Monocoque Racecar Frame - Macleish

8/3/2019 Monocoque Racecar Frame - Macleish

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tZ Department ofVeterans AffairsJournal of Rehabilitation Researchand Development Vol . 30 No. 2, 1993Pages 233249

D esign of a comp osite monocoqu e frame racing wheelchairMichael S. MacLeish, MS; Rory A . Cooper, PhD; Joe Harralson, MS ; James F . Ster IIIHuman Engineering Laboratory, Biomedical Engineering Program, School of Engineering and ComputerScience, California State University, Sacramento, CA 95819-6019 ; Department of Rehabilitation Scienceand Technology, School of Health and Rehabilitation Sciences and Bioengineering Program, School ofEngineering, University of Pittsburgh, Pittsburgh, PA 15261

Abstract Design of present-day racing wheelchairs de-veloped out of necessity and common sense . The chairsfirst used in racing were everyday chairs ; through years oftrial and modification the racing chairs of today evolved.Very little advanced engineering has been applied to thedesign of racing chairs . The Finite Element Analysismodel executed on a computer provided insight intostructural problem areas in the design of unibody frameracing chairs . Slight modifications to the model can beused to investigate new shapes, loads, or materialswithout investing large amounts of time and money.Wind tunnel testing with scale models provided perspec-tives on different improvements to reduce drag . Shapeimprovements may play an important role in reducing theracer's time during competition . Shape may help todecrease drag for the user in either the upright or downposition. Considering that the frontal area increasesaround 30% in the up position with current strut andchassis frames, monocoque shapes should excel . Finiteelement analysis and air drag analysis are important tothe design of a composite racing wheelchair . Compositematerials may promote more efficient and ergonomicracing wheelchairs.

Key words : aerodynam ics, com posite m aterials, ergonom-ics, finite elem ent analysis, racing w heelchair, wheelchairdesign.

Address all correspondence and requests for reprints to : Rory A.Cooper, PhD, Department of Rehabilitation Science and Technology,School of Health and Rehabilitation Sciences, University of Pittsburgh,Pittsburgh, PA 15261 .

INTRODUCTIONDesign for present-day racing wheelchairs de

veloped out of necessity and common sense . Thchairs first used in racing were everyday chairsthrough years of trial and modification the racchairs of today evolved. It was hypothesized thatheir design could be greatly improved by applyinmodern engineering. A literature search was used tidentify how engineering technology could best bapplied. Using available engineering tools, a chawas designed and a monocoque prototype built . monocoque vehicle is one in which the body iintegral with the chassis . This paper presents detailed design methodology and rationale for composite monocoque frame racing wheelchair.Importance of Designing Better Race Chairs

Approximately one spinal cord injury occurevery 45 minutes in the United States . Excluding athe cerebral palsy, muscular dystrophy, and othemobility-impairing diseases, that alone translates tabout 10,000 new wheelchair users per year (1Sports and competition are just as important tpersons with disabilities as to "able-bodied" peoplif not more so (1,2,3,4,5,6) . Competition helpmaintain an individual's fitness while improvinfeelings of self-worth . Lack of physical fitness caresult in obesity and cardiorespiratory ailments twhich chair users are particularly prone (1). Sporhave proven to be an effective way to keep fiimproving the design of the equipment can hel

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234Journal of Rehabilitation Research and Development Vol . 30 No . 2 1993

decrease the incidence of sports-related injuries. Inturn, improved sports equipment will lead to im-proved everyday equipment (2,7,8,9) . Technologydeveloped to enhance the performance of racingchairs may someday become both realizable andaffordable for use in everyday chairs . Increasedmobility for persons with disabilities will help themovercome the stereotypes imposed upon them bysociety . The chair should not limit the individual.History and Rules of Wheelchair Racing

Wheelchair racing was first introduced in 1948(10) . The first chairs were simply modified everydaychairs . Racing did not grow significantly in popular-ity until 1975, when Bobby Hall competed in hisfirst marathon (7,10) . Since then, wheelchair ath-letes have accomplished under 1-hour and 30-minutemarathons and 4-minute miles (2) . Some athletessupport themselves with prize money from theirracing (7).

The National Wheelchair Athletic Association(NWAA), which is the governing body regulating allwheelchair sports in the United States, has devel-oped a set of rules governing allowable designs ofracing chairs. In a wheelchair race, the object is topropel a wheelchair equipped with push-rings over apredesignated course in a minimum amount of time(11) . Chairs are required to have at least threewheels . The rear wheels are permitted a maximumdiameter of 70 cm ; the front wheel(s) are limited toa maximum diameter of 50 cm . Each rear wheel isallowed to have only one push-ring . The greatestwidth of the chair must be measured either at thewheels or the push-rings . The chair cannot rely onany chains, levers, or gears for propulsion ; it mustbe propelled directly through the push-rings. Anystructures for the sole purpose of gaining aerody-namic advantage are prohibited. All of the driver'slimbs must be stable or securely fastened to avoidinjury and the possibility of the driver falling out.The chair must be structurally sound to precludecatastrophic failure during a race (3).Racing Wheelchair Design Parameters

Many factors influence the effectiveness of aracing wheelchair design : weight, materials, design,physical dimensions, fitness and ability of the user,interface compatibility between chair and user, aswell as many external factors such as road surface

and terrain (12) . A description of some of thetechnologies in use or available for use to improveracing wheelchair design follows.

The Frame. The basic frame structure of thechair should provide good positioning of the pilotfor better aerodynamics, propulsion ergonomics,and torso support . It must also be maneuverableand moderately stable, as well as stiff, to promoteefficient transmission of energy to the wheels . Twomain frame types have evolved so far, the cage seatand the bucket seat . Both incorporate a nonadjust-able box design to help maintain the desired stiffnesswith light weight . The cage frame, being closed, canbe made slightly stiffer . The bucket seat frame isopen across the front allowing easier access; it isoften preferred by quadriplegic persons (13) . Theframe struts should fit snugly to the sides of theuser's chest and hips during propulsion . Side guardsmay be added to help protect the user from thewheels (3).The chair's front end can be supported byeither a cantilever or a fork wheel mount . Eachrequires "trail" (i .e ., the distance between thecontact point of the front wheel with the roadsurface to the extension of the pivot axis to the roadsurface) to keep the steering mechanism stable (13).A light front end permits the user to make minorsteering adjustments easily (3) . If the front becomestoo light, the chair may easily tip into a "wheelie"during acceleration.

