Eiffel_proposal for a Tower

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Proposal for an iron tower: 300 metres in height

Claudette Roland and Patrick Weidman

Architectural Research Quarterly / Volume 8 / Issue 3-4 / December 2004, pp 215 - 245DOI: 10.1017/S1359135504000260, Published online: 08 December 2005

Link to this article: http://journals.cambridge.org/abstract_S1359135504000260

How to cite this article:Claudette Roland and Patrick Weidman (2004). Proposal for an iron tower: 300 metres in height. Architectural ResearchQuarterly, 8, pp 215-245 doi:10.1017/S1359135504000260

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theory arq . vol 8 . nos 3/4 . 2004

This translation of the mmoire Gustave Eiffeldelivered to the French Civil Engineering Society in1885 is the byproduct of a quest to understand thephysics underlying the construction of the EiffelTower. Prior to this research, several mathematicalmodels for the skyline shape of the tower had beenpublished. In no case, however, could the proposedphysics of tower construction be traced directly topublications by, or interviews with, Eiffel and hisengineers. The final result of this investigation,published by P. Weidman and I. Pinelis in ComptesRendus Mecanique, vol 332 (2004), shows that the towerwas constructed in a fashion that would eliminatethe load on diagonal elements (trellis bars) of tallvertical structures subjected to the bending momentof a horizontal wind. With this design, the largetrellis bars diagonally criss-crossing each face of thetower could be eliminated and the resulting shapewas that of four elegant curved piers that merge intoa single slender spire at mid-height. Eiffel was proudof his new construction technique and even viewedthe tower as a product of Nature. In his mmoire hestated: Before they meet at such an impressiveheight, the uprights appear to spring out of the

ground, moulded in a way by the action of the winditself. The findings published (in English) in ComptesRendus Mecanique show indeed that the skyline shape,formed by the 29 panels on each tower face, lendsitself to mathematical description: the tower closelyresembles an exponential profile, with widthdecreasing smoothly from bottom to top.

One of the most appealing aspects of translatingthis text was the fact that Eiffel, the quintessentialFrench engineer, had written it himself. In his ownwords, the pioneer architect tells how he created andsold the monument that would become theunmistakable worldwide symbol of Paris and France.The translation would not have been possible byeither translator alone. Ms Roland made every effortto maintain the original flavour of the nineteenth-century French text. Professor Weidman handled theequations and did research on various technical, andsometimes archaic, words appearing in the mmoire.We have kept the translation as close as possible tothe original in style, and retained Eiffelspunctuation whenever feasible, including hisabundant use of commas and semicolons employedto keep various concepts unified.

Editors note:At the translators suggestion, Eiffels text and illustrationshave been printed as closely as possible to the originalformat and layout.

document arq . vol 8 . nos 3/4 . 2004 215

documentIn this previously untranslated text, Gustave Eiffel explains the

technical rationale of his then controversial tower and argues

persuasively for its practical uses and cultural value to Paris.

Proposal for an iron tower: 300 metres in heightClaudette Roland and Patrick Weidman


P R O P O S A L F O R A N I R O N T O W E R

3 0 0 M E T R E S I N H E I G H TDESTINED FOR THE 1889 EXPOSITION

By G . E I F F E L

Ever since my colleagues Messrs. Nouguier, Koechlin and Sauvestre and I have

informed the public of a 300-metre metal tower project intended for the 1889

Exposition, the idea has gained acceptance.

A lot of the French and foreign scientific and political press covered it, and today few

people remain unaware of the projects main features.

There was at first a lot of criticism, particularly with regard to the practical uses of

such a construction, but we also received support and encouragement from eminent

men, which gave us confidence in the viability of the project.

Currently the problem is clearly defined; various possible objections have been

raised, as were indications of genuine possible applications; and it is time for us to

acquaint the Society with the technical aspects of a project with which it already is

generally familiar, and which we have studied in detail.

The idea itself is not new: without going back to the tower of Babel, one will recall

that in 1874, a thousand-foot tower had been proposed for the Philadelphia Exposition;

we do not know why it was not built.

In 1881, M. Sbillot proposed to light up Paris with an electrical source placed 300

metres above the ground. This idea, whose practicality we do not have to discuss here,

has not been carried out to date.

arq . vol 8 . nos 3/4 . 2004 document216

Claudette Roland and Patrick Weidman Proposal for an iron tower

1


Meanwhile, our studies of high metal piers supporting railroad viaducts, such as the

Garabit viaduct, led us to think that piers much higher than those already existing

could be built without great difficulties.

1. General considerations about the construction

of high metallic piers

The main difficulty encountered in the construction of these high piers is as follows:

Normally, an elaborate truss system designed to withstand the force of the wind is

built into the large planes normal to the axis of the viaduct. Since the pillars bases

must be increased in size as their heights increase, due to their great length, the truss

members efficiency becomes practically illusory.

Even if these were designed as caissons, as we were the first to do, so that each one

could withstand both tension and compression, they nevertheless remain a great

problem if the space between the pier footings reaches 25 to 30 metres. It is therefore

much better to completely eliminate these additional, relatively heavy elements and to

shape the piers in such a way that all the shearing forces will be concentrated on the

piers edges, by reducing these piers to four large uprights, without any crossbracing,

and simply linked by a few, interspersed, horizontal belts.

