Post on 06-Aug-2015
Weather-Secure Habitat Dr.Mohideen Ibramsha
1 of 27
The following specification particularly describes the invention and the manner in which
it is to be performed.
Weather_Secure Habitat 2 of 27
Introduction
Due to Global Warming the future weather is not expected to be similar to the past.
Earthquakes, hurricanes, tornadoes, and floods could occur anywhere on earth. We detail
secure habitats for the hostile weather.
Tornado has no effect on buildings with circular exteriors. A hurricane finds it extremely
difficult to uproot a hemisphere or a hemi ellipsoid in which the radius of an upper floor
is less than that of a lower floor. For such buildings the bending force due to the
hurricane decreases at higher levels while the weight of the building increases at the
lower levels. Further as shown in Figure 1 the slope of the building causes the force from
the hurricane winds push the building down increasing the stability of the building.
Floods do not affect a building with entry above ground when the flood height is less than
the entry. A building with triangles formed by pillars and beams is more resistant to
earthquake than without any triangle.
Our buildings have above the floor entry; have circular exteriors; have triangles in the
structural frame; and are hemisphere or hemi ellipsoid shaped with the radius of an upper
floor being less than that of a lower floor.
We demonstrate the feasibility of secure habitats from the smallest size plot of 40’ x 30’
to a plot of 400’ x 400’. Secure habitats could be on a plot of any size, larger than 400’ x
400’ also.
Housing plots are usually in grounds, 60’ x 40’. Some developers offer half a ground plot
also at 40’ x 30’. Until the hemispherical habitats become the norm, we would build
habitats on available plots. Usually the authorities require 10’ clearance abutting the road,
and 5’ clearance on the other three sides. We expect plots for an N feet radius hemisphere
to be (2N + 10)’ x (2n + 15)’ in future. For the present we consider 40’ x 30’; 60’ x 40’;
80’ x 60’; and 120’ x 120’ plots corresponding to half; one; two; and six grounds
respectively.
In India new material is laid on the old road resulting in the approach road going above
the ground floor of houses, even though we normally keep the ground floor about 1’
above the level of the approach road. We design for protection from 8’ high floods. Such
protection would remain valid only if the road repair is carried out by scraping the worn
out road and relaying the new road on the exposed soil.
Assuming that the approach road shall remain as it is at the time of building the habitat,
we design the habitats such that there is no entry point for water at a lesser height. One
way is to have the lower floor of the habitat surrounded by a sloping garden to the height
of 8’. Another way is to build the habitat sitting on pillars that are at least 8’ tall.
Weather-Secure Habitat 3 of 27
Most building authorities permit an FSI of 1.5. There are plans for raising the FSI to 2.
Where the plinth of the hemisphere is small, so that adding a ground level structure to be
surrounded by a garden as tall as the room still keeps the FSI low, a buried lower floor is
adopted.
We adopt this strategy for 40’ x 30’; 60’ x 40’; 80’ x 60’ plots. We consider plots other
than these with less than 6 grounds size at 120’ x 120’ to be rare and hence are not
discussed.
Before giving the detailed description, we consider the prior art and establish that our
invention is different from all the inventions so far.
Weather-Secure Habitat 4 of 27
Prior Art
Hemispherical domes are constructed for a number of years. Some of the famous ones
are considered now.
West Baden Springs Hotel opened for business in 15 September 19021. It has a 200 ft
skylight dome. This dome is supported by 12 trusses2. The distance between the trusses
works out to slightly more than 26’. Possibly the first monolithic dome was built In
Gatlinburg, TN, USA. The domes were built pouring concrete in forms specially
fabricated3. The very first dome built in Gatlinburg is not in use due to a moisture
problem. All domes have problem with refreshing the indoor air and thus well designed
windows need to be part of the domes. A 2,400 sq ft dome home at Cape Romano, FL,
USA lost one window in a storm4. Modern monolithic domes are constructed using an air
form. The air form is inflated; foam is sprayed inside; rebar attached to hooks placed in
foam; shotcrete is sprayed; the air blower is stopped after the concrete sets. The US
authorities have decided as follows:5
The dome, when finished, is earthquake, tornado and hurricane resistant (the US Federal Emergency Management Agency rates them as "near-absolute protection" from F5 tornadoes and Category 5 Hurricanes)
However monolithic domes do suffer from disadvantages. These are considered below.
http://forum.monolithic.org/viewtopic.php?f=2&t=961
A number of problems like cracks in the shell; difficulty in placing windows and doors
because the shotcrete was not uniform and had voids; and echo problems are discussed.
In a two dome garage dropping of a tool at the far end of one dome sounded as though it
was on their leg in the far end of the other dome.
http://en.wikipedia.org/wiki/Talk%3AMonolithic_dome
The above web page comments on the need to spray the shotcrete continuously. This
requirement of continuous shooting of shotcrete makes monolithic suitable for small
domes only; domes of radius 100’ or more could not be monolithic.
http://en.wikipedia.org/wiki/Monolithic_dome
This ‘Article’ part describes problems with the transition from rectangular prisms to
hemispheres like inefficient use of space as the curves of the dome and the straight edges
of furniture and equipments do not match.
1 http://en.wikipedia.org/wiki/West_Baden_Springs_Hotel
2 http://www.insideindianabusiness.com/newsitem.asp?ID=38338 We counted the trusses from the
photograph of the dome. 3 http://www.coastalbreezenews.com/2012/09/07/cape-romano-uncovered/
4 http://www.messynessychic.com/2013/06/12/the-mysterious-dome-homes-marching-into-the-sea-
before-after/domeinside/#main 5 http://en.wikipedia.org/wiki/Monolithic_dome
Weather-Secure Habitat 5 of 27
Possibly the very first patent for a dome was issued on August 26, 1930 to Mr. Conrad
Pantke. A number of patents are issued over the years for constructing the hemispherical
domes. None of these patents describe a dome that has a multi-floor structure inside the
dome except one. That patent describes a dome with two floors without any pillars. Our
domes do have pillars. Further those domes are not repairable, whereas our domes are.
Still we provide the following table indicating the difference between our design and that
of the listed patents.
The following Table considers the patents on domes.
No Patent No P date Title Comment
1 1773851 26/08/30 Space Covering Structure Discussed
Quoting from the patent we have: [subsequent quotes without this explanation]
It will thus be seen that, when these various joints and elements are assembled,
they provide a safe structure, which even tough certain members may be
eliminated or destroyed due to fire, or other causes, will stand up safely, in as
much as the stresses will arch around the space previously occupied by such
eliminated members.
In contrast, we are concerned about the fidelity of the shape of the dome: a hemisphere or
a hemi ellipsoid.
2 2682235 29/06/54 Building Construction Discussed
In contrast to equilateral triangles used in the geodesic design, we use non-equilateral
triangles in our invention.
3 2905113 22/09/59 Self-strutted Geodesic
Plydome
Discussed
If desired, the openings between the sheets can be closed up, this being merely a
function of the selected frequency of the grid in relation to sheet size.
During the 50s openings in domes could be tolerated. With hostile weather we cannot
have any opening in the domes.