Frame size is determined by the user's bodydimensions and stability requirements . The widthmust allow easy access to the push-rings for propul-sion, while providing a stable wheelbase (14) . Cam-bering the wheels can help increase the effectivewheelbase track and improve pushing ergonomics.The wheelbase is also dependent on chair length.Long chairs are dynamically more stable, whileshort chairs have been found to have superiorperformance in short races and can also "draft"behind other chairs more effectively (15,16).

Seat Position . The pilot's position substantiallyaffects the handling characteristics of the chair.Positioning the center of gravity is an importantfactor in race chair design . Presently, positioningdecisions are made using a few rules of thumb andtrial and error (7) . Most seats consist of a nylon orcloth sling with straps, which positions the userergonomically and aerodynamically while helping toremove unwanted motions . A knees-up position


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MacLEISH et al . Monocoque Racing Chai

helps gain more driving force while giving someupper-torso support (3) . This support should not beso much that it restricts the motions required forpropulsion. Other important seat dimensions includethe seat-to-back angle and back height ; these controlthe degree of support that the user has duringpropulsion. Some attempts to make an adjustableseat include a "hill climber" position (13).

The fore and aft position of the seat determineswhere the center of gravity falls relative to thewheelbase. A forward position helps to distributethe load over all the wheels . Positioning the seat toofar forward can result in poor stroke kinematics,increased resistance in the steering, and a largedownhill turning tendency . A good rule of thumbputs the center of gravity somewhere over the backthird of the wheelbase (17) . Downhill turning ten-dency occurs when the center of gravity is forwardof the main wheels and the chair is on a side slope orcrowned road . Its magnitude depends on wheelbase,steering mechanism, total mass of the chair anduser, and their center of gravity . This creates amoment arm which causes the chair to turn down-hill . Moving the center of gravity over the mainwheels removes the moment arm but causes thechair to lose its directional stability (18,19) . Tocorrect these problems, chairs now include a com-pensator connected to the steering mechanism.There are three major types of compensators de-fined by the function of the springs : push-push,push-pull, and pull-pull . Pull-pull is the least effec-tive; the other two are equally acceptable (12).Probably the most important seating considerationis body position relative to the push-rings. Theuser's shoulders should be slightly forward of thepush-rings in order to employ the correct muscles.This enables efficient propulsion and minimizes thepossibility of injury. This position depends on theuser's skill and anthropometric measures, push-ringsize, and the type of competition being raced(2,4,16,20).

The Wheels. Depending on the user's reach,strength, and experience, a 65-70 cm rear wheel isusually used . Smaller wheels, though easier topropel (e .g ., they require less torque), can result inlower top speed. Two tire types are available:clinchers and sew-ups ; the latter are slightly lighterand more expensive (13).

Spokes play an important role in the aerody-namics of the wheel . As they spin, the spokes mix

up the air, creating turbulence. Reducing the number of spokes can reduce turbulence . However, using fewer spokes also decreases the wheel's strengthand stiffness . This can be compensated for by lacingspokes radially instead of crossed (14) . Spoke crosssections can be flat or elliptical to increase theiability to cut through air . Some modern designs usea three-spoke or a monospoke wheel . The monospoke resembles a solid disk ; more expensive andheavier, it is also faster, stiffer, and may possiblyreduce injuries (15) . Specialized Corporation pres-ently markets a tri-spoke carbon fiber, KevlarAramid and glass composite rim which was aerody-namically designed using a super computer (21).

Rims can also be made aerodynamic by utilizinga high flange and a narrow profile . Care must betaken to ensure that the tire and the rim interfacesmoothly to decrease turbulence due to discontinu-ity . High flange rims help to improve wheel stiffness(7,13) . The true aerodynamics of wheel design arenot well understood; wind tunnel testing is needed aspeeds and conditions similar to those encounteredduring racing (15).

Push-rings, attached directly to the spokes vistand-offs, are usually between 12 and 18 inches indiameter . Larger diameter rings allow faster acceleration but may decrease peak speeds (3).

The rear wheels can be mounted rigidly or withquick-release axles . Rigid threaded mounts provide stiffer fit (7,13) . Mounting the wheels with cambegives the chair a larger footprint, increasing itstability. Camber also permits a more natural pushmotion straight down from the shoulders (20) . Toomuch camber often stresses the spokes and decreasewheel rigidity (3) . A camber of about 10 ispreferred by most users but varies between individuals from around 2 to as much as 12 (4) . Alignmenof the wheels is also critical . Tires that toe-in or ouincrease road friction (13,14,20) . Misalignment duto repeated rim removal, frame settling, or abuseduring a race is common . For these reasonsprocedures to correct alignment should be as simpleas possible . One method uses spacers to torque theframe into alignment (11) . Kushall developed amethod in sports chairs which uses a rotating shaffor alignment . Other manufacturers use a mountingplate that can be shimmed to the desired camber andalignment.Using only one front wheel helps reduce rollinresistance and chair weight, but makes the chair less


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236Journal of Rehabilitation Research and Development Vo l . 30 No . 2 1993

stable (13,17). Using larger tires (3550 cm) in placeof small casters helps avoid front wheel flutter,spreads the weight out more evenly, and allows foreasier steering methods (7,19) . However, a smallfront wheel can reduce the chair's aerodynamic drag(15) . Front wheels can be mounted using a fork or acantilever-type design.

Steering mechanisms require some trail . Trailhelps eliminate flutter and makes the steering systemstable (13) . Steering mechanisms and compensatorsare used to allow propulsion through corners andadjust for road crown (22), allowing the user toconcentrate on propulsion.

Aerodynamics. Wind resistance "drag" iscaused by both normal and tangential (skin friction)forces whenever a body moves through the air . Theflow of air over each individual part of the system isinfluenced by the flow over the rest of the system.

Aerodynamic drag is expressed by:C d p airv2A

2gwhere C d = drag coefficient

p air density of airv = air velocityA = frontal areag = gravitational constant

The power consumed in overcoming this forceduring motion is:

Power = Drag force x vTherefore, the power to overcome wind drag isproportional to the cube of the velocity of thevehicle (23) . Obviously, this can become a determin-ing factor in racing competition. As an example:over 80 percent of the energy to propel a bicycle at20 miles an hour goes toward moving 1,000 poundsof air out of the way every minute (24) . Since airdensity and gravity are uncontrollable, there are twoways to maximize velocity by minimizing the dragforce : 1) by reducing the frontal area, or 2) byreducing the drag coefficient . The drag is a functionof the shape and surface finish of the human/vehiclesystem . The shape and surface finish control howthe air passes over the system. Three possible typesof air flow are associated with drag : laminar flow,which governs when the vehicle shape makes gradualtransitions, and the surface is smooth so that the aircan flow smoothly with low drag; turbulent flow,caused by sharp transitions or rough surfaces, which

makes the air eddy over the surface, producingmuch higher drag ; and separated flow, caused bysharp transitions that eddy the air in large swirls,which causes less drag than turbulent flow . Separa-tion is more likely to occur from laminar upstreamflow than from turbulent flow (23) . With this inmind, the shape of the human/chair system shouldbe designed with smooth transitions, a smoothfinish, and the smallest frontal area possible.Smooth transitions and finish should be part ofthe design criteria for the frame, keeping in mindhow the user fits into the flow path . Frontal area isbest minimized by altering the position of the pilot,taking careful note of how the frame fits aroundhim/her. Other considerations, such as helmet shapeand material, water bottle position, and framematerial can also be used to help reduce drag (24).

