HOW TO READ SOLAR CHART?

Sun path diagrams are used to read the solar azimuth and altitude throughout the day and year for a given position on the earth. They can be likened to a photograph of the sky, taken looking straight up towards the zenith, with a 180° fish-eye lens. The paths of the sun at different times of the year can then be projected onto this flattened hemisphere for any location on Earth.

  • Azimuth Lines – Azimuth angles run around the edge of the diagram.
  • Altitude Lines – Altitude angles are represented as concentric circular dotted lines that run from the center of the diagram out.
  • Date Lines – Date lines start on the eastern side of the graph and run to the western side and represent the path of the sun on one particular day of the year. In Ecotect, the first day of January to June are shown as solid lines, while July to December are shown as dotted lines.
  • Hour Lines/ Analemma – Hour lines are shown as figure-eight-type lines that intersect the date lines and represent the position of the sun at a specific hour of the day. The intersection points between date and hour lines give the position of the sun.

Reading the Sun Position (Step-by-Step)

sun path diagram.
  1. Locate the required hour line on the diagram.
  2. Locate the required date line, remembering that solid are used for Jan-June and dotted lines for July-Dec.
  3. Find the intersection point of the hour and date lines. Remember to intersect solid with solid and dotted with dotted lines.
  4. Draw a line from the very center of the diagram, through the intersection point, out to the perimeter of the diagram.
  5. Read the azimuth as an angle taken clockwise from north. In this case, the value is about 62°.
  6. Trace a concentric circle around from the intersection point to the vertical north axis, on which is displayed the altitude angles.
  7. Interpolate between the concentric circle lines to find the altitude. In this case the intersection point sits exactly on the 30° line.
  8. This gives the position of the sun, fully defined as an azimuth and altitude.

– See more at: http://sustainabilityworkshop.autodesk.com/buildings/reading-sun-path-diagrams#sthash.70pW7OPn.dpuf

SHADING DEVICES AND ITS UTILIZATION

HORIZONTAL SHADING DEVICES – OVERHANGS

This diagram illustrates, the basic concept is that an overhang can be positioned to totally allow low winter sun in the entire window while completely shading the entire window from summer sun. The design calculation is performed over a certain period of mid-summer and a certain period of mid-winter, typically a month or two on either side of the two solstices. The calculation is also performed only for a certain period during the day, typically near solar noon since that is when it’s most important to increase solar gain in the winter and reduce gain in the summer (because the sun is most intense then). In fact, it is not usually possible to design a horizontal overhang that works in the early morning or late afternoon because the sun is low in the sky in both the summer and winter.

These are placed horizontally in fron tof the window, in various ways. Their, shape, type, depth and height all differs, all depending on the sun conditions. A window overhang is a (usually) horizontal surface that juts out over a window to shade it from the sun. This is desireable in order to reduce glare or solar heat gain during warm seasons.

Rules of the thumb

Shading devices should be selected according to the orientation of the window. Whilst some orientations are easy to shade, others are much more difficult as the sun can shine almost straight in at times. The table below indicates the most appropriate type of shading device to use for each orientation in the southern hemisphere. These are guidelines and, of course, there are many variations to these basic types.

Orientation Effective Shading
North (equator-facing) Fixed horizontal device
East or West Vertical device/louvres (moveable)
South (pole-facing) Not required

Shadow Angles

When attempting to shade a window, the absolute azimuth and altitude of the Sun are not as important as the horizontal and vertical shadow angles relative to the window plane. These can be calculated for any time if the azimuth and altitude of the Sun are known.

Design Requirements

The design requirements for a shading device depend entirely on a building’s use and local climatic conditions. In a multi storey open plan office building, the occupancy and equipment gains are such that heating is rarely required. In this situation, to avoid unnecessary loads, shading may be designed to completely protect the windows all year-round.

