Figure 71: Use of experimental models

 

content

Vitruvius on limits of models

Construction of the Dome of Florence

Brunelleschi (practice) – Alberti (theory)

Leonardo da Vinci

Since 1600: model experiments

Piere Bouguer (1746), Augustin Louis Cauchy (1829), Joseph Bertrand (1847)

William Froude and Osborne Reynolds

Ludwig Prandtl

Rayleigh and „dimensional analysis“

 

 

Vitruvius on limits of models

 

Around 23 BC Vitruvius (Book X, chapter 16.5-6) describes the following problem:

 

„There are some things which, when enlarged in imitation of small models, are effective, others cannot have models, but are constructed independently of them, while there are some which appear feasible in models, but when they have begun to increase in size are impracticable ...

So too, in some models it is seen how they appear practicable on the smallest scale and likewise on a larger.“ – Translation by Morris Hicky Morgan, 1914

 

„In some machines the principles are of equal effect on a large and on a small scale; others cannot be judged of by models.

Some there are whose effects in models seem to approach the truth, but vanish when executed on a larger scale ...

Thus that which may be effected on a small or a moderately large scale, cannot be executed beyond certain limits of size.“ – Translation by Bill Thayer, ca. 2000

 

Latin and English text see:

Vitruv über Modelle (exemplaria, exempla)

 

 

Construction of the Dome of Florence

 

Rolf Bernzen (1986) and Andres Lepik (1994, 27-38, 59-89) describe in detail the planning and construction process of the Dome of Florence in the years 1285-1471. The most important and interesting phase were the years 1353-67, especially 1366 and 1367, for which years we have a big amount of written documents, mostly notes, architectural tenderings, protocols of debates and  assessments as well as accounting records.

Rolf Bernzen (1986, 89-115) distinguishes for this time two kinds of experiments with the help of models: the ones in thoughts an the ones in practice.

The first ones concern questions of esthetics, conveninecy and adequacy of purpose as well as functionality.

The second ones use models for demonstration purposes, tests of feasability and operationality as well as of statistical calculations and loading capacity (Rolf Bernzen, 1986, 106f).

 

 

Brunelleschi (practice) – Alberti (theory)

 

After 1417 Filippo Brunelleschi experimented with various kinds of models finishing the Cupola of the Dome of Florence.

see in German: Die Modellmethode der Renaissance

 

After 1450 some theoreticians as Leon Battista Alberti, Antonio Averlino, detto Filarete and Francesco di Giorgio Martini described the use of models.

 

see in German:

Leon Battista Alberti: «De re aedificatoria» (1485) über die Modellmethode

see in English:

Figure 50: The first model theory: Leon Battista Alberti (around 1450/1460)

Figure 37: Alberti on models (moduli): De re aedificatoria (written 1450/60)

Figure 38: Alberti on models (exemplaria, exempla): De re aedificatiora (written 1450/60)

Figure 39: Early use of „model“ by Filarete (1464) and di Giorgio (1490)

 

 

Leonardo da Vinci

 

It is not so astonishing that Leonardo da Vinci also can be regarded as one of the first to experiment with models. One of his many fields of interest were “wind and waves”. E. g. he drew and constructed flying apparatus and he studied the art of sailing and the flow of water through a channel.

 

bibliography:

model: special topics – Renaissance: Kunst, Technik und Bildung

 

 

Since 1600: model experiments

 

Experiments with models in modern times started in 1600 with the Dutch engineers Simon Stevin and Cornelius Drebbel as well with the Englisman William Gilbert.

In his book “De Magnete” (1600) Gilbert saw earth as a big magnet. For the experimental proof he took a “terrella” – a little earth – i. e. a globe-shaped magnet he decorated with little jags as “mountains” (image in John Desmond Bernal 1970, II, 409). The illustrations in chapter II of book IV by William Gilbert (1958, 235-240) can be regarded as the first real imagery in experimental science.

 

Favored for experimentation have been, after 1600, model ships – first in England, and shortly after in the Netherlands, France and Russia.

