Various Facts About The Taj Mahal
Date: 08 September 2020
Taj Mahal Central
Dome is “NOT” Asymmetrical
- Dr.Ram Bajaj (Structural Engineer)
If the dimension of the central dome of
Taj Mahal is taken & calculated wrong – then everything, in the proof of
the Central Dome being Asmeymtrical is wrong. The central dome of Taj Mahal is
100% symmetrical.
ताजमहल के मुख्य
गुमंद (Central Dome) की गोलाई की बनावट में बहुत बड़ा
फर्क-मुगल सम्राट शांहजहां से इतनी बड़ी चूक हो ही नहीं सकती।
-डॉ.राम
बजाज (Structural Engineer)
Dr.Ram Bajaj
(Structural Engineer)
General article published in “current science ac.in” by the authors –
Dilip R Ahuja and M.B.Rajani. They are in the National Institute of Advanced
Studies, Bangalore, India.
These experts, on advance studies, have tried their level best to
prove the slight inter factions in the symmetry of central dome by the physical
experiments on a printed photograph of Taj – taken from anywhere and one that
shows part or all of the drum (which is not possible to take from any
photograph of Taj). Figure shown in their study.
1)
They have never mentioned the size of the
photograph – which is very important in their study because-
2)
One way to establish this fact quantitatively is
to take horizontals lies of the dome and measure the two sides across the “central axis”. Figure 2, plots the
radius of the two sides of the “outer
drum” shown in figure-1 which is the photo of Taj Mahal along with smaller
dome of the Taj. How the authors have taken the slices of the drums and plotted
on which size of graph? (Standard printed call based graph will not be easily
available in the market). As the size of
graph is very important because there are more errors in a small sized graph.
3)
The 'so called' measurements taken of slices are
on which calibrated scale of measurement? One cannot measure the length of so
cut slices by using normal 10th class standard of scale.
4)
However, the so measured slices – on such scale
will have a major error in measurement on the scale of drawing of such
photographs on paper graphs as they have the size of a general copy used by the
students of class 10th.
5)
What was the “scale
of drawing” with reference to the cutting pieces of slices of the
photograph?
6)
Conversions of “diameter” & “height of dome”
data’s on such scale of graph & measurement by the 10th class
standard of scale – will never be accurate on such plotting against various
height of dome, meter and radius of outer dome in question for non-symmetry of
the central dome.
7)
Authors have explained it like a “craft class” of
6th standard that is 'carefully cut along the boundary' by a
ordinary scissors (कैंची) will not give a
desirable result (no-not possible) to prove the non-symmetry or imperfections
of central dome of Taj Mahal. Take various sizes of photographs of Taj Mahal by
small & big scanners. You will find that there are a lot of differences
between small photo's compared to bigger photographs.
8)
Remember that the imperfection is the magnitude
of “0.92 meter (maximum) at 19.67 meter height” which was highly unacceptable
to any Mughal Emperor.
9)
Various magnitude of offset shown in the graph at various heights
varies from 0.16 meter to 0.92 meter. These figures are alarming in nature and
more alarming for any structural engineer because when this is clubbed with the
stability of dome – it has certain different meaning and conclusions, as during
earthquake or deadly thunderstorm of having wind velocity more than 134KMPH on
1st June 2020 and which had damaged the structure of our Taj Mahal.
10)
When one folds the picture along the “central axis”one will find that
the two edges do not concede.
How the
authors have come across and found out the central axis of the photographs? The
central axis has to be drawn by a thinner carbon pencil of 4H grade with the
help of a calibrated protector of engineering standards. The author has not
done so.
11)
If you take various sizes of scanned pictures of Taj Mahal and find
out the central axis as suggested by the authors you will get different result
for different sizes of the bigger and smaller photographs of the Taj Mahal.
Then one cannot draw such conclusion on the symmetry of Taj Mahal’s central
dome, without proper central axis.
Now we are coming on the most important
parts of this concluded asymmetry of the central dome of Taj Mahal
The authors of
advanced studies probably must not have the knowledge of the dimentions of the
Taj Mahal; otherwise they would have not made such unrealistic mistake, error
and manipulation of the data's of the Taj Mahal.
