You Go To Church And I Run For The Ship

Tough nut to crack!
Tundra Comic Panel 04.13.2012
Unrealized/UnRecognized Discovery?!!
(You and I both know that not to be the case; here are some caveats Quran 2:41, 2:79, 2:174, 3:77, 3:187, 3:199, 5:44, 9:9, and 16:95...However, that black Audi R8 that keeps popping up sure is tempting,
but like everything else You've thrown my way i have to walk away.)

{Aside: What's up with the 2 Mooning Moscovites kissing on the sofa across from me on 04.11.2012 at Webb Way?--all I have to say about it is, "Only the devil whispers, the rest of us speak aloud.--I do, however, wish to thank her for the help."}

وَالأَنْعَامَ خَلَقَهَا لَكُمْ فِيهَا دِفْءٌ وَمَنَافِعُ وَمِنْهَا تَأْكُلُونَ (16:5
وَتَحْمِلُ أَثْقَالَكُمْ إِلَى بَلَدٍ لَّمْ تَكُونُواْ بَالِغِيهِ إِلاَّ بِشِقِّ الأَنفُسِ
إِنَّ رَبَّكُمْ لَرَؤُوفٌ رَّحِيمٌ(16:7
وَالْخَيْلَ وَالْبِغَالَ وَالْحَمِيرَ لِتَرْكَبُوهَا وَزِينَةً وَيَخْلُقُ مَا لاَ تَعْلَمُونَ (16:8
16:5 And (God) Creates cattle for you....
16:6...to carry your loads..without hardship....Indeed Your Sustainer is Most Compassionate, Beneficent.
16:7...and horses...for you to ride and in which you find beauty...and He Creates things that you have no knowledge yet.

Church Nave vs Naval v Ship's Hull vs Coracle vs Walnut vs Kernel

The ‘nave’ of a church derives from the Latin ‘navis’ for ‘ship', which also gives us the word ‘naval’--having to do with maritime, nautical, seafaring and navigational activities (ie., applications that include seabasing, projective power/force, etc.). While ships primarily refer to seagoing vessels, a ship may also refer to any vessel that traverses a fluid medium, be it water, air/space or 'time'. In the case of a 'space ship' it would be something which flies, ie, 'tayer' refer to 105:3.

Notes: Projective geometry, like affine and Euclidean geometry, can also be developed from the Erlangen program of Felix Klein; projective geometry is characterized by invariants under transformations of the projective group. (re projective power/projective force)
The incidence structure and the cross-ratio are fundamental invariants under projective transformations. Projective geometry can be modeled by the affine plane (or affine space) plus a line (hyperplane) "at infinity" and then treating that line (or hyperplane) as "ordinary". 
An algebraic model for doing projective geometry in the style of analytic geometry is given by homogeneous coordinates. On the other hand axiomatic studies revealed the existence of non-Desarguesian planes, examples to show that the axioms of incidence can be modeled (in two dimensions only) by structures not accessible to reasoning through homogeneous coordinate systems. 
In a foundational sense, projective geometry and ordered geometry are elementary since they involve a minimum of axioms and either can be used as the foundation for affine and Euclidean geometry. Projective geometry is not "ordered" and so it is a distinct foundation for geometry. 
There are many projective geometries, which may be divided into discrete and continuous: a discrete geometry comprises a set of points, which may or may not be finite in number, while a continuous geometry has infinitely many points with no gaps in between. 
The only projective geometry of dimension 0 is a single point. A projective geometry of dimension 1 (1 D) consists of a single line containing at least 3 points. The geometric construction of arithmetic operations cannot be carried out in either of these cases. 
For dimension 2, there is a rich structure in virtue of the absence of Desargues' Theorem. The simplest 2-dimensional projective geometry is the Fano plane, which has 3 points on every line, with 7 points and lines in all arranged with the following schedule of co-linearity...
The simplest 2-dimensional projective geometry is the Fano plane, which has 3 points on every line, with 7 points and lines in all.