4 2914074 24/11/59 Geodesic Tent Discussed
This patent produces conical shapes hanging all over the geodesic dome and such cones
would be blown away by hurricanes and tornadoes.
5 2918992 29/12/59 Building Structure Discussed
the triangular faces of the pieces define regular pentagons and hexagons, with
each pentagon surrounded by hexagons.
We have no pentagons or hexagons in our structure.
6 2929473 22/03/60 Structural Framework Structural member
7 2934075 26/04/60 Inflatable Structure Inflatable
8 2962034 29/11/60 Shelter and method of
making same
Regular polygon
9 2976968 28/03/61 Wall Construction Equilateral triangle
10 2978074 04/04/61 Spherical Building
Structure with Curved
Beams
Isosceles triangles
Weather-Secure Habitat 6 of 27
No Patent No P date Title Comment
11 2978704 04/04/61 Radome Structural
Devices
Discussed
Parallelism is substantially non-existent in the present embodiment, and instead,
the term triangular incrementation is used to describe the orientation which an
antenna device energized by a source of electromagnetic wave energy included
within the radome device sees insofar as transmissibility is concerned.
In our design the ribs that are more or less parallel and the rings that are parallel are
fabricated. Thus electromagnetic energy is possibly blocked from entering the dome.
12 2979064 11/04/1961 Inflatable Building
Construction
Inflatable
13 3004302 17/10/61 Building Construction Strips
14 3006670 31/10/61 Frame for supporting
Domed Structures
Spherical balls
required
15 3018858 30/01/62 Shelter Frame Strut with 2 sections
16 3026651 27/03/62 Building Construction Tetrahedron
17 3042052 03/07/62 Portable Tepee Cone
18 3043054 10/07/62 Spherical Self-supporting
Enclosures
Discussed
In constructing the modules, a flat body sheet of honeycomb material or foamed
plastic may be laid between two skin sheets of fiber resin laminate in wet
condition and the laminate or sandwich so formed may be confined between
spherically curved molding plates where it is held while the materials are bonded
together in any well known manner as by polymerizing agents in the composition
or by heat applied thereto or developed therein. After the spherical laminate sheet
is formed it is cut to the shape and size of the desired module …
The above method of preparing spherically curved sheets requires the spherically curved
molding plates. Without the molding plates the spherically curved sheets of any shape
could not be made. Isosceles triangles forming regular pentagons and irregular hexagons
are used by Mr. Clarence to make the sphere. If we do not use the idea of another
inventor, we are forced to make the first set of spherically curved molding plates using
regular pentagons and isosceles triangles. Once the molding plates are made arbitrary
shapes could be used to make future spherical objects. We agree that once the original
spheres are made using regular pentagons and isosceles triangles, the sphere could be cut
to get molding plates of any shape. Hence the invention requires regular pentagons and
isosceles triangles. Our design has no pentagon at all.
19 3049201 14/08/62 Base Details No overlap
Weather-Secure Habitat 7 of 27
No Patent No P date Title Comment
20 3058550 16/10/62 Structural Unit Discussed
The invention of the geodesic dome by Fuller uses planar sheets to form the triangles,
pentagons, and hexagons. The surface of the dome is not smooth. This patent uses sheets
pressed to approximate the curvature of the dome. In Fuller’s design equilateral and
isosceles triangles are used. Any two triangles in Fuller’s design with a common edge
form a diamond. This patent uses sheets that are diamonds. In the illustration given in
Figure 3A a single diamond is divided into 16 quadrilaterals or triangles and thus reduces
the area of flatness. In general a diamond could be divided into m x n areas where m. n
are greater than or equal to 1. As the numbers m and n increase the flat area decreases
and the diamond sheet approaches the desired curvature. Still it does not become the
desired curvature. Monolithic domes and our invention give the desired curvature to the
elements that make the dome.
21 3061977 06/11/62 Spherically Domed
Structures
Isosceles triangles
22 3063519 13/11/62 Building Structure Like 3058550
23 3063521 13/11/62 Tensile-Integrity
Structures
Discussed
… the length of all booms will be such as to subtend an angle of 25°14’30” of the
sphere. … all utilize one common length of strut …
Since there is just one length of strut, the triangles, pentagons, and hexagons of the dome
are regular. Our design has none of these regular elements.
24 3083793 02/04/63 Membrane Sustained Roof
Structure
Two surfaces
25 3094708 25/06/63 Indoor-Outdoor
Swimming Pool and
Enclosure Therefor
Diamonds of equal
length sides
changing widths
26 3114176 17/12/63 Wood Building
Construction
Plane triangles
27 3129531 21/04/64 Reinforced Building
Structure
Central Post
28 3185164 25/05/65 Three Dimensional
Reticular Structure
Discussed
The element comprises of a core 2 provided with three arms 4, 5. And 6. In
practice the number of arms may vary, depending on the desired geometrical form
of the contour of the structure. … the arms projecting from the core 2 must be
equal …
We have no such requirement.
29 3192669 06/07/65 Skylight Construction Related to
supporting the dome
and not the design
of the dome.
Weather-Secure Habitat 8 of 27
No Patent No P date Title Comment
30 3203144 31/08/65 Laminar Geodesic Dome Spherical equilateral
and isosceles
triangles
31 3220152 30/11/65 Truss Structure Tetrahedron
32 3221464 07/12/65 Tetrahelical Structure Tetrahedron
33 3292316 20/12/66 Self-supporting roof Rhombus, isosceles
triangle
34 3304669 21/02/87 Containers and
Space_Enclosing
Structures
Discussed
Robert C. Geschwender uses tetrahedrons, isosceles triangles, and kites in his
constructions. Our design has none of these structures as the distance between a central
rib and its left neighbor rib need not be same as the distance with the right neighbor rib.
Similarly the distance between a central ring and its bottom neighbor ring need not be
same as its distance with its upper neighbor ring.
35 3314199 18/04/67 Prefabricated Sectional
Building Construction
Discussed
Three butterfly units are used by C. A. Wulf Jr. et al to form a tetrahedron with an
equilateral triangle as base. They form a base rhombus using two equilateral triangles. By
placing a number of rhombuses side by side they create a passage. By keeping the valley
forming edge of the butterfly large enough, the passage is wide to park an automobile.
Thus they create drive-in spaces. There are no tetrahedrons in our design.
36 3323820 06/06/67 Space Frame Structures Unrelated
37 3333375 01/08/67 Frame for supporting a
dome shaped building
Regular hexagon
38 3341989 19/09/67 Construction of
stereometric domes
Regular polygons
39 3380203 30/04/68 Modular Free-span
Curvilinear Structures
Strut connector
40 3407558 29/10/68 Self-supporting structural
unit having a series of
repetitious geometrical
modules
Module has legs
41 3766959 23/10/73 Pivoted Panel Connection
and Hinge
Unrelated
42 3863659 04/02/75 Shelter Structure Pulley, roller, spring
43 3889433 17/06/75 Structural Frame No dome; cylinder
and semi-cylinder
Weather-Secure Habitat 9 of 27
No Patent No P date Title Comment
44 3955329 11/05/76 Hollow Structure interlocking flat
shapes
The following four patents are referred by 3955329
45 604277 17/05/1898 Knockdown House No rings
46 791149 30/05/1905 Building Blocks for
Cylindrical Structures
No rings for the
hemisphere
47 3359694 26/12/67 Domical Building
Structures
Discussed
Walter R. Hein designs a dome given the number of vertices on the dome. Quoting, we
have:
… once the pattern of vertices is established so that the total number of vertices in
the imaginary spheroid is known, the polyhedral angle for each vertex is
calculated by the present invention. Essential to this calculation is an
understanding that in accordance with the present invention, the sum of all such
polyhedral angles of the spheroid is 720° less than the product of 360° times the
total number of vertices on the spheroid, i.e., the polyhedral angles are less than
360° each by an average amount equal to 720° divided by the total number of
vertices.