In a domestic building or one that is occupied 24 hours, the release of stored heat during cold nights in winter can be important. In this case, the shading would be designed to fully protect the windows during the summer months, but to expose them as much as possible to direct sun in winter so that they have a chance to absorb heat during the day. In climates where summers are also relatively cold, the requirement may be to allow full solar access all year round.

Design Steps

To design a horizontal shading device, simply following the following steps.

    1. Determine cut-off date.

This is the date before which the window is to be completely shaded and after which the window will be only partially shaded.

    1. Determine Start and End Times.

These represent the times of day between which full shading is required. Keep in mind that the closer to sunrise and sunset these times are, the exponentially larger the required shade.

    1. Look up Sun Position.

Use solar tables or a sun-path diagram to obtain the azimuth and altitude of the sun at each time on the cut-off date.

    1. Calculate HSA and VSA.

Using the formulae given above, calculate the HSA and VSA at each time.

    1. Calculate Required Depth and Width.

Once again, using the formulae above, calculate the depth and width of the required shade on each side of the window.

DIFFERENTIATED FACADE TREATMENT:

An understanding of solar geometry tells us that the exposure of each facade to the sun is different, and varies by orientation.
Each orientation of the building requires a different approach to the design of shading. 

The northelevation (in the northern hemisphere) essentially does not require shading because except in the summer months in the early morning and late evening, no sun penetration occurs.  At this time of day the sun angle is so low that horizontal projections would be useless as shading devices.  It is best to limit as much as possible fenestration on the north elevation as there will be very little solar heat gain and much direct heat loss from this side. If fenestration is required for daylighting, then it is important to select a highly efficient glazing assembly to reduce energy transfer.

The south elevation (in the northern hemisphere) allows for the easiest control of solar energy.  Shading devices are normally designed as horizontal projections above the windows — the length of the projection is determined as a geometric function of the height of the window and the angle of elevation of the sun at solar noon.  Such shading devices can be designed to completely eliminate sun penetration in the summer and allow for complete sun penetration during the winter when such is desired for passive heat gain.

South Shading
Basic Shading Strategy for a South Elevation

The east and west elevations are both difficult to shade “architecturally”.  The sun angles in the morning and afternoon are low enough to preclude shading using overhangs.  The morning sun is normally cooler and less offensive than the heat and glare of the late afternoon sun.

East and West Facades
Shading Issues with East and West Facades

Shading needs to be provided in the way of landscaping and foliage.  Deciduous trees are effective as they block the sun in the summer when it is not desired and allow sun penetration during the winter.  Fences work to block the sun and view at all times of the year and so are not so climatically responsive.  Vines on more transparent “fence like” elements are effective as they too bear leaves to shade in the summer, and keep their leaves until later in the fall when sun is again desired.  Vines are often used as well on south facing elevations on trellises to achieve seasonal variation in the opaqueness of the overhangs.

Vegetative Shading

Vegetative Shading

The natural environment can be used to shade low rise buildings. Deciduous trees can effectively shade the facade when heat avoidance is desired, and permit solar penetration where passive solar gain is sought. Vines can be used on trellises or trellis like shading devices to the same effect. Vegetative shading also works well with the shoulder heating and cooling seasons. In the spring when heating is still often desirable, leaves are not yet present, allowing continued passive heating. In the fall, when continued warm days might suggest cooling, the leaves have not yet been shed. If natural ventilation is also desired, it is important to allow adequate wind penetration around exterior plantings or potential natural cooling will be blocked.

How Long to Shade For?
Shading devices for heat avoidance need to be designed to be effective beyond the geometry of summer solstice when the sun is highest in the sky. Depending on the local climate conditions, cooling may be a priority from the mid spring to early fall seasons. The length of the south facing shading device should be sized for this extended season.

Shading season
The Shading Season

The diagram above divides the types of shading devices into fixed and movable. Movable shading devices may include awnings, hinged extensions and vegetation. If a mechanically dependent solution, the device needs to be designed for durability.

