Laboratory, computational and field studies of snowboard dynamics Keith W. Buffinton, Steven B. Shooter, Ira J. Thorpe and Jason J. Krywicki Department of Mechanical Engineering Bucknell University Lewisburg, Pennsylvania 17837 Abstract While many studies have documented the dynamic behaviour of skis, similar studies for snowboards have been rare. Characteristics such as board stiffness and damping are acknowledged to be linked to performance, but a quantitative determination of corresponding natural frequencies and damping ratios has to date not been published. The present work uses laboratory, computational and field studies to develop and document an in-depth understanding and quantification of snowboard dynamics. In particular, laboratory tests are used to determine the first three bending and first two torsional natural frequencies and modal damping ratios for eight snowboards from two manufacturers. Computer models are developed using the software packages Pro/ENGINEER and Pro/MECHANICA that accurately reproduce the experimentally measured natural frequencies and that facilitate visualization of mode shapes. Field tests are discussed that provide insights into the strains and accelerations experienced by snowboards while subject to turns, stops and jumps. Quantitative results are shown to correlate well with qualitative descriptions offered by manufacturers and riders. Medium-quality boards designed for beginner riders and characterized as ‘soft’ have lower natural frequencies and larger damping ratios than similar boards designed for advanced riders and characterized as ‘stiff.’ Moreover, boards designed for advanced riders and characterized as ‘high-quality’ have natural frequencies higher than ‘medium-quality’ boards while still exhibiting high damping ratios. Keywords: damping, dynamics, natural frequencies, snowboard, stiffness Introduction Numerous studies have been performed on the dynamic characteristics and performance of snow skis. One of the earliest is Piziali & Mote (1972) in which laboratory and field measurements of frequency response, running Correspondence address: Keith W. Buffinton Department of Mechanical Engineering Bucknell University Lewisburg, PA 17837 Tel: (570) 577-1581, Fax: (570) 577-7281 E-mail: buffintk@bucknell.edu © 2003 isea Sports Engineering (2003) 6, 129–138 pressure distribution and static system characteristics are presented as a guide to future ski research and design. Over the last 30 years, numerous other investigations based on a combination of physics and engineering approaches have been conducted on snow ski performance. Many of these are documented in Lind & Sanders (1996) with more recent investigations presented by Nordt et al. (1999a, 1999b). Although Lind & Sanders offer extensive information on various aspects of the physics of skiing, very little information is offered on the physics of snowboarding. With the rapid growth in recent years of the snowboard industry, investigations have begun to 129 Snowboard dynamics K.W. Buffinton et al. focus attention on the physics-and-engineering characteristics that are unique to snowboards. Swinson (1994) presents a primarily qualitative discussion of both the basic physics of snowboarding and the similarities between snowboarding and skiing. In a more recent article, Michaud & Duncumb (1999) give a theoretical, although greatly simplified, description of the physics of snowboard turning. Their analysis is primarily based on a simple balance of forces and does not offer any quantitative data from either laboratory or field tests. Three articles that do refer to quantitative measurements and analyses of snowboard performance are by Dosch (date unknown), PCB Piezotronics (date unknown) and Sutton (2000). Dosch describes the construction and performance of a high-resolution piezoelectric strain sensor, and as an application, its use in a structural dynamics laboratory ‘to analyze the dynamic behaviour of a new composite snowboard and find the optimal location for a passive damper’. The publication from PCB Piezotronics provides additional information on the analysis referred to by Dosch and states: K2 Corporation, Vashon, WA engaged the structural dynamics lab at Boeing to conduct strain testing on K2 snowboards and skis. Model 740A02 Strain Sensors were placed in various locations on the snowboard and skis to find nodes of maximum strain. Damping devices were then installed in areas of greatest strain to minimize vibrations, giving the user greater control. In his article, Sutton (2000) refers to work done for Walbridge Design & Manufacturing (now Dimension Snowboards) similar to that done for K2. Although Sutton’s article does not offer any quantitative results, he does describe both laboratory tests of snowboard vibration characteristics and field measurements of snowboard strain and acceleration. The