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Biomechanical conditions of maintaining balance in snowboarding
Abstract
BACKGROUND: Snowboarding, along with Alpine skiing, is one of two most popular winter sports. While there are many studies on the mechanical conditions of movement in skiing, there is a lack of studies analysing the forces affecting snowboarders. The difference in body orientation between snowboarding and skiing means that applying the same biomechanical rules to both sports is unjustified and a separate analysis is needed. The most difficult aspect of snowboarding is maintaining the correct body balance which is dependent on the directions and magnitudes of external forces and their torques. Therefore, the aim of this study is to analyse the forces that affect a snowboarder on the slope and the effects of these forces on the maintenance of a stable body posture.
METHODS: The research method used in the work is based on the theoretical analysis of physical phenomena that occur during riding on the snowboard.
RESULTS: The study describes the biomechanical conditions that allow the snowboarder to maintain an upright posture when standing and moving, as well as the forces that initiate movement and decelerate the snowboarder. The physical forces that appear when moving forward and along an arc are analysed, as are the mechanical interdependences that enable effective snowboarding.
CONCLUSIONS: Knowing the rules of forces action is the best method for understanding how a snowboarder move and keep the balance on a slope. The application of theoretical knowledge should improve not only the self-confidence and effectiveness of the snowboarders but also the safety of their riding.
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Introduction. Snowboarding is a sports discipline in which postural control is key to achieving an effective technique. The body is positioned sideways on the snowboard, with only the head facing forward. This study evaluated the effect of several days of intense snowboarding on the parameters of static and dynamic body stability in persons with different levels of skill. Material and methods. A nine-day snowboarding course was designed and conducted with beginner (N = 16) and advanced snowboarders (N = 14) in the mountains in winter. Before and after the course, dynamic body stability was measured on a Biodex Balance System (USA) platform with an unstable surface, and static body stability was measured on a FreeMed Sensor Medica (Italy) stabilometric platform. Results. Measurements on an unstable surface showed significantly weaker (p < 0.01) values of body stability in a lateral stance in the snowboarding stance than in a forward stance and a significant (p < 0.05) improvement in performance after the course. On a stable surface, the improvement in performance (p < 0.05) occurred only among the beginners, in the snowboard basic position. Conclusions. The results confirm that snowboarding, or continuous unstable balance, improves postural control, which leads to the conclusion that the lateral stance on the snowboard is a clearly disruptive factor in natural postural control. This constitutes a considerable difficulty, especially for beginners, who in addition to learning new technical skills, must adapt to continuously shifting balance.
The purpose of this study was to investigate the evolution of ground reaction force during alpine skiing turns. Specifically, this study investigated how turn phases and slope steepness affected the whole foot normal GRF pattern while performing giant slalom turns in a race-like setting. Moreover, the outside foot was divided into different plantar regions to see whether those parameters affected the plantar pressure distribution. Eleven skiers performed one giant slalom course at race intensity. Runs were recorded synchronously using a video camera in the frontal plane and pressure insoles under both feet’s plantar surface. Turns were divided according to kinematic criteria into four consecutive phases: initiation, steering1, steering2 and completion; both steering phases being separated by the gate passage. Component of the averaged Ground Reaction Force normal to the ski’s surface(nGRF¯, /BW), and Pressure Time Integral relative to the entire foot surface (relPTI, %) parameters were calculated for each turn phases based on plantar pressure data. Results indicated that nGRF¯ under the total foot surface differed significantly depending on the slope (higher in steep sections vs. flat sections), and the turn phase (higher during steering2 vs. three other phases), although such modifications were observable only on the outside foot. Moreover, nGRF¯ under the outside foot was significantly greater than under the inside foot.RelPTI under different foot regions of the outside foot revealed a global shift from forefoot loading during initiation phase, toward heel loading during steering2 phase, but this was dependent on the slope studied. These results suggest a differentiated role played by each foot in alpine skiing turns: the outside foot has an active role in the turning process, while the inside foot may only play a role in stability.