If we are dealing with a pier supporting a metal deck, and we consider the effect of

the wind on the deck alone, which is always greater than the effect on the pier itself, we

will simply need, in order to eliminate the crossbracing members of the vertical planes,

to have the two axes of the truss frame go through a single point located at the top of the

pier.

Obviously, in this case, the horizontal wind load can be decomposed directly

according to the axes of the truss systems, and these will not be subjected to any

shearing forces.

If, on the contrary, we are dealing with a very high pier such as our tower, where

there is no longer any horizontal wind stress on the deck at the top, but only the wind

stress on the pier itself, things are different, and it is enough, in order to eliminate the

use of the truss members, to give the uprights a curve such that the tangents to these

2


Proposal for an iron tower Claudette Roland and Patrick Weidman


uprights, brought to points located at the same height, always meet at the crossing

point of the resultant of the stress exerted by the wind on the section of the pier above

the points being discussed.

Lastly, if we want to take into consideration both the wind load on the upper viaduct

deck and the load on the pier itself, the exterior curve of the pier tends closely to a

straight line.

A tall viaduct pier, such as the one we are planning, could thus simply be composed

of four corner uprights, built in the form of caissons. The walls would be hollowed out to

decrease the surface exposed to the wind. The ratio between the height and the base

could be as great as desired to give the construction the necessary strength.

In connection with this, we studied a large viaduct pier 120 metres high with a base

of 40 metres, in whose practical advantages we firmly believe and which we hope to be

able to use one day in a large construction project.

2. Summary description of the features of the

300 metre iron tower

All this research led us to study a tower or pylon, reaching the uncommon height of

300 metres.

Here is a brief description of this tower:

The frame is essentially composed of four uprights forming the edges of a curved

pyramid. Each upright has a square section decreasing in size from the base to the top

and forming a curved caisson with a large lattice, 15 metres wide at the base and 5

metres at the top.

The spacing of the upright footings is 100 metres between axes. These uprights rest

on solid foundation blocks inside of which they are anchored, for added stability.

On the first floor, that is to say approximately 70 metres above the ground, the

uprights are linked by a 15-metre wide, glassed-in gallery, which goes around the

construction.

This gallery, with a surface of 4,200 square metres inclusive of balconies, could serve

as a meeting room either for a restaurant, or various other venues, which we will

discuss later.

3




On the second floor is a square room, also glassed-in, 30 metres wide.

At the top is a 250 square metre glass cupola with an exterior balcony, from which

visitors will be able to enjoy the splendid panoramic views extending as far as 120

kilometres. Also from this terrace, scientific experiments and studies could be

conducted, and an electrical source to light the exhibition could be installed.

In the towers lower portion and on each face is a grand arch 50 metres high and

spanning 80 metres. These arches, with see-through fasciae and tympanums

ornamented with elements of various colours constitute the main decorating feature.

Visitor traffic would flow via lifts placed inside the uprights.

3. Conditions of resistance and stability of the tower;

effects of the wind; foundations; spire at the summit

I arrive now at the conditions of resistance:

The decomposition of the wind forces is established according to the principles we

discussed above.

Let us suppose, for a moment, that we have laid out on the faces of a simple truss

forming a resisting wall the shearing forces of the wind, the horizontal components of

which are:

P, P, P, P.

We know that in order to calculate the forces acting on the three pieces cut by plane

MN, we need to determine the resultant P of all exterior forces acting above the section,

and to decompose this resultant into three forces acting through the cut pieces.

If the shape of the system is such that, for each horizontal cut MN, the two extended

truss frames intersect on the exterior force P, the forces in the truss beam will be zero,

and we will be able to exclude this structural support.

It is the application of this principle which constitutes one of the distinctive features

of our system, and which we believe is worth bringing to the Societys attention.

Consequently, the direction of each upright element deflects following a curve

illustrated in the drawing (fig. 1, pl. 91), and in reality, the exterior curve of the tower

reproduces, at a given scale, the very curve created by the bending moments of the

wind.

4




Since we do not know exactly the effects of the wind, the numbers to be used with

regard to the intensity itself, or the area of the exposed surfaces, we proceeded with

extreme caution.

With regard to the intensity, we considered two hypotheses: the first assumes that

the wind exerts a constant force of 300 kilograms per square metre against the entire

height of the tower. The second assumes that the intensity increases from the base

where it is 200 kilograms, to the summit where it reaches 400 kilograms.

As for the exposed surfaces, we did not hesitate, in spite of its apparent

exaggeration, to admit the hypothesis that, on the upper portion of the tower, all the

lattices of the caissons were replaced by plain walls; on the middle level, where the

voids take on more importance, each front face measured four times its actual iron

surface; below (first floor gallery and upper portion of the arches), the front surface was

solid; and finally, at the base of the tower, the uprights were solid walls and struck twice

by the wind.

These hypotheses are much more extreme than those generally accepted for

viaducts.

Using these surfaces, we calculated the distribution of the intensity of the wind

using both hypotheses, and we can see from the drawing that in both cases the

resulting funicular polygons are nearly identical.

5




In the case of a uniform wind of 300 kilograms against the entire height, the total

horizontal load against the construction is 3,284 tons, and the centre of action is located

92.3 metres above the support. Thus the overturning moment is:

MR = 3,284 92.3 m = 303,113 ton metres.

