn't skew the final results, the tests are put into separate blocks for each pilot, in order to see the effects of the pilot skill more clearly on analysis.
Two factors, binding material, and chitin/material ratio, are being tested for three responses, Force, Aura, and Displacement. A 22 full factorial design with 2 centers and a full replicate, will be conducted on each material associated with this test. A total of 183 runs are needed for all tests, the details of which are explained in further detail in the "Experiment" section.
Stress Test
The purpose of the stress test is to determine if non Aura forces will yield a significant difference in performance. This test involves the use of a rotating pendulum with a set weight of uniform density mounted at the end point. The forces created by this weight can be calculated using torque equations.
Torque = Fxr = F*r*sin(theta)
The radius will not be modified for ease of testing, but by changing the starting inclination of the
Pendulum. The weight can also be increased to provide more gravitational force.
F = m*g*cos(theta)