If we change the number of vertices even by 1 by deleting a vertex or adding a vertex we
need to redesign the complete dome. With 8 vertices with one vertex at the top, one
vertex at the bottom, and 3 vertices each in two planes in between, we get a cube as a
sphere. Our domes are smooth.
48 3485000 23/12/69 Dome Structure and
method for building the
same
Discussed
I claim: 1. A dome structure comprising:
A plurality of superposed edge-overlapping concentric ring members of gradually
smaller diameter, …
In our design we have rings. However their diameters do not gradually decrease. The above
description of gradually decreasing diameter members would form a spiral when connected as
described in the patent.
49 4027449 07/06/77 System for Constructing
Spatial Structures
Spherical nucleus
between struts
50 4233794 18/11/80 Adjustable Connecting
Means for Ceiling
Constructions and the like
Connector; not
related to dome
shape
Weather-Secure Habitat 10 of 27
No Patent No P date Title Comment
51 4357118 02/11/82 Connecting Assembly for
Geodesic Dome
Framework Construction
Connector not dome
52 4491437 01/01/85 Connector for Geodesic
Dome
Two concentric
geodesic domes one
inside another
53 4566818 28/01/86 Ledger Hanger for
Geodesic Domes
Discussed
Second floor inside the dome without pillar from ground transferring the load to the
dome. Our dome need not carry even its own load.
54 4608789 02/09/86 Star Dome Structure Neither hemisphere
nor hemi-ellipsoid
55 4679361 14/07/87 Polyhedral Structures that
approximate a Sphere
Neither sphere or
ellipsoid
56 4796394 10/01/89 Geodesic Structure Growing dome
57 4923544 08/05/90 Method of manufacturing
tetrahexogonal truss
structure
Parallelogram
58 4945603 07/08/90 Concentric Dome Energy
Generating Building
Enclosure
Two concentric
domes
59 5040966 20/08/91 Die for making a
Tetrahexagonal Truss
Structure
Parallelogram
60 5070673 10/12/91 Tetrahexagonal Truss
Structure
Cavity,
Parallelogram
61 5230196 27/07/93 Polyhedron Building
System
Cable
62 5305564 26/04/94 Hemispherical Dome
Building Structure
[lapsed]6
Cells are same size;
frustopyramidal
shape
63 5782035 21/07/98 Multi-purpose automatic
filling and leveling fluid
basin with water transfer
Unrelated
64 5918415 06/07/99 Multi-purpose self-
watering system
Unrelated
65 7464900 16/12/08 Folding Retractable
protective dome for space
vehicle equipment
Collapsible ribs
66 7624705 01/12/09 Small animal habitat Unrelated
6 http://www.google.com/patents/US5305564
Weather-Secure Habitat 11 of 27
No Patent No P date Title Comment
67 7735265 15/06/10 Foam rigidized inflatable
structural assemblies
Inflatable
68 8397678 19/03/13 Small animal habitat Unrelated
69 8782965 22/07/14 Universal Hub and Strut
system for a Geodesic
enclosure
Universal links to
make domes; no
dome design detail
We consider the invention in detail now.
Weather-Secure Habitat 12 of 27
Invention in detail
We consider 40’ x 30’ first. As 5’ clearance is required from 3 sides, the largest circle has
a radius of 10’. We provide a 3’ x 3’ foyer at the 8’ above ground landing for the 10’
radius habitat. The lower floor has a full circle of 10’ radius with a uniform height of 7’8”
which gives the height of the lower floor to be 8’ including the 4” thickness of the
ceiling/floor concrete slab. Where should we place the kitchen, dining, and living space?
The 10’ radius hemisphere has reduced space where a 6’ high individual could stand
straight. This space has a radius of 8’ only.
The occupants of the habitat could tolerate slight inconvenience by sleeping under the
hemisphere. We decide to provide kitchen, dining, and living spaces at the lower level.
The layout of the First Floor is given in Figure 2. [1 is the master bed of size 6’ x 5’; 2
child bed 6’ x 3’; 3 Wash Basin; 4 bath tub with shower; 5 western commode; 6 flush
tank; 7 entry to the apartment; 8 black circle with 0’ clearance; 9 blue circle with 2’
clearance; 10 magenta circle with 4’ clearance; and 11 green circle with 6’ clearance.]
Figure 3 [1 common wash basin, shared by the family and the visitors; 2 stove and oven;
3 spice rack; 4 refrigerator and freezer; 5 washer dryer; 6 six seated dining table; 7 three
seated sofa; 8 four seated sofa; 9 television and other entertainment systems; 10 powder
room under the stairs; and 11 open due to stairs] depicts the arrangement in the lower
floor. In the Figure the space allotted for wash basin; stove and oven; refrigerator and
freezer; and washer dryer are large enough to accommodate the current non-circular
appliances. Having established the feasibility of a couple with two children living inside a
10’ radius hemisphere we consider the plot use alone in what follows.
The area of the floor of a 10’ radius hemisphere is 314 sq ft. The area of a 40’ x 30’ plot
is 1,200 sq ft. The FSI [Floor Space Index] of a home with the lower and upper floors is
(314 + 314)/1,200 = 0.52 only. Accordingly we build the lower floor on ground without
digging below the ground level. To protect from floods up to a height of 8’ we maintain a
garden around the lower level of the house. Instead of providing a door to enter the living
area at the ground level, we enter at the upper level and have provided the internal
staircase. The garden and the steps outside the house to reach the upper floor are depicted
in Figure 4. The elevation is along the line cutting through the steps. The plan shows two
car parks marked by number 1.
Positioning of the 15’; and 25’ hemispheres are displayed in Figures 5 and 6 respectively.
The area under the 15’ hemisphere is 706 sq ft in each floor giving a total of 1412 sq ft.
For the area of 2,400 sq ft, the FSI is 0.58. In contrast to a 15’ radius hemisphere, we
have two floors in addition to the floor at ground for a 25’ hemisphere. The magenta
circle marked 1 represents the area shielded by the garden and the First Floor through
which entry is made. These two floors have a plinth of 1,963 sq ft. We could have a floor
at a height of 8’ and 16’ above the entry level. These have floors with radii of 23.68’ and
19.21’ with plinths of 1,762 sq ft and 1,159 sq ft respectively. The red circle is the floor
Weather-Secure Habitat 13 of 27
with 23.68’ radius marked 2 in the figure. The black circle marked 3 represents the
19.21’ radius floor. The total plinth for the 4 floors is 1,963 x 2 + 1,762 + 1,159 sq ft
adding to 6,847 sq ft. The plot area being 60’ x 80’ = 4,800 sq ft, the FSI is 1.42. We are
justified in having a floor on the ground shielded by the garden.