(1)
Authors have shown the maximum height of central dome of Taj as 30
meters which it is not?
Reference & Courtesy: currentscience.ac.in
(2)
The authors have calculated the measurements of central dome having
cylindrical diameter 31.31 meter at zero meter height as well as at 1.79
meter height (31.31 meter diameter) which is not in actual position.
c
Reference & Courtesy: currentscience.ac.in
At 19.67 meter height the diameter of drum shown by the
author is 24.95 meter which does not concede with actual height at site. Also
it bisects at the radius 13.4 meter=26.8 meter diameter, whereas on the smaller
diameter at 19.67 meter comes out 12.3 meter equal to 24.6 meter, which also does
not concede with actual diameter as well as authors calculation.
(3)
The authors have calculated the maximum diameter of dome as 33.62 at
9.24 meter height of dome with having offset 0.42 meter. Which is not available in
actual dimension.
Reference & Courtesy: currentscience.ac.in
The maximum diameter of dome at 9.24 meter height is 33.62 meter having offset 0.42 meter.
(4)
Diameter of cylindrical portion at zero height is 31.31 meter which is
absolutely wrong, as shown by the Author.
From where
these dimensions are received and calculated for such a serious finding? Where
is everybody's concern for such unremarkable, un-symmetry of central dome of
our Taj.
Now please go through the actual dimensions of the Taj – which is shown here with that the maximum height of the central dome is 24.384 Meter (80ft) and cylinder infernal diameter is 58ft without the thickness of wall
Taj Mahal Wikipedia: As per Google – picture attached. The outer
dome, it rests on a diameter of 17
meters and 68 cm and measures 35 meters high. It rests on a drum of 7 meter
high (This means the height of simple onion type dome is 35-7=28 Meter). A drum
is architectural clement which is in practice, a very large and very low
cylinder arranged vertically and which serves as a support between the building
and the drum – a 7 meter high drum is already very big. It is too big the
building as a whole would look very long. A drum is look like “neck” of the
building. The interior dome is 24M
and 70 cm tall. Authors are out of range from these dimensions.
Reference
& Courtesy: aboutcivil.org
Similar
is the case with the diameter of cylindrical drum – which is shown as 16 meter
radiuses equal to 32 meter diameter of drum.
Reference & Courtesy: currentscience.ac.in
Who is Correct? Author or Google
As per author & red line marked
At the height 24.41 meter the diameter
of the domes are 12.97 meters. Whereas as per Google photo seen is enclosed
here indicates that at the height of 24.4 meter of dome, arch the
diameter of dome is 17.70 meter.
So which dimention of the dome is
correct, reader should judge the facts. The dimention taken by author is wrong.
(5)
In actual the height of complete dome is 35 meters with having neck of
cylinder 7 meters in height.
So when the height of dome
and diameter of dome are differed with the actual measurement of the dome of Taj & the radius of outer
dome, the whole findings of the asymmetry of central dome is determined wrong and not acceptable to any structural engineer.
The plotting
of measurements with reference to 30 meter height and 32 meter diameter of
cylinder drum is unrealistic and does not match with the measurements data
available with the department of ASI & the department of civil engineering,
Roorkee, who has furnished some actual different data’s of measurements for the
working of their different findings at different level.
Note: Civil
Engineering departments of Roorkee and other institution should conclude the
symmetry of the central dome by high resolution-digital theodolite which will give the accurate result of symmetry of
central dome. We have already verified the symmetry of central dome as a
perfect symmetry for which the following photograph of engineering drawing has
the proof of symmetry.
Photograph
with Triangle drawings at different points speaks clearly that the central dome
in question is mostly perfect and symmetrical with reference to any angle of
structural engineering.
On Two Different equilateral Triangle
on Taj - case – 1 for the proof of Symmetry of Taj Dome
Who is right? Judge yourself. Taj Mahal
central dome is 100% symmetrical.
