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“The Art of the Motorcycle”Museum Exhibition

With over two million visitors at fourvenues to date, “The Art of the Motorcycle”exhibition, produced by the Solomon R.Guggenheim Museum in New York City,has been by far the museum’s most suc-cessful exhibition ever. It first opened in1998; Ultan Guilfoyle, former director of theGuggenheim’s Film and Video Productiondepartment, and I were the co-curators. Inselecting motorcycles for this exhibition,we applied three criteria: aesthetic appeal,social significance, and historical or tech-nological importance. Although all threecriteria can be related to materials, here Iwill focus explicitly on some of the tech-nological aspects of motorcycles that in-formed our choices of the specific machinesfor the exhibition. More information onmost of the motorcycles discussed herecan be found in the exhibition catalog (seeBibliography).

Perhaps the single most significantmotorcycle in the exhibition was the1868–1871 Michaux-Perreaux steam veloci-pede, made in Paris (Figure 1a). This wasthe world’s first motorcycle; only one wasever made, and yet it somehow survivedthe Franco-Prussian War and the first andsecond World Wars. It is now owned bythe Musée de l’Ille-de-France in Sceaux, asuburb of Paris. Louis Guillaume Perreauxcreated this machine by installing hispatented steam engine in the first mass-

produced pedal bicycle, designed by theMichaux brothers. A steam engine wasa logical choice for him to use, havingsteadily developed from the work ofThomas Savery and Thomas Newcomenin the 17th century to the point wherePerreaux was able to make one smallenough to use for this purpose. Unfortu-nately for Perreaux, his machine turnedout to be a technological dead-end themoment it was created, since a few yearsearlier, in 1862, his fellow French country-man Alphonse Beau de Rochas hadpublished the technical description of thefour-cycle internal-combustion process.The Michaux-Perreaux engine produces�1–2 hp, and the overall machine weighs195 lb (88 kg). We placed this earliestmotorcycle at the entrance to the exhibi-tion, next to the 1998 MV Agusta F4 (Fig-ure 1b), which at that time represented thelatest achievement in motorcycle design.Significantly, the MV Agusta F4 producesroughly 100 times more horsepower thanthe Michaux-Perreaux, while weighingonly twice as much. As I discuss in thisarticle, it has been the developments inmaterials technology over the centuryseparating these two machines that madethese advances possible.

The Michaux-Perreaux motorcycle hadwheels with iron-covered wood rimsand a 100-psi steam engine held together

with iron rivets. A few years later, thefirst mass-produced motorcycle, the 1894Hildebrand & Wolfmüller, incorporatedthe newly developed drawn-steel tubingand had steel connecting rods directly at-tached to the rear wheel. In both of theseexamples, the designers used some of themost advanced materials available at thetime the machines were created. To followsubsequent developments in materialstechnology, it is particularly useful to tracethe evolution of racing and sportingmotorcycles over the past 100 years, sincethese machines not only quickly incorpo-rated the latest materials advances, butthey also often provided the generalpublic’s first exposure to those materials,whether they were aware of it or not.

The fact that for similar classes of ob-jects (high-speed motor vehicles, for ex-ample) the costs of mass productionreduce to similar numbers of dollars perpound demonstrates why such technol-ogy was typically incorporated first inmotorcycles rather than in automobiles.Since motorcycles are so light comparedwith automobiles, their designs are able toincorporate more state-of-the-art materialstechnology while still maintaining a rea-sonable total cost. Currently, $11,000 willbuy a Suzuki GSX1300R Hayabusa, amotorcycle that is capable of achieving190 mph directly from the dealer’s show-room. In contrast, that same $11,000 willonly buy the least expensive four-doorsedan on the market—a Hyundai AccentGL—whose top speed is a more modest110 mph. Performance in an automobilecomparable to that of the Suzuki motor-cycle certainly is available, but it comes ata price. For $89,000, the Acura/HondaNSX sports car provides the consumer withsomething approaching Grand Prix racing-level technology in a mass-produced auto-mobile. These prices and relative levels oftechnology and performance can be betterunderstood by the following comparison:the NSX costs $27/lb and the Suzuki isroughly the same at $23/lb, while theHyundai costs only $4.80/lb.