Ergonomics . Ergonomics is the science of opti-mizing human work conditions with respect tohuman capabilities . Some major areas addressed byergonomics include health, safety, comfort, andefficiency (20).

The interface between chair and user needsmore research. Quantification of variables andperformance parameters for this biomechanical sys-tem can provide the most useful results (7,8,25).Though some quantifying work has been done,much more is needed (5,6,8,11,12,16,18,19,20,22,25,26) . Some quantified test results have shown howefficiency and speed are related to stroke length andrace length, elbow position, and optimal push-ringdiameter.

The major problem so far is that each chairmust be custom-fitted to each user . Many racechairs are individually hand-crafted (7,13) . No inter-pretable data has been collected that can relate theimportance of anthropometric and other physicalbody measurements to chair dimensions and perfor-mance. Because of this lack of data, it is uncertainwhich parameters are important . Relationships be-tween chair dimensions, chair controller locations,body dimensions, range of motion, physiologicalefficiency, and system performance all need to beresearched. Quantitative results are not only muchmore readily interpretable, but also permit mathe-matical modeling, simulation, and computer analy-sis of the human/chair system.

Materials . Most current racing chairs are madeof high-strength, low-density metals, such as chro-mium molybdenum alloy steel (chromoly), titanium,

Drag Force =


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23MacLEISH at al . Monocoque Racing Ch

or aluminum alloy . These provide the neededstrength, stiffness, and low weight desired for racingchairs . For small-scale projects, chromoly has theadvantage of low material and manufacturing costs.Though composite materials have the desired prop-erties for racing chair design, there have been fewattempts to use them. Composites have seen exten-sive use in many other sports and for high-performance equipment such as fishing poles, golfclubs, tennis rackets, skis, bikes, boats, planes, andrace cars (27,28,29) . For several reasons, the entryof composites into the field of racing chair designhas been slow. High-tech composites are fairly new,being developed only about 20 years ago (29) . Awidespread understanding of their uses and limita-tions is just now becoming a reality . Also, compos-ite materials are still more expensive for manufac-turing purposes than are metals, though they arebecoming more competitive (30).

There are many advantages to using compos-ites . Composite structures can be stronger andstiffer than steel and aluminum at a fraction of theweight . They show superior impact resistance anddissipate less energy into vibration . They can becontoured to almost any desired shape, using fewerjoints and with less wasted material (28).

There are many different types of composites.Three general categories are particulate, laminar,and fiber. Laminated fiber composites provide thenecessary physical attributes for racing chair design.Laminated composites consist of layers of fibers inpredesignated orientations imbedded in a resin ma-trix. The matrix provides ductility and toughness.The fibers add strength and stiffness while keepingthe weight down. A strong bond between the matrixand the fibers must exist to preserve the beneficialqualities of each component (31).

Many different materials can be used for thefibers . The strength of the fiber depends on itsmaterial and diameter (31) . Carbon or graphite offerthe best characteristics for race chair design . Theirhigh stiffness with low density provide the best mixof properties, though the cost is higher . Cost,strength, and stiffness trade-offs must be dealt with(30) . Also, graphite can be laid-up (i .e ., placingresin-impregnated cloth made of composite fibers onthe mold and/or over preceding layers) by hand,unlike many other composites (27) . Often a foamcore is used with the composite lay-up on the outersurfaces . This "sandwich" construction increases

the cross-sectional inertia of the lay-up, reducing thbending stresses while maintaining the weight antensile strength properties of the material (30,31).

The amount of fiber to be used and its directioof lay must be determined . Many weights anweaves of fiber are possible, each with differenworking properties . The term "tow" is used tdescribe the direction which has the most strands ofilaments running parallel . Warp is the direction othe fibers used to hold the tow strands in place . Thdifferent types of weave determine the drapabilitycost, wetability, and stiffness of the cloth (30) . Twmajor categories of tow and warp combinations arcommonly used for hand lay-ups: unidirectional anbidirectional . Unidirectional composites consimostly of tow fibers with just enough warp to hothem in place . Bidirectional composites have an evemix of tow and warp fibers, creating more cloth-likmaterial. A proper understanding of compositlay-up technique can allow passive tailoring to creaan end material with the desired bending and torsiocoupling, taking full advantage of the materialanisotropic behavior (28).

Determining how much material and whadirectional strength is required is not an easy tasCareful planning of the lay-up order and directiocan result in a superior strength-to-weight ratimaterial . Simple isotropic material theories cannobe used with composites . Thermal stresses, residuastresses, hydrothermal factors, and load stresses anstrains must all be considered.

This increased number of variables requirespecial attention. Some work has been done to fnonlinear composite data to statistical curves . Othetheories show some correlation between propertiesuch as density, conductivity, and Young's moduluto a mixture ratio (31) . Many times, the increasedifficulty in analyzing anisotropic materials has leadesigners to default to using quasi-isotropic lay-upthat can be analyzed and laid-up more easily . Thdrawback is over-engineering the material strengtrequired in some directions, resulting in a slightlheavier design.

The most effective analytical methods requirthe use of computers . Computers can be used to dboth micro- and macro-mechanical analysis of thdesign to determine the required ply strength anstacking order . Stiffness characteristics can be estimated using laminated plate theory, and strengthusing modified quadratic failure criteria . Thes


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techniques must be judiciously applied in areas suchas joints or near holes . Use of finite element analysis(FEA) and simulation softwares can determine theload needed to create "first ply failure," forcomplex-shaped designs (29).

When the analysis has been completed, con-struction may begin. Hand lay-up techniques aregood for working on prototypes . Many publicationsoffer guidance on these techniques, giving sugges-tions on the order in which plies should be laid, howto get superior wetting (i .e ., impregnating thecomposite cloth/yarn with resin) without getting airbubbles, how to avoid irritation from the epoxy,and much more. One point, unanimously stressed,was that the most importantant step in doing acomposite lay-up is preparation (27,28,30,32).

