Laboratory, Computational and Field Studies of Snowboard Dynamics

8/8/2019 Laboratory, Computational and Field Studies of Snowboard Dynamics

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MATERIALS ANDSCIENCE IN SPORTSEdited by:

EH. ( Sam) Fmes and S .J . Ha a ke

DynamicsLaboratory, Com putational, and FieldStudy of Snowboard Dynamics

Keith W.Buff ington, StevenB. Shoo ter ,Ira J. Thorpe andJason J. Krywicki

Pgs. 171-183

TIMIS184 Thorn Hill RoadWarrendale, PA 15086-7514(724) 776-9000


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LABORATORY, COMPUT ATIONAL, AND FIELD STUDYOF SNOWBOARD DYNAMICSKeith W. Buffinton, Steven B. Shooter, Ira J. Thorpe, and Jason J. Krywicki

Department of Mechanical EngineeringBu cknell UniversityLewisburg, Pennsylvania 17837

Abstract

While many studies have documented the dynamical behavior of skis, similar studies fo rsnowboards have been rare. Characteristics such as board stiffness and damping areacknowledged to be linked to performance, but a quantitative determination of correspondingnatural frequencies and damping ratios has to date not been published. The present work useslaboratory, computational, and field studies to develop and document an in-depth understandingan d quantification of snowboard dynamics. In particular, laboratory tests are used to determinethe first three bending and first tw o torsional natural frequencies an d modal damping ratios fo reight snowboards from tw o manufacturers. Computer models are developed using the softwarepackages Pro/ENGINEER and Pro/MECHANICA that allow the effects of design changes onnatural frequencies to be investigated and that facilitate visualization of mod e shapes. Fieldtests are presented that provide insights into the strains and accelerations experienced bysnowboards while subject to turns, stops, and jum ps. Results show that quantitative resultscorrelate well with qualitative descriptions offered by manufacturers and riders. Medium-quality boards designed for beginner riders and characterized as "soft" have lower naturalfrequencies and larger damping ratios than similar boards designed for advanced riders andcharacterized as "stiff." Mo reover, boards designed for advanced riders and characterized as"high-quality" have natural frequencies higher than "medium-quality" boards while stillexhibiting high damping ratios.

Materials and Science in SportsEdited by F.H. (Sam) FroesIMS (The Minerals, Metals & Ma terials Society), 2001172


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IntroductionNumerous studies have been performed on the dynamical characteristics and performance ofsnow skis. One of the earliest is Piziali and Mote in 1972 [1] in which they present laboratoryan d field measurements of frequency response, running pressure distribution, and static systemcharacteristics as a guide to future ski research an d design. Over the last 30 years, numerousother physics-and-engineering-based investigations have been conducted of snow skiperformance, many of which were documented in 1996 by Lind and Sanders [2] with a morerecent investigation by Nordt, Springer, and Kollar in 1999 [3]. Although Lind and Sandersoffer extensive information on various aspects of the physics of skiing, very little information isoffered on the physics of snowboarding.With the rapid growth in recent years of the snowboard industry, investigations have begun tofocus attention on the physics-and-engineering-based characteristics that are unique tosnowboards. In 1994, Swinson [4] presented a primarily qualitative discussion of both the basicphysics of snowboarding and the similarities between snowboarding and skiing. In a morerecent article, Michaud and Duncumb [5] give a theoretical, although greatly simplified,description of the physics of snowboard turning. Their analysis is primarily based on a simplebalance offerees and does not offer any quantitative data from either laboratory or field tests.Three articles that do refer to quantitative measurements and analyses of snowboardperformance are given in [6], [7], and [8]. Dosch [6] describes the construction andperformance of a high-resolution piezoelectric strain sensor, and as an application, its use in astructural dynamics laboratory "to analyze the dynamic behavior of a new composite snowboardan d find the optimal location for a passive damper." Reference [7] provides additionalinformation on the analysis referred to in [6] and states:

