The Investigation of the French Curve

City University of New York (CUNY) CUNY Academic Works

Publications and Research New York City College of Technology

2018

Cheriyah Wilmot CUNY New York City College of Technology

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This work is made publicly available by the City University of New York (CUNY). Contact: [email protected] The Investigation of the French Curve Cheriyah Wilmot, Jason A. Montgomery ncarb leed ap

Department of architectural Technology, New York City College of Technology, cuny

Introducton Evolution Demonstration From the Parthenon to shipbuilding to Art Nouveau, curves have played an in- Following the spline, numerous curve templates emerged for use in naval ar- To use this device, a draftsperson finds a close fit along the edge of the tool and tegral part to a successful design in architecture. It can provide optical illusion, chitecture and beyond. They were initially composed of three main elements: repositions it when neccessary to draw a smooth, irregular curve. This could be enhance function, or simply create aesthetics. Over the course of time, differ- molds, sweeps, and single curves. Prior to mass production and plastic, thin pe- used on a drafted version of one’s desired freeform curve or be created from ent devices were created to aid in drawing the curvilinear forms. French Curves ices of rigid, steamed wood were specially cut. Near the beginning of the 19th scratch. are modern templates used in different disciplines to aid in the creation of these century the French Curves appeared. According to the Grand Larousse, the curves. outlines were created out of fantasy “decoupe suivant des courbes de fantasie”. 382 – Example Applications of curves 1 Molds/Sweeps • Set varies upon request by ship- A B C D E F maker • Created prior to Modern Relevance

19th century Fig. C.3: Moulds and sweeps used in ship draughting, adapted by the author from Schnellsegler [8]. 385 frames using “arches of circles called sweeps” (see page 106 in [5]), but the drawings of a West Indiaman of 300 tons (plate XXI), a Collier The Parthenon Corithian pillar Furniture Art Nouveau Brig of 170 tons (plate XXII) and a sloop of 60 tons (plate XXVII), all 5 German Set reedited in Éléments et pratique de l’architecture navale 1805 [6], show The new Academic Building features an auditorium that has a resemblance to that their body plans have been drawn using “moulds” of elliptical or similar shapes.