METHODSCreating the Shape of the Frame

The importance of a favorable aerodynamicshape was discussed during the literature review . Airdrag is reduced by decreasing frontal area andstreamlining the contours of the chair pilot system.NWAA rules state that no items may be added to achair strictly for the purpose of creating aerody-namic advantage . This has been interpreted inseveral cases to mean that nonstructural componentswhich serve primarily to reduce wind resistance areunacceptable. A common test used is : if the chairstill functions with the aerodynamic componentsremoved, those components are disallowed . Someracers currently use strapping and seat bucketswhich serve to reduce aerodynamic drag as well asprovide support . For this reason, design featuresmust demonstrate primary structural and/or safetybenefits ; any accrued aerodynamic improvementmust be secondary . Thus, a space frame beingcompletely structural might incidentally providemuch better contouring aerodynamically than astrut-chassis-type frame.

Determining the Best Shape . Not only shouldthe shape be streamlined, it must also be fit to thepilot's position . To accomplish a prototype design,profile photos were superimposed, in both the upand down positions, with the pilot in his currentracing chair. The rear wheel axle was designed to bein the same position with respect to the seat, toallow the stroke motions to be the same . The front

and rear wheel diameters were chosen by the pilot tobe 16 and 26 inches, respectively. These sizes werechosen to create the desired power gear ratio, whilesimultaneously decreasing rolling resistance . Theaim was to have the frame profile provide minimalaerodynamic drag for the rider in either the up ordown position . Using results from the profile lay-out, clay models of potential chair designs weremade . Width dimensions in the cockpit were deter-mined using dimensions of the pilot . The nose widthwas designed to accommodate the front wheel whileallowing for approximately 15 of steering anglewith a 6 cm cantilever trail arm.

The frame was molded to partially shroud therear wheels with 10 .75 of camber . The shroudingprimarily serves to protect the pilot's arms duringpropulsion and is common practice for racingwheelchairs. Models varied in attack angle of thecontoured nose and rear wheel shrouds . Wheelguards can improve the streamlining of the framewhile improving safety by helping to keep the pilot'sarms from contacting the spinning tires.

Wind Tunnel Testing . Two scale models weremade of plaster of paris . These models weresmoothed, painted, and fitted with wheels and arider model. Model A had a narrow nose, guardsover the wheels, and a steep front-end attack angle.Model B had a slightly wider, round nose, no wheelguards, and a more gradual front-end angle ofattack . The model rider, made of soft clay, wasmounted in race position . Soft clay was used tosimulate the skin and clothing of a real racer . Thesemodels were wind tunnel tested with a stationaryground surface . Drag force was measured in thedirection opposite the wind flow. Drag forces foreach model were recorded at wind speeds from 3,000to 9,000 feet per minute at 1,000 foot per minuteintervals . Because similitude requires the model andthe actual system to have the same Reynoldsnumber, and these wind speeds are slightly low for aone-ninth scale model to exactly simulate the behav-ior of a full-size chair under normal conditions, theresults proved to be worthwhile (Table 1 and Figure1) . The results showed the drag force to be propor-tional to the square of the velocity, as expected . Themodels with a rider in place showed almost twice asmuch drag as their pilotless counterparts. Interest-ingly, model B with its wider nose and no wheelhubs showed slightly less overall drag than thenarrow-nosed model . A 2 x 2 analysis of variance


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23MacLEISH et al . Monocoque Racing Cha

Table 1.Wind tunnel model results.

Drag Force(grams)

Air Speed Model A Model B Model A Model B(m/s) w/Pilot w/Pilot w/o Pilot w/o Pilot15 .2 4 46 43 27 2 620 .3 2 78 75 46 4425 .4 0 110 112 65 6530 .4 8 155 161 82 8835 .5 6 205 21 5 112 12040 .6 4 260 275 132 13745.21 340 360 192 188

2 5 30 35 40Air Speed (m/s)

Figure 1.Wind tunnel results for composite racing wheelchair models.

(ANOVA) showed the effect of the pilot on air dragto be significant (p = 0 .024), and the differencebetween the aerodynamic drag of models A and Bnot to be significant (p>0 .05) . The interaction wasalso not significant (p>0 .05) . Also of importancebut not apparent from the data in Table 1 was thestability of the shapes . Even though model Bshowed less overall drag, it experienced more lateraloscillation during testing than model A. Reaching adefinitive, conclusive decision from this observationis difficult . The increased oscillation of the firstmodel may be attributed to the sharp transition overthe unhubbed rear wheels. Even a slight misalign-ment of one of the rear wheels could exciteoscillations . The lower drag was probably due to therounder nose and smoother attack angle of the frontend. From these observations, the final chair shapewas designed to incorporate a slightly rounder nose,

a gradual attack angle, and guards over the reawheels (Figure 2).Determining the Frame Structure

There is always a trade-off between strengtand weight in any structural design. Carbon graphifibers can increase the strength-to-weight ratioCorrectly identifying high stress areas allows thstrength-to-weight ratio to be optimized . FEA waused to determine the frame contour . FEA uses computer model in which the frame is representeby many small elementary units or "elements .Each element is defined by a shape function : aequation that models the shape of the elemenStresses and displacements across elements can bestimated by minimizing the potential energy equation for all elements simultaneously . Because ocomputational complexity, software packages mube used to determine an optimal solution . The FEpackage ALGOR was chosen to solve this projectfinite element model . Like most FEA softwarpackages, ALGOR optimizes the order of solutiousing complex analysis methods that account foshear, tensile, and compressive loads . It can displathe results in many different ways . The solutionaccuracy depends on the placement, size, and shapof the modeling elements . Areas with a high stresgradient require more elements to give the samdegree of accuracy as regions where the stresses varmore gradually. Some initial assumptions abouwhere the high stress areas might be located must b

Figure 2.Clay model of the aerodynamic composite racing wheelchaspace frame.


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240Journal of Rehabilitation Research an d Developmen t Vol . 30 No . 2 1993

made before the FEA model is created . Moreelements are then placed in anticipated high stressareas. It was assumed that stress would be highernear points where loads were to be applied . There-fore, more elements were placed near wheel, seat,and steering mounts. The results of FEA aresensitive to element shape . The frame, much widerand longer than it is thick, can readily be modeled asa (curved) two-dimensional thin plate. Either three-(triangular) or four- (quadrilateral) sided elementscan be used . Triangular elements appear stifferunder FEA than do quadrilateral elements ; thus,mixing element types should be avoided.