present paper is a detailed elaboration of the snowboard analysis conducted for Dimension Snowboards and in particular provides details of the collection of snowboard vibration data and documents the natural frequencies and damping ratios obtained. The goal of this work is to provide a baseline of information to guide further studies of snowboard characteristics and to suggest methods of 130 evaluating potentially fruitful snowboard design modifications. Presented in the sections below are the results of laboratory tests, computer analyses and field tests on a total of eight snowboards from two manufacturers. Procedures and results of static and dynamic laboratory tests are discussed first. These are followed by a description of the development of a computer model used to simulate characteristics seen in the laboratory and to give additional insights into behaviour. Next is presented a discussion of strain and acceleration measurements taken during field tests. Finally, concluding comments are offered regarding the ways in which the data presented here can be used to guide further snowboard research and development. Laboratory tests Static characteristics Initial laboratory tests were conducted to obtain overall measures of snowboard static characteristics and to provide dimensional information for computer models. Measurements were made of mass as well as chord length, contact length, width, and waist width (see Figure 1). Table 1 lists the values obtained. Measurements, not listed in Table 1, were also made of board thickness (at several locations along the board length), tip radius, tip height, tail radius, tail height and camber (see ASTM, 1995 for detailed descriptions of dimensional terminology). Note that the shaded values in Table 1 correspond to boards used in field testing and that the mass values for these three boards include the mass of testing hardware (strain gauges, cables, etc.). Specifications of material properties given by the manufacturer of all boards (other than Chord length Contact length Waist width Width Figure 1 Principal snowboard dimensions Sports Engineering (2003) 6, 129–138 © 2003 isea K.W. Buffinton et al. Snowboard dynamics Table 1 Mass and principal dimensions Board Mass (kg) Chord length (cm) Contact length (cm) Width (cm) Waist width (cm) 1 2 3 4 5 6 7 8 2.985 3.145 2.715 2.710 3.160 2.720 2.595 2.790 152.4 152.4 152.4 152.4 153.7 148.9 149.7 152.4 121.9 121.9 121.9 121.9 123.2 118.1 129.5 124.5 29.2 29.2 29.2 29.2 29.2 29.2 29.2 29.2 24.8 24.8 24.8 24.8 24.8 25.4 25.4 25.1 board 5) include an Isosport PBT gloss top sheet, a Durasurf 2001 sublimated sintered base, continuous, linear strand, full-length wood cores, thermoset and tri-axial e-glass composites, full-wrap pre-stressed Rockwell 48C edges, and for several of the boards, longitudinally laid carbon strips for added stiffness. Material specifications were not available from the manufacturer of board 5. In addition to the determination of dimensional information, static stiffness tests were performed with each board clamped at its widest point across either the tail or the tip. Weights were hung from the board and the deflection measured at the centre of the widest point of the opposite end of the board. Although a snowboard is a complex composite structure, an estimate of the effective stiffness of the board can be easily calculated using simple beam theory. Specifically, for a uniform cantilever beam, the stiffness EI is equal to PL3/3y, where P is the applied load, L is distance from the support to the load application point, and y is the deflection at the load point. For a typical board, a series of trials produced an effective value of EI equal to 85.8 Nm2. Since the cross-section of a board varies from approximately 1 cm thick and 25 cm wide at the waist to 0.5 cm thick and 30 cm wide at the heel (as given in ASTM, 1995, waist is defined as ‘the narrowest point of the snowboard ski body between the heel and the shoulder’ and heel as ‘the widest part of the tail section of the snowboard ski’), an approximate range for Young’s modulus E is 4.1 to 27.5 GPa. This range serves as a starting point for more accurate iterative procedures described below in the section entitled computational modelling. Dynamic characteristics Free vibration tests were performed on the eight boards available for testing in order to characterize snowboard © 2003 isea Sports Engineering (2003) 6, 129–138 natural frequencies and damping ratios. Natural frequencies and damping ratios are two of the key parameters characterizing snowboard ride, ‘feel,’ and performance. In particular, damping ratios as well as the relative values of bending and torsional natural frequencies directly relate to snowboard controllability and handling. Moreover, a knowledge of the natural frequencies and damping ratios of both high performance boards and those