Materials Used in the EngineThe challenge of creating motorcycles

for racing places high demands on mate-rials. Before World War I, an advancedform of motorcycle racing in the UnitedStates developed on wooden board tracks,resulting in machines like the 1914 Cyclonethat nicely illustrate the dictum of “formfollows function.” The smooth, hard finishof the boards resulted in very low rollingresistance, and the steep banking of theoval racecourses eliminated centrifugalforce as a problem for keeping the ridersfrom sliding off the track, leaving only

The Art and MaterialsScience of 190-mphSuperbikes

Charles M. Falco

AbstractThe following article is an edited transcript of a talk presented in Symposium X at the

2002 Materials Research Society Fall Meeting in Boston on December 2, 2002. FromBessemer steel used on the first motorized bicycle in 1871 to sintered aluminumceramic composites and TiN thin-film coatings used on standard production machinestoday, motorcycles have been at the forefront of the use of high-performance materials.Thanks to developments in materials technology, relatively inexpensive mass-producedmotorcycles are now capable of achieving speeds of �190 mph.

Keywords: advanced materials technology, motorcycles.

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wind resistance as a fundamental limitingfactor on speed. Since the only function ofthese machines was to go as fast as pos-sible around a banked oval track, andsince the only purpose of a brake is toslow a motorcycle, the machines weremade without brakes in order to saveweight. Mufflers were eliminated to saveweight as well, and to avoid restricting thepower. However, although weight wassaved wherever possible on these motor-cycles, in order to extract the maximumpower, the designers had to concentrateon the engine head.

While an engine has a number of com-ponents serving various essential pur-poses, all of the power is produced inthe combustion chamber of the head. Un-fortunately, so is all of the heat. In anyinternal-combustion engine, only 25% ofthe energy extracted from the burning fuelends up as power to the rear wheel, whilethe other 75% is wasted in the form ofheat. The more power generated by anengine, the more heat generated as well.Unless this heat is extracted from theengine, parts will fatigue and fail due totheir reduced strength at elevated tempera-tures. While some of the heat of combus-tion naturally leaves the head through theexhaust pipe in the form of hot combus-tion by-products, the rest must be con-ducted away through the material of thehead itself. Here, the materials properties

of thermal conductivity and strength at hightemperature become key limiting factors.

When the air-cooled BSA “ZB” GoldStar motorcycle engine appeared in 1949,the technology available for casting alu-minum limited the size of the cooling finsthat transfer heat to the outside air andhence limited the amount of power thatcould be produced by this engine. Im-provements in casting technology over thenext seven years resulted in the final “DBD”form of this engine, which had a headwith significantly deeper cooling fins thanthe ZB. During this period, the technologyissue facing BSA’s engineers was not thatof generating more power, but rather ofextracting the additional heat from theengine to prevent component failure inthe engine head.

The heads of the earliest motorcycle en-gines were made primarily of cast iron,which has low thermal conductivity (seeTable I). By the 1920s, iron was replacedwith either brass or bronze in some racingengines, doubling the thermal conductiv-ity and thereby allowing a useful increasein power generated by the engine. Whenthe technology developed to allow durableiron valve seats to be cast into relativelysoft aluminum, thermal conductivity dou-bled again. As Table I shows, if neithercost nor practicality were issues, diamondwould be the optimum choice in thisnatural progression of increasing thermal

conductivity, although silver seems to bea reasonable second choice. Most of the1947 AJS “Porcupine” racing engine wasmade of aluminum, for low weight, butthe head was cast in silver, for high ther-mal conductivity. Notches were cut in itscooling fins to maximize the surface areaand hence its ability to transfer heat to theair. However, since pure silver is soft, a sil-ver alloy was used to make the materialsufficiently hard and durable for use in aracing engine. Unfortunately, by the timesufficient material was alloyed with thesilver to attain the required strength, theresultant thermal conductivity had beenreduced to that of an aluminum alloy, sothe use of silver was quickly abandoned.However, this episode does show thatwhere high-performance motorcycles areconcerned, the cost of materials is not asignificant factor.