GENERAL TYPES OF SHADING DEVICES:

The basic types of exterior shading devices can be identified as HORIZONTAL, VERTICAL OR EGGCRATE. When designing shading devices for heat avoidance it will be important to also weigh the amount of solar penetration that is desired during the heating months. Where the heating degree days greatly exceed the cooling degree days (in COLD climates), be careful not to compromise the potential for solar gain in the winter months. Where the cooling degree days exceed the heating degree days (HOT climates), shading should be effective for a longer period. In some climates this may warrant the virtual elimination of south facing windows, with deference to north facing windows to promote daylighting.

Horizontal shading devices are suited to southern exposures. Roof overhangs can also easily be used to shade southern exposures on low rise buildings. This is perhaps the most economical and potentially aesthetically pleasing solution for residential applications.

Shading Device Types
Basic Typology of Horizontal Shading Devices for Southern Exposures

Where sun is hitting the facade from a south-easterly or south-westerly direction, vertical devices can effectively block the sun. Eggcrates are often used on non true south facing elevations as well.

Shading Device Types
Shading Devices for Non Southern Exposures

The general configuration of the building can also be modified to alter the orientation of windows for heat avoidance.

Sawtooth Configuration

Fins

Oblique shading

Various Planimetric Configurations of Non South Facing Shading Devices

For reasons of both heat avoidance and economy, it is often best to “gang” the south facing shading devices. In order to obtain shading in the late morning and early afternoon when the sun is not at its high point, the shading device should be extended either side of the window opening.

Elevation of Shading Device
Elevation of Shading Device Configurations for South Facing Facades

ISLAMIC TOMBS

The Islamic rule in India saw the introduction of many new elements in the building style.

The main elements in the Islamic architecture is the introduction of arches and beams, and it is the arcuate style of construction while the traditional Indian building style is trabeate, using pillars and beams and lintels. The early buildings of the Slave dynasty did not employ true Islamic building styles and consisted of false domes and false arches. Later, the introduction of true arches and true domes start to appear, the earliest example is the Alai Darwaza by the side of Qutb Minar.

The introduction of decorative brackets, balconies, pendentive decorations, etc in the architecture is an example in this regard. The other distinguishing features of Indo-Islamic architecture are the utilisation of kiosks (chhatris), tall towers (minars) and half-domed double portals. As human worship and its representation are not allowed in Islam, the buildings and other edifices are generally decorated richly in geometrical and arabesque designs. These designs were carved on stone in low relief, cut on plaster, painted or inlaid. The use of lime as mortar was also a major element distinct from the traditional building style.

The general pattern of the tomb architecture is consisted of a domed chamber (hujra), a cenotaph in its centre with a mihrab on the western wall and the real grave in the underground chamber

Seven Cities of Delhi

Qila Rai Pithora

Qila Rai Pithora also known as Rai Pithora’s Fort was a fort city built in 12th-century by Chauhan king, Prithviraj Chauhan. Chauhan Rajputs had taken over the city of Delhi, from Tomar Rajputs. In 1160 AD, the Chauhan rulers took over Delhi from Tomars, along with it the fort city of Lal Kot, the first extant city of Delhi. Thereafter Prithviraj Chauhan whose capital was Ajmer in Rajasthan, enlarged the Lal Kot, which had large rubble walls and ramparts, and renamed it Qila (Fort) of Rai Pithora or Qila Rai Pithora. The combined fort extended to six and a half km, and city existed with the fort, while older Lal Kot served as the citadel. However, the Chauhan’s didn’t rule long over the city, in 1190s the Afghans started attacking. Though Chauhans defeated Muhammad Ghori in the First Battle of Tarain in 1191, a year later in 1192, his general Qutubuddin Aibak defeated Prithviraj Chauhan in the Second Battle of Tarain, ending their dynasty. This in turn established Muslim rule in India, with his Mamluk dynasty also known as Slave dynasty, the first Sultanate of Delhi. However, Aibak didn’t extend or change the fort structure, it remained same through his early successors as well.