Snowboarding requires a lateral positioning of the body. Moreover, a person must continuously control their balance and use this in order to manoeuvre on the slope applying properly pressure on the lower limb closest to the nose of the board (the leading leg). The present study is an attempt to determine the interdependencies between side preference while snowboarding and laterality when performing other tasks. The dynamic stability in the neutral standing position, as well as in the lateral positions (left or right) was also evaluated.
The survey participants (100 active snowboarders) answered a set of questions concerning laterality while carrying out basic everyday tasks and while doing sports. The respondents were divided into two groups based on their preferred leading side in snowboarding. Additionally, in the case of 34 people, muscle torques values of the lower limbs were measured under static conditions and the postural stability was evaluated using AccuSway AMTI platform and Biodex Balance System platform.
Over 90% of the participants declared right-handedness and right-footedness. However, with regard to snowboarding, only 66% indicated their right leg as leading. No significant dependence was found between the directional stance on the board and the leading hand, dominant leg, or leading eye. The stability measurements revealed statistically significant differences between the neutral stance and the lateral positioning.
Based on the study results, it may be assumed that the declared directional stance on the snowboard is not contingent on the person’s basic laterality, and that the lateral stance on the board significantly affects the posture control.
Lower barometric pressure of air at altitude can affect competitive performance of athletes in some sports. Here we report the effects of various altitudes on elite track-and-field athlete's performance.
Lifetime track-and-field performances of athletes placed in the top 16 in at least one major international competition between 2000 and 2009 were downloaded from the database at tilastopaja.org. There were 132,104 performances of 1889 athletes at 794 venues. Performances were log-transformed and analyzed using a mixed linear model with fixed effects for 6 levels of altitude and random quadratic effects to adjust for athlete's age.
Men's and women's sprint events (100-400 m) showed marginal improvements of ~0.2% at altitudes of 500-999 m, and above 1500 m all but the 100-and 110-m hurdles showed substantial improvements of 0.3-0.7%. Some middle- and long-distance events (800-10,000 m) showed marginal impairments at altitudes above 150 m, but above 1000 m the impairments increased dramatically to ~2-4% for events >800 m. There was no consistent trend in the effects of altitude on field events up to 1000 m; above 1000 m hammer throw showed a marginal improvement of ~1%, and discus was impaired by 1-2%. Above 1500 m, triple jump and long jump showed marginal improvements of ~1%.
In middle-and long-distance runners altitudes as low as 150-299 m can impair performance. Higher altitudes (≥ 1000 m) are generally required before decreases in discus performance, or enhancements in sprinting, triple-and long-jump, or hammer throw are seen.
The purpose of this study was to analyze the kinetic friction of different combinations of snowboard base structures and waxes. On a linear tribometer in a cold lab 3 snowboards with 3 different base structures were first waxed with a training wax. Then the friction coefficient was assessed at 2 m/s, 5 m/s and 8 m/s. Subsequently the boards were prepared with a racing finish and the friction coefficient of the boards was measured again.
The effects of base structure and wax on the kinetic friction on snow appear to be strongly interdependent. A wax that takes effect on one board at given conditions must not be working on a board with different base structure. In addition there is a strong influence of the sliding speed. Optimization of race equipment must not only consider the interdependency of base structure and wax but also the relevant competition speed.
Alpine ski racing is a popular international winter sport that is complex and challenging from physical, technical, and tactical perspectives. Despite the vast amount of scientific literature focusing on this sport, including topical reviews on physiology, ski-snow friction, and injuries, no review has yet addressed the biomechanics of elite alpine ski racers and which factors influence performance. In World Cup events, winning margins are often mere fractions of a second and biomechanics may well be a determining factor in podium place finishes.
The aim of this paper was to systematically review the scientific literature to identify the biomechanical factors that influence the performance of elite alpine ski racers, with an emphasis on slalom, giant slalom, super-G, and downhill events.
