Making a Stand for Homegrown Energy

The availability of inexpensive portable-scale solar panels, batteries, and chargers makes building a structure to support them a worthwhile project. For less than $20 and a couple of spare hours, just about anyone with a small space exposed to a few hours of sun should be able to build their own customized stand to meet some of their electricity needs.

solar-stand-lumber-cutTo make the stand suitable for a particular location, (celestial) cube-based geometry is engaged and the following poses an example of how mine came out. To support would might be characterized as a doll house-sized “roof”, I took a piece of 2” X 8” lumber and chop-sawed it at the angle of my latitude (35°). In making this cut, I could use both sides for the base.

On top of the 2” thick edge, I nailed a 1” X 8” board to accommodate the panel. That is all there is to the stand’s structure which is quite easily moved to and away from a sunny spot facing solar noon for a few hours. Other considerations remain. To harmonize the base structure with its surroundings, I took the safe approach and simply followed the home’s 2-tone color scheme to make it seem like a part of it. For those who possess an advanced artistic sense, a color scheme might be chosen to distinguish the stand in a complementary way.


But paint is more than just for aesthetics. For the top sun-facing surface around the panel, a color selection is required to counter the ill effects of the low albedo panel because, truthfully, its blackness absorbs (and re-radiates) sunlight just as the much if not more than the popularly demonized carbon dioxide molecule. Luckily the antidote for this is to simply paint the surface around the panel with a high albedo hue to reflect light right back to space.


Generally speaking, the default color choice for this is (glossy) white. By painting an area white equal to that of the panel, the overall albedo of the stand’s “roof” is increased. This translates to both global and local cooling effects. Regarding the latter, I can confirm a quite a noticeable difference when handling the panel after several hours of exposure. The cooling effect around the panel also makes it run more efficiently. One can fine tune the albedo factor by proportioning exposed area to a desired ratio and/or by tinting the white with softer colors and/or creating a pattern to make the panel less conspicuous and imposing.

My half square foot, 6 watt panel with the corner ear loops cost $50 and the 5000 mAh battery is sufficient to handle my personal lighting needs, as well as being able to charge an AA/AAA battery charger to run other items like bike lights, an mp3 player/radio, and a computer mouse.

All energy sources have their positives and negatives and I believe it is fitting and wise to match each type to its use. In my view, the direct semi-conducting driven process of photo-voltaics should be applied to semiconductor devices – LEDs, computers, TVs, stereos, etc. To do so would take care of a significant chunk of the electricity usage spectrum.

Posted in Code Application, Contemporary Relevance, Cube-based Shelter | Tagged , , | Leave a comment

Bode Wave Development

Thus far, primary elements of bode geometry – point spheres, line edges, and dueling planes (squares and triangles) – have shown they can, by their characteristic arrangements and interplays, readily generate other forms.

For instance, in addition to the intrinsic axes ascribed to any of the bode’s 6 radial line sets, 3 alternative axis types are easily derived from opposing sets of squares, triangles, and edges by reason of their having easily determinable midpoints which are in line with the bode’s center-points. From these, can naturally be generated – with their slopes shaped by the angles of elements spun about, and relative to, the axis employed.

Cuboctahedron Sections

Once cones are generated, parabolas, ellipses, and hyperbolas are created by sectioning the cones with planes intrinsic to the bode. Ellipses are actually sectioned more directly from planes intrinsic to the bode’s intrinsic spheres, which brings me to the crux of this post: Is there something intrinsic to bode geometry that leads to, or naturally expresses waveforms?

Cuboctahedron Wave PrismWhen waves were first applied to the mounds, berms, and architectural embankments of ground design, no explanation was forthcoming of anything bode intrinsic because, frankly I hadn’t given the matter much thought. All that was stated was something to the effect that the wave represented the most elegant transition from one level to another. Bode geometry only came into play to specify a wave’s maximum slope using the analogy of a prism splitting random terrain (white light) into a quantized set of waveforms. Although this might represent a novel application, the wave itself appears to come from outside the realm of the bode.

But if conic sections can be derived so easily, it would seem waves should also, especially in light of the bode’s intrinsic rotational dynamism, and by the notion of the sphere being sectioned more directly than the cone to create an ellipse.

By such considerations, the following constitutes a hodge-podge of observations and musings, beginning with the sectioned circle; its rotation via the preceding rationale; the mathematical and possibly natural relation between it and the wave. By this I refer to the sectioned bode circle in a square context. Pictured thus, relative rotation is only observed by focusing on a point of the circle’s circumference, with such a point being relational – as opposed to the circle’s integral center-point. In this context, “relational” manifests explicitly in terms of other spheres or, in this case, between one sphere and the square.

