Extra-topographic Pad Design

In the last post introducing ET Foundations, the simple circularity characterizing support bases for outwardly-projected constructs was defined by the intersection of the geocentric cuboda’s cylindrically enveloped spheres and earth’s surface.

Derived thus, the cylinder is only one of a handful of basic forms spun about central vertical axes that may guide artifacts intended to set upon the circular pads. In fact, much of the same geometry guiding the supported constructs is employed by the pads themselves.

3D grid mounds and ET pads

As plainly exhibited by the 3D cross-sections of circular landscaping mounds, waveforms represent the smoothest, most elegant transition from one level to another. As such, a pad supporting ET constructs is basically a mound centered by a flat circular plateau.

Recall that the maximum slopes of mound waveforms are keyed to the sloping elements of the vertex-up cuboda, with particular slopes determined by the role played by the mounds in a greater grid context.

Grid juncture review

For example, the 30° sloping edge defines the maximum slope of an inter-grid juncture while the 35° sloping triangle defines the slope of an intra-grid juncture.

To some extent, projected mounds may go beyond filling a context role to actually defining the greater context. For example, a 35° max-slope mound might characterize a pad situated along the direction of a grid line defined by the projection of the edge-up cuboda. In such case, the edge-up cuboda’s 19°, 35°, or 60° angles manifest in a configuration of at least 2 concentric rings.

Concentric ring layout of edge-up oriented pad

The bottom outer slope represents the greater grid by manifesting either of the edge-up’s sloping planes (19°, 35°) with 19° representing the only use of that angle in a circular mound to in effect distinguish its role as a support pad. The inner waveform either possesses the slope opposing the outer waveform or that of the common 60° edge.

As such the slope either goes up in a terraced fashion or down into a crater setting. In either case, the center portion bearing the ET construct is circular and typically flat.

Dual ring pad options

As with landscaping mounds, the waveforms may be quarter or half, with the waveforms’ defining points – crest, trough, and maximum slope – posing natural transition points for the introduction of cylindrical and truncated conical forms.

By the same dual-ring approach, a hexagonal grid foreign to the rectilinear nature of both the polar-rotational and diamond grids may be introduced. In such case, the 2 orientations are integrated by the universal linking intermediary of the cylinder defining their boundary.

Dual-ringed pad layout for triangle-up constructs

In such case, the inner ring – the upper terrace or crater waveform – would have its maximum slope keyed to the triangle-up cuboda bearing the hexagonal pattern. Those slopes correspond to the 55° square or 71° triangle.

The hexagonal pattern is plainly more circular than the rectilinear pattern for basing a circular cross-sectioned artifact. But as a triangle-up cuboda-guided construct must exist in the P-R and/or diamond grid context, how the triangle-up cuboda relates to the host grid is examined.

Rectilinear-hexagonal grid integration

First the 8 directions of the alternating grids are transposed on the circle integrating them both in an orthogonal manner. Then a vertically oriented triangle is positioned via primary and secondary rotations in opposing (left/right) senses and the same is done for the horizontally aligned triangles, with 8 points added to the circle.

ET pad's 24-point structural support configuration

The same maneuvers are implemented with tertiary rotations about the axes of the diamond grid orientation to add 8 more points. All in all, 16 points are added to the 8 provided by the P-R and diamond grids for a total of 24 separated evenly by 15° – just like the hours of the time zones. As each point partakes of both a square and a triangle, the whole layout constitutes a kind of universal configuration for projected constructs having  a circular cross-section.

15-Such sectioning is useful for structuring the support of ET artifacts and is essential to affording access to and through the pads, a major consideration addressed in the next post.

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ET Foundations

For the next few months, posts will concern Extra Topographic Guidelines which constitute Part VII of Geocentric Design Code. In this organizational context, what ET guidelines refers to is a class of artifacts that are viewed as projecting outward from the earth’s surface.

Such constructs can be attached to earth architecturally; attached and emissive as with towers transmitting (and receiving) electro-magnetic waves; or emissive only with totally detached projectiles such as rockets.

Vertically Projected Cylinder of RotationTo build a conceptual base for all 3 possibilities, the topics that concluded Part VI Wheel Extrapolations are evoked. What the disc orientation, and especially the vertical axis wind turbine suggest in the rotation of their cross-sectional geometries is the simplest projective form – the cylinder outwardly directed from earth’s surface, or vertically aligned from a local perspective. Even with more complex forms spun about a vertical axis, cross-sections are circular.

To regard such constructs as arising from the inside out, the geocentric cubodal shell is viewed with the potentiality of its intrinsic structural pattern to include a cuboda inscribed into earth’s surface. Conceptualized thus, the earthbound cuboda (and its internal pattern) is positioned in the same manner used for celestial cubes or the macrocosmic wheel – via primary longitudinal and secondary latitudinal rotations.