Four electronic databases were searched using relevant medical subject headings and key words, with an additional manual search of reference lists, relevant journals, and key authors in the field. Articles were included if they addressed human biomechanics, elite alpine skiing, and performance. Only original research articles published in peer-reviewed journals and in the English language were reviewed. Articles that focused on skiing disciplines other than the four of primary interest were excluded (e.g., mogul, ski-cross and freestyle skiing). The articles subsequently included for review were quality assessed using a modified version of a validated quality assessment checklist. Data on the study population, design, location, and findings relating biomechanics to performance in alpine ski racers were extracted from each article using a standard data extraction form.
A total of 12 articles met the inclusion criteria, were reviewed, and scored an average of 69 ± 13 % (range 40-89 %) upon quality assessment. Five of the studies focused on giant slalom, four on slalom, and three on downhill disciplines, although these latter three articles were also relevant to super-G events. Investigations on speed skiing (i.e., downhill and super-G) primarily examined the effect of aerodynamic drag on performance, whereas the others examined turn characteristics, energetic principles, technical and tactical skills, and individual traits of high-performing skiers. The range of biomechanical factors reported to influence performance included energy dissipation and conservation, aerodynamic drag and frictional forces, ground reaction force, turn radius, and trajectory of the skis and/or centre of mass. The biomechanical differences between turn techniques, inter-dependency of turns, and abilities of individuals were also identified as influential factors in skiing performance. In the case of slalom and giant slalom events, performance could be enhanced by steering the skis in such a manner to reduce the ski-snow friction and thereby energy dissipated. This was accomplished by earlier initiation of turns, longer path length and trajectory, earlier and smoother application of ground reaction forces, and carving (rather than skidding). During speed skiing, minimizing the exposed frontal area and positioning the arms close to the body were shown to reduce the energy loss due to aerodynamic drag and thereby decrease run times. In actual races, a consistently good performance (i.e., fast time) on different sections of the course, terrains, and snow conditions was a characteristic feature of winners during technical events because these skiers could maximize gains from their individual strengths and minimize losses from their respective weaknesses.
Most of the articles reviewed were limited to investigating a relatively small sample size, which is a usual limitation in research on elite athletes. Of further concern was the low number of females studied, representing less than 4 % of all the subjects examined in the articles reviewed. In addition, although overall run time is the ultimate measure of performance in alpine ski racing, several other measures of instantaneous performance were also employed to compare skiers, including the aerodynamic drag coefficient, velocity, section time, time lost per change in elevation, and mechanical energy behaviours, which makes cross-study inferences problematic. Moreover, most studies examined performance through a limited number of gates (i.e., 2-4 gates), presumably because the most commonly used measurement systems can only capture small volumes on a ski field with a reasonable accuracy for positional data. Whether the biomechanical measures defining high instantaneous performance can be maintained throughout an entire race course remains to be determined for both male and female skiers.
Effective alpine skiing performance involves the efficient use of potential energy, the ability to minimize ski-snow friction and aerodynamic drag, maintain high velocities, and choose the optimal trajectory. Individual tactics and techniques should also be considered in both training and competition. To achieve better run times, consistency in performance across numerous sections and varied terrains should be emphasized over excellence in individual sections and specific conditions.
In alpine ski racing the relationships between skier kinetics and kinematics and their effect on performance and injury-related aspects are not well understood. There is currently no validated system to determine all external forces simultaneously acting on skiers, particularly under race conditions and throughout entire races. To address the problem, this study proposes and assesses a method for determining skier kinetics with a single lightweight differential global navigation satellite system (dGNSS). The dGNSS kinetic method was compared to a reference system for six skiers and two turns each. The pattern differences obtained between the measurement systems (offset ± SD) were −26 ± 152 N for the ground reaction force, 1 ± 96 N for ski friction and −6 ± 6 N for the air drag force. The differences between turn means were small. The error pattern within the dGNSS kinetic method was highly repeatable and precision was therefore good (SD within system: 63 N ground reaction force, 42 N friction force and 7 N air drag force) allowing instantaneous relative comparisons and identification of discriminative meaningful changes. The method is therefore highly valid in assessing relative differences between skiers in the same turn, as well as turn means between different turns. The system is suitable to measure large capture volumes under race conditions.
