Half-way Photovoltaics

WBA Solar RoofIn my last post, a prime wheel-based architecture option entailed separating the complementary-sloped roof patterns of cube-based shelter and setting whatever was sculpted from them atop 3D rectilinear annexes appended to WPA’s south and north walls. Then it was suggested that although the equatorial-facing roof had limited area, it was still optimally  oriented for a smaller scale solar system.

The reason I think it would be worthwhile to go for a smaller system is that I believe the common “all-or-nothing” mindset in replacing nuke, coal, or fracked gas power generation with renewables is a false choice.

As a semiconductor-based proposition, photo-voltaic electricity generation should have grown hand in hand with the escalation of electronic goods. However it did not, and its primary role was off the planet powering spacecraft for a long time. Even now, despite the rush of popularity in recent years, PV pitifully represents less than 1% of the electricity generating pie.

The situation can and should be righted by first scaling a PV system to the electricity needed for a home’s consumer electronics – computers, radios, stereos, TVs, etc., and lighting with the advent of light emitting diodes (LEDs). Such a system might be separate from grid electricity to avoid rate arguments and what not. Grid power would be utilized for motorized appliances like refrigerators, fans, washing machines, microwaves, etc.

Here’s an example of how a WBA porch roof would play out. For simplicity, the roof over a 7 X 12 porch at 30° latitude is sheathed by three 4 X 8 plywood sheets. In this area, one 4 X 8 PV panel is placed lengthwise such that 2 feet surround it on all sides.

WBA Photovoltaic

This area might be characterized by substantial trim to soften the roof-as-appliance appearance, and/or be used for albedo compensation. To be mature and real about it, PV should admit its own heat contribution to both local warming (under the roof and inside the house) as well as global entropy and proceed accordingly. Happily the PV negative of waste heat production is easily neutralized by including sufficient white roof area around the panel.

The 32 square foot panel equates to about 600 watts. Next, a modest average of 3 hours of nearly direct sun per day is assumed for a total of 1800 daily watt-hours.

Electronics Power ConsumptionThe table shows a rough consumption approximation of electronic (semiconductor-based) artifacts using ball-park wattages.

Greater WBA Solar Tree FriendilnessThat’s a pretty nice chunk of a home’s power needs met by the panel. If the waste heat generated by the panel (9600 watt-hours) could be tapped for heating water – all the better. An added virtue of the WBA solar alternative is that more space is allowed for trees.

Such an approach would represent a good first step in giving the institution of utility monopolies some healthy competition. When I biked across North America to Alaska years ago, I found attacking the halfway points of hills where their maximum slopes lie was more effective both physically and psychologically than worrying about the top of the hill. I believe the same approach would work well with homegrown electricity generation.

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

Wheel-based Shelter

The intricacy of path geometry’s edge, square, and vertex-up cubodal orientations was applied fully and explicitly in the code’s bridge structure.

Wheel-based shelter (WBA) on the other hand engages most path concepts in its totality, but its structure is very simple – especially the version intended for the Polar-rotational grid which will be the focus of this post.

Mirrored Wheel Port AnnexIn a nutshell, WBA’s  P-R grid version is predominantly characterized by completion of the structure appended to east or west walls of celestial cube-based shelter (CBS)serving primarily as a port for wheeled artifacts as described in Part III. Like that construction, the alignment of WBA is longitudinal only, i.e., its ridgeline is strictly polar (north-to-south).

The origin of such construct arises from the macrocosmic wheel – that great cubodal wheel whose center coincides with earth’s center. With the CBS annex, this wheel was simply rotated latitudinally such that the outer edge of any square paralleled the tangent on the ground.

H-shifted Macrocosmic WheelFor WBA, the hexagonal shift that symbolically neutralizes the wheel’s dynamism is required at this point. The resulting squares sloping from both sides of the same edge guides a symmetric roofline pattern of pitch √2: 1 ( 35°). This is of course set atop the 3D rectilinear construct of walls projected from the celestial co-cube.

With inclusion of round windows derived from rotation of the wheel’s microcosmic representative and set on east and west walls, that’s basically all there is to WBA on the outside.

p-r grid wheel based shelterOn the inside, the same 35° slope guides staircases and structural members – exposed or otherwise – running east and west.

It is important to compare the derivation essentials of WBA, grid berms, and path expressions as each shares the same mirrored (edge-up) slopes, but are functionally different. The symmetry of grid berms was attained by having the edge-up cuboda follow the rotation of the vertex-up cuboda possessing a matching (35°) slope.

Edge-on square slope(s) approaches

Path expression on the other hand was derived by superimposing cross-sectional rotations about travel-aligned axes on either side of the transversely separated road boundaries.

With its longitudinal ridgeline, WBS poses an orthogonal alternative to the CBS latitudinal ridgeline for building sites biased in that direction. In so doing, WBA offers an option in which primary celestial cube projected roof slopes are appropriated by separating them and setting one half atop a structure appended to the WBA south wall and the other half appended to the north wall.

