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Horse and Rider Interaction During Simulated Horse Jumping
Journal of Equine Veterinary Science 70 (2018) 26e31
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Journal of Equine Veterinary Science journal homepage: www.j-evs.com
Original Research
Horse and Rider Interaction During Simulated Horse Jumping Petr Nemecek a, Lee Cabell b, *, Miroslav Janura c a
Department of Anatomy and Biomechanics, Faculty of Physical Education and Sports, Charles University, Prague, Czech Republic Department of Health and Physical Education, College of Education, Arkansas Tech University, Russellville, AR c Department of Natural Sciences in Kinanthropology, Faculty of Physical Culture, Palacky University Olomouc, Olomouc, Czech Republic b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2018 Received in revised form 25 July 2018 Accepted 30 July 2018 Available online 10 August 2018
This descriptive study uses a biomechanical simulation to illustrate the effect of rider’s body position on a horse’s motion during the flight phase of a horse jump. Eleven horses were video-recorded performing six jumps each (three with and three without rider) for a total of 66 jumps. A simulation software program analyzed reference points on the riders’ and horses’ bodies (body position) during the jumps. The rider was modeled as a single-segment trunk with the knee joint fixed to a point on the horse’s side, and with the hip and knee free to flex. The program compared the horses’ movements with and without riders, with the most significant differences seen in the angles between the horses’ necks and bodies. Changes in the angles between the horses’ neck and body segments appeared to compensate for the riders’ movements, enabling the horses to maintain balance throughout the jump sequences. We concluded that a horse adapts to faulty rider position by changing the angle of its neck relative to trunk. This information is relevant to rider and horse safety and to improve jump training and performance. © 2018 Elsevier Inc. All rights reserved.
Keywords: Sport Biomechanics Modelling Equine
1. Introduction The biomechanics of horse jumping have been researched over the past 15 years, with previous studies focusing on linear kinematics. Elements of those studies have included characteristics of gait [1], limb positions [2], movement of the Center of Gravity (CoG) at jump takeoff and landing [2,3], and reaction forces at takeoff [1]. Clayton [3] explored the importance of the horse's angular momentum, as it might be a factor in improving a rider's trunk movements. To date, however, the impact of a variety of other factors that may influence jumping results, including rider posture, remain unexamined. The rider's influence on the horse has been researched only €llhorn et al. [4] examined the interaction of sporadically. Scho horses and riders during basic movements and control of the horse.
Animal welfare/ethical statement: The study was approved by the Charles University research ethics committee and written consent was provided by all participants. Conflict of interest statement: The authors declare no conflicts of interest. * Corresponding author at: Lee Cabell, Department of Health and Physical Education, College of Education, Arkansas Tech University, 1306 N El Paso Avenue, Russellville, AR. E-mail address: [email protected] (L. Cabell). https://doi.org/10.1016/j.jevs.2018.07.001 0737-0806/© 2018 Elsevier Inc. All rights reserved.
The authors identified rider-horse interactions by means of data gathered via artificial neural network and analyzed in the timecontinuous pattern. They concluded that their time courseoriented approach provided a sensitive tool for quantifying the interaction of the rider and horse. Galloux and Barrey [5] investigated the influence of the rider and the principal body segments of the horse on the total angular momentum of the horse-rider system. They concluded that the rider and the horse's trunk provided only a small contribution to total angular momentum; however, during the transfer of horse and rider's combined angular momentum in the jumping flight phase, the horse's forelimbs showed an increase in angular momentum, and its head and neck showed a decrease in angular momentum [4,6]. Following this research, Powers and Harrison [6] examined the relative influence of the rider and specific segments of the horse's body on the net angular momentum of the jumping horse. The authors found minimal rider influence on the moment of forces created by the jumping horse. The horse's trunk contributed less to the net angular momentum than did its head, neck, forelegs, or hind legs. Furthermore, the rider added little to the net angular momentum during the flight phase. The authors noted the transfer of the horse's angular momentum among the individual body segments during the flight phase, most obviously demonstrated in the angular momentum increase of the “chest” extremities corresponding to a decrease in the angular momentum of the horse's