By the 1920s, the excess heat generatedby high-performance motorcycle engineswas reducing the strength of valves to thepoint where the heads of the valves werebeing pulled from the stems by the forceexerted by the valve springs. One solutiondeveloped at that time was to make thevalve stem hollow, then partially fill itwith sodium, a low-density material thatalso has a low melting point and a highboiling point. Under normal operation ofthe engine, the sodium will alternately hitthe hot region of the valve, extract heat

Figure 1. (a) The Michaux-Perreaux steam velocipede (1868–1871).The single-cylinder (22 mm � 80 mm bore � stroke) steam engine in thisfirst motorcycle produces �1–2 hp, and the overall machine weighs 195 lb (88 kg). Used in its construction is iron for the frame, iron-coveredwood rims with iron spokes for the wheels, and leather belts to transmit power to the rear wheel. (b) The MV Agusta F4 (1998). Its four-cylinder,750 cc internal-combustion engine with dual overhead camshafts and four radial valves per cylinder produces 126 hp, and the overall machineweighs 397 lb (180 kg), only twice that of the Michaux-Perreaux. Used in its construction are Cr-Mo steel and Al alloy for the frame, Mg alloy forthe swinging arm and wheel rims, high-strength steel for the chain drive, carbon-fiber composite for the fenders, plastic for the bodywork, and aSi-based microprocessor for controlling fuel injection. (Photographs courtesy of the Solomon R. Guggenheim Museum and MV Agusta.)

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from it, then hit the cooler end and depositthat heat to be conducted away. Later, inthe 1950s, Velocette was one of the firstmanufacturers to use the Ni-based non-ferrous “Nimonic” alloy, developed forjet-engine turbine blades, for exhaustvalves in its racing motorcycles.

The steels used for valve springs werea major limitation to the performance ofengines, until vacuum melt processeswere developed in the 1950s to extractimpurities from the steel. If there were nolimiting factors—the most significant ofwhich are the amount of air that can bedrawn into the combustion chamber andthe strength of the connecting rod—thepower generated by an engine would in-crease linearly with rotational speed (rpm).Thus, neglecting all other factors, thefaster an engine can be made to turn, themore power can be generated. Unfortu-nately, through at least the 1950s, valvesprings often would fatigue and breakwhen engines were operated for significantperiods of time much above 8000 rpm.Different geometrical configurations weredeveloped to reduce or eliminate thisproblem: four valves per cylinder in the1937 Rudge Ulster, each with a smallerand therefore more robust coil spring thanrequired for a two-valve head; hairpin-shaped springs in the 1956 Manx Norton;and torsion bars in the 1965 Honda CB450are several examples. However, once ma-terials scientists developed vacuum-meltedhigh-purity spring steels, the rpm of theengine was no longer limited by valve-spring breakage. For example, the HondaCBR600RR shown in Figure 2 operates at15,000 rpm without problems with itsvalve springs.

Iron is an excellent material to use forthe cylinder of an engine. With the rightamount of carbon in it, the material is self-lubricating, so the piston rings do notabrade, while sealing in the hot gases. The

problem with iron, however, is that it isvery heavy. A lighter material like alumi-num would be preferable, except that it hasfar less abrasion resistance than steel. Inone recent development, aluminum hasbeen impregnated with a ceramic graphitecomposite to combine the weight advan-tages of the aluminum with the tribologicalproperties of the composite. In the Nikasilprocess, patented by the Honda Motor Co.in 1998, SiC in a Ni matrix is bonded to alightweight aluminum cylinder.

A good material to use for the crankcaseof a racing engine is magnesium, due to itslow density. Because Mg does not resistcorrosion well, it is usually anodized orpainted to protect it. Although Mg has alower density than aluminum and thus itsuse reduces the weight of the motorcycle,Mg is more expensive than Al and it is

much more difficult to work with becauseit burns at 454�C in air. However, thesepractical difficulties are offset by its weightadvantage, and as a result, Mg alloys havebeen used in many racing engines, such asthe crankcase of the 1962 Matchless G50.

Materials IssuesTo understand the selection of materials

for constructing racing motorcycles, it isuseful to look at tensile strength, or thespecific strength, which is the tensilestrength normalized to the density of thematerial. As Table II shows, strength andcost typically scale together.

The governing bodies that sanctionraces typically specify limits on both themaximum displacement of the engines aswell as the minimum total weight of themachines. However, the minimum weightlimit does not eliminate the use of thehighest technology in materials, becausethe location of the weight also mattersgreatly. For maximum maneuverability, amotorcycle must have as low a center ofgravity as possible; to prevent the torqueapplied to the rear wheel from elevatingthe front wheel and thereby constrainingthe rider from applying even more power,the center of gravity should also be as farforward as possible. The higher specificstrength of the materials now availableprovides designers with more parametersto position the center of gravity for bestperformance without increasing the over-all weight of the machines.