"Projective geometry" is sometimes used to indicate the generalised underlying abstract geometry, and sometimes to indicate a particular geometry of wide interest, such as the metric geometry of flat space which we analyze through the use of homogeneous coordinates, and in which Euclidean geometry may be embedded (hence its name,Extended Euclidean plane).
The fundamental property that singles out all projective geometries is the elliptic incidence property that any two distinct lines L and M in the projective plane intersect at exactly one point P.
The special case in analytic geometry of parallel lines is subsumed in the smoother form of a line at infinity on which P lies. The line at infinity is thus a line like any other in the theory: it is in no way special or distinguished.
(In the later spirit of the Erlangen programme one could point to the way the group of transformations can move any line to the line at infinity).

The elliptic parallel property is the key idea which leads to the principle of projective duality, possibly the most important property which all projective geometries have in common.

Presumably the nave of a church came to be known as such from a fancied resemblance to a ship shape, but the shared characteristics between a church nave and ship shape is more intricately bound than mere imagination might lead us to believe.

Winchester Cathedral is a good example (images below; Winchester Cathedral's nave and its reflection (reflected across the horizontal x-axis) reminiscent of a ship's hull, compare to a Viking ship's ribs).

Winchester Cathedral (Gothic Architectural Influence)
See Sacred Geometry, Reuleaux Triangle

Upside Down Image of Winchester Cathedral's Nave
Compare with Ship's Hull Planking/Ribs vs
Hull Sections

Viking Vessel Hull Ribs
(See Jonah vs Fish vs Whale vs 'knitted' paths vs.
W-curve-Throw-Woof-Wales-Knots, etc.)

The secondary meaning of nave derives from an Old English word ‘nafu’ (relates to the Arabic, nafs) having to do with the idea of ‘centrality’, like in a ‘hub of a wheel’ (refer to the Hindu concept of 'Chakras'), or connected to the root for the word ‘navel’ from the Latin for umbilicus (relating to womb/matrix/cervix/neck/belly), and/or the Greek omphalos, relating to ‘end of a scroll’ (refer to 105:4 'sijil') and ‘the boss of a shield’, respectively.

Other roots for which describe 'disk, sphere' , 'whirlpool,' and 'bud' --considered a feminine sexual center since ancient times and still in parts of the Middle East, India, and Japan (see Hindu concept of yoni, the Reuleuax triangle, Freemason Symbols/Architecture/Sacred Geometry). 

And that the general layout or plans of a church mimics the shape of a seafaring vessel is more than just a passing fancy. The similarities between a church and ship may even be extended to that of the human form, most conspicously reflected in Native American Kachina dolls.

Amiens Cathedral, France vs Kingston Vessel vs Kachina Doll

(Note the west end/nave/aisle/crossing/transept/choir (lattice)/altar/east end of a typical cruciform church vs stern/transom/aft/engine room/port and starboard/bridge/pilot house/fore (bow or prow) of a ship vs the legs (ground contact/ actuators,--68:42 refers to  سَاقٍ 'saqiin' , refering to the legs or shins of the human body as well as bole/shaft/trunk and in verb form 'to drive') /pelvic region/torso/arms (actuators)/head (sky) of the kachina doll representation of the human form).

The Anatomy of a Church v The Ship v The Human Being

Tradionally churches are oriented facing 'east'  and in a cruciform church as depicted above the entrance is directly opposite the altar, or at the 'west' end which is situated in the church 'facade' (front of the building). In this example, the entrance at the facade of the 'church' corresponds to the  ship's aft which corresponds to the human's feet (where the Human makes contact with the ground, Earth). (This establishes how the orientations of each body correlate--see Special Orthogonal matrix, SO(n, F) )
The relevance or orientation and the Eastward direction may have its basis in navigating and piloting effectively along the Earth's Magnetic Norms , early article with respect to bird flight and overcoming the Earth's Coriolis effect; The Journal o f Applied Physics, Vol. 18, No. 12, A Preliminary Study of a Physical Basis of Bird Navigation, by Henry Yeagley, December 1947)