As for the stabilising moment, the total weight of the construction is as follows:

Metal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,800 tons

Rough-plaster floors 5,500 m2 at 300 kg. . . . . . . . . . . . . . 1,650

Miscellaneous . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Total. . . . . . . . . . . . . . . . . . . . . . . . . . 6,500 tons

The base of the tower being 100 metres, the moment of stability will be:

MS = 6,500 100___

2 = 325,000 ton metres, which is higher than the moment of

destabilisation.

In the second hypothesis, we used a wind varying between 200 and 400 kilograms.

The total horizontal load comes down to 2,874 tons, but the centre of action goes up to

107 metres above the support, and so the destabilising moment is:

MR = 2,874 107 = 307,518 ton metres.

This number is almost identical to the number in the first hypothesis and remains

lower than the stabilising moment.

We could even significantly increase the safety factor by attaching each of the four

upright chords to the foundation blocks using three tie rods of a diameter of 0.11 metre,

involving a masonry cube sufficient to double the factor of safety.

As for the foundations, a few numbers will suffice to show that their execution would

be simple.

They are built as follows:

Each of the corner chords rests on a square, ordinary masonry block 6 metres high

and 8 metres wide, supported by a concrete base 4 metres thick and 9 metres wide.

6




These blocks are crossed by 8-metre long anchors and linked to each other by a wall

one metre thick. This leaves between them a large glassed-in room of approximately

250 square metres, which will be used for access to lifts and to house the machinery.

Under these conditions, the load on the foundation floor would be as follows, based

on a wind of 300 kilograms:

1) Metal upright load:

Weight alone . . . . . . . . . . . . . . . . 6,5004

= 1,625 tons

3,162 tons

Wind load . . . . . . . . . . . . . . . . . . .307,518

= 1,537

2) Masonry load. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5,400

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8,562 tons

which distributed over a surface of 324 square metres, gives per square centimetre:

8,562,000 = 2.6 kg on average

and 4.50 kg on the most compressed edge.

Finally, to estimate the maximum wind load, note that we must use a wind of 300

kilograms, which is so exceptional that it has never been known to occur in Paris, and

we will use a load coefficient of 10 kilograms, which would be the equivalent of a 6 to 7

kilogram load under normal wind occurrences in Paris.

The 10 kilogram coefficient is customarily used in Germany and Austria for large

steelworks not subjected (like bridges) to vibrations caused by trains. We have already

used it ourselves in the Budapest train station, and railway companies in France also

use it for large steelworks.

In our tower, the total coefficient portion due to the loads is 5 kilograms, and it is also

5 kilograms for loads due to winds of 300 kilograms. It will be reduced to 1 or 2

kilograms for ordinary strong winds in Paris.

7



2 100

3,240,000

}


I must also address the potential deflection under the action of the wind in such a

tower. This is an interesting problem, not so much with regard to the deflection which

may occur under the extreme conditions of a wind of 300 to 400 kilograms, which we do

not have to worry about since the summit of the tower would no longer be accessible,

but it is useful to determine if, with ordinary violent winds, people present on the upper

platform would be uncomfortable.

Working with the wind classifications used in Claudels work, and calculating

deflections corresponding to the pressures indicated, we found the deflections to be as

follows:

TABLE of deflections under various winds

These numbers are quite reassuring, and since the oscillations will be extremely

slow because of the great length of the bending portion, the effect will almost certainly

not be felt. It will be much less noticeable than in a masonry lighthouse, where the

mortars elasticity is the major cause of deflection.

8



WIND CLASSIFICATION SPEED PRESSURE DEFLECTIONper second per square metre of the tower

metres kgs. metres

Very strong breeze . . . . . . . . 10.00 13.54 0.038

Breeze affecting top sails . . 12.00 19.50 0.055

Very strong wind . . . . . . . . . 15.00 30.47 0.086

Blustering wind . . . . . . . . . . 20.00 54.16 0.153

Storm . . . . . . . . . . . . . . . . . . . . 24.00 78.00 0.221


4. Lifts

For the lifts to be installed in the tower, which will be of unusual size, we went to M.

Heurtebise, who proposed the following system which seems to us quite workable as

well as capable of ensuring complete safety.

The well known system of hydraulic lifts with compensator created by his company

would activate two articulated shafts running the entire length of the tower, placed

inside one of the four uprights and following its curvature.

Each of these shafts would, every thirty metres (run of hydraulic pistons) receive

cabins which would, thanks to an alternate movement given the shafts, line up in front

of each other at the end of their run. At that point, they would stop for approximately

half a minute, during which time the lower cabin would fill up. Each alternate cabin

would empty its passengers into the facing cabin, and the upper cabin would let out its

passengers on the towers platform. A similar second lift would be used for the descent.

This system would be absolutely safe and would enable a great number of

passengers to go up at the same time, with continuous departures.

The cabins speed would be limited to 50 centimetres per second, since too great a

speed would be uncomfortable for most people. Thus the ascent of the 30 metres

constituting a floor would take one minute. If we include a half a minute stop, the climb

of each 30 metre span will take one and a half minutes, or a total of 15 minutes for the

entire ascent.

With each cabin holding ten passengers and departures occurring every minute and

a half, 400 people per hour could be taken up.