K2 Corporation, Vashon, WA engaged the structural dynamics lab at Boeing toconduct strain testing on K2 snowboards and skis. Model 740A02 Strain Sensorswere placed in various locations on the snowboard and skis to find nodes ofmaximum strain. Damping devices were then installed in areas of greatest strainto minimize vibrations, giving the user greater control.In [8], Sutton refers to work done for Walbridge Design & Manufacturing (now DimensionSnowboards) similar to that done for K2. Although Sutton's article does no t offer an yquantitative results, he does describe both laboratory tests of snowboard vibration characteristicsan d field measurements of snowboard strain and acceleration. The present paper is a detailedelaboration of the snowboard analysis conducted for Dimension and in particular providesdetails of the collection of snowboard vibration data and documents the natural frequencies an ddamping ratios obtained. The goal of this work is to provide a baseline of information to guidefurther studies of snowboard characteristics and to suggest methods of evaluating potentiallyfruitful snowboard design modifications.Presented in the sections below are the results of laboratory tests, computer analyses, an d fieldtests of a total of eight snowboards from two manufacturers. Procedures and results of static anddynamic laboratory tests are discussed first. These are followed by a description of thedevelopment of a computer model used to simulate characteristics seen in the laboratory and togive additional insights into behavior. Next are presented the procedures an d results of strainan d acceleration measurements taken during field tests. Finally, concluding comm ents areoffered and discussed regarding the ways in which the data presented here can be used to guidefurther snowboard research and development.

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Laboratory TestsStatic CharacteristicsInitial laboratory tests were conducted to obtain overall measures of snowboard staticcharacteristics and to provide dimensional information for computer models. Beyond standardmeasurements such as length, waist width, sidecut, and contact length, measurements of boardthickness (at several locations along the board length), tip radius, tip height, tail radius, tailheight, camber, an d weight were obtained. Material specifications given by one of themanufacturers include an Isosport PBT gloss top sheet, a Durasurf 2001 sublimated sinteredbase, continuous linear strand full-length wood cores, thermoset and tri-axial e-glasscomposites, full-wrap pre-stressed Rockwell 48C edges, and for several of the boards,longitudinally lain carbon strips for added stiffness.To perform static tests, a board was clamped at its widest point across either the tail or the tip.Weights were then hung from the board and the deflection measured at the center of the widestpoint of the opposite end of the board. Although a snowboard is a complex composite structure,an estimate of the effective stiffness of the board is easily calculated using simple beam theory.Specifically, for a uniform cantilever beam , the stiffness El is equal to PL3/3y, where P is theapplied load, L is distance from the support to the load application point, and y is the deflectionat the load point. For a typical board, a series of trials produced an effective value of El equal to85.8 N-m. Since the cross-section of the board varies from approximately 0.5 cm thick and 30cm wide at the heel to 1 cm thick and 25 cm wide at the waist, an approximate range forYoung's modulus E is 27.5 to 4.1 GPa. This range serves as a starting point for more accurateiterative procedures described below in the section entitled Computational Modeling.Dynam ic C haracteristicsFree vibration tests were performed on the eight boards available fo r testing in order tocharacterize snowboard natural frequencies and damping ratios. Natural frequencies an ddamping ratios are two of the key parameters characterizing snowboard ride, "feel," andperformance. In particular, damping ratios as well as the proximity of bending and torsionalnatural frequencies directly relate to snowboard controllability and handling. Moreover, aknowledge of the natural frequencies and damping ratios of both high performance boards andthose judged more pedestrian ultimately provide quantitative measures that allow laboratorycharacteristics to be directly related to performance on the slopes. Although the loading,stresses, and strains experienced by snowboards in the field are different than those induced inthe laboratory, a correlation betw een laboratory measurements an d measures of performance inthe field ca n nonetheless be developed.The results described below are all based on free vibration tests in which each board is clampedacross the widest part of the tail. In each test, the board was manually deflected an d released,an d a recording was made with an HP-35665A dynamic signal analyzer of the signal producedby an accelerometer mounted on the board. Measurements were made with the accelerometer atnine different locations on the board (three distributed along the centerline and three distributedalong each edge). At each location, data was automatically taken and averaged by the signalanalyzer over a total of 10 trials for each of two initial shapes: one which would primarily resultin bending vibrations and one which would primarily result in torsional vibrations. Fo r bendingtests, the board was simply deflected vertically at the tip, such that its shape was similar to thefirst bending mode, and released. For torsion tests, the board was twisted at the free end into ashape similar to the first torsional mode and then carefully released. These initial conditions didnot, of course, result in either pure bending or pure torsional responses, bu t they did allow for a