In a plot of 80’ x 120’ we could have just one hemisphere of 35’ radius. In addition to the
floor guarded by the garden, we have floors with 35’; 34.07’; 31.12’ and 25.47’ radii. The
plinths are 3,848; 3,848; 3,647; 3,044; and 2,038 sq ft giving a total of 16,425 sq ft of
plinth. The FSI is 16,425 / (80 x 120) = 1.71. The 35’ radius floor is shown in magenta;
34.07’ radius floor in red; 31.12’ radius floor in blue and the 25.47’ radius floor in black
in Figure 7. In addition we have six car parks. We add more hemispheres instead of car
parks as shown in Figure 8. In addition to the 35’ radius indicated by 1, 2, 3, and 4, we
added two floors of 15’ radius marked 5 and two floors of radius 10’ indicated by 6. The
total plinth now is 16,425 + 1408 + 628 = 18,461 sq ft. The FSI increases to 1.92.
A plot of 120’ x 120’ gives an FSI of 2.50 with 8’ high floors and a FSI of 2.07 with 10’
high floors. We recommend the 10’ high floors permitting large distances between
pillars. With a height of 8’ the beams cannot be deeper than 12” for a clearance of 7’ for
the occupants. However the beams could be 36” deep offering the same 7’ clearance for
the occupants of 10’ high apartments.
A 50’ radius hemisphere in a 120’ x 120’ plot has 7,853 sq ft at a height of 10’; 7,539 sq
ft at 20’ height; 6,597 sq ft at 30’; 5,026 sq ft at 40’; and 2,827 sq ft at 50’ height for a
total plinth of 29,842 sq ft. For protection from floods we leave the ground completely
for car park. All apartments are above 10’ from ground. The layout of the 120’ x 120’
plot is shown in Figure 9.
A family might build a super luxury home at Rs. 10,000 per sq ft and build it for Rs.
29,84,20,000 or Rupees 30 Crores. We consider building 21 family apartments and 37
single person apartments with quality at Rs. 5,000 per sq ft. A young couple would have
a 300 sq ft family apartment at an affordable cost of Rupees 15 lakhs while a single
person has a 100 sq ft apartment costing just Rupees 5 lakhs excluding the cost of
common spaces.
A sample layout of the family apartment is given in Figure 10. We use a bay of 15’ width
and allocate 20.59’ for family apartment as that happens to be the smallest family
apartment in the hemisphere with family apartments. The family apartment [ 1 3’ x 6’
door; 2 3’ x 4’ window starting 4’ above the floor; 3 3’ x 4’ window starting 2’ above the
floor; 4 4-seat dining table; 5 3-seat sofa; 6 2-seat sofa; 7 TV; 8 refrigerator; 9 double
bed; 10 4’ x 4’ window starting 2’ above the floor; 11 safe; 12 bath; 13 western
commode; 14 Wash basin; 15 Microwave oven; 16 cooking space with gas/ electric
stove; and 17 sink] is shown.
Weather-Secure Habitat 14 of 27
Figure 11 gives the layout of a person apartment with 108 sq ft plinth, which is the
smallest person apartment in the hemisphere [ 1 2’ x 6’ door; 2 1’ x 3’ window from 3’6”
above the floor; 3 two-seat dining table; 4 TV above the dining table; 5 3’ x 6’ single bed;
6 refrigerator; 7 wash basin; 8 shower; and 9 Western Commode ].
We find that a total of 24 cars could be parked as depicted in Figure 12. Out of these 10
cars do not have free access. These restricted access parks cannot be sold alone. For
example, park 23 could be owned with park 12 only. Any restricted car park shown in red
in Figure 12 could be owned along with parks that lead to access only. Unsold restricted
access car parks could become flower beds or children playground if properly barricaded.
There are 6 dotted circles with radii 50.00’; 48.98’; 45.82’; 40.00’; 30.00’; and 18.90’in
Figure 13. The 50.00’ radius magenta circle is the floor at a height of 10’ above the car
park. The 48.98’ radius violet circle is the ceiling of the First Floor and floor of the
Second Floor. The ceiling of the Second Floor and the floor of the Third Floor is the blue
circle with radius 45.82’. It is enough to place the apartments within the ceiling circle to
maintain vertical walls. Still no apartment is outside the 45.00’ radius full red circle. This
is because there are no pillars outside the 45.00’ radius circle and we desire to avoid
loading the cantilever supported parts of the hemisphere. The 40.00’ radius orange circle
is the ceiling of the Third Floor and floor of the Fourth Floor. The green circle with
30.00’ radius is the terrace and the ceiling of the Fourth Floor.
The First Floor and the Second Floor have all the 17 apartments numbered 3 to 19. The
Third Floor has 13 apartments numbered 3 to 15. The apartments numbered 3 to 9, a total
of 7 apartments only are found in the Fourth Floor. The plinths of these apartments are
listed in the following table.
Weather-Secure Habitat 15 of 27
No Apartment No First Second Third Fourth
1 3 175 sq ft 175 sq ft 175 sq ft 175 sq ft
2 4 175 sq ft 175 sq ft 175 sq ft 175 sq ft
3 5 172 sq ft 172 sq ft 172 sq ft 172 sq ft
4 6 129 sq ft 129 sq ft 129 sq ft 129 sq ft
5 7 129 sq ft 129 sq ft 129 sq ft 129 sq ft
6 8 129 sq ft 129 sq ft 129 sq ft 129 sq ft
7 9 129 sq ft 129 sq ft 129 sq ft 129 sq ft
8 10 179 sq ft 179 sq ft 179 sq ft
9 11 179 sq ft 179 sq ft 179 sq ft
10 12 179 sq ft 179 sq ft 179 sq ft
11 13 179 sq ft 179 sq ft 179 sq ft
12 14 172 sq ft 172 sq ft 172 sq ft
13 15 129 sq ft 129 sq ft 129 sq ft
14 16 108 sq ft 108 sq ft
15 17 108 sq ft 108 sq ft
16 18 172 sq ft 172 sq ft
17 19 129 sq ft 129 sq ft
Floor total 2,572 sq ft 2,572 sq ft 2,055 sq ft 1,038 sq ft
Hemisphere total 8,237 sq ft
It could be seen that all the apartments are less than 200 sq ft and hence are for an
individual only. We could combine more than one person apartment and use it as family
apartment provided the area of an apartment is at least 200 sq ft. We expect that a just
married couple would have no problem in living in a 200 sq ft apartment. Couples with a
few years behind them might need larger apartments.
To demonstrate the feasibility of different floor layouts in different levels of the
hemisphere, we show different layouts with family apartments. It must be recorded that
some apartments could not be combined and thus would be retained as person apartments
only.
In Figure 13 we see that apartments 4 and 5 share a wall. By removing this wall, we get a
larger apartment. Likewise we get family apartments by combining apartment 6 with 7;
and apartment 8 with 9. The result is shown in Figure 14. To demonstrate that the
apartments in different floors could have different plinth distributions, we combine
different person apartments in Third Floor. The Third Floor layout is found in Figure 15.