The total cost of this apparatus could reach 200,000 francs, excluding the machinery,

250,000 francs if we include it.

5. Using the tower to electrically light

the Exposition

At least for the duration of the Exposition, the top of the tower can be used to house

an electric light source, capable of giving out a warm and pleasant light over the park

and the gardens.

9




If we consider the surface to be lit a circle 1,000 metres in diameter, and as a

condition that there be sufficient light to read a printed page, Messrs. Sautter and

Lemonnier, the well known manufacturers of electrical beacons, while they do not think

this would be the best use of light, estimate that a source placed at the top of the tower

would have to be 3,000 ampres. They base this estimate on the lighting of the quays of

Rouen, for which the source was placed at a height of 13 metres, with an intensity of 24

ampres, and adequately lit a circle 130 metres in diameter.

In our case, the distance between the light and the centre of the circle is

approximately 10 times greater than in Rouen, and it would be necessary to have a

source 100 times more powerful. But since we also have to factor in atmospheric

absorption, the source of light will have to be 125 24, or 3,000 ampres, which will

require a 400 to 500 horsepower generator.

However, 90 ampres is, until now, the maximum that one can practically obtain

with a single lamp.

At most, we would need 33 lamps, but it is better to plan for 48 of various intensities,

which would be positioned around the upper lantern, in three tiers and lighting three

concentric zones.

With light sources of continuous current we dont have to be overly concerned with

aiming the light towards the ground since it has been demonstrated that almost all

rays are naturally projected from bottom to top in the shape of a cone whose

generatrices are 45 degrees from a vertical line, but it will be necessary to train each

lamp so as to produce the maximum intensity in the portion of areas to be lit, and for

that, the best way is to fit each source with a special optical device focused differently

for each one.

6. Construction price

With regard to the cost of our tower, the weight of the metal came to 4,810 tons

distributed as follows:

10




Uprights, with crosspieces . . . . . . . . . . . . . . . . . . . . . . . . 3,500 tons

1st floor gallery = 70 m 15 m 4 = 4,200 m2

2nd floor room = 30 m 30 m = 900 m2

5,110 m2

At 100 kilograms . . . . . . . . . . . . . . . . . . 510

Upper room and platform of 100 m2 . . . . . . . . . . . . . . . 100

Anchors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

Four double arches at the base . . . . . . . . . . . . . . . . . . . 600

Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4,810 tons

which, at 50 cents per kilogram, installed, amount to . . . . . . . . . . . . . . . F 2,405,000

Estimated cost of foundation and masonry for the base . . . . . . . . . 400,000

Various additional glass works, roofing of the halls, etc.,

are estimated at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100,000

The total cost of the construction itself is then . . . . . . . . . . . . . . . . . . . F 2,905,000

to which we must add the cost of the lifts, which, according to M. Heurtebises estimate

will be 250,000 francs, including the necessary machinery.

The total cost therefore is 3,155,000 francs.1

Such would be the real cost of this type of construction. Other estimates published

by outside sources were grossly inflated.

1We researched what the costs would be if the height of the tower were to be reduced, and we studiedtwo other towers, one 250 metres and the other 200 metres. This latter would still be the highest knownmonument.

Applying the same elements of the estimate to these two projects would give the following prices, whichinclude the foundations and the lifts:

Tower 250 metres high and 85 metre base . . . . . . . . . F 2,000,000 Tower 200 metres high and 70 metre base . . . . . . . . . F 1,400,000 .

In the event one of these towers was transferred after the Exposition to another, higher location inParis, the moving costs would be:

For the tower of 250 metres . . . . . . . . . F 500,000And for the one of 200 metres . . . . . . . F 375,000.

11




Of course, we are not including the price of the land, since if the tower is built on the

Esplanade des Invalides, on the Champ de Mars, or any other space within the

Exposition, we would not have to pay for the land occupied.

In fact, we point out that only the surface occupied by the four foundation bases

supporting the tower will actually take up space. There will be room on the remainder

of the land for buildings or parks for public usage.

Now that you are aware of the construction details I have just given you, I dont

think there can remain any more doubts about the ease of assembling and building the

tower.

I will again be able to apply the same methods adapting them to this project to

take advantage of the lower upright anchors I have often used in the past to build

cantilevered constructions such as for example the bridges of Douro, Garabit,

Cubzac, etc.

Based on this experience I am certain that the assembly would not take more than

a year.

7. Choice of material: iron or steel?

Before we go on to list the possible practical uses for such a building, we must say a

few words about our selection of material.

The use of iron or steel appears to be the most appropriate because of the metals

great strength for its light weight, because a small surface would be exposed to the

wind, and because all the building materials involved would work at the same rate of

expansion and compression, which can all be calculated, and therefore give us complete

security.

We hesitated for a long time between iron and steel, but since in this case lightness is

not a concern and would rather be a hindrance with regard to resistance to the wind,

and, since we are dealing with great dimensions, resistance to buckling is the main

concern, and finally, since steel works at a higher coefficient than iron, and bending and

vibrations due to the wind would be greater, we finally selected iron. However, only a

final, detailed study to analyse the costs and comparison between actual metal rates

will determine whether to select iron or steel, and we reserve our choice until then.

12




Finally, metal has a special advantage in that the construction can be dismantled

and for a modest cost the tower could be moved if, for any reason, it had to be

transported to a location other than the Exposition. We estimate the moving costs at

between 6 and 700,000 francs.