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determination of the natural frequency corresponding to a particular mode shape by consideringthe relative amplitudes in the frequency response spectra.Once the averaged data were available, they were saved an d analyzed with a custom-writtenMATLAB program. This program produces a plot of the accelerometer response versus time,performs a fast Fourier Transform (FFT) of the accelerometer response, plots the frequencyspectrum, an d calculates values for the am plitudes and frequencies of the dominant peaks in theresponse and for the modal damping ratio corresponding to each peak (see reference [9] forcomplete details on the theory underlying modal analysis).The measured natural frequencies and modal damping ratios for the first five modes of vibrationof the eight boards investigated are listed below in Tables I and II, respectively. Thecorrespondences between natural frequencies and mode shapes were done based on a knowledgeof the initial conditions (bending versus twisting), the results of previous tests, and theexperience gleaned through testing as well as through the computational modeling described inthe next section. Note in interpreting the table of damping ratios that the algorithm used tocalculate them is based on the half-power point method and thus is sensitive to the proximity ofpeaks in the response spectra. For the results presented here, response spectra peaks werejudged to be sufficiently separated to give meaningful values.

Table I. Modal Natural Frequencies [Hz]Boaai

~3r ~4

"J"~78

Board

~~~4~$

78

lsl Beading

JJj^~2,33

J^2,3752.125

lstleaiiBg

Qjfcg0.074

^^0^4^0.0470.068

2nd Bending 317.015.817.917.517.117.617.417.0

Table II. Modal2nd Bending 3

0.0130.0150.0110.0130.0150.0120.0130.011

^Bending 1st44.340.544.0 ^^43.845.543.9 ~ ~43.442.9

Damping Ratiosrd Bending 1st

0.0200.0100.023aoog~0.0140.008

Torsion

293~~19.9

fe$~~~19.619.4

Torsion

^M3T~0.014

Oil40.0150.015

2*:lolsion;

' '7:54-855.75

~ J l53.654.25

2B(i Torsion

~~~QMl0.012

~ ~ ~ m i0.0150.011

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As mentioned above, a total of eight snowboards were studied. Subjective characteristics of theboards numbered 1, 2, and 5, as offered by the staff of one of the manufacturers, are listed be lowin Table III. These three boards were those also used in the field tests described below in thesection entitled "Field Tests."Table III. Subjective Board Descriptions

Board Length (cm) Carbon Strips Description1 155 Yes "Stiff," intended for advanced riders2 155 No "Soft," intended for beginner riders5 156 n/a "High-quality," intended fo r advanced riders

For the boards used in field testing (indicated in the shaded regions of Tables I and II), one canobserve definite correlations between the subjective descriptions given in Table III and thenatural frequencies and damping ratios given in Tables I and II. Table III describes board 2 as"soft" and intended for beginner riders, board 1 as "stiff and intended for more advanced riders,and board 5 as "high-quality" and also intended for advanced riders. Table I shows that thenatural frequencies for the "soft" board 2 are in fact significantly lower than the naturalfrequencies of the other tw o boards, particularly beyond the frequencies corresponding to thefirst bending and torsional modes. It also shows that the torsional mode frequencies for the"high-quality" board 5 are significantly higher than those of the other two and that it thus has thehigher torsional stiffness desired by an expert rider. In considering Table II , note that althoughthe "stiff board 1 has higher natural frequencies than the "soft" board 2 for modes beyond thefirst, it does not have larger damping ratios and in fact has a significantly lower damping ratiofor the first bending mode. This is an indication that although the stiffness of board 1 makes itmore desirable than board 2 for an advanced rider, its relatively low levels of damping may limitits performance an d perhaps make it prone to chatter. In contrast, board 5 not only has thenatural frequencies indicative of the stiffness desired by an advanced rider but also has dampingratios that would lead to a more rapid attenuation of undesirable behavior than those of board 1.