Chapter 2 The Calfوَإِذْ قَالَ إِبْرَاهِيمُ رَبِّ أَرِنِي كَيْفَ تُحْيِـي الْمَوْتَى قَالَ أَوَلَمْ تُؤْمِن
قَالَ بَلَى وَلَـكِن لِّيَطْمَئِنَّ قَلْبِي قَالَ فَخُذْ أَرْبَعَةً مِّنَ الطَّيْرِ فَصُرْهُنَّ إِلَيْكَ
ثُمَّ اجْعَلْ عَلَى كُلِّ جَبَلٍ مِّنْهُنَّ جُزْءًا ثُمَّ ادْعُهُنَّ يَأْتِينَكَ سَعْيًا
وَاعْلَمْ أَنَّ اللّهَ عَزِيزٌ حَكِيمٌ 2:260

2:260 And when Abraham said, "Lord, show me how you give life to the dead." (God) Said, "Do you not Believe (accept it as True)?" (Abraham) said, "Yes, (of course), but so that I am reassured (with) inner (certainty, in my heart)." (God) Said, "Take 4 birds and train them to obey you, then place a portion of them on each mountain and call them; they will seek you (come to you) at your command (in order); and know/teach that God is Wise, Powerful."

By extension, those forces which are known to effect the 6 modes of motion of a ship (ie., translations--sway, surge and heave and rotations--yaw, pitch and roll) in the water (be it ocean, river, lake or estuary) may be understood in the context of movement in the analogous human (earth) and church (spiritual or sky) 'bodies'. (In 3-D, 6 degrees of freedom refers to these 6 modes of motion, while robotics and gaming applications refer to higher 'degrees of freedom' these are merely incremental of the 6 in general and not in  fact 'additional' degrees of freedom, which may only be accessible from higher dimensions in order to allow truly greater ranges of motion, see affine matrix, projection/perspective, etc.)

Watercraft Rotation
Note Hull Front View vs. S Curve vs. Walnut Shell

The front view of a ship's hull bears a strong resemblance to a shield and in terms of the geometry is reminiscent of a 'bean curve', the smoothed out version described well by Cassini ovals. And the sides of which resemble an upside down 'ship's bell', each half of which can readily be modeled by the cumulative distribution function or S-Curve:
S-Curve Distribution Function
In terms of the mean (mu) and scale (beta, positive)

Bizarro Comics April 4, 2012
(I get it, I get it...
 There really is no need for You to rub it in...)
Coracles are keel-less, flat-bottom boats that are oval in a shape very similar to a half walnut shell (see walnut vs 2-D and 3-D Cassini Ovals, vs. Bean Curve, image below).

The design is intended to evenly distribute the weight of the boat and its load across the structure and to reduce the required depth of water — often to only a few inches, making it ideal for use on rivers (see Rivers of Time).

The coracle, called quffa in Arabic, is mentioned in the Bible, Exodus 2:3 as the water craft in which Moses's mother launched Him down the river to protect Him from Pharoah's decree to do away with the first born male children while the Israelites were dwelling in Egypt.

It was also frequently mentioned by my Dad whenever He wanted to remind any of us not to rush into anything in the form of a rhetorical question, "Must we jump from the quffa onto it's ears (handles)?" The short answer, 'tho none is called for to answer a rhetorical question is, "No, no, for the simple reason that you may find yourself in an awkward position that looks something like Dilbert in the comic panel here."
Dilbert April 15, 2012
What it looks like to jump from the coracle onto its handles.

The Welsh apparently have a saying about it, too. Since it is a light-weight flat-bottom boat, it can be carried by one man (or woman) on his (or her) back, the saying goes, "the load of a man is his coracle".

While inherently unstable by design because it sits "on" the water, rather than "in" it, a coracle can easily be carried by currents and the wind,  the coracle makes for an effective fishing vessel since it hardly disturbs the water or the fish, being easily manuevered with one arm, while the other arm tends to the net. (Generally 2 coracles are required for 1 net).

Walnut, 2-D Cassini Ovals & 3-D Cassini Ovals vs.
2009 Homework Assignment (compare with geometry of Wankel engine)& Bean Curve

Coracles vary in design, as they are tailored to the river conditions where they are intended to be used. In general there is one design per river, but this is not always the case.