8. Use of masonry

Apart from metal, we also wanted to investigate the use of masonry, and we studied

two solutions, one, a combination of masonry and iron, and the other, masonry alone.

Lets say right off that after some research, we found that these alternatives would be

much inferior to using metal alone, if not outright impossible.

Attempting a combination iron and masonry would expose us to all the

inconveniences of a mixed solution where heterogeneous factors such as flexibility,

strength and expansion would enter into play, and it is enough to say that we

encountered so many difficulties that it made it impossible to carry out such a project.

As for the use of masonry alone, we dont believe it is possible unless we wanted to

set aside all price considerations.

Here is a summary of our findings:

The first thing to worry about is which coefficient of resistance per square

centimetre to use.

Indeed, in research for large masonry works, considerations of tipping over under

force of wind are not as important as those relative to wind resistance itself.

In addition, there is a capital consideration to be taken into account in this research,

without which one would be in error, if the potential height of an edifice was calculated

based solely on the toughness of the stone used in its construction, as though it were a

monolith, and if it was assumed that by using porphyry or granite one could build a

taller tower than with good limestone.

Indeed, if we dont want to do simple mathematical abstractions and if we stay

within the reality of facts, which is that we are working here on a large construction,

where materials have to withstand a very great load, we must not forget that these

materials, with surfaces more or less well squared off, will not simply be stacked up on

top of each other. They will inevitably be separated by mortar beds intended to ensure

adequate pressure distribution.

13




Thus the stability of the work requires that this mortar not be crushed. So in the

construction of such masonry work we have to factor in the point of crushing of the

mortar, rather than that of the stone, which, if factored in alone, would mislead us into

believing we could build to fantastic heights far beyond all practical limits.

The necessary condition is that the materials used be stronger than mortar, their

surplus strength only providing additional security which cannot be evaluated.

Now, the maximum resistance indicated in classical buildings for cement mortars is

between 150 and 200 kilograms per square centimetre.

If we accept as the practical maximum 1/10 of this resistance, as is usually

admitted, a masonry construction in cut stone should not bear loads greater than 15 to

20 kilograms per square centimetre. Quite exceptionally, and going beyond the usual

safety point, getting, so to speak, into the danger zone, we could go as far as 25

kilograms. A limit of thirty kilograms becomes almost unacceptable for large works. In

any case it is quite an extreme limit.

Navier cites the buildings having the greatest loads. They are:

Pillars of the dome of the Invalides, in Paris . . . . . . . . . . . . 14.76 kgs

of Saint Peter of Rome . . . . . . . . . . . . . . . . . . . . . . . . . . . 16.36

of Saint Paul of London . . . . . . . . . . . . . . . . . . . . . . . . . . 19.36

Columns of Saint Pauls outside the walls, in Rome . . . . . . 19.76

Pillars of the tower of the Saint-Merri church, in Paris . . 29.40

of the dome of the Pantheon in Paris. . . . . . . . . . . . . 29.44

He even adds a 45 kilogram figure for the All Saints Day Church in Angers, but this

doesnt seem to be a convincing example since the church is in ruins.

The conclusion drawn from this table is that the limit of resistance of the

constructions considered the most daring is, as we were saying earlier, between 15 and

20 kilograms per square centimetre, going up to 30 kilograms in two of the buildings.

9. Washington Monument

But there exists a more striking example of construction which was just inaugurated

and about which I would like to give a few interesting details since they are so timely.

14




15




I am referring to the great stone obelisk known as the Washington Monument,

which is currently the highest in the world. (See figure on opposite page.)

This building, entirely constructed in marble-covered granite is 169.25 metres high.

It is square from top to bottom. At the base, the foundations are 16.75 wide. At the top,

below the pyramidon, it is 10.50 metres wide. The pyramidon itself is 16.86 metres

high. Inside this obelisk a rectangular space has been hollowed out such that the

thickness of the walls at the top is 0.50 metres and at the base, 4.5 metres. Its exterior

batter is 3.15 metres for a height of 152.4 metres, or 0.0206 metre per metre. The

interior space contains a steam lift, which was used to transport the building materials

and is now used for carrying up visitors.

The weight of the construction above the foundations is 45,000 tons, distributed on a

223 square metre base, giving a compression coefficient of 20 kilograms per square

centimetre.

If we account for the effect of a 300 kilogram wind, the wind stress coefficient is 6.5

kilograms per square centimetre, for a total stress of 26.5 kilograms per square

centimetre.

Such is the limit that even with choice materials and a particularly careful

execution,American engineers, who are not known for lacking boldness, did not dare go

beyond, and for good reasons.

Allow us to digress here on the subject of this monument and say that this is not an

encouraging example in favour of stone for the construction of a tower.

The construction of the first project was started in 1848. It was to include a 600-ft

pyramid, or a height of 183 meters, standing in the middle of a pantheon with a

colonnade forming a peristyle. But when, in 1854, the pyramid reached the height of 46

metres, it was seen to be leaning in such a frightening way that the work was stopped.