 

A unique theoretical approach to the heuristics of small scale models has been given by the clegyman Simon Sturtevant (1612 – see Fig. 51)

 

In his text book „Della fortificazione“ (1596) the Florentine architect of fortifications, Buonaiuto Lorini, warned to not trust too much in conclusions deduced from experiences made with models (Wolfgang Lefèvre et al., 2003, 78).

 

According to the thesis by Moritz Weber (1919, 364) already Aristotle has studied the static behavior of geometrically simular wooden staffs against bending in his „Mechanica Problemata“.

In 1638 Galilei (see Viktor A. Stoff 1969, 122) made static considerations on the similarity of machines and found out that the firmness resistance of a construction piece does not increase proportionally to its linear dimensions (1890, 106-109). But only Isaac Newton in his „Principia mathematica“ (1687) was the first to  clear the concept of „mechanical similarity“. He searched for the conditions under which two processes of geometrical similarity behave in mechanical similarity.

 

bibliography:

Model: The 66 most important publications from 6 centuries

model: special topics

 

 

Pierre Bouguer (1746), Augustin Louis Cauchy (1829), Joseph Bertrand (1847)

 

In a technological encyclopedia of the 18th century (J. K. G. Jacobsson, 1783, 79) we read that since the investigations into the building of ships and model ships by Pierre Bouguer (1746) attention has been paid to understand that the small copy can by no means demonstrate the same behavior as the original in its true size with regard to masts and rigging. After all nobody can scale down the wind.

 

It was only in the 19th century the problem was tackled mathematically, e. g. by

·        Augustin Louis Cauchy (1829),

·        Joseph Bertrand (1847, 1848),

·        William Froude (1870) and

·        Osborne Reynolds (1883).

Hermann von Helmholtz contributed the nice study: „Über ein Theorem geometrisch ähnliche Bewegungen flüssiger Körper betreffend, nebst Anwendung auf das Problem, Luftballons zu lenken“ (1873). Later (1889) he developed a „Theory of wind and waves“.

 

 

William Froude and Osborne Reynolds

 

An important impulse for studying hydrodynamic drag for big ships with models was the desaster of the big ocean liner „Great Eastern“ (1858): the motor was to weak to propel the ship forward at a reasonable speed. The English engineer William Froude soon began to experiment with little models. Later he had a 90 meter channel in which to drag model ships. He found that models of different size with similar shaped hull produced different patterns of waves even if they were dragged at he same velocity.

Not much later, in the 1880s, the English engineer Osborne Reynolds experimented with flowing liquids in tubes.

 

Since then several model laws adopted the names of Cauchy, Froude und Reynolds.

 

 

Ludwig Prandtl

 

As early as in 1901 the Wright brothers built a little wind tunnel to test their airplanes, especially the wing shapes. In 1908 the German physicist Ludwig Prandtl built the first wind tunnel of "continuous circuit" design. He experimented with turbulent flows and developed the „Prandtl-Zahl“ (viz. Margaret Morrison, 1999, 53-65).

The first full-scale airplane to be tested in a wind tunnel was the „Sperry M-1 Messinger“ in summer 1927. The outer parts of the wings had to be cut off (Thomas A. McMahon, John Tyler Bonner, 1985, 81).

 

 

Lord Rayleigh and „dimensional analysis“

 

A seminal article on „The Principle of Similitude“ by Lord Rayleigh in 1915 broadened the way to „dimensional analysis“ (e. g. Percy W. Bridgman, 1922).

 

In Germany the so-called „Ähnlichkeitmechanik“ was treated by Moritz Weber (1919, 1930, 1942).

 

A broad overview on experimenting with scale models is given by  Henry Louis Langhaar in his book: „Dimensional analysis and theory of models“ (1951).

Other overviews are by Jon Valer L. Chirila (1967), Jürgen Zierep (1972; Engl. 1971), Walter Rehwald (1975) and Johann Stichlmair (1990).

 

 

Bibliography

 

model: special topics – Ähnlichkeitslehre in der Strömungstheorie: Modellregeln