Cuboctahedron Wave Generation

Between the sphere and the square, the relational contact points define the 2 axes of an X,Y plane such that the position of a rotated point can be described separately in 2 dimensions of the square grid’s orthogonal lines. When the ratio of the point’s horizontal and vertical distances to the radius changes via rotation keyed to the arc length subtended, the plot of the relation is a wave. Does this mean waves are derived from bode geometry as the conic sections are?

Relative rotation of the sectioned (sphere) circle in the square grid context. Does nature care about such ratios? Perhaps only if the ratios are parameterized with time inferred by rotation.

What about the circle’s relational points? When the parallel (square) planes of the celestial co-cubes are rotated relative to each other, so go the relational contact points and their wave-manifested ratios, a happenstance that lends CBA yet another dimension of expression. Although this wave connection is somewhat compelling, the relation to bode geometry is not immediate.

Circle Wave Relationships

With the rolling wheel, on the other hand, the cycloid of one revolution equals one wavelength of the rotated circle. However, there is still no specific bode association, let alone a unique one. The superimposed square to triangle transformation arcs supply an alternative mechanism for rotation, but does this translate to a generated wave? Length of the arc comes into focus with π, but there is still no intrinsic bode distance between spheres that involve that constant. How about rotation of the triangle about the common edge to superimpose itself on the square?

In the model of electro-dynamic behavior posed by bode geometry, triangles oscillating on either side of a propagating line reflect the mutually orthogonal electric and magnetic fields embedded in the bodally arranged octahedral spheres. Alternatively, the shortest line distance between vertically aligned points of the triangle-up bode looks like it could correspond to a matter wave. If either or both of these present a sound correlating picture of EM and/or gravitational behavior, the bode can be said to possess the wave intrinsically. After all, alternators are circularly rotating devices with no apparent wave connection, but that is exactly what they make.

Cuboctahedron Matter and Electromagnetic Waves

I am skeptical. It seems more likely that the bode pattern infinitely generated poses a good representation of the space-time fabric through which waves travel. I.E., waves are not something in the bode that can be evoked and brought to life, but are caused by a disturbance, be they electrons, winds blowing across the water, or a meteor crashing into our plastic crust.

One last matter: In formulating the wave mathematically, the maximum slope and the radius of the generating circle from which the ratios are described occupy the same place in the equation. What connections can be made, especially in the context of bode geometry?

Circle Radius-Wave Slope Relationship

For one, spheres may seek to touch diagonally across the square by enlarging their radii, with a similar situation found in the triangular cluster. Radii also undergo a change with formation of the ellipse as a rotated sectioned sphere circle, with the circle’s relational points becoming foci. Relational contact points of other spheres angled away from the reference unity sphere poses another scenario. Otherwise, something akin to shoaling relates size and slope as a wave is created or transmitted through the faceted bodal prism.

Posted in Code History, Cube-based Shelter, Derivations, Extra-topographic Guidelines, Ground Rules, Polytechnic Integration, Rolling Transport, Wheel Extrapolations | Leave a comment

If I We’re a Landscaper

In overhauling and expanding the code’s formal PDF, I have come to appreciate just how much space is devoted to abstract reasoning behind the applications, and how far GDCode may seem to be removed from reality.

But in reviewing the math for wave-formed landscaping recently, I found it easier to make the connection with the volume of DIRT required to realize a plan. Before showing how useful the formulas are, here’s a brief description of how they were derived:

For half waves spun about their crests or troughs to shape mounds or round berms and embankments I used the thin shell integration method on the wave equation Y = M cos X, with Y being the height, M the maximum slope, X the radius and dx the thickness of the cylinder. I treated a quarter wave section at a time and spun from both directions to account for concave rounding situations.

Landscaping Wave Volumes

After integrating the convex crest quarter wave section, I divided this generalized volume by that of the cylinder bounding it to obtain a proportionality constant. For the concave trough volume, the convex crest volume is subtracted from the same cylindrical volume and divided by same to obtain its proportionality constant.

Wave Volume Integrations

The same procedure was used for the concave crest and the convex trough, but as these are separated from the pivot, the integrating limits are shifted from π/2 to π and proportioned to the volume of the (thick) cylindrical shell bounding them. I then I found I could multiply the proportionality constants by the volume of a wave-bounding cylindrical shell in a specified situation to obtain a real waveform’s volume.

I am not absolutely certain that this is a valid approach for volumes of waves spun about axes, but it seems reasonable and the relative size of the constants derived are consistent with what one would expect. For the derived constants and formulas, check out the new PDFs when they are published in a few weeks on this website.

Wave Area

What I am more certain of is taking the area of the wave cross-section and multiplying it by the length of an architectural embankment to determine its volume. Still, it seems strange that the constant does not depend on slope but the more one studies a range of slopes the more this makes sense.