Mehrauli

Mehrauli is one of the seven ancient cities that make up the present state of Delhi. The Lal Kot fort was constructed by the Gurjar Tanwar chief Anangpal I around 731 AD and expanded by AnangPal II in the 11th century, who shifted his capital to Lal Kot from Kannauj. The Gurjjar Tanwars were defeated by the Chauhans in the 12th century. Prithviraj Chauhan further expanded the fort and called it Qila Rai Pithora. He was defeated and killed in 1192 by Mohammed Ghori, who put his general Qutb-ud-din Aybak in charge and returned to Afghanistan. Subsequently in 1206, after the death of Mohammed Ghori, Qutubuddin enthroned himself as the first Sultan of Delhi. Thus Delhi became the capital of the Mamluk dynasty of Delhi(Slave dynasty), the first dynasty of Muslim sultans to rule over northern India.  Mehrauli remained the capital of the Mamluk dynasty which ruled until 1290. During the Khilji dynasty, the capital shifted to Siri.

Balban’s tomb, Mehrauli

In 12th-century Jain scriptures, the location is also mentioned as Yogninipura, now noticeable by the presence of the “Yogmaya Temple“, near the Qutub Minar complex, believed to have been built by the Pandavas.

Siri

siri was built by ala ud din khilji in 1303. the site of the city is partially ocupied by the vllage of shahpur but hardly any of the wall remained by sher shah to build the walls of the city. the walls were 17 feet in thickness but only mounds of Earth remained to mark their positions. inside yhe city there were palace of 1000 pillars, but this is also gone, the only thing which remained is the hauz khas of ala ud din.

Tughlakabad

Tughlabad was founded by tughlaq Shah about 1321 and was constructed very rapidly. The city may be approached from three sides. [There is a road from Qutb Minar, there is one from railway station of tughlakabad and there is a rough track ]  the citadel is approached by a small postern gate it has very fine arched roof and well cut stone , there is no sing of hinge to any door. there is reservoirs and undersround passage.

The Tumb Of Tughlakabad

this lies about midway in south westurn side of the city and opposite the citadel it is built in a fortified way which was once sorrounded by water, held up a dam held accros the valley near muhammadabad fort. the interior of the fortified enclosure is raised and probably built above an outcrop rock. the shape of the fort is irregular and defence mechanism was provided at the corners.in the acrade to the left lies a grave which is reputed with bones of thuglaq Shah’s favourite dog.

the King’s tomb is massive and plain

Firozabad

One of the Tughlak rulers,Firoze Tughlak created the fourth city of Delhi , Firozabad or Kotla Firoze Shah next to the river Yamuna. This was a large enclosure of high walls , containing palaces , pillared halls , mosques, a pigeon tower and a water tank. On the top of his palace, Firoze planted an Ashokan pillar from 1500 years ago. He also built several hunting lodges in and around Delhi, as well as mosques, some of which still remain. Apart from raising new buildings, Firoze Shah also repaired old ones,such as Sultan Ghori’s tomb,Qutub Minar,Suraj Kund and Hauz Khas. ( Firoze Shah’s tomb, a lofty structure, lies in Hauz – Khas. ) After Firoze Shah’s death, the sultanate became politically unstable and in 1398, the Turk ruler of Samarkand Taimur invaded India – creating havoc in the cities of Delhi, looting, killing and plundering. He captured Firozabad, prayed at the mosque and went back to Samar – kand with the goodies.Today, Kotla Firoze Shah is famous for its sports stadium – a common venue for cricket matches. The Sayyid and Lodhi dynasties that followed the Tughlak dynasty were far more concerned with restoring stability than patronisation of arts or architecture. Tombs erected in the honour of the rulers are the only monuments of these times (most famous: the tombs at the Lodhi Garden).Architectural glory returned with the Mughals.

Dinpanah (shergarh)

The second Mughal Emperor Humayun in the year 1533 A.D. founded the city of Dinpanah (Refuge of the Pious). This he did after holding consultations with various learned men and various scholars.  The city was also located in very close proximity to the shrine of Delhi`s most revered saint, Nizam ud Din Auliya.