This investigation was designed to (a) develop an individualized mechanical model for measuring aerodynamic drag (F(d) ) while ski racing through multiple gates, (b) estimate energy dissipation (E(d) ) caused by F(d) and compare this to the total energy loss (E(t) ), and (c) investigate the relative contribution of E(d) /E(t) to performance during giant slalom skiing (GS). Nine elite skiers were monitored in different positions and with different wind velocities in a wind tunnel, as well as during GS and straight downhill skiing employing a Global Navigation Satellite System. On the basis of the wind tunnel measurements, a linear regression model of drag coefficient multiplied by cross-sectional area as a function of shoulder height was established for each skier (r > 0.94, all P < 0.001). Skiing velocity, F(d) , E(t) , and E(d) per GS turn were 15-21 m/s, 20-60 N, -11 to -5 kJ, and -2.3 to -0.5 kJ, respectively. E(d) /E(t) ranged from ∼5% to 28% and the relationship between E(t) /v(in) and E(d) was r = -0.12 (all NS). In conclusion, (a) F(d) during alpine skiing was calculated by mechanical modeling, (b) E(d) made a relatively small contribution to E(t) , and (c) higher relative E(d) was correlated to better performance in elite GS skiers, suggesting that reducing ski-snow friction can improve this performance.
An application of Newton's second law to a snowboarder dropping off a vertical ledge shows that the average normal force during landing (force exerted by the ground on the snowboarder) is determined by four factors. It is shown that the flexing of the legs, the softness of the snow, the angle of the landing surface and the forward motion of the snowboarder can contribute significantly to reducing the force on landing. A judicious choice of the geometry of the jump leads to a force on landing that is equal to the force that the snowboarder would feel if they were standing at the landing point independent of the height from which the snowboarder jumps. Thus we are able to explain with a relatively simple model why a snowboarder may jump from rather high ledges and land comfortably. The physics here is also applicable to jumps in other sports including skiing and mountain biking. The importance of knowing the limits of models is discussed and some of the limits of this model are pointed out.
The aerodynamics of the skier’s equipment and the effect of postural changes on the aerodynamic forces acting on the skier during downhill speed racing have been studied theoretically. The aerodynamic characteristics of skier and equipment have been determined by a source panel method based on the velocity potential theory. The calculations indicate that the skier’s torso should be slightly lifted from the tangential direction of downhill during skiing, thus causing a lift force and reducing the friction between the skis and snow. The drag of the torso—tilted by a few degrees—will remain almost the same as the drag of the torso in strict tangential direction. The force acting on the skier’s legs can be directed according to individual needs. The shape of the leg spoilers will give the wanted drag/lift ratio. The optimum shape of the helmet depends on the skiing style. The results introduced here are obtained from theoretical calculations, and their validity should first be tested in a wind tunnel and finally during the normal skiing performance. The calculated drag forces, which are based on the velocity potential theory, do not include the base drag of the skier’s body.
This paper documents a five year testing program that identified factors affecting the aerodynamic drag (Fd) of alpine skiers. Wind tunnel Fd measurements of world class alpine skiers and air permeability measurements of ski suits were conducted to determine the effect of fabric permeability on suit Fd. Frontal area (Ap) measurements were combined with Fd data to determine the drag coefficient (Cd) of the athletes in various skiing positions. Differences in Fd of ski suits were most pronounced between downhill (DH) race suits and those designed for Giant Slalom (GS) competition where protective padding increased Fd by up to 7.1%. In general, suits that were stretched from multiple wearing or that were undersized had greater permeability and higher Fd. Alternatively, skiers who wore a loose fitting suit or multiple suits that increased the skier’s Ap experienced up to 5.2% of additional Fd, estimated to slow a skier by 0.19 s over a 250 m straight glide section of a downhill race course. Pre-season wind tunnel testing to optimize body positioning and ski suit size selection, followed by custom suit fitting have been important to the competitive success of the Canadian Alpine Ski Team.