Developing the Model . A computer model wasbased on the more aerodynamically shaped claymodel (Figure 3a, b, c) . A reference line was scoreddown the length of the clay model ; a similar line wasplaced on the profile drawing . The line on theprofile drawing was used to determine the angularorientation of the frame in space and relative towheel positions. Cross-sections were sliced perpen-dicular to the scored line from the tip to the tail ofthe model. The width of each cross-section was 7 .5mm to preserve the shape of the model and createsufficient elements. These cross-sections were tracedonto grid paper. For each cross-sectional slice,points chosen along its contour defined the curve.Extra points were placed in areas where high stresseswere expected . Horizontal and vertical positions ofall points were recorded along with slice depth tocreate x, y, and z coordinates for each point . The yand z coordinates were then plotted back onto gridpaper. This insured that the model shape had beenpreserved and allowed for lines to be drawn in toconnect the points. These lines created the edges ofthe elements of the FEA model . The elements wereconfigured as quadrilaterals whenever the framegeometry allowed; otherwise, triangular elementswere created . Once a satisfactory shape was deter-mined, all three coordinates were multiplied by nineto return the dimensions to the full-scale coordinatesused to develop the model on ALGOR . The pointswere connected with lines as had been done beforeby hand . The model was rotated back to its worldposition as calculated by the profile drawing and thescore line. The resulting FEA model consisted of 411points, 844 lines, for a total of 435 elements . Beforeany FEA results can be attained, material propertiesmust be specified for the elements, and the loadsmust be assigned to the model. Additional nodes

(a )

(b )

(c)Figures 3a,b,c.Computer finite element model of aerodynamic compositeracing wheelchair space frame.

RACE CHAIR BODYFINITE ELEMENT MODEL

WA* L o r .. - s r a = ,e


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24MacLEISH et at . Monocoque Racing Cha

were added to areas which showed high levels ofstrain . The analysis was then repeated with themodified mesh.

Modeling Material Properties . Material proper-ties were determined by testing specimens made ofquasi-isotropic carbon fiber and of a quasi-isotropiccarbon fiber and glass mix . These materials werechosen because of their good drapability andwetability (18,27) . Load and strain data collected forthese specimens led to the results shown in Figure 4aand Figure 4b . The glass did not add any strength tothe material, only bulk, but it did give a better finishwhich would be less abrasive to the pilot, being lesssusceptible to environmental wear . Peculiar units ofmeasurement are required to allow ALGOR, whichwas designed to use English units, to process theFEA model, which was formulated in metric units.

x10 4

Figure 4a.Stress and strain data for carbon fiber test specimens.

[Slope =4 .91

Figure 4b.Stress and strain data for carbon fiber-glass test specimens .

Ultimate strength = 2,000 kg/cm2 (28 ksi), Youngmodulus = 458,000 kg/cm2 (6,5000 ksi), Poissonratio = 0 .325 . These results concur sufficiently witthose published. Similar materials such as T300, ASand IM6 composites have Young's moduli of 10 .107 .95, and 11 .36 msi, and Poisson's ratios of 0 .300 .28, and 0 .30, respectively (29) . Our first FEAmodels employed elements with the properties oone layer of quasi-isotropic carbon fiber . From thresults of the one-layer models, areas that requirestrengthening were located . These areas werstrengthened by multiplying the thickness of thelements by some multiple of a single layer or badding core material to the center of the quasiisotropic lay-up . Since the tensile strength waalready adequate for the in-plane loads, foamprovided a good core material to improve thbending stiffness without adding weight . For coreareas, the properties can be estimated by noting thaPoisson's ratio does not change when a core iadded. Young's modulus can be estimated using thprimary flexural modulus of the composite lay-up.

The primary flexural modulus is determined bfirst integrating over the thickness of the compositdefined by its ply stiffness matrix Q

E0 0

cWhere h = the laminate thickness

z e = the top face of the coreDij = (3)Qij[(h/2)3 (c/2) 3 ]

Where c = the core thicknessThe primary flexural modulus, Eflex, can be determined by first normalizing the moment of inertiamatrix:

3

o 0o 0o 0o oo oq 0

-2000 -1000 5 0 0 00 0 0 2000 3 0 0 0S t r a i n ( m i c r o s t r a i n )

2 .5

2

1 .5C I)

0 .5

00000000EPS-T 000o 0o 0

slope = 6 .514O 0

EPS-L00 00 0

IEPS - L

1000 2000 3000Strain (microstrain)

4000 5000

E uE 01 - u2 1 - u2uE E 0

1-u2Q] _

2(1 + u)Where E = Young's Modulus

v = Poisson's RatioThe flexural stiffness, D, becomes

h2[D] = 2 [Q ] z2 dzz


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12[D]h 3

and then finding its inverse matrix[d*] = [D*] -1

whose major element is d, t * .1

Ef1ex d* 1 1Loading the Model. A number of cases of

frame loading were chosen to mimic loads that arace chair might experience in a race . Loadingpoints were determined from the grid drawings. Sixpoints were used to mount the seating system ; fourpoints were used to mount the three wheels and acompensator (Figure 5 ) . The position of the com-pensator mount was determined geometrically . A22-cm lightweight stainless steel push-pull compen-sator was manufactured . On a top view of the frontof the frame, drawn using the coordinates of theFEA model, the position of the front wheel wasdrawn with a 6 cm cantilever trail arm. The size ofthe moment arm created by this mounting schemecan be determined from the drawing. Three loadcases were designed to model possible pilot posi-tions, and four load cases were used to modelpossible road shocks.

Figure 5.Loading points for finite element analysis . À' and `B' are theright and left rear seat mounts ; `C' and D' are the right and leftcenter seat mounts; È' and are the right and left front seatmounts; `G' and `H' are the right and left rear wheel mounts;Ì' is the compensator mount ; and `J' is the front wheel mount .

In Figure 5, À' and `B' are the right and leftrear seat mounts ; `C' and D' are the right and leftcenter seat mounts ; E' and F' are the right and leftfront seat mounts ; `G' and are the right and leftrear wheel mounts ; Ì' is the compensator mount;and `J' is the front wheel mount . Pilot loads wereestimated using a 70 kg pilot distributed over six seatmounts while holding the wheel mounts fixed . Theseat mounts protrude inward with an estimatedmoment length of 1 cm. Three load cases were used:loads distributed toward the rear seat mount, loadsequally distributed over the seat mounts, and loadsdistributed toward the front seat mount . The pilotloads were all in the back third of the wheelbase.Road loads, applied while fixing seat mounts, weredetermined using the forces resulting from theworst-case pilot position during seating loads . Frontwheel impact loads were determined for the pilot inthe forwardmost position ; rear wheel loads werethose for the pilot in the rearmost position . Loadswere also applied to the compensator mount tomimic jarring of the front wheel in either direction.The compensator spring constant was determined tobe 80 lbs/in . Moments for the front wheel weredetermined using the frame geometry, and momentsfor the rear wheels were determined knowing thecamber, wheel radius, and an estimated typicalmounting distance . For all load cases, these staticforces were multiplied by three to allow for theeffects of dynamic loading (31).