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head and neck. The net angular momentum was found to be almost constant during the flight phase for the horse under conditions with and without a rider. The model in this study did not take the horse limb movements into consideration. The simulation was simplified and did not include influences on the flight phase of a jump. However, by omitting the limbs, neck movements were the model horse's only measurable response to perturbations. This is, admittedly, a weakness of this study. Regardless, the simplified simulation's primary purpose was to show the horse's neck ability to respond to incorrect position of the rider during the flight phase. The researchers are aware of this limitation but maintaining this study could become the foundation for further, more precise, horse-andrider modeling during the flight phase of a jump. Patterson et al. [7] researched the differences between the experienced and novice riders and described the net head acceleration, arm position, and their overall acceleration. Other authors investigated the interaction between horse and rider at different trots [8], and biomechanics of a jump of a horse over the obstacles with and without the rider was researched by Lewczuk et al. [9]. This study hypothesized that nonzero angular momentum of the rider's body is created during rider movement backward (or forward) at horse takeoff and then the rider's CoG is misaligned with the horse's takeoff force vector. In other words, when the rider moves incorrectly (i.e., movement that changes the common CoG), the horse compensates for the rider's shift by moving its neck and head in the opposite direction. This study examines the role of the horse's neck in compensating for errors in rider trunk position and independent balanced seat [10] during the flight phase of a jump. The purpose of this descriptive study was to show that simulation confirms that a balanced posture of the rider allows the horse to improve its jumping height ability for 10e20 cm and increase success in clearing obstacles.
horse's takeoff force vector. These body positions are described in the model that defines the rider's trunk during the flight (Fig. 1). Each recorded jump trial began one canter stride before the horse's takeoff, continued through takeoff, and the “flight phase” over the obstacle and the landing, and concluded with one full canter stride after landing [3]. The horses were videotaped jumping over obstacles 0.8, 1.0, and 1.2 m in height and six separate recordings were taken of each horse (i.e., once over each of the three obstacle heights with and without a rider), for a total of 66 trials [11] over a 6-day period. In addition, the horizontal distance from a horse's takeoff to its landing was measured using a tape measure and recorded. The three obstacle heights were chosen to see whether the height of the obstacle influenced the jumping style of the horse. The video images were transferred to the Adobe Photoshop program (version 7.0 CE; Adobe Systems Incorporated, San Jose, CA, USA) to manually digitize the jump-flying sequences. The analysis was twofold: images of the horses alone were analyzed, then the video images of each horse with its rider were overlaid onto the images of that same horse without a rider to compare the horse's neck position during flight during the two different testing states (i.e., with and without rider). Angles between body segments of the horse and rider were measured using a commercially available program (QuickPHOTO Industrial 2.3, PROMICRA s.r.o, Prague, Czech Republic). A script written in MATLAB (MathWorks, Nattick, MA, USA) and a program written in Cþþ (Borland Cþþ Builder, Embarcadero Technologies, San Francisco, CA, USA) were used to calculate basic kinematic parameters (i.e., linear and angular velocities and accelerations of the horse and rider's trunk). The video and data were used to create a model for analysis, which represented as realistic a situation as possible by combining mechanical measurements and the empirical experience of the rider.
2. Materials and Methods
Incorrect rider movements were defined by a model created with the help of a rod to establish the ideal position of the rider's trunk with respect to the horse's neck. Rider errors and ideal
The study was approved by the institutional research ethics committee and written consent was provided by all participants. Five male professional riders (33 ± 3.77 year old) who achieved the “Silver Tour” jumping level volunteered in the study, and 11 horses of various breeds, sex, and age (8.55 ± 0.39 year old), trained at the medium proficiency level, were used for data collection. Other horses’ body parameters include height (1.70 ± 0.06 m), length (1.69 ± 0.08 m), trunk circumference (1.95 ± 0.11 m), length of back (1.47 ± 0.10 m), and body mass (555 ± 81.27 kg). Thirteen retroreflective markers were attached unilaterally on obvious anatomical locations to define rigid body segments of the horse and rider and construct a biomechanical model. The body segments were defined as the horse's neck segment and rider's trunk segment. Markers were placed on the following locations of each horse (chin, ear, withers, shoulder, elbow, tail root, and knee) and its rider (heel, knee, hip, shoulder, and top of head). The horse and rider body positions were videotaped using one static digital camera (Sony DCR- TRV 110E, Sony Corporation, Tokyo, Japan; shutter speed 1/1000 seconds, video resolution 400 Kpix) that allowed for two-dimensional (2-D) analysis of their motions. The camera, used for qualitative assessment, was placed 13 m distance from the horse and rider, and perpendicular to their movement. The riders, while riding on a horse, were asked to take three body postures by feeling. One was the correct rider position and two were incorrect positions, specifically, ahead of and behind the movement. “Ahead of” (or “behind”) the movement indicates the rider leans his trunk more forward (or backward) than the
2.1. Model of the Horse and Rider Body Systems and Their Simulation
Fig. 1. Theoretical model of movement of the rider's trunk, represented by a rod pivoting around the center of rotation. Abbreviations: L0, length of rod; r, position vector; rD, vector pointing to the CoG of the rod; 0, center of rotation (origin of the perpendicular Cartesian axes); u, angular velocity; 4, angle between position vector r and axis x; q, angle between the rod and axis x.