Substituting aluminum for cast iron in apart doubles or triples its strength whilereducing the weight by one-third, but itdoes so at a fivefold increase in cost. While

Table I:Thermal Conductivity and Density of Selected Materials.

Thermal Approx.WeightConductivity Density of Heada

Material (W�cm K) (gm�cm3) (lb)

Carbon steel 0.61 7.9 25Iron 0.80 7.9 25Brass (60% Cu, 40% Zn) 1.05 8.2 26Al alloy (0.6% Mg 0.6%, 0.4% Si) 2.00 2.7 9Aluminum 2.37 2.7 9Gold 3.15 19.3 61Copper 3.98 9.0 28Silver 4.27 10.5 33Diamond 9.07 2.3 7

a Assuming a 500 cc single-cylinder engine.

Figure 2.The 2003 Honda CBR600RR with its fairing (front and side bodywork) removed,showing most of the major components discussed in this article. (Courtesy of AmericanHonda Motor Co. Inc.)

The Art and Materials Science of 190-mph Superbikes

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there is no cost advantage to making thissubstitution, the savings in weight is clearlya performance advantage. Carbon-fiber-reinforced resins also exhibit much higherspecific strength than standard structuralmetals, but at a much higher cost. Theentire front fork assembly as well as thewheel rims of the 1995 Britten were madewith carbon-fiber composite to gain thatweight advantage over the competingmaterials, which would have been steelor aluminum. This sort of weight-savingsubstitution can be, and is, carried to ex-tremes. A plastic front fender on a motor-cycle weighs only a few ounces, so theweight saved by replacing it with onemade of carbon fiber is tiny. Even thoughthe cost increases greatly when carbonfiber is used for such a purpose, a signifi-cant number of buyers are willing to paythat cost for even a trivial performanceincrease. As a result, carbon-fiber compo-nents are to be found on many of today’sproduction motorcycles.

The 1932 MGC featured a fuel tankmade from cast aluminum. Taking advan-tage of the relatively thick and strongaluminum casting, the designer, MarcelGuiguet, was able to form a fuel tankthat also served as the main structuralbackbone of the frame. Unfortunately, thetungsten–inert gas (TIG) welding process,which prevents the formation of alumi-num oxide, had not been developed atthat time, so Guiguet had to resort tocrude aluminum struts bolted to the tankto connect it to the rear portion of the frame.Today, thanks to finite element analysis, adesigner can optimize the design of everycurve and segment of a complex frameand then use robotic welding to form theindividual components into an overallframe of whatever complexity is needed.

The forks of a motorcycle have to com-press and extend to absorb the irregu-

larities of the road. To absorb even thesmallest irregularities requires the surfacesin contact with the bushings in the forks tohave the lowest possible coefficient of fric-tion. One approach to accomplishing thishas been to deposit a titanium nitride filmon the polished steel of the fork legs. Theexpense of the process to deposit this ma-terial is irrelevant in terms of the increasein performance. For roughly $30,000, the180-mph 2003 Ducati 999R has TiN-coatedfork legs, a magnesium headlight assem-bly, and the entire fairing—the bodyworksurrounding the front and sides of themotorcycle—is made of a carbon-fibercomposite. Since the bushings in the forksalso contribute to the friction, a recentdevelopment from Honda is a compositesynthetic polymer/metal (Syntallic) bush-ing designed so that the coefficients ofboth static and dynamic friction are asclose to zero as possible (Figure 3).

The 2001 Honda “New American Sports”concept motorcycle was designed with asingle-sided front fork and rear suspen-sion. This asymmetric design requires avery high-strength material for support.The front fork is made from a carbon-fibercomposite and the leg is TiN-coated. Thisis not the first time such a single-sidedfront suspension has been used, althoughin an earlier example, the designer wasmore interested in saving material than inachieving high performance.

In the late 1940s, industrial productionin Germany was still recovering from thewar, and engineering materials were inshort supply. In this economic climate,Norbet Riedl designed the 1949 ImmeR110 with a single-sided front suspension(Figure 4).