judged more ‘pedestrian’ ultimately provide quantitative measures that allow laboratory characteristics to be directly related to performance on the slopes. Although the loading, stresses and strains experienced by snowboards in the field are different from those induced in the laboratory, a correlation between laboratory measurements and measures of performance in the field can nonetheless be developed. The results described below are all based on free vibration tests in which each board was clamped across the widest part of the tail. In each test, the board was manually deflected and released, and a recording was made with an HP-35665A dynamic signal analyser of the signal produced by an accelerometer mounted on the board. Measurements were made with the accelerometer at nine different locations on the board (three distributed along the centreline and three along each edge; see Figure 2 for a view of the experimental set-up and accelerometer locations). At each location, data were automatically taken and averaged by the signal analyser over a total of ten trials for each of two initial shapes: one which would primarily result in bending vibrations and one which would primarily result in torsional vibrations. For bending tests, the board was simply deflected vertically at the tip, such that its shape was similar to the first bending mode, and released. For torsion tests, the board was twisted at the free end into a shape similar to the first torsional mode and then carefully released. These initial condi- 131 Snowboard dynamics K.W. Buffinton et al. A B C Test stand 1 2 3 Figure 2 Accelerometer locations and experimental set-up for free vibration tests. tions did not, of course, result in either pure bending or pure torsional responses, but they did allow a determination of the natural frequency corresponding to a particular mode shape by considering the relative amplitudes in the frequency response spectra. Once the averaged data were available, they were analysed with a custom-written MATLAB program. This program produces a plot of the accelerometer response versus time, performs a fast Fourier transform (FFT) of the accelerometer response, plots the frequency spectrum and calculates values for the amplitudes and frequencies of the dominant peaks in the response as well as the modal damping ratio corresponding to each peak (see Ewins, 2000 for complete details on the theory underlying modal analysis). The measured natural frequencies and modal damping ratios for the first five modes of vibration of the eight boards investigated are listed in Tables 2 and 3, respectively. Also listed in parentheses in Table 2 are the natural frequencies calculated with the software package Pro/MECHANICA and discussed in the following computational modelling section. The correspondences between natural frequencies and mode shapes were done based on a knowledge of the initial conditions (bending versus twisting), the results of previous tests, and the experience gleaned through testing as well as through the computational modelling described in the next section. Note in interpreting the table of damping ratios that the algorithm used to calculate them is based on the half-power point method and is thus sensitive to the proximity of peaks in the response 132 spectra. For the results presented here, response spectrum peaks were judged to be sufficiently separated to give meaningful values. Also note that windage (the contribution of aerodynamic drag to overall damping) is significant. The values given in Table 2 Experimental (and Pro/MECHANICA) modal natural frequencies [Hz] Board 1st bending 2nd bending 3rd bending 1st torsion 2nd torsion 1 2.25 (2.21) 2.25 (2.19) 2.375 (2.35) 2.33 (2.28) 2.375 (2.36) 2.375 (2.32) 2.375 2.125 54.7 (50.8) 52.5 (50.6) 54.8 (53.3) 55.75 (51.8) 59.9 (54.9) 53.1 (53.0) 53.6 54.25 2 3 4 5 6 7 8 17.0 (16.8) 15.8 (16.6) 17.9 (17.8) 17.5 (17.3) 17.1 (17.8) 17.6 (18.1) 17.4 17.0 44.3 (40.9) 40.5 (40.5) 44.0 (43.4) 43.8 (42.2) 45.5 (43.3) 43.9 (43.8) 43.4 42.9 19.3 (19.2) 19.2 (19.1) 20.3 (20.1) 19.9 (19.6) 20.75 (20.9) 19.5 (19.5) 19.6 19.4 Table 3 Experimental modal damping ratios Board 1st bending 2nd bending 3rd bending 1st torsion 2nd torsion 1 2 3 4 5 6 7 8 0.039 0.062 0.036 0.074 0.058 0.034 0.047 0.068 0.012 0.011 0.011 0.012 0.032 0.011 0.015 0.011 0.013 0.015 0.011 0.013 0.015 0.012 0.013 0.011 0.009 0.012 0.020 0.010 0.023 0.008 0.014 0.008 0.015 0.015 0.013 0.014 0.020 0.014 0.015 0.015 Sports Engineering (2003) 6, 129–138 © 2003 isea K.W. Buffinton et al. Table 4 Subjective board descriptions Board Length (cm) Carbon strips Description 1 2 5 ‘Stiff’, intended for advanced riders ‘Soft’, intended for beginner riders ‘High-quality’, intended for advanced riders 155 155 156 Yes No ? Table 3 are thus not representative of the true levels of structural damping present in the boards but