Internal Pattern Expressions of the Geocentric Cubodal Shell

So viewed, circular cross-sectioned cylindrical forms can be projected by bringing the cuboda’s spherical expression into play – with spheres centered at any intrinsic pattern intersection. Although radially-aligned spheres are the most natural way to conceptualize such, there are actually 3 additional ways by which to meld spheres with cylindrical forms for a total of 4 possibilities corresponding to the basic cubodal orientations.

Cubodal Pattern Cylindrical Projections

The radial possibility has already been employed with grid juncture and architectural corner mound waves spun about the vertex-up cuboda. These were applied to landscaping in Ground Design and infrastructure in Wheel Extrapolations. The relevant point here is that they exhibit circular cross-sectioned foundations. Such employment can theoretically be extended to city planning.

Tic Tac Toe City Planning Centeredness

To see how, organizing rectilinear grid geometry for such purpose is briefly explored. In the “tic tac toe” plat, the center square of 9 functions as a block’s common area, neighborhood park, and – progressing outward – to a city square and beyond. Clearly the configuration exhibits a centered-ness evocative of the circle. Another layout possibility that is somewhat more complex entails an alternation of P-R and Diamond grids.

Centered Diamond and Polar-Rotational Grid AlternationIn the larger sense of such alternation, the 2 grids may be linked circularly to facilitate efficient transportation and some utilities flows. The details of connecting radial directions to tangential circular curves required for access are determined by the form type – wave, cone, etc. – and the greater context of the cross-sectioned sphere’s orientation.

The advantage of the vertex-up orientation and its radial alignment (aside from supplying a nice range of slopes) is that spheres along those lines are just in contact and thus exhibit an essential continuity which frees any cylinder melding of them from proportional specifications. Conversely, the lack of continuity characterized by the 3 non-radial orientations is accounted for as illustrated below.

Continuous and Separated Cylindrically-paired Sphere ProjectionsThe height-to-diameter ratio of the conceptual square-up cylinder is √2:1 and √3:1 for the edge-up. The triangle-up is √6:1 as was previously derived for propeller hubs. At this point, these cylinders are conceptual and are addressed mainly to show the possibility of their potentiality by reason of their axes coinciding with locally vertical or earthly radial lines. However the cubodal geometry is oriented, lines always converge at earth’s center. The other main point is (again) the fact of their cross-sections being circular, which will be the 2D foundation geometry of all constructs presented in Part VII.

The vertical axis wind turbine was the best example of the triangle-up orientation in relation to the earth’s surface and as such poses a hexagonal grid foreign to the rectilinear patterns of the P-R and Diamond Grids. How this is resolved in surface and 3 dimensions will be the topic of the next post along with the aforementioned access problems.

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The Geo D’code Intro Video

With the Part VI series of posts on Wheel Extrapolations complete, and I now wrestle with how to proceed in the expansion of Extra-topographic Guidelines (Part VII), I am posting the video intro to all of Geocentric Design Code in the interim.

Although I am not thrilled with how the slide show quality is diminished by its conversion to the video format, I still think it can impart a simple sense of how the code’s universal geometric form applies to a considerable range of constructs – in less than 5 minutes.

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The Illustrated Gallery of Wheel Extrapolations’ Concepts

This post will be the last of the series on Wheel Extrapolations begun 6 months ago. As a portal to the introduction of an endeavor that is virtually all graphics, I view the gallery as a kind of icing on the cake. With the artwork, I have gotten more playful, especially in contrast to the previous posts’ PDF which is very conservative and formal – “just the facts.”

Part VI Gallery Post Graphic

My hope for these illustrations is that they convey, with no more text than guiding titles, the notion of how the simple cuboda can with its crystalline variegation, address artifacts that are wheel-related be they dynamic; template neutralized; or macrocosmically projected. Neglected in the posts and PDF but included here is the means for obtaining visual perspective in flight.

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The Part VI Wheel Extrapolations PDF Beta

Part VI has presented the most challenging subject matter to date, which is one reason why there have sometimes been 2 week gaps between posts and the whole endeavor has taken half a year. But it is done and I am satisfied with how it all took shape. 

One challenge is that information held by the seemingly simple cuboda grows with each new perspective and insight. A form that can be reasonably applied to differing architectural functions as well as such varied constructs as roads, farm fields, bridges, dams, airplanes, marines vessels, their propulsion, satellites and other spacecraft is a form to be reckoned with. Click on the graphic to check the out the completed PDF.

Wheel Extrapolations Intro Graphic

Expanding the whole code document from an existing 70 to a planned 92 pages has resulted in surprising new ground. The most significant is the dynamic transformation concept with the one instance related being just the tip of the iceberg, I think. Then there are the items that were not in the posts that usually led my thinking process such as the whole plane angle of attack. There will be one more Part VI post to introduce the gallery of Wheel Extrapolations’ concepts.

Posted in Code Application, Code History, Contemporary Relevance, Derivations, Polytechnic Integration, Rolling Transport, Wheel Extrapolations | Leave a comment