The New Expanded Cube-based Shelter PDF

Here finally is the new CBS pdf. It encapsulates the topics of the last 5 1/2 months in a formal and efficient manner. Key equations derived are included, but not the derivations themselves, although I have tried – where there is space – to give a sense of how they were worked out. Post equations for the cylindrical sun chart were all done over and based on the local celestial sphere model. This PDF is in “beta” and is subject to change by the time I am ready to consolidate the expansions of all 7 parts in a more comprehensive PDF.

CBS Abstract

This PDF constitutes the essences of the CBS style. A reminder: copyright only protects distribution of an idea’s expression, not the idea itself, so the CBS style appeals to you feel free to use its guidelines at no cost. Naturally, acknowledgement would much be appreciated. Forthcoming are important enhancements and options for transporter accommodations in parts III and IV, as well as relevant landscaping and shaping guidelines in Part V.  Next, after a short pause, I will start Rolling Transport topics.

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Spheroidal Circus

Because sun path geometry loomed big and important, so I took the time to analyze it. Conversely, because correcting for earth’s oblate spheroid shape involved angles of about 0.1 degree, I hadn’t looked as closely as I should have on this. The reason I looked at all was because the angles translated to lengths measurable with typical field measurements.

Even so my heart wasn’t fully in the effort and that proved costly. The first mistake I made from the git-go a few years back stemmed from ignorance regarding established definitions of latitude, particularly the geodetic norm. Duly corrected, I promptly went on to the second mistake applying the correction to the roof, which I discovered just the other day seemed to be in the wrong direction. Disbelieving I could make such a blunder, I reasoned out a new “new right correction” but something still didn’t seem right, something to do with how the roof correction varied with changes in latitude.

Mystified and frustrated, I magnified the picture to get a clearer trigonometric handle on the variance, assigning angles to acutely converging lines, and then made a startling discovery: Geodetic latitude is exactly equivalent to the prime cube projection’s angle of incidence and thus the roof is in no need of correction whatsoever.

Oblate Spheroidal Discrepancy

Incredulous, I searched for the reason and came to this: Because geocentric and geodetic latitudes are equivalent at the equator and poles, so tangents at those boundary latitudes are exactly in tune with the prime cube projection’s planes, and as latitude changes between 0* and 90*, the geodetic origin slides along its major equatorial axis to assure repeating and complementary angles made with the rectangle framed by earth and cube vitals.

That no complicated easy-to-screw-up roof correction is required should be good news for home builders to whom the CBS style appeals but already have enough to contend with non-standard roof pitches. With no correction to roof needed or wall recommended, does the correction angle have any application? Just one: A flat roof attuned to the co-cube projection following geocentric latitude is not flat relative to the spheroid’s intersection tangent. For latitudes 35* and 55* the correction angle is about .17 degrees or a rise of about 3/16″ over a 5′ run, and sufficient to drain water.

But what about the CBS style attribute that states the smaller a structure is the more precisely it conforms to co-cube projection purity and is thus better. How does this latest oblate revelation effect that? Viewing the projection along a line of longitude, the statement stands.

But by analysis of the picture below from a latitudinal profile perspective, oblate discrepancy is actually lessened, if a structure is extended toward the pole, but at the expense of either structural or right-angled integrity.

co-cube oblate discrepancy

On the other hand, extending toward the equator worsens the oblate discrepancy, yet in so doing incurs the same expense.

What can be concluded from this is that smaller improves accuracy in one dimension unambiguously. The other plane dimension will always be off by the oblate discrepancy formula no matter how small. If so why be concerned about size? Because size inevitably distorts the 3D rectangular construct’s right-angled integrity, a separate matter from latitude conflicts. But in having to live with the oblate discrepancy in one dimension, this flaw in the co-cube projection – the egocentric projection – can look to the universal prime cube projection embodied with the ‘s geometry as pure and inviolate provoded its scale is small. In the matter of dueling latitudes, the normal of the geodetic latitude can be said to carry out the guidance of the co-cube projection rotated about geocentric latitude.

A more sublime implication of this circumstance is that “smaller is better” is not in itself a cure-all philosophy. If carried to its extreme there is still a problem that can only be surmounted by looking to the universal and overarching absolute. Along that line, what is worth remembering is that if this geometric situation parallels sublime reality, it is nevertheless not that reality itself. Even so, the upshot of all this confusion is that the code has come out of it better than ever, smelling like a rose, even if its author has been made to look like a clown in the process.

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The Mirror Roof Option

CBS Mirror RoofIn early Spring 1997, when the (celestial) Cube-based Shelter revelation transpired at the bottom of an existential crisis, a natural reflex to the style’s asymmetric profile was to include roof slopes that mirrored the roof slopes projected from the prime celestial cube, as if those projection’s planes were reflected off the ground. I’m sure the underlying reason for the inclusion was to make the CBS style more socially acceptable and not too different.

Transportation Accommodation

As the code developed through subsequent years, more practical reasons came to light for including the mirror roof as an option. Foremost is the roof’s ability to house transportation artifacts by the widened dimension of the shallower slope. This application is especially relevant if access to the road is not favorable using the style’s essential projection. How the mirror roof is used to effect such won’t be detailed until Polytechnic Integration is delved into, possibly months from now, but the PDF includes the basics of that derivation.