The objective of this study was to devise a method of kinetic analysis of the ground reaction force that enables the durations and magnitudes of forces acting during the individual phases of ski turns to be described exactly. The method is based on a theoretical analysis of physical forces acting during the ski turn. Two elementary phases were defined: (1) preparing to turn (initiation) and (2) actual turning, during which the center of gravity of the skier-ski system moves along a curvilinear trajectory (steering). The starting point of the turn analysis is a dynamometric record of the resultant acting ground reaction force applied perpendicularly on the ski surface. The method was applied to six expert skiers. They completed a slalom course comprising five gates arranged on the fall line of a 26° slope at a competition speed using symmetrical carving turns (30 evaluated turns). A dynamometric measurement system was placed on the carving skis (168 cm long, radius 16 m, data were recorded at 100 Hz). MATLAB procedures were used to evaluate eight variables during each turn: five time variables and three force variables. Comparison of the turn analysis results between individuals showed that the method is useful for answering various research questions associated with ski turns.
The aims of the present study were to develop a method for classifying slalom skiing performance and to examine differences in mechanical parameters. Eighteen elite skiers were recorded with three-dimensional kinematical measurements and thereafter divided into a higher (HP) and lower performance group, using the ratio between the difference in mechanical energy divided by the mass of the skier and section entrance velocity (Δe(mech)/v(in)). Moreover, the skiers' velocity (v), acceleration (a), center of mass turn radii (R(CM)) and skis' turn radii (R(AMS)), ground reaction forces (GRF) and differential specific mechanical energy [diff(e(mech))] were calculated. v and diff(e(mech)) were different between the performance groups (P<0.001 and <0.05), while no inter-group differences in R(CM), R(AMS), a and GRF were observed. A relationship between R(AMS) and diff(e(mech)) was demonstrated (r=0.58; P<0.001). The highest GRFs were related to the lowest diff(e(mech)) and a was related to GRF (r=-0.60; P<0.001). The Δe(mech)/v(in) predicted the performance over short course sections. The HP skiers skied with a higher v and a similar range of diff(e(mech)). We suggest that shortest R(AMS) and the highest GRFs should be reduced in elite slalom in order to increase performance.
There have been considerable changes in equipment design and movement patterns in the past few years both in alpine skiing and ski-jumping. These developments have been matched by methods of analysing movements in field conditions. They have yielded new insights into the skills of these specific winter sports. Analytical techniques have included electromyography, kinetic and kinematic methods and computer simulations. Our aim here is to review biomechanical research in alpine skiing and ski-jumping. We present in detail the techniques currently used in alpine skiing (carving technique) and ski-jumping (V-technique), primarily using data from the authors' own research. Finally, we present a summary of the most important results in biomechanical research both in alpine skiing and ski-jumping. This includes an analysis of specific conditions in alpine skiing (type of turn, terrain, snow, speed, etc.) and the effects of equipment, materials and individual-specific abilities on performance, safety and joint loading in ski-jumping.
Whether you are a first time skier or regularly take to the slopes, your chances of an enjoyable – and injury free - holiday are greatly enhanced if you prepare for the physical exertion of skiing.
This book offers readers a fitness programme specifically designed for the rigours of skiing. The book begins with an overview of the most common injuries that skiers suffer, plus a look at what areas of fitness you need to focus on in order to get the most out of your skiing - strength, CV fitness and flexibility.
The book has two sections, one aimed at those new to skiing and one aimed at the more advanced skier. Both sections will include programmes to be undertaken in the months and weeks leading up to the skiing trip, but there will also be year round programmes that can be incorporated into the reader's regular exercise programme, offering year round skiing fitness.