Computational ModelingThe dimensional, natural frequency, and damping information described in the preceding sectionwas used in conjunction with the software package Pro/ENGINEER to construct a solid modelfor five of the eight snowboards investigated in the preceding section. These models were thenused for finite element analyses performed using Pro/MECHANICA to investigate both staticand dynamic characteristics. In performing these analyses, relatively simple material propertieswere used. Although the actual structure of a typical snowboard is a built-up laminatecomposite, and in fact Pro/ME CHAN ICA allows for the analysis of such structures, the boardswere modeled as having uniform mass density and transversely isotropic stiffness properties.This greatly simplified the modeling and property determination processes, as well assignificantly reducing computation time, while still yielding results in close agreement withexperimental observations.For a completely general transversely isotropic material, there are six material parameters thatmust be specified independently. These six parameters are mass density (/?), Young's moduli(Ei an d E 2=Ei) , Poisson's ratios (vi i=v$i an d v 2), and the shear modulus [Gu=Gi3i noteG23=j/2(l+Vj^)]. Further simplification was achieved in the modeling process here by letting

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E\=E2=E$ and y^=v$\=v$2- This reduced the number of independent parameters to four yet stilllead to computational results that were in close agreement with those observed experimentally.To determine a value for p, the mass of the board was measured an d then divided by the volumecalculated by Pro/MECHANICA from the measured dimensions used to create the model. Inthis w a y , the total mass of the each model was always equal to the actual mass of each of theboards. A value for Poisson's ratio (v= vz\= v$\= 1^2) was not determined ex perimentally but wassimply set to 0 . 3 , which is typical of most materials. Values fo r Young's modulus(E=E\=E2=E3) and the shear modulus (G=Gi2=Gu) were determined by matching values ofnatural frequency calculated with Pro/MECHANICA to those me asured experimentally. Thiswas an iterative process begun by selecting a reasonable initial value for E (such as thatdetermined in the Static Characteristics subsection of the Laboratory Tests section above),calculating a corresponding initial value for G such that G m m a i = E in i ti a i I 2(1+v), and then usingthese values in Pro/MECHANICA to calculate the first five natural frequencies. Th e frequencycalculated for the first bending mode was then compared to the first bending frequencydetermined experimentally. For a fully isotropic material of uniform cross-section, an exactlycorrect updated value for E could be calculated from the selected initial value of E m M a i , thecalculated frequency ( f c a i c ) , and the corresponding experimentally determined frequency ( f e x p )using E = E i n i t i a i ( f e x p l f c a i c )2 - This relationship, and a similar one for G, were used in an iterativeway (with a bit of manual tweaking) to converge on values of E and G that yielded naturalfrequencies that were in close agreement with experimental results. Here "close agreement"means within 0 . 1 2 5 Hz ( t h e resolution of the experimental measurements) with occasionalslightly greater variations for the third bending an d second torsional modes. The valuesdetermined for Young's modulus and the shear modulus for the five boards studied are givenbelow in Table IV.

Table IV. Young's Modulus and Shear ModulusBoard Young's Modulus ( G P a ) Shear Modulus ( G P a )

12347

1 8 . 7 41 7 . 8 51 8 . 7 01 7 . 5 01 6 . 6 0

3 . 6 03 . 4 73 . 5 33 . 5 33 . 2 5

Beyond simply calculating natural frequencies, Pro/MECHANICA also enabled the modes ofvibration to be easily visualized. Typical mode shapes for the first four modes of vibration of anunconstrained board are shown in Figure 1. Shown in the upper left is the first bending mode,while the second and third bending modes are shown in the lower left an d upper right,respectively. The first torsional mode is shown in the lower right. The lighter tones in thefigures correspond to larger displacements; note that the displacements are exaggerated toemphasize the characteristic shapes of the modes.

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Figure 1: Mode shapes.Field Tests

Field testing was undertaken to develop a database of strain and acceleration information thatwould quantify typical snowboard maneuvers and provide input for future laboratory testingequipment (see the Discussion and Conclusions section below). Field testing was done withboards numbered 1, 2, and 5, as identified above, after 7 MicroMeasurements strain gages andon e accelerometer (PCS model 3 53 A) were attached to each. A photograph of one of the boardswith strain gages and accelerometer attached is shown in Figure 2.