P H • Set of 34 one template of the Burmester Set. Even though it was built digitally using para- A plate with the title “Moulds and Sweeps used in Ship Draughting” 381 2 Copenhagen in Hedderwick’s book “A Treatise on Marine Architecture”, published 1830 [7], illustrates David Steel’s verbal description of moulds. e • Possible Ori- metric design, it is possible that the building was hand drawn prior. plate shows 17 “Moulds being Portions of Circles” with radii from 3 to 22 feet (not all radii mentioned by Steel are presented here) and 26 Set other moulds, many of their contours set into one another. Most of *+2-%#$/3 ''-%#$/.-!.!-1! *+2-%#$/3 ''-%#$/.-!.!-1! gin: Germany them show a hyperbolic shape, only few of them seem to be parts of Objective elliptical curves. • Set of 43 [9]. Set German C.6: Fig. -!/%)#$+!.%)%1%') 1'- $%/! /0-!-*..%. %+'%)-2*(+-%.*) -*0!./**&!)/-' C.7 Fig. in here shown is which of selection a curves, of type same the $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. !/%' /%*) * -!/! "-*( %/2/! $!**&.*) 1980 – 1580 Instruments Drawing in shown are Curves French Other [9]. • Possible Origin: 103. page on [10] nition of “French Curve” in e Random House Dictionary Dictionary House Random e in Curve” “French of nition de e The objective of this project is to investigate the origins of the French Curve in o 15 of Fig. C.7 and the Diction- the and C.7 Fig. of 15 N to similar very curve a shows [11] naire usuel illustré [12] gives as examples for “pistolets à dessin” three three dessin” à “pistolets for examples as gives [12] illustré usuel naire Copnhagen, C.7. Fig. of 17 and 7, 4, os N to similar curves terms of its history, evolution, usage, and mathematical composition. century 19th early the in manufactured rst were Curves French in France and sold in sets. e material was pearwood, lime or other other or lime pearwood, was material e sets. in sold and France in Fig. C.2: Copenhagen Set [9]. or celluloid vulcanite, century 20th the in Later wood. stable similar Denmark [10]. used were acrylic added to the Copenhagen Set the French Curve No 4, others the French geometrical from derived not were Curves French of outlines e Curves No 4 and No 21 (see Figs. C.2 and C.7). the in stated is it as cut, but hyperbolas or parabolas ellipses, as curves • Advertised in des suivant (“découpé fantasy of curves following [13], Larousse Grand courbes de fantaisie”), ending in spirals, curls or corner points. French French points. corner or curls – spirals, in ending fantaisie”), 386 de courbes D S decora- or design other any and architecture in used were Curves tive work; their use in naval architecture, specially to draw the body body the draw to specially architecture, naval in use their work; tive 1805 In the chapter “Explanation of the terms used in shipbuilding” in e 6 French Curves élémentaire Traité in d’Étroyat by described been had ship, a of plan Shipwright’s Vade-mecum [5, p. 118] Steel explained the term “moulds” simply it called (he Curve French e [14]: Navale d’Architecture in the familiar way as fullsize templates to cut the timbers for frames, cur- strong a with lines draw to served bord, thin of out cut “pistolet”), vature which could not be achieved with an ordinary spline. He pictured pictured He spline. ordinary an with achieved be not could which vature stem etc. But then he continued that the term mould is also given *+2-%#$/3 ''-%#$/.-!.!-1! Method similar [14], in C.5 Fig. I, (planche Curve French a of sample one only to “thin exible pieces of peartree or box, used in constructing the draughts and plans of ships, which are made in various shapes; viz. to • Set of 28 the segments of circles from one foot to 22 feet radius, increasing six inches on each edge, and numerous elliptical curves with other gures”. +'%)-2*(+-%.*) -*0!./**&!)/-' 1'- $%/! /0-!-*..%. % -!/%)#$+!.%)%1%') ( ere is no further description of “other gures”). In a footnote to * !/%' /%*) $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. • Possible Origin: "-*( %/2/! $!**&.*) -!/! 3 English Set this explanation the name of a dealer was given where “moulds, &c. of 383 Information was gathered primarily from online databases. Primary and Second- every sort requisite for marine drawing may be had”. is advertisment indicates that in 1805 these moulds were already known and demanded Paris, France tools and must have come into use some years earlier. • Set of 14 Steel never mentioned the use of these “moulds” in his description ary sources were analyzed to extract information in order to complete the objec- of constructing the body and the half-breadth plan (page 186 and • Possible Origin: *+2-%#$/3 ''-%#$/.-!.!-1! following in [5]). He described only the old fashion of drawing the • “decoupe suiv- Fig. C.7: French Curves (not on uniform scale!) [9]. scale!) uniform on (not Curves French C.7: Fig. tive. Dates of significance (where available) were collected and organized from ant des courbes THe new Academic Building Front Elevation French Curve United King- -!/%)#$+!.%)%1%') 1'- $%/! /0-!-*..%. %+'%)-2*(+-%.*) -*0!./**&!)/-' $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. !/%' /%*) * -!/! "-*( %/2/! $!**&.*) the earliest to the latest to determine origin. This provided a visual evolution of Fig. C.4: English Set [9]. de fantasie” Fig. C.8: Burmester Curves [9]. Curves Burmester C.8: Fig. dom e plate (see Fig. C.3) has been redrawn from a small reproduction in Schnellsegler 1775–1875 [8] and a scale in feet has been added to the For curves. these of use and form show to above) C.7 Fig. in 26 o N to circular moulds. ere is no scale given for the other 26 moulds nor French cut perfectly where trade the to referred he information further the drafting tools for curves. contours de variés pistolets . . (“. sizes and contours various of Curves is it known if all of them are of the same scale. e e purchased. be could .”) . . decoupés parfaitement grandeurs, de et way d’Étroyat dealt with this subject indicates that the use of French French of use the that indicates subject this with dealt d’Étroyat way Conclusion

O 20 1850. by matter routine a been had architecture naval in Curves *+2-%#$/3 ''-%#$/.-!.!-1!

e various sets of curves for the special purpose of drawing ship lines shown here (Figs. C.4, C.5 and C.6) are taken from a catalogue of a dealer and manufacturer of drawing tools [9]. ey represent the 7 The Burmester +'%)-2*(+-%.*) -*0!./**&!)/-' 1'- $%/! /0-!-*..%. % -!/%)#$+!.%)%1%') !/%' /%*) * !/%' /%*) $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. status of these traditional drawing tools which they had reached by the "-*( %/2/! $!**&.*) -!/! beginning of the 20th century and which lasted as long as these curves were manufactured. e numbering of the curves is arbitrary and serves Set Predeccesor: The Spline only as identi cation for ordering single curves out of a set. A scale The creation of curves has evolved from using a compass and splines to us- in millimeters is added at the side to give the approximate size of the original curves. ese curves were originally cut out of thin bords of steamed wood of the pear-tree, the box-tree or white beach. By steam- ing the wood warping was avoided. Later in the 20th century various • Set of 3 ing The Burmester Set. This resulted from the need to convert scaled draw- plastic materials, transparent or coloured brown, were used. 4 Hamburg Set – 384 Splines are thin pieces of bendable wood. Their curved form are held in place E S • Possible Origin: ings to full-sized creations. As the need grew, individually created pieces became e English Set (Englischer Satz, see Fig. C.4) looks like a subset of • Set of 44 the 26 moulds Peter Hedderwick presented in his book [7] (see Fig. C.3) and which Steel [5] described as “numerous elliptical curves with Hamburg, Ger-