CBS Annexes

Such modest, scaled-down CBS expression,  subservient to WBA as it is, would typically serve as porches, sunrooms, or bed-loft-over-bathroom nests, with the equatorial-facing appendage providing a smaller but optimally-aligned area for a limited solar system.

WBA is naturally more accommodative of wheeled artifacts than CBS and its greater conventionality makes this style more appealing to those averse to the CBS tilt. All in all WBA has wider architectural applicability than CBS going beyond residential into realms ranging from commercial to churches.

Whatever the function, a few options avail themselves to this style. They include rounding the ends fully with straight conical forms, or doing the same over a relatively smaller radius with bay windows.

wheel-based architecture options

Additionally, seeing that WBA is connected to and otherwise associated with wheel and path, curved roofs with 35° or 90° terminating tangents (as with Quonset huts) can substitute for straight slopes. Curves with 35° tangents can be parabolic or circular.

.   .   .   or wave-formed. This option also plays out in WBA embanking options, but the rules for such engage the more complex ideas of path and are thus explored in a separate forthcoming post.

Posted in Code Application, Contemporary Relevance, Cube-based Shelter, Derivations, Ground Rules, Rolling Transport, Wheel Extrapolations | 1 Comment

Bridge Parabolas Revisted

While constructing the post on code bridges, a dim sense questioned the necessity of restricting verticals from merging with the parabolic curve only where tangents are consistent with cubodal geometry, i.e., at edge and vertex-up cubodas’ 60° and 30° angles

However, the light bulb didn’t come on until after I published the post. It makes perfect sense for circles to be subject to the tangent rule as well as their cyclical wave spin-offs which can at least be viewed mathematically as trigonometric expressions of circles in the context of an orthogonal (rectilinear) coordinate system and which have but distinctive tangents – 0° and a maximum slope.

What is different about parabolas is their reflection of all lines directed parallel to the axis of symmetry through a single point – the focus. Viewing this phenomenon in reverse, any line directed from the focus to the parabolic curve invariably reflects parallel to all the others no matter where it hits the curve or at what the tangent. In contrast, any line directed from the center-point of a circle simply reflects back at the opposite angle, and thus the reflection of a non-cubodal angle is also non-cubodal.

parabolic reflections

With the parabola’s axis of symmetry oriented vertically, wherever a vertical line hits the parabolic curve, it will be reflected through the focus and hit the curve again, wherefrom it will be reflected vertically in the opposite direction. The parabola’s universal production of code consistent (but taken for granted) vertical lines, regardless of the intermediary reflected angle (or tangent angle), means verticals can be applied anywhere on the curve deemed necessary with arches or suspended cables.

Nevertheless the previous specification of verticals only making contact at the curve’s 30° and 60° tangents still holds for terminating points.

parabolic termini

The reason for this is all these angles are part of (the only) trifectas in which tangents, verticals, and reflection angles are all code consistent.

orthogonal parabolic reflectionInterestingly, there are a few other parabolic tangents that pose less code consistency than 30° and 60° but more than the mundane continuum of tangents. At the 45° tangent the reflected angle is horizontal. This angle evokes the shallowest and deepest to the square and vertex-up cubodas respectively and represents the angle of the grid juncture’s inherent slope to which elements fuse. Also shown in the illustration is a circle nested into the curve with a radius equal to the focus distance. Not being a mathematician, I don’t know to prove such a circle is the largest possible without contacting the curve beyond the vertex, but I suspect very strongly that it is so. I also don’t know if this has any significance, but in light of the parabola’s correspondence with other physical phenomena, it would seem to be a distinct possibility.

Verticals merging at the 35° tangent and expressive of the intra-grid juncture bounce to the focus at a 19° angle as it does with the 55° complementary angle – a combination that ties the cuboda’s edge and square-up positions together to suggest that the cuboda – like the parabola – has its own innate reflective properties.

cubodal parabolic reflections

Verticals merging with the parabola’s 15° (and complementary 75°) tangents reflect plus or minus 60° lines. Thus vertical members joined to the 15° tangent poses a halfway point between the 30° parabola’s 0° vertex and its termini. These combinations pose another argument for allowing verticals at any tangent as a complete 180° reflection entails two tangents. These being complementary, they add to the code-consistent 90°.

Allowing universal placement of the verticals facilitates connection coordination with hexagonal truss junctures – after the hex structure is sized to the length to height ratio of the curve. If not done, the hex structure can still be built up around the curves midpoint.

arched code bridge example

To fully utilize the parabola’s attributes, it seems reasonable that the focus (or directrix) correspond to basic bridge point. Otherwise the structure can again be built up to center the focus – with a circle placed there signifying the proverbial keystone.

12-GDCode-wise, it wouldn’t be wrong to follow the previous post’s rule – just unnecessarily restrictive and possibly very unwise. Therefore, in light of these new assessments, my previous statement that the circle afforded more flexibility than the parabola in the context of bridge arcs was precisely backwards.

Posted in Code Application, Code History, Derivations, Wheel Extrapolations | 1 Comment