Initial Model Findings and Improvements . EachFEA solution for the loaded model required simulta-neous reduction of 2,443 equations . Areas requiringstrengthening were identified by using the resultsfrom the single thickness model . Areas with deflec-tions exceeding one-hundredth mm, or with stressesexceeding one-third the ultimate strength of thematerial were strengthened . A safety factor of threewas applied to account for the effects of fatigue andpossible unexpected loadings (Figure 6a and Figure6b) . With only a single quasi-isotropic carbon fiberlayer, stresses at some points on the frame exceededfour times the ultimate strength of the material . Thehigh stress areas were divided into those thatexceeded the ultimate strength and those that ex-ceeded one-third of the ultimate strength . The smallareas with the highest stresses, such as wheelmounting sites, were enhanced with a 1-inch core.High stresses near the cockpit were enhanced with ahalf-inch core. Other high stress areas were strength-

LOPDING POINTS

9 611361 3 . 0 6 F I l e : c Z a 3 6 i 1 L 6 7 1 1 :5 5 LC L 3 Vudl6 Lo' -62 La =


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24M a cL E IS H e t a l . Monocoque Racing Cha

SVII W 3.84 rfie :c 1428

IMPROVED MATERIAL,Quas-IsoropcFoam CoredMuti Thc

OUT

Figure 7a.Material layout for quasi-isotropic cored body (left side).Figure 6a.Areas exceeding safety factor of three for single isotropic layer

with pilot loads .

IMPROVED MAT LAYOUTQuaml- I aotropic

Foam CoredMuti Thckress

SOIEW 3 .84 PI 49 14 : L C 12 3 W La. LFigure 6b.Areas exceeding safety factor of three for single isotropic layerwith road loads.

ened with quarter-inch core material . Double thick-ness quasi-isotropic carbon fiber was used in transi-tion to the lower stress areas . The final materiallay-out may be seen in Figure 7a and Figure 7b . Theproperties for the cored areas were estimated usingthe flexural modulus as previously described . Thiscombination of decreased modulus with an in-creased thickness resulted in improved strength ; aresult typical of flexural estimation.

Improved Model Results . Figures 8a, 8b, and 8cand Figures 9a and 9b show stress contours of thereinforced model in the pilot and road load cases,

Figure 7b.Material layout for quasi-isotropic cored body (right side).

respectively. Results from the modified model methe stress and deflection requirements . The stresscale on the improved material model was differenfrom that used with the single thickness layer omaterial. The cored FEA models are shown on scale of 0-400 kg/cm2 , while the single-layer modewere displayed on a scale of 0-1,000 kg/cm2 . Thhighest stress level found for the improved model any of the loadings was only 635 kg/cm (almost 1times less stress than in the original model) . Locations of high stress areas from road loads are almoopposite the position of high stress areas from thpilot loads. This could help avert any failure due combinations of loading .


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244Journal of Rehabilitation Research and Development Vol . 30 No. 2 1993

PILOT LOBORFT3 U M M 3 .11 rI le :eg2c 90,1L8 f4 :28 CC t, 3 tki~i6

STRESS CONTOURSQuest-IsotropicCored Body

LORD F'OR GIRD14 :28

400 .00500 .00520 .002 .0.00240.00200.00160.00120 .000 . .00040 .0000 .0000

Figure 8a.Stress contours for quasi-isotropic cored body : pilot load aft.

Figure 8b.Stress contours for quasi-isotropic cored body: pilot loadcentered.

R E S U L T SBuilding a Prototype

Building the prototype required creating amold . When the lay-up was completed, the framewas seamed and trimmed. Next, the wheel andsteering mounts and seat were attached to the frame.Finally, the wheels were aligned.

Building the Frame . Full-size patterns of theright and left halves of the chair were cut usingcross-sectional data. These patterns were traced ontoStyrofoam and cut using a hot wire . Cross-sectional widths, cut with a band saw, were glued

Figure 8e.Stress contours for quasi-isotropic cored body: pilot loadforward .

TRESS CONTOURSOussI -Isotropic

red Body

'400 .00 .500 .0032 0.002 4 0 : a;200 .0010 0 .00I ]20.00eO . .I D RIGHT REAR WHEEL LOAD00.0 .000046 tile . b 3c 9841,69 . 09 :00 LC 3, 4 WM, l,o. -66 I . 13 6.

Figure 9a.Stress contours for quasi-isotropic cored body: road load rightrear wheel.

together to form right and left halves of the chair.The two halves were sanded to smooth the surfacecontour. Sanding was also used to recess corematerial. The molds were covered with plastic wrapusing double-stick tape to prepare them for lay-up.(The plastic wrap protects the foam from the resinand makes the finished shell easier to release .) Alarge aluminum sheet sprayed with mold-release wasused as a work table . The carbon fiber was cutdirectionally to allow enough pieces to create aquasi-isotropic lay-up for each mold half . Somepieces required seams to cover the entire mold. No

STREOS CO\ITOURS


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24MacLEISH et at . Monocoque Racing Ch

Figure 9b.Stress contours for quasi-isotropic cored body : road load leftrear wheel.

seams were placed directly over other seams toeliminate stress risers created by increased thicknessat the seam (30) . The two frame halves were moldedby using standard hand lay-up procedures . Thefoam cores were puttied in the center of the lay-upusing a microbubble slurry . A flange, left at theedge of the mold on the aluminum, helped to insurethe lay-up's integrity at the edges and to create aneasy way to match molded halves . Fiberglass wasused for the outermost layer . After 2 days the moldswere released and trimmed . The two halves werematched and bolted together along the flange . Seatand front wheel holes were cut, and the inside seamwas sanded rough. Using long strips of carbon fiber,the inner half of a quasi-isotropic seam was created.When the seam dried, the outer flange was removed.The outer seam area was then sanded rough tocreate a bonding surface and the second half of thequasi-isotropic seam laid . Some extra material waslaid-up around wheel and cockpit openings toincrease their strength, and fiberglass was placed inareas that might contact the pilot . The rough frameand seat are shown in Figure 10.Attaching Wheel and Steering Mounts . ClickStuds (Click Studs, Bergdahl Associates, Inc ., Reno,NV), were used to mount the wheels and steeringmechanisms because they do not require drillingholes that may degrade the integrity of the framematerial. The studs are surface-mounted using anepoxy cement . When properly adhered to a graphitesubstrate, each 1 .25-inch mounting base can support

550 lb in tension of 1300 lb in shear . Used in thfashion proposed in the models, most of the load expected to be in shear . The front and rear wheelmount to faceplates, which attach to the ClicStuds . The compensator mounts directly to a stainless steel stud, slightly larger than a Click Studwhich had a face better suited for tightening . Thwheel mounting plates were machined from alumnum 7075, T6 because of its high strength-to-weighratio .