Quranic Reference to Vessels, Ships, Ark, Orbits, Boats/Coracles & Orbits

Walnut Halve Shell, Vietnamese Coracle
 (Watercraft, Ship, Naval Application),
Boat Hull, Whole Walnut (note flange)

The Teifi coracle, for example, is flat-bottomed to negotiate shallow rapids, common on the river in the summer, while the Carmarthen coracle is rounder and deeper, better suited to negotiate the tidal waters on the Tywi, where there are no rapids.

Traditional Teifi coracles are made from locally harvested wood — willow for the lats (body of the boat), hazel for the weave (Y bleth in Welsh — the bit round the top) — while Tywi coracles have been made traditionally made of sawn ash.

Teifi coracles use no nails, and rely on interweaving the lats for structural coherence (see 'cracking open an alien spaceship'), while the Carmarthen ones use copper nails and no interweaving.

Modern working coracle boats are made of fiberglass.

The general idea for integrating the conepts above:
(2-D representation from 3-D or higher dimensional equivalents involve orthonormal projection, reflection, translation, etc. to conceptualize real-world equivalents which may account for why UFO witnesses percieve the craft morphing/transfigures when it impinges on Earth's airspace).

Proportions Based on a Kernel

Walnut Shell Cross Section vs
Wankel Engine (note Reuleux Triangle)
While the coracle resembles the shape of a half walnut shell, the cross-section of a walnut shell is characteristic of the compression chamber of the Wankel rotary engine.

In the basic single-rotor Wankel engine, the oval-like epitrochoid-shaped housing surrounds a rotor which is triangular with bow-shaped flanks (reminiscent of the Reuleaux triangle, a three-pointed curve of constant width, but with the bulge in the middle of each side a bit more flattened).

In the Wankel engine, the expansion phase of the cycle is much longer than that of the Otto cycle, and the four strokes of a typical Otto cycle occur in the space between a 3-sided symmetric rotor and inside the housing.

The central drive shaft, called the eccentric shaft or E-shaft, passes through the center of the rotor and is supported by a fixed bearing.

The shaft turns 3 times for each rotation of the rotor around the lobe and once for each orbital revolution around the eccentric shaft.

The Wankel engine cycle is shown in the diagram below.

In the diagram above:
The "A" marks one of the three apexes of the rotor
The "B" marks the eccentric shaft and
And the “white portion” is the lobe of the eccentric shaft

The Wankel engine is actually a variable-volume progressing-cavity system. There are 3 cavities per housing, all repeating the same cycle.

Eccentric shafts do not have the stress-raising internal corners of crankshafts and Wankel engines also generally have a much higher redline than a reciprocating engine of similar power output. This is in part because the smoothness inherent in circular motion, but especially because they do not have highly stressed parts such as a crankshaft or connecting rods.

Points A and B on the rotor and e-shaft turn at different speeds--point B moves 3 times faster than point A, so that one full orbit of the rotor equates to 3 turns of the e-shaft.

The shape of the rotor between the fixed corners is meant to minimize the volume of the geometric combustion chamber and a maximize the compression ratio.

The symmetric curve connecting two arbitrary apexes of the rotor is maximized in the direction of the inner housing shape with the constraint that it not touch the housing at any angle of rotation (an arc is not a solution of this optimization problem).
While the Wankel engine has some disadvantages compared to conventional 4-stroke engines, having to do with thermal boundry layer, apex seal failures, and slightly higher fuel consumption, it has certain performance and safety advantages that make it difficult to overlook as a viable future engine technology.
Wankel engines have certain advantages over conventional 4-stroke engines; they are considerably lighter, simpler, and contain far fewer moving parts than equivalent piston engines.

When operating within their original design parameters Wankel engines are almost immune to catastrophic failure.

Because valving is accomplished by simple ports cut into the walls of the rotor or side housings, they have no valves or complex valve trains; and since the rotor rides directly on a large bearing on the output shaft, there are no connecting rods and there is no crankshaft.

The elimination of reciprocating mass and the elimination of the most highly stressed and failure prone parts of piston engines result in high reliability, a smoother flow of power, and a high power-to-weight ratio.