Work only resumed in 1877. The height originally planned was reduced by 100 ft and

definitely fixed at 160 metres. Then the foundation was underpinned. The size of the

base was considerably increased by adding around it numerous new concrete blocks

sunk deeper, giving a total footing of 38 metres, bringing the foundation surface from

600 square metres to 1,500 square metres. The maximum stress on the lower bed of the

foundation reaches 6 kilograms. Nevertheless, additional settling continued to occur

unevenly on each of the faces, measuring approximately 10 centimetres since the

beginning.

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It is only after great difficulties were overcome that, in 1880, work was resumed on

the upper portion. It went on steadily at the rate of approximately 30 metres per year,

and the monument was inaugurated last February 21. The total costs to date are

6,225,000 francs, and it is estimated that additional work will cost 870,000 francs,

bringing the total to 7,095,000 francs. As for the Pantheon, planned as decoration for

the monument, it was permanently postponed due to the considerable expense of

building it.

This is an example of cost figure which must be remembered, keeping in mind that

the edifice is overly simplified, reduced in effect to a large chimney, which is, after all,

only 170 metres high.

What would this price become for a 300 metre pyramid?

We tried to estimate it, and, by figuring a pier of equal strength for a coefficient of 30

kilograms, we arrived at a cube no less than 70,000 cubic metres, excluding the

foundations. If we estimate a cubic metre at 200 francs, the total cost would be 14

million. As for the foundation, its upper diameter would be approximately 30 metres,

its lower diameter 70, and its height approximately 20 metres, arriving at a cube of

38,000 cubic metres, which, at 50 francs per cubic metre, would cost 2 million, or a

total of approximately 16 million.

If we wanted to ornament this pyramid with a Pantheon and special decorations, the

numbers would be greatly increased, and we abandoned the idea of estimating the cost,

even approximately.

In summary, the difficulty of the foundations, the dangerous risks which could arise,

such as either uneven settling of the ground (settling which does not have serious

consequences in the case of a metal tower), or the uneven settling of mortars and their

inadequate hold within these large blocks, the difficulty and slowness of construction

generated by building the necessary enormous masonry cube, and the considerable cost

of the building, all these factors convinced us that a masonry tower, difficult to project

in theory, would in practice present great dangers and inconveniences, the least of

which would be a disproportionate cost for the goal to be attained.

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10. Conclusion in favour of metal

Thus we believe that iron or steel are the only materials leading to the solution of the

problem. Besides, in antiquity, in the Middle Ages and during the Renaissance, the use

of stone was pushed to its extreme limits of boldness, and it seems hardly possible to go

beyond what our predecessors achieved with the same materials, all the more so since

there has not been any notable progress in this direction in the art of construction for a

long time.

Therefore, such as we are planning it, this edifice of unusual height rationally

requires a material not necessarily new, but one that has not yet been industrially

available to the engineers and architects who preceded us. This material is iron or

steel, through the use of which the most difficult construction problems are solved

simply, and with which we commonly build either frameworks or bridges with a span

which would have seemed quite unachievable in the past.

Now for the shape of the edifice.

The one we are submitting for our tower might possibly be improved after further

studies, but we feel that it already demonstrates a striking feeling of strength and size,

as well as adaptation to the goal to be achieved.

Before they meet at such an impressive height, the uprights appear to spring out of

the ground, moulded in a way by the action of the wind itself.

Of course, shapes can be discussed, this one like any other, however, we are pleased

to be in the position of having received the endorsement of many artists and prominent

architects.

11. Use of the 300 metre tower

One of the most frequent objections raised by the public over the construction of this

tower has been its lack of practical use.

We are now quite confident that the practical applications of this tower are real, as

we will demonstrate later by examining some of its applications one by one.

First of all, with the popularity among the public of previous ascensions in the

Giffard captive balloons and in the Trocadero lifts, there is no doubt that people would

greatly enjoy, without incurring any danger or exertion, visiting the various floors

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of our tower which will offer them quite an extraordinary panoramic view, as far as 120

to 130 kilometres, from a birds-eye view, as though from a balloon, without interference

by the foreground such as when climbing a mountain when the feeling of distance and

height is missing. The brilliant lights of Paris by night would be a wonderful sight

which so far has only been experienced by aeronauts.

There is therefore no doubt that this tower would be one of the most popular

attractions in the Exposition, and that once it is completed, many people would

continue to visit it either during the day or in the evening.

But, outside of this application of a special nature, science would find there a vast

field of observation.

12. Opinion of M. Herv-Mangon

With regard to meteorology, we cannot do any better than show you a few excerpts

from M. Herv-Mangons March 3 report to the French Meteorological Society:

I am quoting these excerpts verbatim:

The usefulness of building an open metal tower structure of great height to house

certain scientific instruments and from which to carry out experiments and studies at

various elevations above ground level has often been brought to the attention of the

French Meteorological Society.

There exist masonry towers in several observatories, however they present more

inconveniences than advantages for the installation of meteorological instruments.

In the sun, the mass of the construction heats up, the wall surfaces produce eddies

which impede the study of rain, mist, snow and dew, even conducted at a great range;

all hygrometric or thermometric data become inaccurate or deceptive.

The 300 metre iron tower proposal established by M. Eiffel and Messrs. Nouguier

and Koechlin, engineers, and M. Sauvestre, architect, is therefore of considerable

interest to meteorologists.

It would enable us to conduct many meteorological studies and experiments of the

greatest interest, among which we will randomly mention the following:

The law of temperature decrease with height would easily be observed, and the

variations due to the wind, clouds, etc., would certainly supply ample data which is

completely lacking as of now.