nonetheless give indications of the relative levels of damping in the boards tested. Subjective characteristics of boards 1, 2 and 5, as offered by the staff of one of the manufacturers, are listed in Table 4. These three boards were those also used in the field tests described below in the section entitled field tests. For the boards listed in Table 4 (also indicated in the shaded regions of Tables 1, 2 and 3), one can observe definite correlations between the subjective descriptions given in Table 4 and the natural frequencies and damping ratios given in Tables 2 and 3. Table 2 shows that the natural frequencies for the ‘soft’ board 2 are in fact significantly lower than the natural frequencies of the other two boards, particularly beyond the frequencies corresponding to the first 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 the higher torsional stiffness desired by an expert rider. In considering Table 3, note that although the ‘stiff’ board 1 has higher natural frequencies than the ‘soft’ board 2 for modes beyond the first, it does not have larger damping ratios and in fact has a significantly lower damping ratio for the first bending mode. This is an indication that although the stiffness of board 1 makes it more desirable than board 2 for an advanced rider, its relatively low levels of damping may limit its performance and perhaps make it prone to chatter. In contrast, board 5 not only has the natural frequencies indicative of the stiffness desired by an advanced rider but also has damping ratios that would lead to a more rapid attenuation of undesirable vibration than those of board 1. Computational modelling The dimensional, natural frequency and damping information described in the preceding section was © 2003 isea Sports Engineering (2003) 6, 129–138 Snowboard dynamics used in conjunction with the software package Pro/ENGINEER to construct a solid model for six of the eight snowboards investigated in the preceding section. These models were then used for finite element analyses performed using Pro/MECHANICA to investigate both static and dynamic characteristics. In performing these analyses, relatively simple material properties were used. Although the actual structure of a typical snowboard is a built-up, laminate composite, and in fact Pro/MECHANICA allows for the analysis of such structures, the boards were modeled as having uniform mass density and transversely isotropic stiffness properties. This greatly simplified the modelling and property determination processes, as well as significantly reducing computation time, while still yielding results in close agreement with experimental observations. For a completely general transversely isotropic material, there are six material parameters that must be specified independently. These six parameters are: mass density ( ρ), Young’s moduli (E1 and E2 = E3), Poisson’s ratios (ν21 = ν31 and ν32), and the shear modulus (G12 = G13). Note also that G23 = E3/2(1+ν32). Further simplification was achieved in the modelling process here by letting E1 = E2 = E3 and ν21 = ν31 = ν32 . This reduced the number of independent parameters to four yet still led to computational results that were in close agreement with those observed experimentally. To determine a value for ρ, the mass of the board was measured and then divided by the volume calculated by Pro/MECHANICA from the measured dimensions used to create the model. In this way, the total mass of the each model was always equal to the actual mass of each of the boards. A value for Poisson’s ratio (ν = ν21 = ν31 = ν32) was not determined experimentally but was simply set to 0.3, which is typical of most materials. Values for Young’s modulus (E = E1 = E2 = E3) and the shear modulus (G = G12 = G13) were determined by matching values of natural frequency calculated with Pro/MECHANICA to those measured experimentally. This was an iterative process begun by selecting a reasonable initial value for E (such as that determined in the Static characteristics sub-section of the Laboratory tests section above), calculating a corresponding initial value for G such that Ginitial = Einitial / 2(1+ν), and then using these values in Pro/MECHANICA to calculate the first five 133 Snowboard dynamics K.W. Buffinton et al. natural frequencies. The frequency calculated for the first bending mode was then compared to the first bending frequency determined experimentally. For a fully isotropic material of uniform cross-section, an exactly correct updated value for E could be calculated from the selected initial value of Einitial, the calculated frequency ( fcalc ), and the corresponding experimentally determined frequency ( fexp ) using E = Einitial ( fexp/fcalc )2. This relationship, and a similar one for G, as well as a bit of manual tweaking were used in an iterative way to converge on values of E and G that yielded