Volume is important for two simple related reasons. Obviously, when one lays out a landscaping plan, quantity of dirt required is of great importance. The second value comes at the end of the embanking procedure which commences with determining and marking the wave’s height and width and their relationship keyed to the maximum slope chosen from a small set of options.

Waveform Embanking Basics

The next task is to stake out a string to signify the maximum slope which is half way between both the height and width. The next thing is to drive pointed rods every few feet with flat pieces angled to the maximum slope secured to the rod at the height of the string and extending upward.

Waveform StakingNext the dirt is piled in such a way that the crest and trough are horizontal and the steepening curvature of slope from the crest jives with the stakes’ board slope along the string. Upon satisfying these basic conditions, any remaining dirt is placed at the most glaring deficits eyeballed. If dirt is consumed before satisfying these conditions, material shift from excess to deficits is in order.

In my mind, this procedure was the most one could do without getting into high tech instruments. Then I explained what I was doing to my father (whose livelihood entailed working with road construction engineers) and he quickly pointed out the identical mirror image nature of the top and bottom wave portions.


Straight Slope embankments with mirror waves

Properly enlightened, I saw that the dirt volume in its entirety could then be piled up in a straight slope from top to the outward boundary. Dirt could then be sluffed away from the midline and placed directly above the string with full knowledge that the two volumes are equal as should be. Much better way. To perfect the slopes, mirror guides can be cut from a sheet of plywood.

This would work well for a symmetric wave and even though such is unnecessary or even impractical in many situations, it still poses the simplest, most elegant default waveform. All that remains is to plant the ground cover decided upon and wait for the waveform to unite the abode with the earth.

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Embarrassing Moments (of Inertia)

Several weeks after having started an expansion of my comprehensive GDCode PDF this past May, I was trying to verify some math formulas I had derived 2 years prior pertaining to rotational inertia, and which were posted under the title “Intrinsic Wheel Quantification”.

Spoke Moment of InertiaI remember the engaging challenge of finally putting a calculus education (received 3 decades prior) to practice. To test myself, I started with a simple spoke moment and came up with the same expression that tables stated!

However, for displaced lines perpendicular to a line extended from the axis and representative of bodal wheel triangles and hexagons, I should have caught on to how the expression arrived at was perhaps a bit more complicated than it should be, but I deemed my procedure sound and posted without verifying because no tables listed the configurations (as simple as they are), and I was not yet aware of how handy the parallel axis theorem is.

But in reviewing my work recently, I thought to use the theorem which gave me a very different expression. So I then went through the old procedure and got the same expression as before. Which one was right? The answer eluded me until studying similar problems in my Mary Boas.

Mass element on a curveIt seems the way I had specified infinitesimal mass (dm) was not up to par, and required the Pythagorean Theorem for a radius that varies with angle. Thus, I made another go at it and my answer seemed to improve in simplicity but still did not agree with what the parallel axis theorem yielded.

Perhaps I had misapplied the theorem and didn’t fully comprehend what the conditions of its use were. But after much digging, thought, and rereading, I determined that the answer it gave me was correct and something was still awry with my calculus approach. Finally, I looked at the angle I had used to set up the trigonometric relationships and discovered that although it was the right angle in a generalized sense, the reference axis I used didn’t properly account for the changing radial distance to the mass element.

Triangle Rotational Inertia

In making the correction, the complementary angle was found to be the relevant one and so ascribed, the limits of integration were changed also. Going through the problem set up accordingly, the expression arrived at agreed with what the parallel axis theorem yielded both for the triangle above and the hexagon below.

Hexagon Rotational Inertia

As I write this the thought occurred to me that the reason I made this mistake was because I had grown accustomed to using spherical coordinates in a certain way.

The reason I sweated all this was because I wanted to make another go at getting the moment of inertia for the 2/3 circular arc element hypothetically inscribed into the wheel as something of special GDCode application. Proceeding forward with confidence in how to set up the problem, the shear complexity of the trigonometric expressions stopped me  with integral tables promising no help and I was too tired to go the substitution route.

Rim Arc Rotational Inertia

So I derived the element’s center of mass. Then after deriving the moment from the center of the completed circle with constant radius, I used the parallel axis theorem in reverse to obtain the rotational inertia about the axis passing through center of mass. With that expression, I used the theorem in the conventional manner to find the moment of inertia about the wheel axis – an expression that agreed with what I had posted the first time!


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geO d’code lingo

Just a few words to bring attention to the glossary of terms in the navigation bar. In developing Geocentric Design Code over the last 15 years, I have found it best to come up with special terms and phrases to make the delivery more palatable.  Although it is a work in progress (with links to illustrations in future plans), I think it poses an adequate quick reference tool for anyone seriously hoping to grasp the code – as it stands now.

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