  Its high walls of rubble masonry with a slight batter, 4 m. thick and as much as 21 m. high in places, have a battlemented parapet above the row of arrow-slits, behind which all along the circumference are built a series of chambers in a two-aisle depth. There are massive bastions on the four corners, in addition to five bastions in the western wall, and three gates, all double-storeyed, one on each side except on the east. The gates have a veneer of red and buff sandstones, with an ornamental use of white and black marble and coloured tiles.
                              The three main gates of the fort were Bara Darwaza, (Big Gate) facing west, which is still in use today, The South Gate, popularly known as the Humayun Gate (either because it was constructed by Humayun, or because Humayun’s Tomb is visible from there) and the Talaqi Gate, often known as the “forbidden gate”.
                              Despite the immense exterior, few of interior structures have survived except the Qila i Kuhna Mosque and the Sher Mandal, both of which were said to be constructed Sher Shah Suri.
Shahjahanabad

Humayun’s son Akbar is known as one of the greatest Mughal emperors . However, he concentrated his construction feats in Agra and the later abandoned city Fatehpur Sikri. It was his grandson Shahjehan, the man who gave the Taj Mahal to the world, who created the city of Shahjehanabad, the seventh city of Delhi – in the area that is now known as Old Delhi. The Jama Masjid and the Red Fort are two excellent examples of the architectural splendour of the 17th c.

The architecture of the city of Shahjahanabad is something which cannot be described in a paragraph or two. It was a detailed city (rectangular in shape) (built on the banks of River Yamuna, which has now changed course) with many architectural and visual marvels. The main palace (or citadel) in which the emperor Shah Jahan and the succesive rulers of the Mughal Dynasty lived until 1857 A.D. was known as the Lal Qila (Red Fort). It was called so because of its Red Sandstone walls (Initially the walls were being made of mud until Shah Jahan ordered them to be decorated with red sandstone). The fort covers approximately 125 acres of land.The city of Shahjahanabad as such had eight gates which were locked during night time (in the 17th, 18th and the 19th century). The city had many bazaars, some of which exist even now, for example Khari Baoli (which is today Asia’s largest wholesale spice market). The area of Chandni Chowk (Moonlit Square) (which was also the main street of Shahjahanabad) had many bazaars as well. Some shops in this area are several centuries old ! Other important monuments in Shahjahanabad are Ghalib ki Haveli (the house of famous poet Mirza Ghalib), Jama Masjid (Friday Mosque) (an imposing mosque made of Red Sandstone), St James Church (First Church of Delhi), Sunehri Masjid, Gurdwara Sis Ganj e.t.c.

Golden Ratio in Art & Architecture

“Mathematics is the majestic structure conceived by man
to grant him comprehension of the universe”-
 
LE CORBUSIER

In simple terms, the golden ratio (also known as the divine proportion or thegolden mean), is a mathematical constant that appears repeatedly in nature and artwork.

Expressed as an equation, when a is larger than b, (a + b) divided by a is equal to a divided by b (just look at the image below), which is equal to about1.618033987. That number, often represented by the Greek character “phi,” is the golden ratio.

The same theory can be used to construct a rectangle, called the golden rectangle. An image that follows the golden ratio can be placed neatly inside a rectangle that obeys the ratio.

To construct a golden rectangle, choose a number that will be the length of the rectangle’s short side.

For argument’s sake, let’s say 500 pixels. Multiply that by 1.618. The result, 809 pixels, is the length of the long side of your rectangle. Therefore, a rectangle that is 500 pixels by 809 pixels is a golden rectangle. It obeys the golden ratio.

The human face follows the ratio as well, and we find people whose faces are truer to the ratio more attractive. Seashells, classic Renaissance masterpieces, architecture from antiquity

ADVANTAGES:

It Allows For Varying Shapes

Of course, not all buildings are going to be perfectly rectangular. Whether the natural landscape, existing lot boundaries, or personal style dictates that the structure take on a different formation, architects need to be a way to accommodate an array of shapes. Luckily, with just a few extra amendments to the golden rectangle, architects can easily apply the ratio to any shape that they can dream up.

