Full Wheel/House Fusion

The Rolling Transport series of posts concluded with 2 approaches to accommodating wheeled artifacts architecturally. Although there is nothing really lacking in the usefulness of these simple configurations – IMO they serve their purpose very well – the wheel slot and the wheel port annexation are only 2-dimensional.macrocosmic wheel-house fusion

To begin the series of posts on Polytechnic Integration, a deeper connection between template-guided transporter and CBS architectural forms is sought by once again looking to the macrocosmic wheel. After longitudinally aligning its central hexagonal edges via primary rotation, the great wheel undergoes secondary rotation such that any one of its outermost edges is oriented horizontally at a specified latitude.

Zooming in on the spot with the wheel’s innate microcosmic representative in attendance (below), perspective is turned to a polar view with edges of plane types sloping from each side of the horizontal edge identified.

hexagonal shift of microcosmic wheel

Next, the wheel’s natural halves are separated and – with the triangularly sloped side held in place – the sloping square side is rotated 60° such that a sloping triangle mirrors that of the fixed side in the same hexagonal shift that formed the basis of the transport template.

Then focus sharpens on the matched triangles which are detached from the microcosmic wheel and juxtaposed against the CBS home’s latitude dependent roof.

Roof Fusion of Cubodal Wheel

To make the fit, the angle of the sloping triangles is adjusted such that the outer points contact the roof/wall juncture and the central ridge joining the triangles maintains a horizontal bearing.

The precise angle of adjustment (Φ) is of course related to the slope of the CBS roof (Δ)which in turn is either equal to the latitude (Θ) or complement (90° – Θ), and is given by the fusion formula:

Φ = ArcSine [ (√3/3) TanΔ ]

In temperate latitudes of both north and south hemispheres, both polar and equator-facing roofs are receptive to these fusions. Outside these latitudes the fusion is can only be implemented on one roof.

Such latitudinal variation makes “triangular wings” an apt term for the mirrored pair. Spreading the wings to their extreme forms the rudiments of a hexagonal pattern viewed from above, while completely folded, they pose one triangle from either profile.

With the tri-wings fitted to the (rectangular) roof, the overhanging portion is clipped flush with the wall to leave 2 half triangles while appearing as nothing more than a highly specified cross gable.

Cross Gable Wheel Port

As such the gable’s slope gives indication of latitude from a polar perspective (with the fusion formula solved for such) to round out expressions of the celestial cube projections from all directions viewable from the ground.

Together the clipped triangular wing halves combined are of course equal to one triangle – the simplest expression of the planar cuboda’s wheel orientation. Considerable time and thought went into this approach with several previous approaches rejected as lame and I wasn’t exactly thrilled by this solution. Why? Because it wasn’t unique or novel. But as its sensibility quietly grew on me, I came to wonder if perhaps the advent of the cross gable was an instance where the code’s fundamentals were being followed in a groping way.

Whereas architectural annexations and wheel slots only involve walls, this fusion involves both the co-cube projection and the added dimension manifested by the roof. Neutralizing the macrocosmic wheel via symmetry of the h-shift bestows upon the transporter an apt place of rest, while tension created by the difference between template and adjusted angles can be viewed as building potential energy to charge the transporter for its intended work.


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Polytechnic Intro

The middle part of Geocentric Design Code’s 7 parts can definitely be the most dry, complex, and out of range for all but the very motivated, but, it is also necessary. To ease the pain, here’s some air for Part IV’s title: Polytechnic Integration is the incorporation of polytechnic functionalities by way of polyhedral integration.

The poly- prefixed words are linked by the requirement that functional constructs designed must effectively respond to, or harness natural law (physics), and by the most simplified geometric representation of that law. By definition, the word polytechnic pertains to a variety of technical arts and applied sciences.

The word “polytechnic” also has special significance for the place of my birth and upbringing in the San Luis Obispo area of California. In my time Cal Poly has always hovered over the region as the dominant institution, economic force, and transient population, but I had little appreciation for the college until attending a “Poly Royal” – the school’s annual open house of yesteryear, while a teen. It was then that the meaning of “polytechnic” was driven home with exhibits and projects ranging from architectural to agricultural to just about every engineering field. After this one exposure opened my eyes to what the greater world was doing, I sometimes felt as if I was absorbing polytechnic  creativity from the air.

A half century later, the notion of a polytechnic spectrum called to a burgeoning design code upon the fusion of transporter and architectural forms, specifically a full fusion as opposed to the superficial integration of the methods described in recent posts. Delving into the deeper (3D) fusion engaged geometric relationships that I found could reasonably be applied to other connections.

In reviewing the existing Part IV’s 10 pages (of the 70-page PDF) however, I found the presentation of integrating ideas and applications so unintelligible Part IV might as well be titled Polytechnic Entanglement; and If accessible to hard core interest, it is surely devoid of any inspirational merit. So preparing for an expanded revision similar to what the first 3 parts have undergone, I have wrestled with how to make the material more easily digestible.

Ever striving for a linear approach where each concept builds logically upon what has preceded it, I have found that Part IV is not so simply organized because it theoretically could start with any one of a handful of basic concepts. In fact, I have even entertained the idea of switching Part IV and Ground Design because treatment of the latter doesn’t absolutely require the concepts of the former.