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position were defined empirically, not scientifically. The model is exhibited in Fig. 1. A simulation was constructed to confirm this position, and graphs were created. Fig. 1 describes the model with a pivoting rod. The rod describes the simulation of rider's trunk movement during a jump with respect to the angle of imaginary takeoff. If the rod is in the takeoff axis, the reaction to centripetal force is not exerted on the rod. The more the rod deviates (greater angle) from the axis, the larger reaction centripetal force is exerted on the pivoting rod. The calculations were used to build a numerical model that allowed simulation of the jump action of a horse with its rider. Through this simulation, different rider positions can be modeled with respect to horse positions and this information can be used to improve rider positions. Using video data from the real jumps, the following mathematical model was constructed to illustrate possible relationships between the rider's and horse's positions during the flight phase of the jump. In this model, the horse and rider were treated as two different rigid bodies, subject to the equations of motion [12e15]. All equations are in the Appendix. The forward dynamics simulation is based on a numeric solution of these equations by the Euler method, which replaces differentiation. In the case of known linear velocity (vn) and coordinate (rn) in time (t), these values were calculated (with index n þ 1) in duration t þ h from relations (with known force Fa), which depends on rn (Equations 19e22). The value of integration (h) is calculated in the simulation program, using velocity data from several simulation views, that is, selected as small as possible based on computer calculation. If the variables (r, 4) are given, then the above formulas are employed to derive the following values in arbitrary time (t ¼ nh), quantity of motion (p), velocity (v ¼ p/m), angular momentum (J), and angular velocity (u ¼ J/I in duration t ¼ 0 [initial value]). Force resultant (Fn), moment of forces (Mn), and moment of inertia (In) must be calculated for every stride. There are two active forces in this model: 1. Gravitational force, which affects the horse's CoG, was measured by the methods of Buchner et al. [16] and Springings and Leach [17]. The rider has zero angular momentum, and the rider's force moment is calculated with respect to the horse's CoG. The force direction is along the y-axis, and the value Fg ¼ mg. 2. Interaction force (between horse and rider) has its point of action where the rider's knee meets the horse, and the force moment is generally nonzero. Because the calculation of this force is complex, a simulation model is beneficial. In this case, a spring model with a damping was used (Taylor's potential expansion), in which the rider's knees are connected to the saddle. The net (resultant) force is the sum of two vectors: one is proportional to the difference between position vectors and the other is proportional to the difference between the instantaneous velocities. During the first approach, a force acts as a spring and is followed by a simple harmonic motion (Taylor's potential expansion). Before this simulation process, it is necessary to know and input the initial conditions into the modeling program. These include the dimensions of the horse's and rider's body segments and their associated masses, the angles between the body segments, and the coordinates of the CoG of every segment. The net CoG of the horse [16] and the rider [18] is calculated by the formula in Equation 23. The initial input values, determined by the positions of the individual body segments, were (1) the initial angle of lean of the horse's neck and rider's trunk and (2) the initial velocity of the horse's and rider's CoG, and the initial angular velocities of all segments [19].