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The amount of rain falling at various heights on the same vertical has been widely

estimated. Such an interesting problem for the theory of formation of the rain would be

solved by a few years of observations made with about fifteen precipitation gauges

positioned at regular intervals along the height of the tower.

Mist, fog, dew often form in layers thinner than 300 metres, thus we could observe

these meteors throughout their entire depth, take air samples at various levels,

measure the volume of water in its globular state held suspended in each layer. This

liquid volume is much greater than its equivalent in steam, and its knowledge would

explain why clouds of small volumes sometimes pour out such considerable amounts of

water on the ground.

The hygrometric state of air varies with height. Nothing would be easier than to

study these changes if we could simultaneously observe instruments placed relatively

far apart above each other. Evaporation would also occasion very useful experiments.

Atmospheric electricity, about which we still have only imperfect knowledge, should

be the subject of the most active research in the towers observatory. The difference of

electrical tension between two points located 300 metres above each other is probably

great, and would cause very interesting phenomena.

Wind velocity usually increases rapidly as it gets farther away from the ground

surface; the tower would enable us to determine the law of increase of this speed up to

300 metres and probably slightly higher. Independently from its theoretical interest,

this determination would supply useful information to the aerostation.

Air transparency could be observed from the tower, in exceptionally favourable

conditions, following either a vertical, or vectors of a given inclination.

Independently from the meteorological observations I have just mentioned and

which are my only concern here, a 300 metre tower would also enable the realisation of

a large number of experiments impossible to attempt today. For example, it would

make it possible to set up manometers of up to 400 atmospheres, which could serve to

experimentally calibrate the manometers of hydraulic presses, and to establish

pendulums with oscillations lasting over a quarter of a minute, etc., etc.

Without further developing, due to lack of time, a programme of studies which a 300

metre tower would make possible, I am convinced that the Society will join me in my

wish to see the realisation of this magnificent edifice proposed by M. Eiffel for the 1889

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Exposition, and whose usefulness as a scientific research instrument cannot be

doubted.

13. Opinion of Admiral Mouchez

Admiral Mouchez, director of the Observatory, wrote us a letter from which are the

following excerpts:

I hasten to inform you that I have seen your proposal for a 300 metre tower with the

greatest of interest. I very much desire the realisation of the project because I believe

that in addition to the general interest presented by such a monument, it will be

extremely useful for various scientific matters and specifically for the study of the lower

layers of atmosphere, which have some influence on the precision of astronomical

studies. A height of 300 metres would enable us to regularly observe the frequent

inversions of the law of decrease of temperature with height, and in better conditions

than on a mountain.

We will also be able to study humidity variations, atmospheric electricity and wind

variations in force and direction.

Comparisons between four similar sets of registering instruments placed at ground

level, at 100, 200 and 300 metres would certainly give greatly interesting results.As for

astronomical observations, I dont believe it would be as useful. It is, however, certain

that in the middle of the city of Paris, the atmosphere at that height would be much

purer than in our observation rooms; most of the city smoke and dust would be left

below us.

With regard to meteorological observations and the atmospheric studies I was

mentioning, a masonry tower would take away a great part of the precision and interest

from observations that would be made in an iron tower; with the latter, instruments

would be completely isolated in the atmosphere; with a masonry tower, they heat up and

cool off along with the tower and are alternatively in the shade or in the sun, etc., and

the conditions are quite different.

An iron tower would unquestionably be superior for meteorological observations.

You did not tell me the approximate cost of this tower; whatever it is, I

wholeheartedly wish that your project will be realised.

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14. Opinion of M. Pierre Puiseux

From a specifically astronomical point of view, M. Pierre Puiseux, astronomer at the

Paris Observatory, was kind enough to give us the following information:

Undoubtedly the projected tower will enable applications useful in astronomical

studies. The motion of the platform under the influence of the wind probably precludes

observations intended to determine the precise position of the stars, but it clears the

way for most physical astronomical research. Spectroscopes to analyze the light of the

sun and the stars, to observe the movements of the stars by the displacement of the

rays, would function better at an altitude of 300 metres than on ground level. The

elimination of dusts and local mists would make it possible to follow the sun closer to

the horizon, which would be a great advantage for the study of telluric lines due to solar

light absorption by the atmosphere.

A camera to photograph the sun or the moon would also be practical; its utilisation

would mostly serve during the passages of Mercury or when eclipses occur near the

horizon. Since photographing stars or nebulae requires a long exposition time, it is

therefore most susceptible to being affected by the wind and should be reserved for

calm nights. It will be necessary to make sure that the lateral translation of the

instrument has no negative influence. The most important is that the optical axis

remains parallel to itself. It seems difficult to decide, prior to the experiment, if the

motions caused by the wind will in fact be of this nature. In any event, the physical

aspects of the moon, the planets, the nebulae will be able to be studied and charted

under favourable conditions.

A searcher or a wide aperture telescope installed at the top of the tower will enable

us to follow those stars which are low on the Paris horizon. These observations, of

course, would not be as good in terms of accuracy as those made in fixed observatories,

but they could be made in the event the latter were no longer possible. Now, we know

that it is important to obtain measurements, even approximate, as soon as possible for

newly discovered stars.