The ratio can be applied to achieve a variety of shapes. Image Via: Bernard Andre Photography

It Brings Balance and Height

As a general rule, we gravitate toward buildings that appear balanced. Though “modern” marvels of construction may be fun to look at, we tend to write them off for day-to-day use because they the space is perceived as less functional than their more conventionally structured counterparts. One of the simplest ways to impart a sense of balance to a structure is to base it off the principles of the golden rectangle.

To explain it simply, a golden rectangle signifies any shape that can be wholly divided into up into a square and a rectangle that, when combined, establish a ratio of 1:1.61. Since both the lengths and widths of these shapes correspond to the ration, the theory states that you should be able to continue dividing the resulting rectangles into smaller and smaller segments while still maintaining the ratio’s proportions.

The inverse is also true. If an architect wants to make a structure larger or smaller to accommodate their clients’ needs, as long as they follow the principles laid out by the ratio, they have the ability to correctly alter a building’s proportions with just a few simple calculations.
Notice how even the rectangles appear. Image via: Rinox Inc

It Makes Buildings Aesthetically Pleasing

Architecture isn’t just about form and function. It’s also about physical appearance. Just as the design elements you include in your interior design set a tone for the rooms within your home, the way that a building looks has an impact on its surrounding area. Add to that the personal satisfaction that an architect must feel when their work is well received and it’s no surprise that the ratio plays a role.

Studies have shown that, when it comes to conventional attractiveness, we subconsciously gravitate towards others whose proportions most closely conform to the golden ratio. With that in mind, it is such a stretch to believe that we would gravitate towards buildings whose proportions match that ratio as well?

Architects keep the golden ratio in mind when it comes time to decide how a building’s  floor plan will flow. It’s used when determining features such as how to properly determine a buildings layout, space out windows, and determine where a door should be placed in a room. While these proportions are considered of secondary importance to the building’s structural integrity, adherence to the ratio increases chances that people will find the building aesthetically pleasing.

Architects also use the ratio to determine factors like window  and door placement. Image Via: Phinney Design Group

http://www.hongkiat.com

http://www.wikipedia.org

MODULAR MAN

Le Corbusier developed the Modulor in the long tradition of Vitruvius, Leonardo da Vinci’s Vitruvian Man, the work of Leon Battista Alberti, and other attempts to discover mathematical proportions in the human body and then to use that knowledge to improve both the appearance and function of architecture. The system is based on human measurements, the double unit, the Fibonacci numbers, and the golden ratio. Le Corbusier described it as a “range of harmonious measurements to suit the human scale, universally applicable to architecture and to mechanical things”.

With the Modulor, Le Corbusier sought to introduce a scale of visual measures that would unite two virtually incompatible systems: the Anglo Saxon foot and inch and the French metric system. Whilst he was intrigued by ancient civilisations who used measuring systems linked to the human body: elbow (cubit), finger (digit), thumb (inch) etc., he was troubled by the metre as a measure that was a forty-millionth part of the meridian of the earth.

The graphic representation of the Modulor, a stylised human figure with one arm raised, stands next to two vertical measurements, a red series based on the figure’s navel height (1.08 m in the original version, 1.13 m in the revised version) then segmented according to Phi, and a blue series based on the figure’s entire height, double the navel height (2.16 m in the original version, 2.26 m in the revised), segmented similarly. A spiral, graphically developed between the red and blue segments, seems to mimic the volume of the human figure.

Practical application

Le Corbusier used his Modulor scale in the design of many buildings, including:

Unité d’Habitation in Marseille

In his first book on the subject The Modulor, Le Corbusier has a chapter on the use of the modular in the Unité d’Habitation. The modular governs: the plan, section and elevations; the brise-soleil; the roof; the supporting columns and the plan and section of the apartments. It was also used for the dimensions of the commemorative stone laid on 14 October 1947. A version of the Modulor Man was cast in concrete near the entrance.