The resultant (net) force (F), the linear momentum (M), and the moment of inertia (I) were calculated. The coordinates (r, 4), together with the dimensions of body segments and the relative angles between them, are used for the calculation of the CoG for each segment. The relative angles between body segments were not influenced by the external forces. To imitate the rider and horse actions, under the three conditions of the rider being in front, behind, or on the horse's CoG, it is necessary to define the rider's trunk position accordingly before calculating the net force, linear momentum, and moment of inertia. Specifically, change in the angle (q) between the horse's trunk and rider's trunk affects the moment of inertia of the horse and its angular velocity. In addition, the angle of the horse landing is calculated at every step of the landing and is compared with the predicted angle of horse landing during the constant angular velocity. The moment of inertia and angular velocity of a horse change with each stride. Finally, in response to the rider's movements, the horse constantly changes its moment of inertia and angular velocity to land the jump at the correct angle, that is, the angle at takeoff with rider's body equals zero angular momentum. His body's CoG is in line with the horse's takeoff force vector. 3. Results The simulation program was written such that the values of mass of each segment and its length were variably set, which increased the scope of the program. Another factor, shown in the software, was the shift of overall CoG of the rider versus the overall CoG of the horse either in the forward or backward direction (Fig. 2), so the rider's trunk does not lie parallel with the vector of horse's takeoff. The figures show a different initial body position than the position at the beginning of the flight phase to which the horse must respond. In the simulation program, the horse's position was set and the body position of the rider was changed to the correct position, to the position ahead of the movement, and to the position behind the movement. The results are shown in Fig. 3 which illustrate how the angles between horse's neck and trunk change. This simulation program allows the researchers to see errors a trainer cannot see, and those that are undetectable based on the trainer's observation or the rider's perception. This further gives trainers the opportunity to work with the horses in a way that allows them to take advantage of their full potential. It is possible to differentiate between the effects of rider postures on jumping horses using a model created from data gathered from single jumps and rider irregularities. Inherent in the validity of this tool is prior analysis of the horse's jump without a rider because of the different modes and natural styles of the riderless jump in each single case. This model shows that, for all horses, only one segment, the horse's neck, can correct the rider's position errors relative to the horse's CoG. The errors of rider position and effects of resulting irregularities are illustrated in Fig. 3, where the displacement of the rider's CoG forward and backward against the horse's CoG (when the rider's body is not positioned parallel to the vector of the horse's takeoff) is depicted. The following figures are taken from the simulation program and length ratios corresponding to the simulation model. Fig. 2 depicts the rider and horse starting positions at the initial “takeoff phase” of the jump, to which a horse must react. It shows the same position for the horse but different positions for the rider. Fig. 2 does not show any substantial changes in the horse's neck with respect to rider's trunk while the individual rider's trunk positions start to project into the horse's neck positions during the flight phase. Fig. 2 shows different body positions of the rider influencing the horse, which instinctively balances “errors” of the
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Fig. 2. Model of the horse with the rider in three different positions. Abbreviations: R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front of the horse's CoG.
Jumping is a popular equestrian activity that requires significant communication between horse and rider. Riders can communicate and interact with their horses in a number of ways, mainly via changes in the rider's body position and use of the rider's limbs [12].
The relationships between horses and riders are interactive and complex [13]. There are different approaches to analyze the interaction between the horse and rider that are based on biomechanical simulation [14]. Powers and Harrison [6] presented a theoretical model that demonstrated the interaction between the horse and rider. In this model, both horse and rider are represented as separate information-processing units. De Cocq et al. [8] used three models of force-driven spring (-damper)-mass systems for modeling horse-riding technique at trot. In their system, horses may be required to carry an inanimate load (dead weight) or an animate load (rider). The determination of the close relationship between the three interacting systemsdhorse, saddle, and riderdis difficult to characterize using a limited number of biomechanical parameters. All three components have their own geometry, inertia, elasticity, degrees of freedom, etc. [15]. Therefore, this study has been simplified by using a model that specifically focuses on CoG to determine the interaction between horse and rider, and the horse's compensation for rider errors as evidenced through changes in both the horse's and rider's CoG. The individual length ratios were taken into consideration and influenced the creation of simulation. The authors are aware that each horse is different and has a different style of jumping. A variety of jumping horses were sought for this study and an average jump
Fig. 3. The angle between horse's neck and trunk from takeoff (time 0 seconds) to landing of the jump. Abbreviations: H, horse without a rider; P1, angle begins to differ between the three rider's positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front of the horse's CoG.