natural frequencies that were in reasonable agreement with experimental results. The resulting computationally determined natural frequencies for the six boards studied are given in parentheses in Table 2. The frequencies obtained for the first bending, second bending and first torsional modes of vibration are all within 2% of the experimental results. For the third bending and second torsional modes the frequencies are all within 8% (typically 5%). Values determined for density, Young’s modulus and the shear modulus for the six boards studied are given in Table 5. Beyond simply calculating natural frequencies, Pro/MECHANICA also enabled the modes of vibration to be easily visualized. Typical mode shapes for the first four modes of vibration of an unconstrained board are shown in Figure 3. The lighter tones in the figures correspond to larger displacements; note that the displacements are exaggerated to emphasize the characteristic shapes of the modes. Field tests Field testing was undertaken to develop a database of strain and acceleration information that would quantify typical snowboard manoeuvres and provide input for future laboratory testing equipment (see the Discussion and conclusions section below). Field Table 5 Density, Young’s modulus and shear modulus Board Density (kg/m–3) Young’s modulus (GPa) Shear modulus (GPa) 1 2 3 4 5 6 1170 1230 995 1060 1147 1013 17.5 18.0 16.8 16.9 19.5 16.6 3.55 3.70 3.30 3.32 4.13 3.25 134 Figure 3 Mode shapes. Shown in the upper left is the first bending mode, while the second and third bending modes are shown in the lower left and upper right, respectively. The first torsional mode is shown in the lower right. testing was done with boards 1, 2 and 5, with seven MicroMeasurements strain gauges and one accelerometer (PCB model 353A) attached to each. As shown in the photograph of one of the boards in Figure 4, three strain gauges, numbered 1, 3 and 6, are located along the longitudinal centreline of the board and these measure strain along the longitudinal axis. Gauge 1 is at the centre of the board, gauge 3 is at the widest point of the tail, and gauge 6 is at the widest point of the tip. Two gauges are located along each edge of the board and these measure strain perpendicular to the longitudinal axis of the board. On one edge these gauges are numbered 2 and 5, and on the other, 4 and 7. An accelerometer is located on the longitudinal axis of the board at its centre and measures acceleration perpendicular to the surface of the board. Cables connect each of the gauges and accelerometer to a 24-pin connector mounted near the centre of the board on an L-bracket. The cables are attached to the board and coated with a heavy-duty adhesive; the strain gauges are coated with a thin layer of polyurethane as well as silicone rubber. The cables are also covered with a layer of waterproof tape. The locations of the strain gauges were chosen to provide an accurate indication of the bending and torsion that the board experiences during use. The gauges placed along the centreline measure bending strains at the tip, centre and tail of the board. The Sports Engineering (2003) 6, 129–138 © 2003 isea K.W. Buffinton et al. 2 5 1 6 3 4 7 Figure 4 Strain gauge locations. gauges placed along the edges are strained when the board is in torsion or when riding on one edge and bent transversely. The accelerometer was added to give a measure of the overall excitation of the board as it traverses the snow. During testing the connector mounted on each of the boards was mated to a cable that communicated the strain gauge and accelerometer signals to an IBM ThinkPad laptop computer carried in a padded backpack worn by the professional snowboarder performing the testing. The computer was equipped with data acquisition hardware and custom software written in Visual Basic. The Visual Basic program controlled data acquisition commencement, rate and duration, provided a time-stamp for each data set, and plotted the data on the screen at the conclusion of each run. The program and laptop computing environment provided a powerful tool for data collection, storage and analysis yet was still robust enough to tolerate the low temperatures and rough jostling experienced during runs. A variety of scenarios were investigated during field tests. Of primary importance were measures of performance during turning, stopping and jumping. A total of six scenarios were developed and executed by one of our professional riders over a two-day period. On the first day, relatively gentle turning and stopping manoeuvres were done on a beginner’s slope on groomed, man-made snow. First, a series of gentle, wide-radius turns around cones placed on the slope were performed, as shown in Figure 5, and these were followed by a series of narrow-radius turns. Stopping manoeuvres were also investigated, using both the toe-side