The Taj is in an equilateral triangle
in which three sides are equal and three internal angles are also congruent to
each other and are each 60O.
Equilateral Triangle proofs that from
any point on the central line of Taj – the straight line measured distance –
measured (by engineering drawing compass) within onion shaped dome must be equal
and is equal at any point, please measure with engineer divider.
Hence, the central dome is most-most
symmetrical from any side.
On different equilateral Triangle as
shown in figure-case – 2 for the Symmetry of Dome
Who is right? Judge for yourself. Taj
Mahal central dome is 100% symmetrical.
Reference & Courtesy: BMKTCN-DHXD
Case – 3 for the proof of Symmetry of
Central Dome of Taj
Who is right? Judge for
yourself. Taj Mahal central dome is 100% symmetrical. Actual picture of Taj
Mahal. Lke authors – Asymmetry on picture.
Square lines are drawn by the civil
engineering drawing-instruments & 4HH pencil on the actual picture of
central dome of Taj Mahal. The distance between central line and curved
portions of central dome – comes same at any bisects at the dome. Two bisects
and the distance of arch between two vertical lines of square are same.
From the central line of central dome –
horizontal distance measured from any centre point – dome touches the arch of
central dome.
Both side distances are equal as
measured by the highly accurate engineering drawing compass and divider. This
proves that the Taj Mahal's central dome is symmetrical from any side of dome.
One can plot – these various distances
on graphs and complete the dome – you will find that the dome of both sides are
equal.
Equilateral Triangle of Taj of
Different Diamention than case 4 – Triangle is bigger & taken from four
minar centre.
Who is right? Judge for yourself. Taj
Mahal central dome is 100% symmetrical.
In general the height of an equilateral
triangle is equal √3/2
time a side of the equilateral AB or BC or AC. All heights come to the same. So
the Dome is in Symmetry.
h = √3/2 AB side of Triangle
h = √3/2 BC
h = √3/2 AC
All must be equal and comes to be equal
when measured on any size – print of this Taj – including triangle and the
heights comes equal when we calculate, when measured a scan print of this Taj
Mahal of various sizes, the height comes to same, in the various prints taken.
Do it yourself and get the symmetry of Taj Mahal central onion dome. Measured
the length of side AB, BC or AC by civil engineering drawing divider.
Area=√3/4 a2 (Equilateral)
Height=√3/4 a
Equilateral
Triangle of Different size than–smaller size & smaller base as compared to
case-5.
Who is right? Judge for
yourself. Taj Mahal central dome is 100% symmetrical.
The area of equilateral triangle is
equal to ½ height x length of any side
Area = √3/4 x (length of any side of Triangle)2
Area = √3/4 x (AB)2
or
Area = √3/4 x (BC)2
Area = √3/4 x (AC)2
All must be equal and are physically
equal, when measured by civil engineering divider. Here we have measured all
the sides of Triangle – which are equal to 10.41cms, on the print of this
photo. Do it yourself and get the proof of symmetry of Taj Mahal onion dome.
Important Conclusion on Symmetry of Taj
Note: All the five different cases
studied for the symmetry of central dome of Taj Mahal and proofs that the
central dome of Taj Mahal is most symmetrical in nature.
Case 6
Who is right? Judge for
yourself. Taj Mahal central dome is 100% symmetrical.
Reference & Courtesy: currentscience.ac.in
Actual height of the central dome –
includes the portion of cylindrical drum – where the onion type’s central dome
sits (बैठता है)
80ft=24.38 meter. Whereas author has shown his height of central dome –
30M-1.79=28.21 meter in his picture.
Diameter of central drum is 58ft=17.67
meter + thickness of both walls.
Other Asymmetry – proved by the author
Northern Ends of
Platform are not differently sinking
(A)
It is also (Not) apparent that the northern and southern ends of
platform on which Taj sits are differently sinking over time with northern end
towards the river having sunk 35mm
(In 350 years of existence of Taj) more than the southern end (Two side cannot
sink differently).