Fig. 4. The trajectory of the COG of the rider during the jump. Abbreviations: P1, angle between the horse's neck and trunk begins to differ between the three rider's positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front the horse's CoG. Origin of the perpendicular Cartesian axes is the horse's takeoff.
rider. These changes are also clearly visible in the last portion of Fig. 3. Each simulation scenario began with the horse's body always in the same initial position, changing only the rider's posture to positions “in front of horse's CoG,” or “on the horse's CoG,” or “behind the horse's CoG” in the simulation program. One advantage of this simulation software is that the human and equine anatomical and biomechanical characteristics can be modified to match the actual segment body mass and length of real-life subjects. The inclination of the rider's trunk is graphically represented in Fig. 4. Each rider's trunk position is depicted with comparisons to the jump of a horse without a rider. When the rider's trunk is “in front of the horse's CoG” position, the horse balances force by raising its head and neck, as seen in Fig. 2. When the rider is positioned “behind the horse's CoG” position, the horse lowers its head and neck. 4. Discussion
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was created because the horse's neck length and its mass may significantly influence the curve of jump. All of these were parts of simulation where individual length and mass parameters could be established. The results of studies dealing with the influence of the rider on the execution of movement are not clear. Peham et al. [20] indicate the motion of the horse-professional rider system is more consistent than that of the horse-hobby rider system. On the other hand, in their study dealing with the influence of rider experience on jump kinematics, Powers and Kavanagh [12] indicate inertial effect of the rider on the jumping horse as minimal. This model is able to capture detailed differences in the horse's reaction to rider errors. Because similar studies have not been widely published, it is a challenge to compare this study with similar research. For example, Patterson et al. [7] claim that an experienced horse jumps the same way with either an expert or novice rider. However, the model in this study suggests the horse instinctively corrects balance for a rider's error, regardless of whether the rider is an expert or novice. A similar study by Powers and Harrison [21] shows the rider's influence is minimal. That minimum can be the deciding factor for the horse‘s overall performance during a jump. The model can be used for specific demonstrations of rider position errors on a horse. Further, the model allows researchers to set initial parameters such as the length of body segments and their masses. The model, however, only analyzes the flight phase, which follows the takeoff phase. In this phase, the rider must assume specific body positions as determined by the parameters of the simulation. This model is initiated from the jump execution and therefore the horse and its body segments must always be set to the same initial positions. After the horse positions are established, the rider and his body segments are set to the various body positions so the model will show exactly how the errors are manifested in the horse's activity, thereby validating the calculated presumptions. This simulation model demonstrates relative angles between the horse's neck and trunk (Fig. 3, Table 1) as the horse balances the rider's movement using these two body segments to avoid faulty jumps or falls. When the rider maintains a correct posture, the horse jumps almost as without a rider, which is its natural movement. Different takeoff conditions and velocities affect horse and rider movements, and it is challenging to identify horses' and riders' errors. Moreover, the mental and physical preparation of the horse and rider, and the trainer's skills affect jump movements [22]. A limitation of this model is that these parameters cannot be included in the software program. The simulation program defines the total numerical error as the following: e ¼ h/t, where h is the integration step of simulation, that is, the velocity of the simulation jump, and t is the total duration of simulation (t z 1 s). The total approximate error is 0.001/1 ¼ 0.1%, and the maximum relative error (Erel) is 1%.