For simplicity, we retain the same layout for the Second Floor and the First Floor, shown
in Figure 16. The apartments and their plinths of the hemisphere with family and person
apartments are listed in the table below.
Weather-Secure Habitat 16 of 27
No First Floor Second Floor Third Floor Fourth Floor
No Plinth sq ft No Plinth sq ft No Plinth sq ft No Plinth sq ft
1 3 355 3 355 3 355 3 175
2 4 108 4 108 4 355 4 348
3 5 355 5 355 5 172 5 258
4 6 172 6 172 6 129 6 258
5 7 129 7 129 7 308
6 8 308 8 308 8 129
7 9 108 9 108 9 308
8 10 129 10 129 10 172
9 11 308 11 308 11 129
10 12 172 12 172
11 13 129 13 129
12 14 172 14 172
13 15 129 15 129
Floor total 2,574 2,574 2,057 1,039
Hemisphere total 8,244
The difference of 7 sq ft between the totals [8,237 as single person apartments and 8,244
as mixed apartments] is due to ignoring the fractions of the plinths of the apartments.
We consider the person apartments only for the location of the pillars, beams, pillar-
beams now. Pillars from ground are permitted only when the pillar does not affect the
movement of cars on ground. However the lift and the stairs are essential and we have
bifurcated one park way and located them. The pillars that support the lift are at
(48.5’,60’) where the X coordinate is 48.5’ and the Y coordinate is 60’. The X coordinate
is zero at the left and increases in the right direction. The Y coordinate is zero at the
bottom and increases upwards. The other three lift pillars are: (56.5’, 60’); (48.5’, 68’);
and (56.5’, 68’). The stairs are supported by the lift pillars and the four pillars: (45’, 60’);
(45’, 71.5’); (60’, 60’); and (60’, 71.5’). These pillars are not shown in Figure 17 in
which we show another 40 potential pillars. The pillars that have the same X coordinate
have their number displayed for the bottom most and the top most pillars. The X and Y
coordinates along with their heights of the pillars are listed in the table below. The pillars
reach the floor of the circle enclosing the pillar. The table lists a total of 66 pillars
including the pillars that were added as the design continued till end.
No X coordinate Y coordinate Height
1 20.00’ 39.38’ 30.00’
2 15.40’ 54.00 30.00’
3 15.00’ 60.00’ 30.00’
4 20.00’ 80.61’ 30.00’
5 39.00’ 20.20’ 30.00’
6 39.00’ 45.39’ 50.00’
7 39.00’ 54.00’ 50.00’
Weather-Secure Habitat 17 of 27
No X coordinate Y coordinate Height
8 39.00’ 60.00’ 50.00’
9 39.00’ 71.50’ 50.00’
10 39.00’ 99.80’ 30.00’
11 60.00’ 15.00’ 30.00’
12 60.00’ 17.57’ 30.00’
13 60.00’ 24.80’ 40.00’
14 60.00’ 36.78 50.00’
15 60.00’ 45.39’ 50.00’
16 60.00’ 54.00’ 50.00’
17 60.00’ 83.21’ 50.00’
18 60.00’ 95.19’ 40.00’
19 60.00’ 102.42’ 30.00’
20 60.00’ 105.00’ 30.00’
21 79.00’ 19.20’ 30.00’
22 79.00’ 24.89’ 40.00’
23 79.00’ 36.78’ 50.00’
24 79.00’ 45.39’ 50.00’
25 79.00’ 54.00’ 50.00’
26 79.00’ 60.00’ 50.00’
27 79.00’ 71.50’ 50.00’
28 79.00’ 83.21 50.00’
29 79.00’ 95.19 40.00’
30 79.00’ 100.79 30.00’
31 100.00’ 39.38’ 30.00’
32 100.00’ 45.39’ 30.00’
33 100.00’ 54.00’ 40.00’
34 100.00’ 60.00’ 40.00’
35 100.00’ 71.50’ 30.00’
36 100.00’ 80.61’ 30.00’
37 104.00’ 50.56’ 30.00’
38 104.59 54.00’ 30.00’
39 105.00’ 60.00’ 30.00’
40 104.00’ 89.43’ 30.00’
The following pillars are added for earthquake protection.
41 39.00’ 24.80’ 30.00’
42 39.00’ 36.78’ 40.00’
43 39.00’ 83.21’ 40.00’
44 39.00’ 95.19’ 30.00’
45 20.00’ 45.39’ 30.00’
46 20.00’ 71.50’ 30.00’
The following virtual pillars were added for Fourth Floor
47 26.25’ 81.47’ 30’ 40’
Weather-Secure Habitat 18 of 27
No X coordinate Y coordinate Height
48 39.00’ 89.20’ 30’ 40’
49 60.00’ 100.00’ 30’ 40’
50 79.00’ 95.19’ 30’ 40’
51 95.40’ 78.61’ 30’ 40’
52 100.00’ 60.00’ 30’ 40’
53 96.67’ 44.02’ 30’ 40’
54 79.00’ 24.80’ 30’ 40’
55 60.00’ 20.00’ 30’ 40’
56 39.00’ 30.79’ 30’ 40’
57 22.76’ 45.39’ 30’ 40’
58 20.00’ 60.00’ 30’ 40’
To support the Terrace we add the following virtual pillars
59 30.00’ 60.00’ 40’ 50’
60 39.00’ 81.42’ 40’ 50’
61 60.00’ 90.00’ 40’ 50’
62 90.00’ 60.00’ 40’ 50’
63 89.39’ 54.00’ 40’ 50’
64 60.00’ 30.00’ 40’ 50’
65 39.00’ 38.57’ 40’ 50’
66 30.60’ 54.00’ 40’ 50’
To facilitate the drive way in the car park, no pillars were allowed outside the circle of
45’ radius. However the First Floor has a 50’ radius floor. We support the additional 5’
by cantilevers. There are main beams at a distance of 19’ and 21’. Normally the support
beams are drawn perpendicular to the main beams. The cantilevers are drawn radial to
minimize the length of the cantilever. The beams supporting the First Floor with a radius
of 50.00’ are shown in Figure 18. The green beams join the adjacent pillars on the 45’
radius circle. They are sixteen in number. The longest of these beams connects pillars 30
and 36 and has a length of 29.12’. A beam of length 30’ is expected to have a depth of
30”. Since we have 10’ between floors, we decide to have uniform depth of all beams to
be 36” allowing the longest beam to be 36’ in length. We need to add additional pillars to
reduce the beam length if necessary.
Normally we run beams from pillar to pillar. In Figure 18 these beams are shown in
green. We have major beams – 2 in the X direction and 5 in the Y direction – that also
run pillar to pillar. However these are shown in red to emphasize that they are major
beams. Every apartment has a non-load bearing brown beam. These brown beams are
beam to beam connections and support the weight of the partition wall only. These
partition walls could be as light as two plywood sheets with fluffy cotton in between for
sound insulation. It is found that the interconnections between the pillars and beams form
a number of rectangles. If a tornado creates a twist on the structure, the indeterminate
rectangles become parallelograms and the floor does not remain circular. For the floor to
maintain its shape we introduce a number of beams shown blue in Figure 19. We have
Weather-Secure Habitat 19 of 27
introduced 37 blue beams just to retain the shape of a floor in case an earthquake occurs.