Explanation: These findings of 35mm of civil engineering
department of Roorkee in the year 1989-1992 has clearly stated that it has a
slope for the purpose of draining the rain water from the platform but not any
settlement or sinking, because they have checked this sinking very minutely
with reference to the fixed point of Taj. There is no further sinking-as far as
their data’s is concern.
Slope
in the northern side of platform for the purpose of drain the rainwater.
The slight
sinking would have not caused the rigid dome to become more asymmetrical over
time fill this year (August 2020). As symmetry of this is wrong.
All the four smaller
Chhatari are covered by Red stone – so question does not arises for any
Asymmetry
(B)
Base of one Chhatari is left (Figure 1) in red sandstone and not
covered with marble. An asymmetrical example quoted by author.
Taj shows that the red stone are fixed
on all the four minor dome at the plinth
Explanation: Not one Chhatari or smaller dome is not left to
cover with marble. But in fact all the four chhatari of smaller size has fixed
red stone on the plinth of the chhatari. Probably, the authors were not having
the bird view of Taj Mahal. The bird view will explain automatically. This
asymmetry to the authors. However in engineering subject the plinth is always
covered with red stone-which is not having much importance to the visitors.
Others asymmetry in
the structure
The authors should
know that in the first floor of the main building and gallery, the lime plaster
has been on the dome instead of covering by marble slab by the designer of Taj
Mahal. Will you count this non-marble fixing in the 1st floor &
galleries are asymmetrical examples of Mughal Emperor.
(C)
The four minarets of Taj Mahal are out of plumb-are they supposed to
be asymmetrical in your nature. They are purposely constructed out of plumb
leaning outside from the central platform. Authors will count this fixture for
non-symmetry in the structure.
The Four Minarets of Taj Mahal are out
of Plumb & Technically built perfectly stable
Technically
when any structure constructed out of plumb, we have to reduce the dead loads
of due to the minarets on top, so that it did not tilt big due to high-velocity
wind. That is why there is three section or floors in the minarets & the
highest length of height is the top portions. Please note.
However,
one must also know the facts that these four minarets are built for the purpose
of watch & ward of the area, where the watchmen have to stand on the top of
the Chhatari of these minarets and need the balconies placed at three stages of
its total height for the stability of minarets.
The
designer of such hudge most famous structure had purposely made “out of plumb”
because in case of any worst happening due to the earthquake or thunderstorm,
these minarets did not fall on the Main Taj Mahal. Because of it’s “out of
plumb” – outward towards the ground.
(D)
Nobody knew this, that the south-west minaret is more plumb out than
the back-minarets of northern bank. Please go through my book & papers
published. President Donald Trump was standing near this south-west
minaret of the Taj Mahal and was discussing the leaning of minarets with our
guide. Why these minarets leans more than other 3 minarets.
President Trump (USA) Visiting Minarets
Reference
& Courtesy: Times Now
The finial pinnacle is not tilled from the central axis by 3O
angle
The Taj is definitely renowned for its bilateral
symmetry. There is “No” imperfection in its symmetry. As per the author, the
FINIAL (Pinnacle) h=35ft over the central dome is tilted from the vertical axis by about 3O
(angle as measured at the bottom of dome, smaller it measured at ground level).
The tilt could not have occurred – when bronze replica was installed in 19th
century. But still have the 100% vertical on its axis.
The central line shown in these
photographs – concede with the centre line of the finial (pinnacle-35ft) as
well with the central dome.
However, one should understand the
technicality of the tilted finial. If by any chance it is tilted by 3O
from the central axis, it would have blown out from its bottom by the high
speed wind velocity of 150kmh. When there are serious damages on Taj has
occurred recently in the year 2018 & June 2020.
Technically the wind forces of 150kmh,
will certainly loose its rigidity from the joints. Vibrations force of
unbalance finial (tilted by 3O) and the pressures – created at the
different points at finial will create the unbalanced dynamic – displacement of
finial and will blow it down to the earth. Please do not try – such type of
unsymmetrical in the Main Taj Structure.