and heel-side of the boards. Data were collected at the rate of 100 Hz over a period of 25 to 30 seconds, which was typically slightly longer than the total run time. Each run was video-recorded, © 2003 isea Sports Engineering (2003) 6, 129–138 Snowboard dynamics which also provided an audio record of times at which turns were executed as read aloud from a digital timer. The data collected gave a wealth of information about the behaviour of the board. The beginning of each run started at the top of a small ridge (see the upper left corner of Figure 5), about 1–1.5 m above the slope. As the rider dropped down from the ridge to begin his run, the board was bent significantly, as registered by compressive strains measured by the strain gauge in the middle of the board. Compressive strains were measured on alternating edges of the board as the rider traversed back and forth across the slope. The accelerometer registered the greatest vibration when the board was on edge and the vibration greatly diminished during the transitions between edges when the running surface was relatively flat on the snow. On the second day of testing, more aggressive manoeuvres were investigated. These were all performed 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. Data were again collected at the rate of 100 Hz over a period of 30 seconds. Each run was video-taped and jump times were recorded. Typical data collected during a halfpipe run (see Figure 6) gave a clear indication of both the strains and level of vibration involved. The output of the accelerometer in particular definitively showed the times when jumps were occurring and the rider was in the air, as indicated by the disappearance of the high frequency vibration caused by contact with the snow. The strain gauges were also relatively quiet during air time. Figure 5 Wide-radius turn. 135 Snowboard dynamics K.W. Buffinton et al. Figure 6 Half-pipe run. Discussion and conclusions One of the primary goals of this research has been to correlate relatively vague qualitative descriptions of board performance, such as ‘soft,’ ‘stiff,’ or ‘highquality,’ with the quantitative measures of board characteristics represented by modal frequencies and damping ratios. These data have also been shown to provide the basis for the parameter identification needed to develop accurate computational models. The data presented here have not been available before and serve as a foundation for further studies. There are a number of refinements and extensions to this work that could be pursued. Beyond simply more testing of more boards, a greater effort could be made to develop a database of quantitative performance characteristics and rider observations. In particular, a directed survey of rider commentary should be done that collects input from a number of riders on the same and different boards. An attempt should be made to elicit input that goes beyond comments such as ‘soft’ and ‘stiff’ and asks the rider to focus on issues such as bending, twisting, damping and chatter. Another avenue for further research is forced excitation. As has been done for skis, a snowboard could be attached to an electro-dynamic shaker and subjected to excitation through a range of frequencies. This would allow for more definitive determinations of natural frequencies and damping ratios beyond those based simply on free vibration tests. 136 Yet another area for further investigation that builds on the results presented here is stiffness and damping control. Ski manufacturers, such as K2, have had active stiffness and damping control in ski products for a number of years and stiffness and damping control have recently appeared in snowboards, as indicated by PCB Piezotronics (date unknown). Optimal placement of stiffness and damping controlling materials could be determined through computer simulation and then the actual effect on natural frequencies and damping ratios measured both in the laboratory and in the field. As mentioned in the computational modelling section, more elaborate computer models beyond those described here can be easily envisioned that more accurately represent a board as a composite laminate structure. Such a model would require significantly more development time, as well as a much more in-depth determination of material properties, but would allow more detailed tracking of the effects of changes in the design and structure of the board. It is unclear, however, whether the effort associated with the development of such a model would yield sufficient additional insight to make it justifiable. One continuation of the current work that could be undertaken even with the current computer models is a study of the effect of adding stiffeners, such as carbon strips or Kevlar strands, to the snowboard structure. While determining the exact net effect of such additions using the current