Aerodynamic properties are one of the factors that determine speed performance in Alpine skiing. Many studies have examined the consequences of this factor in downhill skiing, and the impact of postural modifications on speed is now well established. To date, only wind tunnel tests have enabled one to measure aerodynamic drag values (a major component of the aerodynamic force in Alpine skiing). Yet such tests are incompatible with the constraints of a regular and accurate follow-up of training programs. The present study proposes an experimental model that permits one to determine a skier's aerodynamic drag coefficient (SCx) based on posture. Experimental SCx measurements made in a wind tunnel are matched with the skier's postural parameters. The accuracy of the model was determined by comparing calculated drag values with measurements observed in a wind tunnel for different postures. For postures corresponding to an optimal aerodynamic penetration (speed position), the uncertainty was 13%. Although this model does not permit an accurate comparison between two skiers, it does satisfactorily account for variations observed in the aerodynamic drag of the same skier in different postures. During Alpine ski training sessions and races, this model may help coaches assess the gain or loss in time induced by modifications in aerodynamic drag corresponding to different postures. It may also be used in other sports to help determine whether the aerodynamic force has a significant impact on performance.
Objective: To examine possible bilateral strength asymmetries between the front (FL) and the rear leg (RL) in elite snowboard athletes due to the imposed asymmetrical position on the board.
Design: Observational study.
Setting: Department of Biomedical Sciences for Health, University of Milan.
Participants: Thirty-three elite male snowboarders: twelve alpine athletes (SBalp), eleven snowboardcross athletes (SBx) and ten freestyle athletes (SBfs).
Intervention: Open and closed kinetic chain exercises.
Main Outcome Measures: Maximal isometric voluntary contraction (MVC) and vertical jump force (VJFT).
Results: Only SBalp athletes presented MVC and VJFT values in RL 9.9% and 11.3% greater than the corresponding value in FL (P < 0.001), respectively. No significant differences were observed in SBx and SBfs.
Conclusion: A muscle strength asymmetry between FL and RL was detected only in elite SBalp. This asymmetry is lower than the ±15% cut-off interval used to define clinically relevant bilateral strength asymmetry, and is likely to be explained by technical aspects. Indeed, only SBalp athletes naturally distributed the center of mass, and thus the weight, towards RL to have a good board control. This feature likely reflects a greater adaptation of the muscle characteristics.
In simulation of skiing the force between ski and snow is a decisive factor. We decompose the reaction force into a penetration force normal to the snow surface, a shear force, and friction. Thus, two portable measurement devices were developed to study the penetration and shear force for compacted snow
on groomed ski slopes. The penetration force was assessed by measuring the penetration depth of a ski-tool
loaded normal to the snow surface. For the shear force the tangential load was measured when snow begins
to fail. Overall 236 penetration and 108 shear experiments were conducted on different types of snow. The penetration force was proportional to the volume of snow displaced by the ski-tool. The failure shear force
was proportional to the penetration depth times the length of the tool. The constants of proportionality, H_V and S_f, are material parameters of snow. The snow hardness, H_V varied between 0.04 and 90 N/mm3 and the failure shear stress, S_f between 0.04 and 0.40 N/mm2. In another investigation skiing turns were simulated using the presented snow reaction forces. Maximum deviations between computed and real trajectories
were less than 1% of the overall length of the runs.
A wind-tunnel experiment was performed to measure the aerodynamic forces acting on an alpine skier running down a slope at top speed and to clarify their relation to his postural changes. Throe wind velocities (10, 20, 30ms) were chosen. Two male Japanese top alpine skiers served as subjects. The following results wero obtained: (1) measured values of drag ranged from 11.76 N (10 ms to 256.27 N (30 ms). (2) Measured values of lift ranged from 4.9 N (10 ms to 113.68 N (30 ms. (3) The aerodynamic advantage of the so-called ‘ egg-shaped ’ posture in alpine skiing has been established. (4) Even at the lowest posture, however, lateral extension of the arm causes a substantial increase in drag (50 N for 30 ms of wind velocity), which is comparable with the increase caused by raising the trunk. (5) For further application, drag area and lift area were calculated. (6) Using the above measured values, the influence of postural changes upon velocity, distance covered and consequent performance are discussed.
Chapter 12 Equilibrium and Elasticity.