Table 1 Values of the angle between horse's neck and trunk in the key simulation points. P1
R1 R2 R3 H
P2
The accuracy of the simulation of the horse jump depends on two factors. First is the accuracy of the data describing initial conditions (such as the horse and rider's body dimensions and masses, angles between body segments, etc). The condition values, given by the simulation program at takeoff, can be changed to reflect measured errors of the rider and horse. However, these values can influence only the total amount of the calculated phenomena, that is, the initial angle changes occur only along y-axis. This phenomenon can be assumed to represent actual and measurable changes because the simulation is shown under real conditions. The second factor in determining accuracy is more important: it is the inaccuracy inherently resulting from using mathematical calculations to simulate motion. The size of such an error depends on the size of the integration used (Equations 24e27). This can also be set in the software program; in this model, the integration h ¼ 1.024 ms was used to obtain the graphs. 5. Conclusions The Figures and Table were based on data that were the output from program SIMULATION. The calculations in the simulation model supported the study's hypothesis that the horse accommodates incorrect rider movement through its neck movement, that is, the horse moves its neck in a specific direction to maintain balance despite rider error. Because the horse's neck is the only free-moving segment that can balance errors made by the rider, its mass and created internal forces are important. It is the only segment that can balance the error made by the rider. This simulation program allowed the examination of rider errors and asymmetries that cannot be seen clearly by the trainer's eye, or felt by a rider, and is also customizable to specific horses and riders because the human and equine anatomical and biomechanical characteristics can be modified to match actual real-life subjects. The program facilitates improved quality and effectiveness of the horse's training and jumping height ability by affording trainers better teaching methods. It has the potential to reduce trauma to the horse's body, reduce incidence of falls, and improve safety for both the horse and rider. In the future, the study should be further explored and developed and could be used to educate trainers and create new software programs that, after video recording, would show the rider's incorrect body positions. Acknowledgments The authors are grateful to the late Professor Vladimir Komarek from Czech University of Life Sciences Prague, who coordinated the research study and to Jiri Cerny for programming the code in Cþþ used in this project. Supplementary Data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jevs.2018.07.001. References
P3
Time (s)
Angle (deg)
Time (s)
Angle (deg)
Time (s)
Angle (deg)
0.150 0.150 0.150 0.150
57.6 57.6 57.6 57.6
0.381 0.361 0.341 0.341
69.8 71.3 71.2 71.2
0.582 0.590 0.604 0.549
123.3 120.8 114.4 123.3
Abbreviations: H, horse without a rider; P1, angle between the horse’s neck and trunk begins to differ between the three rider’s positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front the horse's CoG.
[1] Leach DH, Ormrod K, Clayton HM. Standardized terminology for the description and analysis of equine locomotion. J Equine Vet Sci 1984;16: 522e8. [2] Clayton HM. Time-motion analysis of show jumping competitions. J Equine Vet Sci 1996;16:262e6. [3] Clayton HM. Terminology for description of equine jumping kinematics. J Equine Vet Sci 1989;9:341e8. €llhorn WI, Peham C, Licka T, Scheidl M. A pattern recognition approach [4] Scho for the quantification of horse and rider interactions. J Equine Vet Sci 2006;(36):400e5.
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[14] Powers PNR, Harrison AJ. Models for biomechanical analysis of jumping horses. J Equine Vet Sci 1999;19:799e806. [15] Witte K, Schobesberger H, Peham C. Motion pattern analysis of gait in horseback riding by means of principal component analysis. Hum Mov Sci 2009;28:394e405. [16] Buchner HHF, Savelberg HHCM, Schamhardt HC, Barneveld A. Inertial properties of Dutch warmblood horses. J Biomech 1997;30:653e8. [17] Springings E, Leach D. Standardized technique for determining the center of gravity of body and limb segments of horses. J Equine Vet Sci 1986;18: 43e9. [18] Fredriksson I, Gernandt A, Hendlund G, Sederholm L. Horses and jumping. London: Pelham; 1976. [19] Fuss FK, Fuss AH. Angular acceleration in horse jumping. J Biomech 1998;31(Suppl. 1):180. [20] Peham C, Kapaun M, Licka T, Scheidl M. Motion pattern consistency of the rider-horse system. ISBS 16 Proc. https://ojs.ub.uni-konstanz.de/cpa/article/ view/1641. [Accessed 30 May 2008]. [21] Powers PNR, Harrison AJ. Effects of the rider on the linear kinematics of jumping horses. Sports Biomech 2002;1:135e46. [22] Dobes J. Riding: training a rider and a horse in jump riding, variety and dressage (in Czech). Prague: Olympia; 1986.