The front wheel was mounted first and adjustewith spacers until it was vertical. The rear wheewere mounted and aligned using an alignment too(11) .The Seating System . The pilot of the chair mube securely seated in the proper position in order t

get the best foundation from which to drive thchair. Using a Pin Dot seat molding frame (Pin DoProducts, Niles, IL), a plaster mold was made of thpilot's back and seat in his racing position . The seawas laid-up by using the same technique as with thchair mold in Figure 10 . Fiberglass was chosen fothe lay-up material because it would be less irritatinto the pilot . The seat was mounted to the chaiframe using Click Studs . Two rails, also fasteneonto Click Studs, allow adjustment of seat position

Finishing. A smooth finish was needed in ordeto decrease aerodynamic drag and skin irritationThe body was sanded to remove any majodiscontinuities. The texture was then smoothed, amuch as possible, using primer paint . Finally,

Figure 10.Rough lay-up of composite space frame and seat .


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gloss paint coat was applied . Figure 11 shows thefinished chair.Expenses . Table 2 gives a rough estimate ofmaterial costs required to build this prototype.These costs alone make this racing wheelchairexpensive compared to contemporary tubular chassisdesigns . Labor costs would also be relatively high;however, costs could be reduced if the chair wentinto commercial production and materials werepurchased in larger quantities . If performance wasimproved, there would still be interest by elite

Figure 11.Completed composite space frame racing wheelchair.

Table 2.Prototype budget.Bidirectional Woven Graphite 42" x .013", 8HS Weave, 32 yds.

@ $70 .00 = $2,240 .00Unidirectional Graphite 5" x .006 " , Plain Weave, 20 yds.@$1 .35=$27.00Safe-T-Foxy Resin, 2 Gallons, $100 .00Foam Cores and Microbubble Filler, $50 .00Foam for Mold Shape, Styrofoam, $50 .00 MoldingSupplies:Paint Brushes, Rollers, Rubber Gloves, Wrap, Saw Blades,

Contact Cement, Cleaners, $100 .00Modeling Supplies : Clay, Plaster, Mold It, Epoxy Glue,Paint, Sandpaper, Graph Paper, $40 .00Photography Supplies: Film and Developing, $75 .00Mounting Studs, Click Studs, $25 .00Wheel Mounts, Steering Mount, and Compensator Material

and Machining, $140 .00TOTAL $2847 .00

athletes, despite the high cost, since racing wheel-chairs are special purpose vehicles.Testing the Prototype

The new design was tested to measure itsimprovement over existing designs . The pilot hasused the chair several times . The best testing,through repeated usage in a competitive situation, isyet to come . Several simple performance checkswere possible, however.At 32 pounds, the complete composite chair isnearly twice the weight of a typical race chair . Thepilot noted that although the chair acceleratedslowly, it handled well at road speeds . It is difficultto determine, without performing destructive test-ing, whether the unibody frame is actually stifferthan its strut-chassis counterparts . The chair has avery stiff ride. The pilot felt as if he had a firm baseto transmit force to the push-rings . He reported thatthe rear wheel positions were slightly too wide forhis preference and the seat was too far forward . Theseat position was moved all the way back on theadjustable rails . The unibody design prevents mov-ing the seat any farther back without alteringstructural integrity . The width, however, can becorrected with a simple modification of the wheelmounts . The unibody frame allowed the pilot totuck in his arms when coasting, which improved theaerodynamics.

FUTURE IMPROVEMENTSPositioning ImprovementsIn future designs, care should be taken to allowample adjustment of seat position . With a unibodydesign this is critical . In this design, trying tocontour the back of the frame too close to the pilotresulted in limitations on the seat movement.Aerodynamic ImprovementsThe preliminary aerodynamic studies with thewind tunnel and plaster models could also have beenimproved. The wind tunnel did not account forground motion and air viscosity effects . Only forcesin the axial direction could be measured ; lift andtwist forces were not accessible . The models them-selves were not exact . Spoked wheels were difficultto model, and the surface finish could only simulatethat of the final chair . Increasing the number of


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24MacLEISH et ai . Monocoque Racing Ch

shapes and possible pilot positions would be useful.A better wind tunnel and improved modeling tech-niques might be able to determine the best helmetdesign and clothing material . Besides using animproved wind tunnel and models, better resultsmight have been attained through FEA on acomputer. Simulation may possibly offer a moreaccurate and cost-effective alternative.

Apart from possible modeling refinements, themanufacturing process could be improved to pro-duce a more aerodynamic frame . The final surfaceof our frame was lumpy because of the imperfect fitof the core pieces . The easiest "fix" for this is to usea female mold instead of a male one. Then thesmooth, aerodynamic shape would be preserved onthe outside, and the lumpiness from the core wouldbe on the inside. Measuring the frontal area usingphotos and a planimeter could, in the future, be auseful way to compare the aerodynamics of theprototype with more traditional chairs, giving fron-tal area values for quick comparison. This could beuseful to future designs.Structural Im provements

Though the FEA results helped optimize thestructural strength, thus keeping the weight at aminimum, the final chair was still much heavier thandesired. Perhaps this occurred because the shape ofthe chair and its strength were optimized separately.Optimizing them together might give a weight anddrag compromise which would result in the bestoverall chair, one that would be better than eitherthe best-shaped or lightest-structured chair . Theweight problem could also be addressed by removingmaterial . The initial structure was designed using asingle layer of material . High stress areas werebeefed up, but low stress areas were left alone . Byusing a finer weave material or leaving lighteningholes, weight in the low stress areas could have beensignificantly reduced . Taking advantage of thenonhomogeneous properties of composites couldgreatly reduce the weight of the chair . Not everyelement requires the same strength in every direction(the back region of the frame is a possible candidatefor redesign).