Are we justified in increasing the cost? It is estimated that an earthquake could reduce the
GDP of a nation.7 At least for the future constructions we should introduce additional
beams to convert rectangles to triangles so that the GDP of the nation does not suffer due
to an earthquake. We strongly feel that the additional cost due to the beams for
earthquake protection is highly justified.
Under an earthquake a floor of a building could slip with respect to the floor above or
below that floor. Even though the floor retains its shape during an earthquake, such
slippage between floors results in destruction of the building. We add inclined pillar-
beams between the adjacent floors to avoid such slippage. Figure 20 shows the 4 pillar-
beams between the First Floor and the Second Floor along a main beam in the X
direction. The pillar-beams connect the bottom of pillar 2 with the top of pillar 7. This
pillar beam crosses a service lane near the floor. We expect the service personnel to jump
over the exposed pillar-beam. The rest of the pillar-beam is inside the partition wall of
Apartment 15 adjoining the corridor. The next pillar-beam starts at the top of pillar 7 and
connects the bottom of pillar 16. The exposed part of this pillar-beam in the corridor is
above 7’ and thus causes no difficulty to the occupants. Likewise the other 2 pillar-beams
do not cause any difficulty. These 4 pillar-beams divide the vertical rectangle into 8
triangles and these triangles resist any slippage between the floors of First Floor and
Second Floor in the X direction. Similar pillar-beams are placed between pillars (41, 13,
22); (42, 14, 23); (45, 6, 15, 24, 32); (46, 9, pillar at the corner of the stairs, 27, 35); (43,
17, 28); and (44, 18, 29).
To avoid slippage along the Y direction, we place pillar-beams using a different strategy
to ensure proper placing of doors and windows of the apartments using the corridor. We
show the pillar-beams along the corridor connecting pillars 21 to 30. On this corridor are
apartments 11, 10, 6, and 5. The pillar-beams are shown in Figure 21. There are no
apartments between pillars (21, 22) and (29, 30). For the other 6 apartments the entry is
in the triangles shown in red. The windows are in the triangles shown in blue and green.
The doors and windows are sized such that they do not touch the pillar-beams. Like these
4 apartments, apartments 14 and 15 have three triangles at the entry. The other
apartments have the main beam running at the back of the apartment. The windows of the
kitchen and bathroom of the remaining apartments are adjusted after deciding the pillar-
beams.
The First and Second Floors have all apartments because the ceiling of First Floor has
radius of 48.98’ greater than 45’. Likewise the ceiling of Second Floor having a radius of
45.82’ is greater than 45’. Thus both the First Floor and the Second Floor have all 17
apartments numbered 3 to 19 When it comes to the Third Floor, the ceiling of Third Floor
has radius of 40’ only. Because this is less than 45’, the Third Floor has 13 apartments
7 http://www.stuff.co.nz/business/rebuilding-christchurch/4984173/Quake-rebuild-will-eat-into-GDP
Reconstruction after the Canterbury earthquakes is likely to eat up about 7.5 per cent of 2011 GDP, according to the International Monetary Fund.
Weather-Secure Habitat 20 of 27
only numbered 3 to 15. All the pillars are within the 45’ radius and the Third Floor is
fully supported.
When we consider the Fourth Floor with a radius of 40’, the pillars 1, 2, 3, 4, 45, 46, 5,
41, 44, 10, 11, 12, 19, 20, 21, 30, 31, 32, 33, 35, 36, 37, 38, 39, and 40 do not support the
Fourth Floor. The result is the Fourth Floor needs a cantilever of 20’ if we require all
pillars to start from ground. A cantilever of 20’ is not acceptable.
A beam could support distributed and concentrated loads. As a beam could support
concentrated load also, we have the freedom to start a pillar above the ground level sitting
on a beam. We call such pillars ‘virtual pillars.’ The virtual pillars that support the Fourth
Floor start from the beams of the Third Floor. These virtual pillars are shown in Figure
22. These virtual pillars are numbered 47 to 58. The virtual pillars 48 and 56 do not lie on
the 40’ radius circle. As the apartments of the Third Floor are within the 40’ radius circle,
we need to check whether virtual pillars 48 and 56 obstruct any apartment. From Figure
13 we find that there are no apartments in the places occupied by the virtual pillars 48
and 56. The beams supporting the Fourth Floor are shown in Figure 23. Any beam from a
virtual pillar is shown in brown,
Similar to the Fourth Floor, the Terrace also needs virtual pillars. The virtual pillars
numbered 59 to 66 along with the pillars from the ground inside the 30’ radius circle
support the Terrace. The virtual pillars and the beams that support the Terrace are given
in Figure 24.
Now we consider the rich who normally live in ‘Farm Houses.’ The attraction for living
in such houses is the greenery that surrounds the house on 4 sides. If the occupants
maintain a terrace garden the house is surrounded by greens on 5 sides. In a multistory
hemispherical complex we provide greens on all six sides of the house. We use 40’ wide
bay for the apartments. One set of pillars support an apartment and the entry corridor of
6’. Another set of pillars support the 4’ wide service lane and an apartment of 40’. Thus
the main beams are at a distance of 46’ and 44’ alternately.
We design the support beams to be 54” deep permitting the support beams to have a
maximum length of 54’. To provide a clearance of 7’ 6” for the occupants, we keep the
floor at heights of 12’ each. The design of the pillars and support beams is similar to that
of the 50’ radius hemisphere just described. We do not consider the design of pillars and
beams for the sake of brevity.
We consider the location of the apartments only now. To avoid the possibility of the
plinth of the apartments decreasing as we move up, we start the design with the top floor.
We have selected a hemisphere of 200’ radius. The terrace is the 15th
floor at a height of
180’ above the bottom of the hemisphere. The hemisphere starts at a height of 12’ leaving
a gap of 12’ for the car park. As the main beams have a minimum gap of 44’ we do not
design the car park as it would be very easy to design it for those who design car parks.
Weather-Secure Habitat 21 of 27
There are no apartments in a bay adjoining a bay with apartments to ensure that the
apartment has greens in front and back. We leave a gap of 12’ between apartments in the
same bay so that the apartments have greens on all the 4 sides in the same floor. The bay
above and the bay below a bay with apartment are left for greens to satisfy the
requirement that all 6 sides of an apartment has greens.
As the ground is used for car park, the bottom most of the floors, called First Floor at 12’
above ground is fully used for greens. The apartments in the top floor, Fourteenth Floor
are given in Figure 25. As a luxury apartment we desired to have at least 3,200 sq ft of
plinth. At the Fourteenth Floor there are only two apartments of plinth 1,600 sq ft each in
the displayed quadrants. Only one of the two could be selected. We arbitrarily chose the
one in the first quadrant in preference to the one in the fourth quadrant. We show the
apartments in the first and fourth quadrant only. There are apartments in the second and
third quadrants that are symmetric to those shown in the figures. As 1,600 sq ft is small,
we hope to link the apartment in the Twelfth Floor with the one identified in the
Fourteenth Floor. Hence the 1,600 sq ft apartment in the Fourteenth Floor is called ‘A1
top.’