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Journal of Equine Veterinary Science journal homepage: www.j-evs.com
Original Research
Horse and Rider Interaction During Simulated Horse Jumping Petr Nemecek a, Lee Cabell b, *, Miroslav Janura c a
Department of Anatomy and Biomechanics, Faculty of Physical Education and Sports, Charles University, Prague, Czech Republic Department of Health and Physical Education, College of Education, Arkansas Tech University, Russellville, AR c Department of Natural Sciences in Kinanthropology, Faculty of Physical Culture, Palacky University Olomouc, Olomouc, Czech Republic b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 13 February 2018 Received in revised form 25 July 2018 Accepted 30 July 2018 Available online 10 August 2018
This descriptive study uses a biomechanical simulation to illustrate the effect of rider’s body position on a horse’s motion during the flight phase of a horse jump. Eleven horses were video-recorded performing six jumps each (three with and three without rider) for a total of 66 jumps. A simulation software program analyzed reference points on the riders’ and horses’ bodies (body position) during the jumps. The rider was modeled as a single-segment trunk with the knee joint fixed to a point on the horse’s side, and with the hip and knee free to flex. The program compared the horses’ movements with and without riders, with the most significant differences seen in the angles between the horses’ necks and bodies. Changes in the angles between the horses’ neck and body segments appeared to compensate for the riders’ movements, enabling the horses to maintain balance throughout the jump sequences. We concluded that a horse adapts to faulty rider position by changing the angle of its neck relative to trunk. This information is relevant to rider and horse safety and to improve jump training and performance. © 2018 Elsevier Inc. All rights reserved.
Keywords: Sport Biomechanics Modelling Equine
1. Introduction The biomechanics of horse jumping have been researched over the past 15 years, with previous studies focusing on linear kinematics. Elements of those studies have included characteristics of gait [1], limb positions [2], movement of the Center of Gravity (CoG) at jump takeoff and landing [2,3], and reaction forces at takeoff [1]. Clayton [3] explored the importance of the horse's angular momentum, as it might be a factor in improving a rider's trunk movements. To date, however, the impact of a variety of other factors that may influence jumping results, including rider posture, remain unexamined. The rider's influence on the horse has been researched only €llhorn et al. [4] examined the interaction of sporadically. Scho horses and riders during basic movements and control of the horse.
Animal welfare/ethical statement: The study was approved by the Charles University research ethics committee and written consent was provided by all participants. Conflict of interest statement: The authors declare no conflicts of interest. * Corresponding author at: Lee Cabell, Department of Health and Physical Education, College of Education, Arkansas Tech University, 1306 N El Paso Avenue, Russellville, AR. E-mail address: [email protected] (L. Cabell). https://doi.org/10.1016/j.jevs.2018.07.001 0737-0806/© 2018 Elsevier Inc. All rights reserved.
The authors identified rider-horse interactions by means of data gathered via artificial neural network and analyzed in the timecontinuous pattern. They concluded that their time courseoriented approach provided a sensitive tool for quantifying the interaction of the rider and horse. Galloux and Barrey [5] investigated the influence of the rider and the principal body segments of the horse on the total angular momentum of the horse-rider system. They concluded that the rider and the horse's trunk provided only a small contribution to total angular momentum; however, during the transfer of horse and rider's combined angular momentum in the jumping flight phase, the horse's forelimbs showed an increase in angular momentum, and its head and neck showed a decrease in angular momentum [4,6]. Following this research, Powers and Harrison [6] examined the relative influence of the rider and specific segments of the horse's body on the net angular momentum of the jumping horse. The authors found minimal rider influence on the moment of forces created by the jumping horse. The horse's trunk contributed less to the net angular momentum than did its head, neck, forelegs, or hind legs. Furthermore, the rider added little to the net angular momentum during the flight phase. The authors noted the transfer of the horse's angular momentum among the individual body segments during the flight phase, most obviously demonstrated in the angular momentum increase of the “chest” extremities corresponding to a decrease in the angular momentum of the horse's
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head and neck. The net angular momentum was found to be almost constant during the flight phase for the horse under conditions with and without a rider. The model in this study did not take the horse limb movements into consideration. The simulation was simplified and did not include influences on the flight phase of a jump. However, by omitting the limbs, neck movements were the model horse's only measurable response to perturbations. This is, admittedly, a weakness of this study. Regardless, the simplified simulation's primary purpose was to show the horse's neck ability to respond to incorrect position of the rider during the flight phase. The researchers are aware of this limitation but maintaining this study could become the foundation for further, more precise, horse-andrider modeling during the flight phase of a jump. Patterson et al. [7] researched the differences between the experienced and novice riders and described the net head acceleration, arm position, and their overall acceleration. Other authors investigated the interaction between horse and rider at different trots [8], and biomechanics of a jump of a horse over the obstacles with and without the rider was researched by Lewczuk et al. [9]. This study hypothesized that nonzero angular momentum of the rider's body is created during rider movement backward (or forward) at horse takeoff and then the rider's CoG is misaligned with the horse's takeoff force vector. In other words, when the rider moves incorrectly (i.e., movement that changes the common CoG), the horse compensates for the rider's shift by moving its neck and head in the opposite direction. This study examines the role of the horse's neck in compensating for errors in rider trunk position and independent balanced seat [10] during the flight phase of a jump. The purpose of this descriptive study was to show that simulation confirms that a balanced posture of the rider allows the horse to improve its jumping height ability for 10e20 cm and increase success in clearing obstacles.