Temperature variations with altitude would also constitute an interesting field of

study for meteorology and astronomy. All the theories of refraction given to date are

based on unwarranted hypotheses, often contradicted by experience.

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15. Opinion of Colonel Perrier

Finally, Colonel Perrier, whom we had consulted regarding optical telegraphy

applications, confirmed to us that such a tower would be extremely useful and would

allow types of communication not yet in existence, but about which he did not want to

elaborate, which we understand, as to where they would be located.

He was also kind enough to summarise the areas that the construction of the iron

tower might help clarify.

Astronomy: Law of refraction, spectroscopy, telluric lines.

Plant Chemistry: Plants at 300 metres, air composition, carbonic acid.

Meteorology: Winds, temperature, hygrometry, electrical state, lightning, upper air

streams.

Physics: Deviation of a falling body. Atmospheric electricity.

Foucaults experiment to demonstrate the rotation of the earth.

War: Optical telegraphy.

The range of possible experiments is quite wide, and will go on increasing as science

progresses.

I believe you will be doing something worthwhile by building this gigantic tower.

Based on the expertise of the prominent men I have just named, I believe I can

positively state that the scientific usefulness of the planned tower has been

demonstrated, and that we will have with us the entire scientific community in support

of our project.

16. Summary and conclusion

In summary:

1. The potential for the execution of the project I have the honour of presenting

cannot be seriously doubted: the nature of the material we have selected, the degree of

certainty with which we can adapt the result of our calculations to it, a degree much

greater than the one included in the use of masonry, the knowledge acquired by todays

engineers in the construction of great metalworks, everything assures us that we may

assert that no hazards are to be feared.

23




2. The cost of this work, that I have estimated at 3,150,000 francs, is based on very

advanced detailed studies, and has been sufficiently examined to not be subject to great

variations if we move on to the execution stage.

3. The uses of this tower will be great from a scientific point of view and very

important militarily.

4. Not only would it be one of the great attractions of the Exposition, but after the

Exposition, it would remain one of the most interesting monuments in Paris, and

certainly one of the most visited.

Finally, if I may add, such a tall tower which goes far beyond anything achieved until

now, may be worthy of personifying, not only the art of modern engineering, but also the

century of Industry and Science in which we live, the road to which was paved by the

great scientific movement of the end of the eighteenth century and by the revolution of

1789, to all of which this monument would be erected as an expression of Frances

gratitude.

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25




Plate 91

The fold-out drawing on the following page designated Pl.91 shows, from left to

right: moment distributions on the tower computed from two different wind load

distributions; plan and elevation views of a tower footing resting on its partially buried

caisson structure; and an overhead detail and a horizontal cut of the massive bolt

structure holding a footing to its caisson.

Information concerning estimates of loads and moments based on two different wind

models, with augmented tower surface areas as described in 3 to provide an ample

factor of safety, are given below:

Diagram of wind resistance

Case 1: Wind of 300 kg from the base to the summit.

Case 2: Wind increasing from 200 kg at the base to 400 kg at the summit.

Surfaces and corresponding forces

Below the table two calculations are presented. The first is the determination of

forces in the primary rafters and the second is a calculation of the surface area of each

foundation necessary to distribute the tower weight and the forces wrought by the wind

according to the two wind load models. In the lower left corner are two polygon force

diagrams for wind distribution models presented on a scale of 0.001 m per 60,000 kg.

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Nos. of Height of Area of 1st wind model 2nd wind model

elements surface surface Wind force Total Wind force Totaland forces element element per sq. m wind force per sq. m wind force

Summit 400 kg 1 76 m 359 m2 300 kg 285,000 kg 375 356,250 2 64.5 1064 300 319,200 328 348,9923 18.5 583 300 174,900 300 174,9004 11.5 391 300 117,300 290 113,3905 39 1236 300 370,800 274 338,6646 7 360 300 108,000 58 92,880 7 42 3003 300 900,900 242 726,7268 41.5 3361 300 1,008,300 215 722,615

300 m 3,284,400 kg 2,874,417




This and following two pages: Eiffel's fold-out Plate 91




AcknowledgementsWe have benefited from constructivecomments on the accuracy oftranslation from Edward Allen at MIT,Professor Bernard Amadei at theUniversity of Colorado, AndrzejHerczynski at Boston College andStephane Eisen a recent graduatefrom the University of Colorado. Themmoire was originally publishedunder the title Projet dune Tour enFer de 300 Mtres de Hauteur Destine LExposition de 1889 in Bulletin de laSociet des Ingnieurs Civils de France, 38,pp345370 with one fold-out plate.

BiographiesClaudette Roland is a freelancetranslator in Los Angeles whosetranslation credits include museumcatalogues, art criticism essays andfilm scripts.

Patrick Weidman is a Professor atthe University of Colorado. Hereceived postgraduate degrees fromCaltech in Pasadena, the Von KrmnInstitute for Fluid Dynamics inBelgium, the University of SouthernCalifornia in Los Angeles and is afellow of the American PhysicalSociety.

Translators addressesClaudette RolandPO Box 24035Los AngelesCA 90024, [email protected]

Professor Patrick WeidmanDepartment of Mechanical

EngineeringUniversity of ColoradoBoulderCO 803090427, [email protected]

Documents

Eiffel_proposal for a Tower