Figure 2: Strain gage locations.As shown in the figure, three strain gages, numbered 1, 3, and 6, are located along thelongitudinal centerline of the board and measure strain along the longitudinal axis. Gage 1 is atthe center of the board, gage 3 is at the widest point of the tail, an d gage 6 at the widest point ofthe tip. Two gages are located along each edge of the board and me asure strain perpendicular tothe longitudinal axis of the board. On one edge these gages are numbered 2 and 5, and on theother, they are numbered 4 and 7. An accelerometer is located on the longitudinal axis of theboard at its center and measures acceleration perpendicular to the surface of the board. Cablesconnect each of the gages and accelerometer to a 24-pin connector mounted near the center ofthe board on an L-bracket. The cables were attached to the board and coated with a heavy-dutyadhesive; the strain gages were coated with a thin layer of polyurethane before being coatedwith a silicone rubber. The cables were also coated with a layer of waterproof tape.

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The locations of the strain gages were chosen to provide an accurate indication of the bendingand torsion that the board experiences during use. The gages placed along the centerlinemeasure bending strains at the tip,center, and tail of the board. The gages placed along theedges are strained when the board is in torsion or when riding on one edge and benttransversely. The accelerometer was added to give a measure of the overall excitation of boardas it traverses the snow.During testing the connector mounted on each of the boards was mated to a cable thatcommunicated the strain gage and accelerometer signals to an IBM ThinkPad laptop computercarried in a padded backpack worn by a professional snowboarder performing the testing. Thecomputer was equipped with data acquisition hardware and custom software written in VisualBasic. The Visual Basic program controlled d ata acquisition commencement, rate, and duration;provided a time-stamp for each data set; and plotted the data on the screen at the conclusion ofeach run. Th e program and laptop computing environment provided a powerful tool for datacollection, storage, and analysis yet was still robust enough to tolerate the low temperatures andrough jostling experienced during runs.A variety of scenarios were investigated during field tests. Of primary importance weremeasures of performance during turning, stopping, and jumping. A total of 6 scenarios weredeveloped and executed by one of our professional riders over a two-day period. On the firstday, relatively gentle turning and stopping maneuvers were done on a beginner's slope ongroomed man-made snow. The day was overcast and windy with the temperature atapproximately 38; the rider weighed approximately 150 Ibs. First, a series of gentle wide-radius turns around cones placed on the slope were performed, and these were followed by aseries of narrow-radius turns (Figure 3 shows the rider executing a wide-radius turn). Stoppingmaneuvers were also investigated, using both the toe-side and heel-side of the boards. Data wascollected at the rate of 100 Hz over a period of 25 to 30 seconds, which was typically slightlylonger than the total run time. Each run was video recorded, which also provided an audiorecord of times at which turns were executed as read aloud from a digital timer.

Figure 3: Wide-radius turn.Typical results for a series of wide turns using board 5 are shown in Figure 4. The graphdisplays the readings obtained from the seven strain gages and the one accelerometer. Thevertical axis of the graph has units of micro-strain, and the horizontal axis has units of seconds.Note that each of the strain gage readings has been offset from zero for clarity of presentation.The topmost line (corresponding to gage 1) has been offset by 8000 micro-strain from its

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average value, the second line (corresponding to gage 2) by 7000 micro-strain, and so onthrough the seventh gage, which has been offset by 2000 micro-strain. For clarity, theaccelerometer output has been scaled by a factor of 1000, with the actual peak voltage recordedequal to approximately 1.25V.When viewed closely, the graph gives quite a wealth of information about the behavior of theboard. The beginning of each run started at the top of a small ridge (see the upper left corner ofFigure 3) , about 3 to 4 feet above the slope. As the rider dropped down from the ridge to beginhis ran, the board was bent significantly, as registered by the compressive strains measured bygage 1 in the middle of the board and as indicated in Figure 4 at approximately 3 seconds. Thecompressive strains produced on alternating edges of the board as the rider traversed ba ck an dforth across the slope can also be clearly seen in Figure 4. The first turn is at approximately 8seconds, at which time the compressive strains registered by gages 4 and 7 on one edge of theboard switch to the other edge of the board as measured by gages 2 and 5. The next turn atapproximately 11 seconds returns the strains to gages 4 and 7 and so on for the turns atapproximately 15 and 20 seconds. Also note that the accelerometer registers the greatestvibration when the board is on edge and that the vibration greatly diminishes during thetransitions between edges when the running surface is relatively flat on the snow [see theaccelerometer signal (the bottom-most line on the graph) at approximately 8, 11, 15 and 20seconds].