Because of the churning of the wheels and thenonaerodynamic shape of the pilot, the air flow inthe back region is not laminar . Turbulent flowcreates the largest drag . A sharp disturbance up-stream in the structure can cause full-scale separa-

tion, lowering the overall drag force : material in threar structure of the frame might be reduced so thonly as much material remained as was needed tmaintain the stiffness . This would be clarifieduring a more complete aerodynamic and structuraoptimization.

Integrating a seat base into the unibody framwould remove the need for any extra hardware thincreases the system's weight . It is important tallow for full adjustability of seat position.Frame weight might be further decreased bimproving the lay-up technique . Because the corpieces did not fit perfectly, a slurry of resin anmicrobubble was used as filler . This filler was mucheavier than the core material . The core reinforcment was 1 inch, 0 .5 inch, and 0.25-inch-thicmaterial . It is important that the transitions fromone core thickness to another are continuouAlthough the layout process would be more diffcult, an exterior mold would make the exteriotransitions smoother. Also, during hand lay-upspecial care must be taken to insure that the materiais completely impregnated with resin. This may havled to using excess resin in the material . Usingtechnique known as vacuum bagging, excess resican be sucked out, leaving only the resin that required.

Several Click Studs had to be replaced . Athough the studs were strong, the epoxy adhesivhad difficulty standing up to impact loads . Rouging up the bonding surfaces and increasing thmounting area might help to improve their strength

More tests should be run on this chair tdetermine its strengths and limitations. The safefactor of three may be more conservative than wanecessary. Some of the weight increase may turn outo be acceptable due to the decreased drag anincreased frame stiffness . A kinematic analysis othe pilot may permit interface improvement.

DISCUSSIONThe FEA model executed on a computer pro

vided insight into structural problem areas in thdesign of unibody frame racing chairs . Slight modfications to the model can be used to investigate newshapes, loads, or materials without investing largamounts of time and money . With aerodynamFEA software, the model could provide perspective


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248Journal of Rehabilitation Research an d Developmen t Vol . 30 No . 2 1993

on different improvements to reduce drag . Shape REFERENCESimprovements may play an important role in reduc-ing the racer's time during competition by helping todecrease drag for the user in either the upright ordown position. Considering how much the air flowis deflected by current strut frames and that thefrontal area increases around 30 percent in the upposition, monocoque shapes should excel . Futurework on unibody race chairs could start from thisdesign and attempt to improve upon it by reducingthe weight of the chair, to bring it in line with thatof current strut-chassis chairs, or could try to showthat the drag of the unibody chair compensates forits extra weight.Although this composite chair weighs morethan its competitors, the extra weight is compen-sated for in other ways (e .g ., the lack of joints andother high stress areas in the unibody style mightmake the chair stiffer and safer).It is important to remember that the race chairis only part of the system. The racer's weight, whichvaries significantly between individuals, also affectsthe ease with which the system can be propelled.

Other ways to improve the chair were discov-ered during construction: using a female, instead ofa male, mold could improve the outer surface shapeand texture; vacuum bagging excess resin couldreduce the weight of the frame ; and adhesive ClickStuds provided an easy way to mount things to theframe without deteriorating the integrity of theframes structure (but stronger bonds should besought out).

The molded seat made with the Pin Dotmolding system turned out well . The seat providesthe support and positioning needed to effectivelypropel the chair . These findings clearly indicate thatthe application of engineering technology can im-prove the design of the racing wheelchairs.

ACKNOWLEDGMENTSCarbon fiber material was donated by Hexcel Corpo-

ration, Click Studs were donated by Bergdahl Associates,and wheelchair components were supplied by EagleSports Chairs . Additional support was provided by theRehabilitation Services Administration, U .S . Departmentof Education (#H129E00005), and California State Uni-versity, Sacramento, CA . The authors thank TomAndersen, Dave VanSickle, Ken Stewart, Dr . ChuckWashburn, and Dr . Leo Dabaghian for their assistance .

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1983 :54(3) :229-33.5 . Ridgway M, Pope C, Wilkerson J . A kinematic analysis

of 800-meter wheelchair racing techniques . Adapt PhysAct Q 1988 :5(2):96-107.6 . Sanderson DJ, Sommer HJ . Kinematic features of wheel-chair propulsion . Biomechanics 1985 :18(6) :423-9.7 . Cooper RA . The racing wheelchair . SOMA Eng HumBody 1990 :4 :28-34.8 . Depauw KP . Sports for individuals with disabilities : re-search opportunities . Adapt Phys Act Q 1988 :5 (2) :80-9.9 . McFarland SR, Scadden LA . Marketing rehabilitationengineering . SOMA Eng Hum Body 1986 :1 :19-23.

1 0 . Cooper RA . W heelchair racing sports science : a review. JRehabil Res Dev 1990 :27(3) :295-312.1 1 . Cooper RA . Racing wheelchair rear wheel alignment . JRehabil Res Dev 1989 :26(1) :47-50.1 2 . Cooper RA . Racing Wheelchair crown compensation. JRehabil Res Dev 1989 :26(1) :25-32.1 3 . Cooper RA . Racing chair lingo . . . or how to order aracing wheelchair . S ports 'N Spokes 1988 :13(6) :29-32 .1 4 . Quickie Designs Inc. The perfect fit, an adjustment guideto your manual wheelchair . Fresno, CA: Quickie DesignsInc ., 1990.1 5 . Kyle CR . Aerodynamic wheels . Bicycling . Dec :I985 :121-

4.16 . York SL, Kimura IF . An analysis of basic constructionvariables of racing wheelchairs used in the 1984 Interna-tional Games for the Disabled . Res Q Exerc Sport1987 :58(1) :16-20.17 . Cooper RA. Racing wheelchair roll stability while turn-ing . In: Proceedings of the 13th Annual RESNA Confer-ence, 1990 June; Washington, DC : RESNA Press,1990 :65-6.18 . Brubaker EC. Wheelchair prescription : an analysis offactors that affect mobility and performance . J RehabilRes Dev 1986 :23(4) :19-26.

19. Brubaker CE, McLaurin CA, McClay IS . Effects of sideslope on wheelchair performance . J Rehabil Res Dev1986 :23(2) :55-7 .20 . Van der Woude LHV, Veeger HET, Rozendal RH.Ergonomics of wheelchair design : a prerequisite foroptimum wheeling conditions . Adapt Phys Act Q1989 :6 :106-32.21. Soviero MM . Reinventing the wheel . Pop Sci1990 :Oct :76.22 . Cooper, RA . An international track wheelchair with acenter of gravity directional controller . J Rehabil Res Dev1989 :26(2) :63-70 .


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