Figures 26 and 27 display the apartments in the Thirteenth and Twelfth Floors. On the
Twelfth Floor we find ‘A1 bottom’ in the first quadrant with a plinth of 3,200 sq ft.
Combining ‘A1 top’ and ‘A1 bottom’ the plinth of apartment A1 is 4,800 sq ft making
apartment A1 possibly a super luxury. Apartment A3 is a trapezoid and not a rectangle.
As a rectangle it would have just 2,800 sq ft area. We decided to relax the rule of having
a rectangle, hoping that such occasions would be rare. Indeed apartment A3 is the only
one which is not a rectangle. It has a plinth of 3,000 sq ft.
Figures 28 to Figure 36 display the apartments in Eleventh Floor to Third Floor.
Apartment 32 in the Third Floor has a plinth of 2,395 sq ft only. Still it is not called ‘A32
top’ as the First Floor is reserved for Flower Bed only. Likewise the Second Floor
displayed in Figure 37 also has no top part of any apartment. Apartment 40 is displayed
in Figure 37. The total number of apartments in the first and fourth quadrants is 40 giving
the total number of apartments inside the 200’ radius hemisphere to be 80. The plinths of
these apartments are listed in the following table.
No Apartment No Symmetric Apartment No Plinth sq ft Bottom plinth sq ft
1 1 41 1,600 3,200 (4,800)
2 2 42 3,200
3 3 43 3,000
4 4 44 3,200
5 5 45 3,200
6 6 46 1,600 3,200 (4,800)
7 7 47 3,200
8 8 48 3,200
9 9 49 3,200
Weather-Secure Habitat 22 0f 27
No Apartment No Symmetric Apartment No Plinth sq ft Bottom plinth sq ft
10 10 50 3,200
11 11 51 1,600 2,400 (4,000)
12 12 52 1,600 3,200 (4,800)
13 13 53 3,200
14 14 54 1,600 2,400 (4,000)
15 15 55 3,200
16 16 56 3,200
17 17 57 1,600 1,600 (3,200)
18 18 58 3,200
19 19 59 3,200
20 20 60 3,200
21 21 61 3,200
22 22 62 1,600 2,400 (4,000)
23 23 63 3,200
24 24 64 3,200
25 25 65 2,400 2,400 (4,800)
26 26 66 3,200
27 27 67 3,200
28 28 68 3,200
29 29 69 2,400 2,400 (4,800)
30 30 70 3,200
31 31 71 1,600 2,400 (4,000)
32 32 72 2,400
33 33 73 3,200
34 34 74 2,400
35 35 75 3,200
36 36 76 3,200
37 37 77 3,200
38 38 78 3,200
39 39 79 3,200
40 40 80 2,400
1,11,000 25,600
Quadrants 1 and 4 1,36,600 sq ft
All 4 quadrants 2,73,200 sq ft
We have used 200’ radius on the ground. The area of circle with 200’ radius is 1,25,663
sq ft. If the rules permit building on a circular plot, then FSI = 2,73,200 / 1,25,663 = 2.17.
Given that the FSI is 2 in most places, we need to add 10,937 sq ft of plot to the circular
plot. If we take a square plot of 400’ side, the FSI is 2,73,200 / 1,60,000 = 1.70. We have
used pillars at a distance of 46’ or 44’ using beams of depth 54” or 4’6”. If we have used
pillars at 21’ or 19’ distance, we use beams of depth 2’ only. Then every floor is just 10’
high. We would have 18 floors instead of 14. With the Ground Floor dedicated for car
Weather-Secure Habitat 23 of 27
park and the First Floor for flower beds, we have apartments in 12 floors now. With 18
floors, we would have apartments in 16 floors. Assuming a linear relation between the
number of floors and the area of the apartments, the FSI of 1.70 becomes 1.70 x 16 / 12 =
2.26. We conclude that a hemisphere of radius 200’ offers luxury apartments comparable
to the rectangular prisms. The major difference is the rectangular prism is not as strong as
the hemisphere with respect to earthquakes, floods, hurricanes, and tornadoes.
The apartments described from the smallest with a 10’ radius hemisphere to the 200’
radius hemisphere need to be provided with the hemispherical dome. We detail the steps
involved in designing the dome.
The smallest dome has a radius of 10’ and a surface area of 628.31 sq ft. Figure 38 shows
the plan of a cloth that provides for half the hemisphere. We take another cloth that is a
mirror reflection of the wing shaped cloth. By first stitching the two vertical lines
together we get a butterfly shape. In the butterfly stitch the points with the same color.
We get a closed shape with the bottom open. Arrange the bottom on a 10’ radius circle
and inflate. The cloth would assume a hemispherical shape. The area of the single wing
shown is 312.61 sq ft close to the actual 314.15 sq ft. The difference is because of the
straight line connections between the points. We have added the two cones and their
cloths nearby. These cones are given to show that the procedure used to get the
hemisphere’s cover works for other shapes as well as long as the shapes have a circular
cross section on every horizontal plane. Monolithic Domes are made by preparing air
forms like the one shown in Figure 38 and blowing concrete slurry on the cloth from
inside. Such a monolithic dome does suffer some drawbacks.
The air pressure under the cloth must be just right; over pressure causes the shape to
approach an ellipsoid and under pressure leads sagging at the top. To avoid such
problems we build a cage using metallic strips. For ease of manual assembly we use
strips of about 2’ length. The rib of a 10’ radius hemisphere is 15.70’ in length on the
surface of the hemisphere.
The elevation and plan view of the cage is given in Figure 39. Just to demonstrate that the
ribs and the rings could be at arbitrary gaps, we use 2’2” and 1’10” alternately for the
location of the rings. The ribs are at 2’2” and 1’10” at the bottom and they shrink
proportionately as they approach the top.
In the plan view of Figure 39 a scaffold is shown in blue. A worker standing on this
scaffold cannot reach any of the points shown on the dotted orange line or above. To
reach them we need to provide 6 ‘maintenance windows,’ three of which displayed.
Another three in the shadow and are not shown. The plan and elevation are shown in the
same color. These windows are removable so that a worker standing inside the
hemisphere could reach each of the 8 cells touching the maintenance window. Any
damage caused by debris in a hurricane or tornado could be repaired through the
maintenance window. It is possible that a window is designed for some other purpose by
Weather-Secure Habitat 24 of 27
the architect. In that case we do not provide any maintenance window for the cells that
are close to the useful window. The useful window must be removable to perform the
maintenance work after a natural event. Figure 39 shows three maintenance windows in
blue, green, and red. Their plans and elevations have the same color. Through the
windows we reach down to the dotted red line. We could reach the brown line above also
through the windows. The space above the brown line could be reached from the top. The
top is covered by a two piece lid which could be removed if desired. Thus the whole
hemisphere is reachable for repair and maintenance.
We concentrate on making the surface of the hemisphere a true hemisphere. We fix a
cloth of appropriate shape against the desired space; blow air from inside so that the cloth
assumes the spherical gradient all over; and spray cement solution or some other binder
to freeze the cloth as true spherical surface. Once the cloth dries and becomes rigid, we
apply plaster inside to the desired thickness. We recommend leaving the metal strips
inside the plastered wall to form a Faraday Cage offering protection from an EMP
[Electro-Magnetic Pulse] attack as well. If desired the strips could be designed to have
protrusions to pull them out after the plaster has set. Before considering the metallic
strips, we detail the process of preparing the cloth.