*+2-%#$/3 ''-%#$/.-!.!-1! *+2-%#$/3 ''-%#$/.-!.!-1! other gures”. mass-produced sets. Manufacturing competition within Europe is present due by weights. Their purpose is to create “fairness” in the hull form of a ship. Na- • Possible Origin: val architects aimed to achieve smooth, gradual lines that alter the overall perfor- many to the various location-based naming of these sets. Due to the name French Hamburg, Ger- -!/%)#$+!.%)%1%') 1'- $%/! /0-!-*..%. %+'%)-2*(+-%.*) -*0!./**&!)/-' $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. !/%' /%*) * -!/! "-*( %/2/! $!**&.*) • Mathematically mance of a ship. many derived Curves, manufacturers in France could’ve created the evolved set first. The evo- Fig. C.5: Hamburg Set [9]. Set Hamburg C.5: Fig. lution could have also stemmed from the fact that splines/molds cannot be used Proccess of Shipmaking S H e English Set and part of the Copenhagen Set were obviously com- obviously were Set Copenhagen the of part and Set English e Nowacki, H, and Wolfgang Lefèvre. Creating Shapes in Civil and Naval to produce small curves with ease in a schematic drawing. However, the stan- bined to form the Hamburg Set (Hamburger Satz, see Fig. C.5). At At C.5). Fig. see Satz, (Hamburger Set Hamburg the form to bined 26 was created for this set by reducing in in reducing by set this for created was 26 o N curve “new” one least Architecture: A Cross-Disciplinary Comparison. Leiden: Brill, 2009. 25. o N curve scale Internet resource. dardized set that is mass produced today is called the Burmester set instead of G S G

e youngest set is the German Set (Deutscher Satz, see Fig. C.6). C.6). Fig. see Satz, (Deutscher Set German the is set youngest e It seems that this set was a combination of several curves from the the from curves several of combination a was set this that seems It the French Curves. If there is a connection between the new academic building THe Burmester new twelve about which to Set Hamburg the and Set Set:Copenhagen Composition curves were added (see lower part of Fig. C.6). Timmermann wrote wrote Timmermann C.6). Fig. of part lower (see added were curves [4] that these new curves had been adapted to the change in geometry geometry in change the to adapted been had curves new these that [4] of iron and steel hulls. steel and iron of and the Burmester set, then relevance still exists for architects to create in reality The highly commercialized BurmesterC F set was mathematically formulated by “French Curves”, in the narrower sense of the word as it is used in in used is it as word the of sense narrower the in Curves”, “French and replicate digitally.

Britain, indicates that these drawing tools originated in France where where France in originated tools drawing these that indicates Britain, *+2-%#$/3 ''-%#$/.-!.!-1! the German mathematician, to linked are names Both Ludwigdessin”. à “pistolets called were Burmestercurves these near the mid 19th century. It

+'%)-2*(+-%.*) -*0!./**&!)/-' 1'- $%/! /0-!-*..%. % -!/%)#$+!.%)%1%') !/%' /%*) * !/%' /%*) $//+!**& !)/-'+-*,0!./ *('% %/2/! $!**&. poses a similarity to three of the forms in the"-*( %/2/! $!**&.*) -!/! French Curves set. This custom Discussion set of curves separates itself from its predecessors because it was derived from Splines and Weights Drawings Construction These conclusions provide a reference point into the limitations of a curve. mathematics. They provide a historical background of the current method to produce curva- Half Ellipse Parabola ture: Parametric Design. [Instead of a fixed set of algorithms that exist in the Burmester set, parametric design allows changes in the algorithms (parameters), Parabola Logarithmic Spiral resulting in a limitless way to create curves.] This can provide a starting point for

Logarithmic Spiral Partial Spiral students who explore curvilinear forms. It can also provide context for the students who draft using these templates. Future research can look into the process Euler Spiral Euler Spiral of algorithms that Ludwig Burmester put into his mathematically-derived set.

Built Vessel Recognizable Curves