Wide Turns w/ Board 5 (1/11@4:15:27)Turns @ 8,11,15, 20 Seconds

Time (s)

Figure 4: Wide-radius turn data.On the second day of testing, more aggressive maneuvers were investigated. These were al lperformed in a snowboard park and included steep descents with a large jump, riding a half-pipe, and riding a quarter-pipe. Snow conditions were again groomed, man-made powder. Theday was sunny, although breezy, with the temperature at approximately 32. The second day oftests were done by a professional snowboarder who weighed approximately 160 Ibs.Data wasagain collected at the rate of 100 Hz over a period of 30 seconds. Each ran was video taped andjump times were recorded.Data collected during a half-pipe ran are shown in Figure 5. The strain gage readings haveagain been offset for clarity. The top seven curves correspond to the seven gages, numberedconsecutively from the top. The curve representing the accelerometer output is at the bottomand is again scaled by a factor of 1000. The most readily discernible features of this figure

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correspond to jumps that occur as the rider exits and re-enters the half-pipe. These jum ps takeplace at 7.5,10, 13, 16, 19, 22, and 24.5 seconds. As can be seen, the output of theaccelerometer is approximately constant throughout the time when the rider is in the air. Theoutputs of the strain gages are also relatively quiet during air time. Unfortunately, because ofthe aggressiveness of these maneuvers, a problem was encountered with th e connection to thebattery supplying the excitation voltage to the strain gages, which can be seen at the pointswhere all seven gage output voltages simultaneously drop.

Half Pipe w/ Board 5 (1/12@1:38:50)Jumps @ 7.5,10,13,16,19,22, and 24.5Seconds

Time (s )

Figure 5: Half-pipe data.Discussion an d Conclusions

One of the primary goals of this research has been to correlate relatively vague qualitativedescriptions of board performance, such as "soft," "stiff," or "high-quality," with thequantitative measures of board characteristics represented by modal frequencies an d dampingratios. These data have also been shown to provide the basis for the parameter identificationnecessary for the development of accurate compu tational mod els. The data presented here haveno t been available before and will serve as a foundation fo r further studies.There are a number of refinements and extensions to this work that could be pursued. Beyondsimply more testing of more boards, a greater effort could be made to develop a database ofquantitative performance characteristics and rider observations. In particular, a directed surveyof rider commentary should be done that collects input from a number of riders on the same anddifferent boards. An attempt should be made to elicit input that goes beyond comments such as"soft9 an d "stiff and asks the rider to focus on issues such as bending, twisting, damping, andchatter.Another avenue for further research is forced excitation. As has been done for skis, asnowboard could be attached to an electro-dynamic shaker and subjected to excitation through arange of frequencies. This would allow for more definitive determinations of naturalfrequencies an d damping ratios beyond those based simply on free vibration tests.Another area for further investigation that builds on the results presented here is stiffness anddamping control. Ski manufacturers, such as K2, have had active stiffness and damping controlin ski products for a number of years and stiffness and damping control have recently appearedin snowboards [7]. Optimal placement of stiffness an d damping controlling materials could be181