What injury can occur to a rock climber hanging by a crimp hold?
12-1 What Is Physics?
12-2 Equilibrium.
12-3 The Requirements of Equilibrium.
12-4 The Center of Gravity.
12-5 Some Examples of Static Equilibrium.
12-6 Indeterminate Structures.
12-7 Elasticity.
Review & Summary Questions Problems.
Chapter 13 Gravitation.
What lies at the center of our Milky Way galaxy?
13-1 What Is Physics?
13-2 Newton's Law of Gravitation.
13-3 Gravitation and the Principle of Superposition.
13-4 Gravitation Near Earth's Surface.
13-5 Gravitation Inside Earth.
13-6 Gravitational Potential Energy.
13-7 Planets and Satellites: Kepler's Laws.
13-8 Satellites: Orbits and Energy.
13-9 Einstein and Gravitation.
Review & Summary Questions Problems.
Chapter 14 Fluids.
What causes ground effect in race car driving?
14-1 What Is Physics?
14-2 What Is a Fluid?
14-3 Density and Pressure.
14-4 Fluids at Rest.
14-5 Measuring Pressure.
14-6 Pascal's Principle.
14-7 Archimedes' Principle.
14-8 Ideal Fluids in Motion.
14-9 The Equation of Continuity.
14-10 Bernoulli's Equation.
Review & SummaryQuestionsProblems.
Chapter 15 Oscillations.
What is the "secret" of a skilled diver's high catapult in
springboard diving?
15-1 What Is Physics?
15-2 Simple Harmonic Motion.
15-3 The Force Law for Simple Harmonic Motion.
15-4 Energy in Simple Harmonic Motion.
15-5 An Angular Simple Harmonic Oscillator.
15-6 Pendulums.
15-7 Simple Harmonic Motion and Uniform Circular Motion.
15-8 Damped Simple Harmonic Motion.
15-9 Forced Oscillations and Resonance.
Review & Summary Questions Problems.
Chapter 16 Waves--I.
How can a submarine wreck be located by distant seismic
stations?
16-1 What Is Physics?
16-2 Types of Waves.
16-3 Transverse and Longitudinal Waves.
16-4 Wavelength and Frequency.
16-5 The Speed of a Traveling Wave.
16-6 Wave Speed on a Stretched String.
16-7 Energy and Power of a Wave Traveling Along a String.
16-8 The Wave Equation.
16-9 The Principle of Superposition for Waves.
16-10 Interference of Waves.
16-11 Phasors.
16-12 Standing Waves.
16-13 Standing Waves and Resonance.
Review & Summary Questions Problems.
Chapter 17 Waves--II.
How can an emperor penguin .nd its mate among thousands of huddled
penguins?
17-1 What Is Physics?
17-2 Sound Waves.
17-3 The Speed of Sound.
17-4 Traveling Sound Waves.
17-5 Interference.
17-6 Intensity and Sound Level.
17-7 Sources of Musical Sound.
17-8 Beats.
17-9 The Doppler Effect.
17-10 Supersonic Speeds, Shock Waves.
Review & Summary Questions Problems.
Chapter 18 Temperature, Heat, and the First Law of Thermodynamics.
How can a dead rattlesnake detect and strike a reaching hand?
18-1 What Is Physics?.
18-2 Temperature.
18-3 The Zeroth Law of Thermodynamics.
18-4 Measuring Temperature.
18-5 The Celsius and Fahrenheit Scales.
18-6 Thermal Expansion.
18-7 Temperature and Heat.
18-8 The Absorption of Heat by Solids and Liquids.
18-9 A Closer Look at Heat and Work.
18-10 The First Law of Thermodynamics.
18-11 Some Special Cases of the First Law of Thermodynamics.
18-12 Heat Transfer Mechanisms.
Review & Summary Questions Problems.
Chapter 19 The Kinetic Theory of Gases.
How can cooling steam inside a railroad tank car cause the car to be
crushed?
19-1 What Is Physics?
19-2 Avogadro's Number.