While the fork leg of the Imme was sig-nificantly heavier than that of an individualleg of a standard set of forks, the fact thatonly one was required reduced the overall

amount of material needed for the frontsuspension. Riedl’s clever use of materialsextended to other components. The exhaustpipe of the Imme was made from muchthicker steel than normally would be usedfor this component, but by doing so it wasable to simultaneously serve as a single-sided rear-suspension leg. We can specu-late that Riedl got the idea for his frontsuspension from the design of the single-strut landing gear of the MesserschmittMe109, the most widely used fighterplane flown by the German Air Force dur-ing World War II. Aircraft design, espe-cially that of fighter aircraft, has many ofthe same requirements as motorcycle de-sign: the highest quality materials, at thelightest weight, with the highest perform-

Table II:Tensile Strength of Selected Materials Used in Motorcycle Construction.

Max.WorkingSpecific Strength Temperature Relative Cost

Material (N m�kg) (�C) (cast iron � 1)

Cast iron 52 300 1Stainless steel (18% Cr, 8% Ni) 98 600 8Tempered steel (0.5% C) 119 550 5Aluminum alloys 70–155 180 5Magnesium alloys 105–125 * *Nimonic 115 (Ni alloy) 134 900 *Titanium alloy (6% Al, 4% V) 280 500 25Maraging steel 299 * *Carbon-fiber-reinforced resin 1140 �200 30

Note: Specific strength � tensile strength�density.*Data not provided. Figure 3. A composite low-friction

synthetic polymer, deposited on abronze substrate for rigidity, providesthe load-bearing surface of a 45-mm-diameter bushing. (Courtesy ofAmerican Honda Motor Co. Inc.)

Figure 4.The 1949 Imme R110,designed to economize on the useof materials by incorporating suchinnovations as single-sided front andrear suspensions, the latter servingdouble duty as the exhaust pipe.(Courtesy of the Solomon R.Guggenheim Museum.)

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ance. The design is further enhanced when-ever an individual component can servemore than one function. Other examplescould be cited, such as the rotary engine ofthe 1922 Megola, or the styling of the 1957Aermacchi Chimera, where aircraft tech-nology directly led to developments inmotorcycle technology.

Magnetic properties of materials playan essential role in ignition systems. Untilthe early 1960s, most high-performancemotorcycles used magnetos for their igni-tion systems, since this device eliminatesthe weight and potential unreliability ofa battery. A magneto generates the highvoltage for a spark plug by simply spin-ning a coil of wire in a magnetic field. (Al-though this statement is true in principle,to actually understand the operation of amagneto in detail would require a lengthytreatise.) Since the larger the magneticfield, the smaller the coil needed to gener-ate a given voltage, and thus the smallerand lighter the total magneto, it is quite ad-vantageous to use magnets that have thehighest available energy product (mag-netic field B times magnetic intensity H).As a result, during the first half of the20th century, when magnetos were essen-tial components in racing motorcycles,these electrical devices were at the fore-front of the use of the latest magnetic ma-terials. Magnetos moved through steelsof tungsten, chromium, cobalt, and thennickel, then quickly made the transition toAlnico shortly after it was developed inthe 1930s. The anisotropic grain structurein this family of aluminum-nickel-cobaltalloys gives it particularly favorable mag-netic properties. Subsequent improvementsin varieties of Alnico continued to be in-corporated until the early 1960s, when themagneto itself ceased to be used in thelatest racing motorcycles.

The same principle of rotating a coilof wire through a magnetic field is usedto generate electrical power for auxiliaryfunctions like lights. Today’s sportingmotorcycles are expected to supply over500 W of electrical power, five times thatof a similar-weight machine of only 30 yearsago, and improved magnetic materialshave helped make this possible withoutan unacceptable increase in the weight ofthe electrical system.

Antilock brakes have certain advantagesfor some motorcycles, but the additionalweight of the system is a significantlymore serious problem than it is for a muchheavier automobile. However, small sen-sors based on high-performance giant-magnetoresistance materials for determiningwheel speed are now commercially avail-able, and antilock braking systems are beingincorporated in an ever-wider number ofmotorcycle models. For some years, mag-

netic sensors have been common items onracing motorcycles, used in data-acquisitionsystems that monitor suspension travel inorder to rapidly determine for each race-track the optimum spring rates and com-pression and rebound settings for theshock absorbers.