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determined through computer simulation and then the actual effect on natural frequencies anddamping ratios measured both in the laboratory and in the field.As mentioned in the Computational Modeling section, more elaborate computer models beyondthose described here can easily be envisioned that represent a board as a true composite laminatestructure. Such a model would require significantly more development time, as well as a muchmore in-depth determination of material properties, but would allow for more detailed trackingof the effects of changes in the design of the structure of board. Whether the effort associatedwith the development of such a model would yield sufficient additional insight to make itjustifiable however is unclear.One continuation of the current work that could be undertaken even with the current computermodels is a study of the effect of adding stiffeners, such as carbon strips or Kevlar strands, to thesnowboard structure. W hile determining the exact net effect of such additions using the currentmodels is not feasible, identifying trends in changes in the relative frequencies of bending andtorsional modes is. Such studies would accelerate the design process and allow for theconsideration of a much wider range of design modifications.Not discussed in this paper is work that has already occurred that extends the foundation of thesnowboard research presented here. In particular, a dynam ic testing machine was developed atBucknell University that simulates the behavior of a snowboard, as actually observed in fieldtests, while turning, stopping, an d jumping. A photograph of the testing m achine simulating aheel-side turn is displayed in Figure 6. The four pneumatic actuators simulate the ability of arider to apply forces either at the toes or heels of either leg. The displacement of each actuator,an d the force applied, is controlled through a Visual-Basic-based graphical user interface. Theuser can select either manual mode for development of a particular maneuver or scenario modethat allows for continuous execution of already developed and stored maneuvers. While amaneuver is being performed, data from strain gages and accelerometers can be recorded toensure that the maneuver recreates that seen on the slopes and to track changes in behavior asmodifications are made to board design.

Figure 6: Snowboard testing machine.

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AcknowledgementsMany individuals contributed to the work described in this paper beyond those listed as authors.Bucknell mechanical engineering students Michael E. Morris and Christopher V. Nowakowskicontributed to the laboratory testing. Chris an d fellow mechanical engineering student E. BlairSutton used their expertise with Pro/ENGINEER to aid in the development of the computermodels. Mike, Chris, and Blair with mechan ical engineering students Frederick E. Luchsingerand Timothy J. Nageli worked as a well-coordinated team while enduring the discomfort ofwinter temperatures during field testing. Bucknell College of Engineering DevelopmentEngineer Wade A. Hutchison contributed greatly to the collection of field data through thedevelopment of Visual Basic software that communicated with data collection hardware.College of Engineer Electronics Technician Thomas J. Thul, Laboratory Technologist James B .Gutelius, Jr., and Product Development Laboratory Technician Daniel G. Johnson providedelectronics expertise, strain gage preparation, and machining skills tha t were important elementsin the success of the project. The project would never have taken place without theentrepreneurial spirit and commitment to innovation of Walbridge Design & Manufacturing,Inc. (now Dimension Snowboards) of York, Pennsylvania. Professional snowboarders JaySmith and Todd Aldridge contributed their skill, expertise, and patience in performing themaneuvers requested in field testing. Seven Springs Mountain Resort in Champion,Pennsylvania graciously provided accomm odations, lift privileges, and slope access for the fieldtesting. Financial support for the project was provided through a grant from the Ben FranklinTechnology Center of Northeast Pennsylvania for which the Small Business DevelopmentCenter at Buckn ell handled administrative support.

References1. R.L. Piziali and C.D.Mote, Jr., "The Snow Ski as a Dynamic System," ASME Journal ofDynamic Systems. Measurement, and Control 94 (1972), 133-138.2. D. Lind and S.P. Sanders, The Physics of Skiing: Skiing at the Triple Point (NewYork, NY:Springer-Verlag, 1996).3. A.A.Nordt, G.S. Springer, and L.P.Kollar, "Simulation of a Turn on Alpine Skis," SportsEngineering, 2 (1999), 181-199.4. D.B. Swinson, "Physics and Snowboarding," The Physics Teacher, 32 (1994), 530-534.5. J. Michaud and I. Duncumb, "Physics of a Snowboard Carved Turn"(http://www.bomberonline.com/Bo 1999).6. J.J. Dosch, "Piezoelectric Strain Sensor" (Unpublished technical report, PC B Piezotronics,Inc., 3425 Walden Ave.,Depew NY 14043).7. "Extreme Testing, Supreme Performance" (Model 740A02 dynamic ICP piezoelectric strainsensor advertising flyer, PCB Piezotronics, Inc., 3425 Walden Ave.,Depew NY 14043).8. E.B. Sutton, "Better Snowboards by Design," (Paper 2000-IMECE/DE-18 presented at the2000 AS ME International Mechanical Engineering, Orlando, Florida, November 5-10,2000).9. D.J. Ewins, Mo dal Testing: Theory. Practice an d Application (New York, NY: John W ileyand Sons, 2000).

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Laboratory, Computational and Field Studies of Snowboard Dynamics