Instead of selecting a cell different from the maintenance windows, we describe the
process for the green maintenance window. In Figure 38 we have developed a cloth to
form a 10’ radius hemisphere. For a cone we form a circular segment with radius equal to
the line joining the apex with a point at the bottom. We extend this process to any
structure which has the same distance to all points at a horizontal plane. The intersection
of the structure with every horizontal plane is a circle, with all circles having the same
center in plan. Instead of the straight line connecting the apex with a point on any
horizontal circular intersection, we find the length of the string along the curvature of the
object between the apex and the selected point. In Figure 40 the apex is 1 and the points
of interest are those inside the green polygon in the plan along the dotted red line. The
string length is given by the arc 12 shown in the elevation. The length of the circular
arc between 34 in the plan should be the length of the arc with a center and radius
equal to the string length. To maintain symmetry, we have half of 34 on the left and the
other half on the right. We divide the length along the rib into 10 equal parts, giving 11
horizontal circles. The bottom most circle is the blue circle while the top most circle is
the green one. We list the string length, the arc length, and the subtending angle on each
side corresponding to the half arc length for the 11 rings below.
No Ring arc string Angle
1 Blue 2.786826837388657’ 7.707963267948968’ 10.357691809463495˚
2 Blue + 0.1 2.730981625703501’ 7.515135224880602’ 10.410572557799377˚
3 Blue + 0.2 2.672911662015854’ 7.318242587158437’ 10.463342491101492˚
4 Blue + 0.3 2.612468595145274’ 7.116935359881187’ 10.516002818858988˚
5 Blue + 0.4 2.549483646342933’ 6.910814989896926’ 10.568554728105412˚
6 Blue + 0.5
[Green - 0.5]
2.483763446866371’ 6.699424304112744’ 10.620999384002745˚
Weather-Secure Habitat 25 of 27
No Ring arc string Angle
7 Green – 0.4 2.415084709006854’ 6.482234606217968’ 10.673337930406004˚
8 Green – 0.3 2.343187303234138’ 6.258628885370287 10.725671490409121˚
9 Green – 0.2 2.267765115497280’ 6.027879602208813’ 10.777701166873005˚
10 Green – 0.1 2.188453745173699’ 5.789118746146116’ 10.829728042936114˚
11 Green 2.104813593915855’ 5.541296601282292’ 10.881653182509153˚
The cloth to cover the green window is shown in red in Figure 41. The interface between
the blue and the red region looks straight. Is that a straight line? There is a very slight
curvature giving a distance of 0.00719902394601’ between the straight line joining the
ends and the middle of the curve. This gap is 0.0863” and is negligible in engineering
terms. In any case the hemispherical shape is produced by the metallic strips that define
the ribs and rings to be described. In practice the edge would be cut as a straight line and
an error so small would not affect the resulting hemispherical surface. The resulting
hemispherical surface would be as true as possible.
The blue and the magenta strips are pasted over the left rib and bottom ring of a selected
quadrilateral. When the next quadrilateral of the ring in the right side gets the blue strip
pasted, the green strip is pasted on the cloth of the next quadrilateral. Thus we paste the
blue, green, and magenta strips of all the quadrilaterals of a ring. The orange strips are
clipped to the metallic strips of the upper ring. Now we blow air on the cloth forcing the
cloth to assume the true hemispherical curvature. While the airflow is maintained, we
spray the cement solution or some other drying solution on the cloth. We apply plaster to
more than half the depth of the metallic strips. If we desire to reuse the metallic strips, we
paste the full hemisphere to half depth of the strips, allow the hemisphere to dry and
harden, and pull the metallic strips out. The plaster remains in place because we have
allowed holes on the outer edges of the metallic strips permitting the plaster to be
connected across the strip.
The first rib strip connected to the foundation strip is shown in Figure 42. The three 1”
diameter holes at the bottom are used to align the first rib strip with the vertical
foundation strip. There is a 0.1” cut half way at the top of rib in the horizontal direction to
accommodate a 0.2” thick ring part. The three 1” diameter holes at the top of the rib strip
are used to align the next rib strip to achieve true 10’ radius hemisphere rib structure. The
lowest two ribs are shown in Figure 43. All other rib and ring elements are formed
likewise. The smallest hemisphere with 10’ radius could be formed with bamboo strips as
well.
Erect a temporary pole in the center with a circle of radius 1.5253’ of cane. Take 14’2”
long thin bamboo strips and attach one end with the circle at the top and the other end at
the corresponding point at the edge of the 10’ radius floor slab. The strip would assume
the shape of a circular curve of 10’ radius with the centre at the centre of the floor. Place
as many strips as desired with spacing of 6” or about at the edge of the floor. Use ropes or
bamboo strips to form rings tying the bamboo strips to form rings. Once the cage is
formed using the bamboo ribs and bamboo or rope rings, the circle at the top would be
Weather-Secure Habitat 26 of 27
held in position by the hemisphere. Remove the temporary pole and cover the top hole
with a circular lid woven with bamboo strips. Cut windows and doors as required. Cover
the hemisphere with waterproof cloth all over except the door and windows. Use curtains
for the door and the windows.
For hemispheres with two or more floors use the metallic or bamboo strips of appropriate
length to form that section of the cage between the floor and ceiling. Plaster or cover with
waterproof cloth as desired.
In the description we have the skin enclosing the building inside. It is very easy to
visualize a stricture with floors enclosing the described circular floors and providing the
skin as described on the circles in the floors and ceilings with extended floors jutting
outside the skin. Such trivial extensions do not exempt the buildings from the protection
offered to this patent.
Weather-Secure Habitat 27 of 27
I Claim:
1. We claim a hemispherical or hemi ellipsoidal habitat of at least two levels with or
without plants inside meant for human occupancy.
2. The hemispherical or hemi ellipsoidal skin of the habitat of claim 1 could touch or
not touch the internal building, but carries no load of the internal building.
3. The skin of claim 2 could be with holes allowing natural ventilation or without
holes allowing ventilation through windows only.
4. The radius of the hemisphere or of the hemi ellipsoid of claim 1 could be from 10’
upwards.
Ibramsha Mohideen
Weather-Secure Habitat 1 of 1
Abstract
Due to Global Warming the future weather is not expected to be similar to the past.
Earthquakes, hurricanes, tornadoes, and floods could occur anywhere on earth. We detail
secure habitats for the hostile weather.
Tornado has no effect on buildings with circular exteriors. A hurricane finds it extremely
difficult to uproot a hemisphere or a hemi ellipsoid in which the radius of an upper floor
is less than that of a lower floor. Floods do not affect a building with entry above ground
when the flood height is less than the entry. A building with triangles formed by pillars
and beams is more resistant to earthquake than without any triangle.
Our buildings have above the floor entry; have circular exteriors; have triangles in the
structural frame; and are hemisphere or hemi ellipsoid shaped with the radius of an upper
floor being less than that of a lower floor.