A Materials Story of SocialSignificanceIndustrialized Countries versusDeveloping Nations

In this article, I have mostly addressedsome of the highest levels of materialstechnology available, as used in racing andsporting motorcycles. In industrializedcountries, a typical consumer wants amotorcycle with the highest possiblehorsepower and the lightest weight, alongwith a stylish appearance and innovationslike antilock brakes. To meet these goals,typical construction materials may includehigh-Si-content forged-Al pistons, pressure-cast Al engine heads, Ti for valves androds, alloy steels for other engine parts,Mg for engine and frame components,and carbon-fiber composites for the bodyparts. However, in large parts of theworld, motorcycles have a very differentfunction, where they often provide theonly means of personal transportation. Ina developing country, motorcycles mustbe inexpensive, easy to maintain, and ableto operate on low-octane fuel. Thus, thematerials for their construction are castiron for cylinders, gravity-cast Al for en-gine heads, low-grade steels for engineparts, and cold-drawn-steel tubing forthe frame.

In the future, new materials and fabri-cation technologies will play a major rolein the motorcycles of both industrializedand developing nations. In the former case,higher-strength composite materials wouldallow designers to produce smoother,rounder, more organic shapes, such as seenin the Yamaha Morpho concept motor-cycle of the early 1990s. To the extent thatsuch materials could replace relatively ex-pensive metals like stainless steel, theyalso could help provide more people indeveloping nations with the benefits ofpersonal transportation. On this subject, itis appropriate to end with a quote fromthe eminent physicist Freeman Dyson: “Thetechnologies that raise the fewest ethicalproblems are those that work on a humanscale, brightening the lives of individualpeople. For my father 90 years ago, tech-nology was a motorcycle.” For a signifi-cant fraction of the world’s population,these words still apply today.

AcknowledgmentsI am pleased to acknowledge Ultan

Guilfoyle, for a wide variety of significant

contributions related to the work describedhere, and the staff of the Solomon R.Guggenheim Museum. Many people inthe motorcycle industry have been veryhelpful, with special thanks to GaryChristopher of American Honda and TimBuche of the Motorcycle Industry Council.

Bibliography1. J. Bradley, The Racing Motorcycle: A TechnicalGuide for Constructors (Broadland Publications,York, UK, 1996).2. G. Cocco, How and Why: Motorcycle Designand Technology (Giorgio Nada Editore, Vimodrone,Italy, 1999).3. F. Dyson, Can Science Be Ethical? (HarvardUniversity Press, Cambridge, MA, 1997).4. C.M. Falco, in The Art of the Motorcycle (exhi-bition catalog), edited by M. Drutt and T. Krens(Solomon R. Guggenheim Museum, New York,1998).5. P.E. Irving, Motorcycle Engineering (TemplePress, London, 1961).

Charles M. Falco, a professor of opticalsciences at the University of Arizona inTucson, holds the university’s Chair inCondensed Matter Physics. He has publishedmore than 250 research articles on variousaspects of materials physics and has givenover 200 invited talks on his research atconferences and research institutions in20 countries. He is a fellow of the AmericanPhysical Society and the Optical Society ofAmerica. Falco’s current research involves thegrowth and study of magnetic ultrathin filmsand spintronics devices by molecular-beamepitaxy. Falco has assembled one of the mostextensive private libraries of English-languagemotorcycle books, comprising more than 90%of all such books published. He brought thisscholarly background in the subject when in1998, he co-curated an exhibition at theSolomon R. Guggenheim Museum titled“The Art of the Motorcycle.” This industrialdesign exhibition set an all-time attendancerecord for the museum and subsequentlytraveled to the Guggenheim Bilbao (Spain)and to the new Guggenheim Museum inLas Vegas. For this work, Falco sharedan award from the U.S. Chapter of theAssociation Internationale des Critiquesd’Art with fellow co-curator Ultan Guilfoyle,Guggenheim director Thomas Krens, andarchitect Frank Gehry. Recently, Falco andartist David Hockney discovered opticalevidence that painters in the early Renaissanceused optical projections as aids in their workseveral hundred years earlier than historianshad previously realized had even been possible.This work has been reported in newspapersand magazines around the world, includinga documentary on BBC and a segment on theCBS news program “60 Minutes.” Falco canbe reached by e-mail at falco@u.arizona.edu.