Another reason for the mirror roof is that in the event of location in a neighborhood or tract of homes, the neighbors are not forced to face the rear end of the CBS orientation, which might be construed as unsociable at best and disrespectful at worst. The thinking is this: the roof I look at is just like the roof from where I look.

Visual Sociability

Along those same lines, it will be shown that the method of transportation accommodation can be extended to go beyond visual sociability to include actual physical connection of CBS structures, even to the extent of surrounding space as in courtyards.

Celestial Projection DistinctionThe code rule for mirror roofs is that, if employed, they should not obscure expression of the essential CBS geometry from either the east or west side. This may simply mean including a telling plank along east or west walls. I have not yet thought up any uses for the steeper mirror roof, but if this and the shallower reflection are used together, special care should be taken to not confuse which is which because the mirror roof is just that, a reflection of CBS geometry not the original.

 

 

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CBS Breathability

This post will try to convey a sense of how natural ventilation can be enhanced by Cube-based Shelter’s characteristic geometry. As such, breathability is an extension of the style’s passive solar design attributes with the goal being to minimize the need for fans and air conditioners.

So far the only references made to address natural cooling entailed shutting out high sunlight from equator-facing wall glazing with a flat roof extension and specifying a high albedo solar roof base such that the area remaining after PV panel placement is sufficient to produce a net cooling effect.

At the lower end of the solar roof, the horizontal extension should situate high enough to allow air currents (from the general direction of the equator) passage through vents over glass doors and windows. If not, slatted vents might be incorporated between glass elements on that wall. The porch area defined by the flat roof can be employed to effect additional cooling by supporting a shallow water reservoir that cools as it evaporates.

Equatorial Air Ventilation

Or, the reservoir might supply water for a wicking material like burlap stretched vertically to the ground, with the resultant cool air produced from evaporation caught in the path of air movement into the house. Alternatively, the outside vertical plane defined by the roof extension can be a air permeable green walls of climbing flora, that create shade, and cools air by evapotranspiration.

Once inside, air may exit through vents on east and west walls. Of upmost importance is that the warmest and uppermost air have a means to escape which is afforded by quarter circle roof ridge vents.

Circular Ventilation

As with portholes indigenous to those planes vents are fully circular, or can share circular areas with glass partitioned according to CBS Geometry.Vent slats might also be rotated vertically to admit change of season air from the general direction of the poles.

In the absence of external air movement to tap into, the CBS cross-section poses a geometry having implications worth considering.  As a general principle, asymmetry begets movement. How that principle plays out physically with disparately angled ceiling slopes would most likely be initiated by air rising from the floor or a heat source like people. Like the sun’s radiation falling on the uneven terrain of mountain ranges to induce microclimate breezes, the resulting temperature and pressure differences arising from the varying planes of the interior terrain should induce air movement.

Asymmetric Ventilation

Conversely, the symmetry posed by the cross-sections of a flat or symmetrically sloped ceiling would more likely cause air movement to reach an equilibrium, and stagnate. Not that the CBS cross-section would induce a howling vortex, but the notion that subtle currents would naturally move in a pattern following the asymmetry’s intrinsic circular basis certainly seems reasonable. That movement would likely be biased in a counter clockwise direction in winter from low sun striking the most exposed floor area near the most glazing, and clockwise in summer from striking the polar side of the house. As air encounters the hard (90*) angle at the ceiling’s apex, stopped momentum would tend to encourage air toward east and west wall vents.

This dynamic can be enhanced by tapping into solar chimney effects that create and releases heat from the sun upward during the warmer months to draw up cool air from below into a circulation pattern.

To control and guide these air movements to need, the open beam ceiling joists of the CBS grand room structure can be used to support light movable horizontally-oriented panels.

Panel Ventilation

Or the joists can serve to hang drapes and or sliding vertically extended panels.

Heat flow considerations require that adequate insulation be provided for all the home’s glazing, perhaps sliding Styrofoam-cored panels for doors, and  upholstered cylindrical foam pads for portholes. Sloped Ceiling InsulationWith regard to the roof, recent building code specifications apparently do not distinguish between R-Values required for flat ceiling and a sloped roof even as the latter is in fact part wall to the extent of its steepness. To avoid installing unnecessary insulation (along with the extra material to accommodate it), a way to calculate the R-value for a particular slope in a particular climate zone is given by the above. For example if you are at 40* latitude and your climate requires R38 for the ceiling and R20 for the walls, the R value for your equator-facing roof is R34. The formula – being reverse  engineered as it is – may be oversimplified; but if it errs, I believe it does so on the side of caution, yielding more insulation than necessary. Even so, if you intend to size your roof thickness and insulation with this equation, check with your building inspector first.

Such are the low entropy ways in which CBS geometry addresses comfort. Additional approaches will come with cool tubes buried in earth embankments which will be described later with posts regarding Ground Design. For now, the embanking specifications can be viewed in this PDF.

 

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