Conclusion
The central dome of
Taj Mahal is mostly & perfectly symmetrical with reference to any “angle”
of structural engineering concerns. From the above facts & finding which speaks
clearly, that the central dome of Taj Mahal in question for asymmetry is not at
all asymmetrical.
निष्कर्ष
मुगल सम्राट बादशाह
शांहजहां से इतनी बड़ी गलती हो ही नहीं सकती कि ताजमहल के मुख्य गुमंद की गोलाई की
बनावट में बहुत बड़ा अन्तर रह जावे।
-डॉ.राम बजाज (Structural
Engineer)
0.92 meter maximum
difference in two part of central dome is impossible. Before proving none
symmetry of central of Taj – one must have the knowledge of “How to construct a
spherical dome of Brick Masonry
In short, for construction
of spherical dome, we have to put a fixed centre of dome – permanently without
any disturbance to this centre, till the spherical dome or in our case the
“onion type bulb” dome of Taj Mahal is fully completed.
Then from this
centre of dome, during the construction of brick dome, we have to lay down each
and every layer of bricks of spherical dome with respect to this permanent
marked centre by the help of string-revolving around this centre. This string
or some wooden from of circle is meant for the diameter of the dome at that
layer of bricks.
So by doing this
revolving the string around centre, the exact diameter of dome is constructed
without any “error” in diameter of dome at any place in that layer of bricks.
Each & every
layer of bricks laid down for the purpose of construction is thoroughly checked
by the experts working on the construction of dome with I respect to the
radius.
If any layer of
radius of bricks laid down is out of plumb from the centre, the next layer of
bricks on dome will immediately known to the experts constructing the dome and
will immediately rectified any mistake, which is out of circle. Hence there
cannot any chance that each & every brick laid on one half part of circle
(dome) is smaller and other half part of circle (dome) is bigger like a tune of
0.92 meter as calculated by the above authors mentioned in this report,
the graphs.
For the references
various photographs are displayed here to understand by a layman – the actual
procedure of construction of spherical dome.
So, inclusion the
spherical dome cannot be constructed with having two half of dome having
different nature of radius without any knowledge of the experts constructing
the central dome of Taj Mahal.
Various photographs showing the various stages of laying the
layer of bricks in circle with the help of centre marked and string or having
the wooden frame to check the diameter at any place of that layer which is is
in progress
Dome Part – 1
Dome Part – 2
Actual Article Reproduced here with any correction
Dr.Ram Bajaj
& his team of experts on spot at Taj Mahal-analysis at various visits.
Various Pictures
taken by our Experts Team – working of Taj Mahal. These are the pictures during
lockdown period.
Structural Analysis of Taj
Mahal at various Technical Angles
Various actual views &
pictures of Taj Mahal & River Yamuna-during lockdown period (COVID-19)
April 2020 for analysis.
Their pictures were taken from
the northern side of Taj Mahal and position of Yamuna River-during lockdown
period April 2020 by our team-for analysis.
The
contaminated Yamuna River-during lockdown period-for analysis
Road Bridge-where few vehicles
are moving on the Yamuna River bridge crossing-Agra during COVID-19 lockdown.
A
famous temple of Agra near Taj Mahal is during COVID-19 period April 2020.
Not a single person is seen at Yamuna River of Agra-even Dhobhis who washes the clothes at Yamuna River-are also not seen.
A team member working on the Taj Mahal,
standing behind the back portion of Taj Mahal having Yamuna River. (North Side)
Dr.Ram
Bajaj – Structural Engineer on spot at Taj Mahal-analysis at various visits.
Dr.Ram
Bajaj & his team of experts on spot at Taj Mahal-analysis at various
visits.
Dr.Ram Bajaj
Ph.D, M.Structural Engineer,
B.E. (Civil
Engineering) From
B.I.T.S, Pilani
M.A. (Economics)
M.A. (Public
Admin.)
M.Com (Fin. Man.)
L.L.B.
Diploma In
Interior Decoration M.I.E.
F.I.V
Chartered
Engineer
Structural
Engineer
Approved Valuer
Note: Your advise will be highly appreciated.
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