Church of Sainte Marie de La Tourette

In the Church of Sainte Marie de La Tourette Le Corbusier floors the majority of the church in pale concrete panels set to Modulor dimensions. Also, the engineer Iannis Xenakis applied the Modulor system to the design of the exterior vertical ventilators or “ondulatoires”.

Carpenter Center for the Visual Arts

In the Carpenter Center the Modulor system was used for the brise-soleil distances, the floor to floor heights, the bay distances and the column thicknesses. Le Corbusier conceived that the dimensioning of the entrance ramp would be “visible essay on the mathematics of the human body“.

In Le Corbusier’s buildings and art a recurrent silhouette appears. It’s a stylised human figure, standing proudly and square-shouldered, sometimes with one arm raised: this is Modulor Man, the mascot of Le Corbusier’s system for re-ordering the universe. You’ll find him in two major exhibitions showing now: Cold War Modern at the Victoria & Albert Museum and a retrospective in Liverpool, the first big Corb show in the UK for 20 years.

The Modulor was meant as a universal system of proportions. The ambition was vast: it was devised to reconcile maths, the human form, architecture and beauty into a single system. This system could then be used to provide the measurements for all aspects of design from door handles to cities, and Corbusier believed that it could be further applied to industry and mechanics. The fundamental “module” of the Modulor is a six-foot man, allegedly based on the usual height of the detectives in the English crime novels Corbusier enjoyed. This Modulor Man is segmented according the “golden section”, a ratio of approximately 1.61; so the ratio of the total height of the figure to the height to the figure’s navel is 1.61. These proportions can be scaled up or down to infinity using a Fibonacci progression. In devising this system, Corbusier was joining a 2000-year-old hunt for the mathematical architecture of the universe, a search that had obsessed Pythagoras, Vitruvius and Leonardo Da Vinci.

Le Corbusier developed the Modulor in 1943, and the first volume of his study of it was published in 1950. From the Unité d’Habitation in Marseilles (completed 1952) onwards, Corbusier applied the Modulor to his buildings, including the government complexes he built in Chandigarh, India, and his rural retreat, Le Cabanon. It won widespread praise, and was used by architects and designers including Georges Candilis and Jean Prouve; no less a figure than Albert Einstein said: “It’s a tool that makes the good easy and the bad difficult.” But it was not widely adopted, perhaps because Corbusier wanted to patent the system and earn royalties from buildings built using it.

However, the fact that Corbusier showed Modulor to Einstein betrays how proud he was of his creation. He became transfixed, attributing mystical virtues to the system and seeing it as part of the fundamental architecture of the universe itself. The quixotic search for a key that can unlock the secrets of architecture obsessed him, as it has others through the ages. The quest continues: architectural historian Charles Jencks, who has written extensively on Le Corbusier, identifies Peter Eisenman and Cecil Balmond as the inheritors of the spirit that drove the creation of the Modulor.

The Modulor was, however, as arbitrary as any human measurement: its six-foot basis was plucked out of the air, there was no reason the Modulor Man couldn’t be five foot ten or six foot two. As is often said, a six-foot rule is hardly fair to women and children. Also, Corbusier’s own application of it was somewhat haphazard. Jencks points out that the children’s bedrooms in the Unité are six feet by 23 feet, not exactly an elegant proportion. If it’s flawed, if it never became the universal measure Corbusier wanted, why honour it? Why even remember it?

It goes without saying that things that are in proportion to one another are naturally more pleasing to the eye. But what’s really important is that the Modulor puts the human form back at the centre of design. In the present architectural climate of post-modern free-for-all, driven by computer processors and buoyed by parametric ideology, biomorphism runs riot, but human proportions are out of the picture. Maybe this is the result of an understandable discomfort with the idealisation of the human body. But we should overcome that discomfort to obtain the magical comfort of inhabiting spaces that we know were designed with our forms in mind.