19-3 Ideal Gases.
19-4 Pressure, Temperature, and RMS Speed.
19-5 Translational Kinetic Energy.
19-6 Mean Free Path.
19-7 The Distribution of Molecular Speeds.
19-8 The Molar Speci.c Heats of an Ideal Gas.
19-9 Degrees of Freedom and Molar Speci.c Heats.
19-10 A Hint of Quantum Theory.
19-11 The Adiabatic Expansion of an Ideal Gas.
Review & Summary Questions Problems.
Chapter 20 Entropy and the Second Law of Thermodynamics.
Why is the popping of popcorn irreversible?
20-1 What Is Physics?
20-2 Irreversible Processes and Entropy.
20-3 Change in Entropy.
20-4 The Second Law of Thermodynamics.
20-5 Entropy in the Real World: Engines.
20-6 Entropy in the Real World: Refrigerators.
20-7 The Ef.ciencies of Real Engines.
20-8 A Statistical View of Entropy.
Review & Summary Questions Problems.
Appendices.
A The International System of Units (SI).
B Some Fundamental Constants of Physics.
C Some Astronomical Data.
D Conversion Factors.
E Mathematical Formulas.
F Properties of the Elements.
G Periodic Table of the Elements.
Answers to Checkpoints and Odd-Numbered Questions and Problems.
Index.
A ski-snow interaction model is presented. The force between ski and snow is decomposed into a penetration force normal to the snow surface, a shear force parallel to it, and friction. The purpose of this study was to investigate the benefits of a hypoplastic vs an elastic contact for penetration in the simulation of skiing turns. To reduce the number of influencing factors, a sledge equipped with skis was considered. A forward dynamic simulation model for the sledge was implemented. For the evaluation of both contact models, the deviation between simulated trajectories and experimental track data was computed for turns of 67 and 42 m. Maximum deviations for these turns were 0.44 and 0.14 m for the hypoplastic contact, and 0.6 and 7.5 m for the elastic contact, respectively. In the hypoplastic contact, the penetration depth of the ski's afterbody maintained nearly the same value as the part under maximum load, whereas it decreased in the elastic contact. Because the shear force is proportional to the penetration depth, the hypoplastic contact resulted in a higher shearing resistance. By replacing the sledge with a skier model, one may investigate more complex skier actions, skiing performance, or accident-prone skiing maneuvers.
Aerodynamic loads contribute more than 80% of the total drag on speed skiers when passing through timing gates at the end of the straight downhill course. Measurements of aerodynamic drag on a variety of competitive speed skiers obtained in a subsonic windtunnel, are presented here to quantify the influence of position, helmet, leg fairings, poles and ski-suit features when skiers are in competitive speed skiing tuck positions. Results show that drag is reduced significantly by reductions in either the frontal area or the size of recirculation regions around the body, particularly those in the downstream wake of the legs and buttocks. Equipment designed to improve stability is also shown to facilitate a decrease in the integral of drag over a competitive run because the optimal tuck can be more easily identified and maintained.
Wrist injuries are frequently observed after falls in snowboarding. In this study, laboratory experiments mimicking forward and backward falls were analysed. In six different falling scenarios, participants self-initiated falls from a static initial position. Eighteen volunteers conducted a total of 741 trials. Measurements were taken for basic parameters describing the kinematics as well as the biomechanical loading during impact, such as impact force, impact acceleration, and velocity. The effective mass affecting the wrist in a fall also was determined. The elbow angle at impact showed a more extended arm in backward falls compared to forward falls, whereas the wrist angle at impact remained similar in forward and backward falls. The study results suggest a new performance standard for wrist guards, indicating the following parameters to characterize an impact: an effective mass acting on one wrist of 3-5 kg, an impact angle of 75 degrees of the forearm relative to the ground, and an impact velocity of 3 m/s.
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Mechanical model of the relationship between the body mass of snowboarders and time needed to descend on slope
- Spasić M
Mechanical model of the relationship between the body mass of snowboarders and time needed to descend on slope
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