There are compelling resons for making the switch, but I have decided the overall flow would best be served by keeping the same order. What needs changing is the order within the subjest’s material. What I am going to start out trying is the easy-to-picture (and apply) fusion of shelter and transport, and then describe the underlying geometry afterwards which can then proceed to be applied in other key practical situations.

In the most plain terms, what amounts to a triangle-to- (cube) square fusion will turn, and ultimately proceed, to the opposite process where the square is fused into the triangle. By so doing, applicability of the triangular transport template will be expanded to guide sea and air transporters, as well as working mobile artifacts such as agricultural machinery, fishing boats, and exploration spacecraft.

Exactly how these will take shape awaits Part VI, but to prepare for them Polytechnic Integration will mostly be geometric gymnastics with just enough application examples to make it real. In embarking on this expansion I don’t foresee any new math beyond the simple trig expressions stated in the existing version, but I can’t truly predict what will come to light diving deeper into the applicability of code geometry in the next few months.

What gives Part IV its character and demands special treatment for it is revealed in linking intermediaries developed which manifest the difference between centuries’ long use of the cube for artifact design and addition of the more physically attuned cuboda straddling and orienting both the cube and the sphere. In the end, appreciation for the universal link of the latter will make the earth ripe for such interpretation in Part V Ground Design.

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Illustrated Rolling Transport

In addition to the PDF, I have endeavored to express Rolling Transport concepts in a way that involves minimal test – the titles to a gallery of illustrations. Although these have sufficient detail to deduce most of what the code brings to rolling mobility, the illustrations are mainly intended to serve as an intuitive intro that will hopefully spark some interest and complement the informal lecture-like nature of the posts and the formal PDF. Thus I have also included a link to the gallery at the beginning of the Rolling  Transport Page. To Rolling Transport Gallery Development of similar galleries also attended the previous topical series of posts which are the Orientation Gallery situated at the beginning of the Orientation page, and the Cube-based Shelter Gallery at the beginning of the CBS page. These are also accessible on the sidebar to the home page. Actually the galleries would have been more effective at the beginning of the each part’s posts, but they were not ready then because they were being developed in parallel with the posts – during lower energy times of non-analytical moods.

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Final Rolling Clarifications

In crafting the PDF that paralleled Rolling Transport posts for the last 5 months, some material required much creative condensing. In so doing, the description of some key points pertaining to the cubodal wheel were either omitted or left open to misinterpretation.

One example is the dismissal of radial spokes in having any value transmitting torsional forces. With regard to the axis of rotation, this is true because the sine of the angle between the force transmitted and the moment arm is zero. Viewed differently, the nearer the angle approaches an optimal 90°, the more likely the spoke will be snapped at the very small contact area provided by the axis.

Such conditions are avoided by appropriating off-axis spokes that are optimally aligned, that is tangential to the circle of rotation instead of perpendicular. Also, by inscribing hexagonal geometry into the rim, forces are shifted or apportioned into components that work their way to the rim.

Radial Spoke Torsional Engagement

Omitted at this point was how a tangential component worked on the radial spoke to effect torque not only on the axis but also on the continually moving instantaneous point of contact between wheel and the rolling surface. Thus radial spokes may play a significant role in a driven wheel, provided they are rigidly connected to the hub and not hinged, or are widened with hexagonal geometry for maximum strength and minimum weight.

When the cubodal hub was introduced, I don’t think the term was made clear, and its graphic representation could have easily given one the impression that the hub was in fact a cuboda. What is actually meant by the term is that the hub employs cubodal geometry in the context of being circular or cylindrical.

Hexagonal layers

In practice, using cubodal geometry means appropriating its layers, which are hexagonal, or reduced to the base form – triangular. The hub’s components such as flanges can be shaped thus (after all hexagonal nuts and bolt heads are in common use) but more likely they will be circular and spokes will then be arranged in a hexagonal pattern.

There is no more compelling need for the layered approach than what is posed by an hypothetical fusion of the cuboda wheel in its 2 alternative profile orientations that are shifted by 30° to pose a complex tangle of lines and planes. However, by isolating only corresponding layers of each orientation, integration is quite manageable. (Although previously derived and then applied in a few instances, the layered approach only involved one orientation to avoid too many concepts at once).

Simplification of Cubodal Wheel Orientations

With template-guided fixed wheel constructs, fusing layers of disparate orientations requires a special intermediary described in Part IV. But because the intermediary is circular, this is not necessary because a rolling entity provides its own circle of rotation. The actual fusion is no more complex than what might first be pictured (above) – transposed hexagons with 12 evenly spaced points.

Regarding a real wheel exhibiting depth in which it is important to stagger this dimension’s structure for lateral stability (as well as expressing the wheel’s inherent asymmetric dynamism), oppositely oriented triangles from each orientation can be fused as shown below in a simple straight approach. (triangular points may of course be rounded, convexly or concavely).

Integrated Cubodal Wheel Orientations

Cross bracing guided by cubodal lines joining layers is applied only to crossings from a specific cubodal (and thus hexagonal) orientation. Radial spokes extending from respective greater hexagons, as well as spokes extended from their sides come to a total of 36 – the same number in common use with contemporary bicycles. All of the above can be inferred by the PDF’s text and graphics, but is not spelled out as it probably should be.

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