models is not feasible, identifying trends in changes in the relative frequencies of bending and torsional modes is. Such studies would accelerate the design process and allow for the consideration of a much wider range of design modifications. Not discussed in this paper is work that has already begun that extends the foundation of the snowboard research presented here. In particular, a dynamic testing machine has been developed at Bucknell University that simulates the behaviour of a snowboard, as actually observed in field tests, while turning, stopping and jumping. A photograph of the testing machine simulating a heel-side turn is shown in Figure 7. The four pneumatic actuators simulate the ability of a rider to apply forces either at the toes or heels of either leg. The displacement of each actuator, and the force applied, is controlled through a VisualBasic-based graphical user interface. The user can select either ‘manual mode’ for development of a Sports Engineering (2003) 6, 129–138 © 2003 isea K.W. Buffinton et al. particular manoeuvre, or ‘scenario mode’ that allows for continuous execution of already developed and stored manoeuvres. While a manoeuvre is being performed, data from strain gauges and accelerometers can be recorded to ensure that the manoeuvre reproduces that seen on the slopes and to track changes in behaviour as modifications are made to board design. Acknowledgements Many individuals contributed to the work described in this paper beyond those listed as authors. Bucknell mechanical engineering students Michael E. Morris and Christopher V. Nowakowski contributed to the laboratory testing. Chris and fellow mechanical engineering student E. Blair Sutton used their expertise with Pro/ENGINEER to aid in the development of the computer models. Mike, Chris and Blair with mechanical engineering students Frederick E. Luchsinger and Timothy J. Nageli worked as a well co-ordinated team, while enduring the discomfort of winter temperatures during field testing. Bucknell College of Engineering development engineer Wade A. Hutchison contributed greatly to the collection of field data through the development of Visual Basic software that communicated with data collection hardware. College of Engineering electronics technician Thomas J. Thul, laboratory technologist James B. Gutelius, Jr. and Product Development Laboratory technician Daniel G. Johnson provided electronics expertise, strain gauge Figure 7 Snowboard testing machine. © 2003 isea Sports Engineering (2003) 6, 129–138 Snowboard dynamics preparation and machining skills that were important elements in the success of the project. The project would never have taken place without the entrepreneurial spirit and commitment to innovation of Walbridge Design & Manufacturing, Inc. (now Dimension Snowboards) of York, Pennsylvania, USA. Professional snowboarders Jay Smith and Todd Aldridge contributed their skill, expertise and patience in performing the manoeuvres requested in field testing. Seven Springs Mountain Resort in Champion, Pennsylvania, USA graciously provided accommodations, lift privileges and slope access for the field testing. Financial support for the project was provided through a grant from the Ben Franklin Technology Center of Northeast Pennsylvania (USA) for which the Small Business Development Center at Bucknell handled administrative support. References ASTM (1995) Standard Terminology Relating to Snowboarding. ASTM Designation: F 1107–95, American Society for Testing and Materials, 100 Barr Harbor Dr., West Conshohocken, PA, USA. Dosch, J.J. (date unknown) Piezoelectric strain sensor. Unpublished technical report, PCB Piezotronics Inc., 3425 Walden Ave., Depew, NY, USA. Ewins, D.J. (2000) Modal Testing: Theory, Practice and Application, New York, John Wiley and Sons. Lind, D. & Sanders, S.P. (1996) The Physics of Skiing: Skiing at the Triple Point, New York, Springer-Verlag. Michaud, J. & Duncumb, I. (1999) Physics of a snowboard carved turn. <http://www.bomberonline.com/ Bomber_Files/Articles/JackM8/jackm8.html>. Nordt, A.A., Springer, G.S. & Kollár, L.P. (1999a) Computing the mechanical properties of alpine skis. Sports Engineering, 2, 65–84. Nordt, A.A., Springer, G.S. & Kollár, L.P. (1999b) Simulation of a turn on alpine skis. Sports Engineering, 2, 181–199. PCB Piezotronics (date unknown) Extreme testing, supreme performance. Model 740A02 dynamic ICP piezoelectric strain sensor advertising flyer, PCB Piezotronics Inc., 3425 Walden Ave., Depew, NY, USA. Piziali, R.L. & C.D. Mote, C.D., Jr. (1972) The snow ski as a dynamic system. ASME Journal of Dynamic Systems, Measurement and Control, 94, 133–138. Sutton, E.B. (2000) Better snowboards by design. ASME International Mechanical Engineering Congress and Exposition, 2000-IMECE/DE-18. Swinson, D.B. (1994) Physics and snowboarding. The Physics Teacher, 32, 530–534. 137