The surface/volume-ratio  (S/V) problem is so complex that a direct comparison between a reciprocating piston engine and a Wankel engine cannot be readily assessed. The flow velocity and the heat losses behave quite differently.

Surface temperatures behave absolutely differently; the film of oil in the Wankel engine acts as insulation (and contributes to some smoking on start up). Engines with a higher compression ratio have a worse surface/volume ratio.

The surface/volume (S/V) ratio of a Diesel engine is much worse than a gasoline engine, but Diesel engines are well known for a higher efficiency factor than gasoline engines. Diesel and alternate fuel versions of Wankel engines have been developed by Deere and others, and the Wankel engine lends itself to hydrogen fuel (fuel cell) applications.

Comparing engines of equal power, a naturally aspirated 1.3-liter Wankel engine with a naturally aspirated 1.3-liter four-stroke reciprocating piston engine with equal power, such a four-stroke engine is not possible and needs twice the displacement for the same power as a Wankel engine.

The extra or "empty" stroke(s) should not be ignored, as a 4-stroke cylinder produces a power stroke only every other rotation of the crankshaft. This doubles the real surface/volume (S/V) ratio for the four-stroke reciprocating piston engine and the demand of displacement.

So the Wankel engine has higher volumetric efficiency and a lower pumping loss since it has no choke valves.

Because of the quasi-overlap of the power strokes that cause the smoothness of the engine and the avoidance of the 4-stroke cycle in a reciprocating engine, the Wankel engine is very quick to react to throttle changes and is able to quickly deliver a surge of power when the demand arises, especially at higher rpm. This difference is more pronounced when compared to four-cylinder reciprocating engines and less pronounced when compared to higher cylinder counts.

Due to a 50% longer stroke duration than a four-cycle engine there is more time to complete the combustion. This leads to greater suitability for direct injection.

In addition to the removal of internal reciprocating stresses by virtue of the complete removal of reciprocating internal parts typically found in a piston engine, the Wankel engine is constructed with an iron rotor within a housing made of aluminium, which has a greater coefficient of thermal expansion--ensuring that even a severely overheated Wankel engine cannot seize, as would be likely to occur in an overheated piston engine. 

This is a substantial safety benefit of use in aircraft, since there are no valves and valve trains to burn out, jam, break, or malfunction in any way, again increasing safety.

A further advantage of the Wankel engine for use in aircraft is the fact that a Wankel engine generally has a smaller frontal area than a piston engine of equivalent power, allowing a more aerodynamic nose to be designed around it.

The simplicity of design and smaller size of the Wankel engine also allows for savings in construction costs, compared to piston engines of comparable power output. 

And the Wankel engine is capable of running at very high speeds and operates almost noiselessly.

A Wankel engine that loses compression, cooling or oil pressure will lose a large amount of power and fail over a short period of time. It will, however, usually continue to produce some power during that time. Piston engines under the same circumstances are prone to seizing or breaking parts that almost certainly results in major internal damage of the engine and an instant loss of power.

For this reason, Wankel engines are very well suited to applications in remote places where a failure could result in fatalities; and aircraft, where abrupt failure is likely to lead to a crash or forced landing.

{ok, ok, I am more than a  little weirded out that someOne is asking just how long this has been going on--not only did I think You Knew but I thought You Planned it!}

Quran Surah 7 Al-A3Raf
  فَأَرْسَلْنَا عَلَيْهِمُ الطُّوفَانَ وَالْجَرَادَ وَالْقُمَّلَ وَالضَّفَادِعَ وَالدَّمَ
آيَاتٍ مُّفَصَّلاَتٍ فَاسْتَكْبَرُواْ وَكَانُواْ قَوْمًا مُّجْرِمِينَ (7:133

7:133 That We Sent them floods, and locusts, and lice, and frogs, and blood; Separate Signs (of severence, disentanglement, judgment, to decide...), yet they (continued) in their arrogance and were an immoral (criminal) community. (133/7==19)

Green Frog vs Origami Frog

Green Frog vs. Walnut Halves vs.Kernel
Child Pose Yoga Position vs Walnut Kernel (See Above)