horse's takeoff force vector. These body positions are described in the model that defines the rider's trunk during the flight (Fig. 1). Each recorded jump trial began one canter stride before the horse's takeoff, continued through takeoff, and the “flight phase” over the obstacle and the landing, and concluded with one full canter stride after landing [3]. The horses were videotaped jumping over obstacles 0.8, 1.0, and 1.2 m in height and six separate recordings were taken of each horse (i.e., once over each of the three obstacle heights with and without a rider), for a total of 66 trials [11] over a 6-day period. In addition, the horizontal distance from a horse's takeoff to its landing was measured using a tape measure and recorded. The three obstacle heights were chosen to see whether the height of the obstacle influenced the jumping style of the horse. The video images were transferred to the Adobe Photoshop program (version 7.0 CE; Adobe Systems Incorporated, San Jose, CA, USA) to manually digitize the jump-flying sequences. The analysis was twofold: images of the horses alone were analyzed, then the video images of each horse with its rider were overlaid onto the images of that same horse without a rider to compare the horse's neck position during flight during the two different testing states (i.e., with and without rider). Angles between body segments of the horse and rider were measured using a commercially available program (QuickPHOTO Industrial 2.3, PROMICRA s.r.o, Prague, Czech Republic). A script written in MATLAB (MathWorks, Nattick, MA, USA) and a program written in Cþþ (Borland Cþþ Builder, Embarcadero Technologies, San Francisco, CA, USA) were used to calculate basic kinematic parameters (i.e., linear and angular velocities and accelerations of the horse and rider's trunk). The video and data were used to create a model for analysis, which represented as realistic a situation as possible by combining mechanical measurements and the empirical experience of the rider.
2. Materials and Methods
Incorrect rider movements were defined by a model created with the help of a rod to establish the ideal position of the rider's trunk with respect to the horse's neck. Rider errors and ideal
The study was approved by the institutional research ethics committee and written consent was provided by all participants. Five male professional riders (33 ± 3.77 year old) who achieved the “Silver Tour” jumping level volunteered in the study, and 11 horses of various breeds, sex, and age (8.55 ± 0.39 year old), trained at the medium proficiency level, were used for data collection. Other horses’ body parameters include height (1.70 ± 0.06 m), length (1.69 ± 0.08 m), trunk circumference (1.95 ± 0.11 m), length of back (1.47 ± 0.10 m), and body mass (555 ± 81.27 kg). Thirteen retroreflective markers were attached unilaterally on obvious anatomical locations to define rigid body segments of the horse and rider and construct a biomechanical model. The body segments were defined as the horse's neck segment and rider's trunk segment. Markers were placed on the following locations of each horse (chin, ear, withers, shoulder, elbow, tail root, and knee) and its rider (heel, knee, hip, shoulder, and top of head). The horse and rider body positions were videotaped using one static digital camera (Sony DCR- TRV 110E, Sony Corporation, Tokyo, Japan; shutter speed 1/1000 seconds, video resolution 400 Kpix) that allowed for two-dimensional (2-D) analysis of their motions. The camera, used for qualitative assessment, was placed 13 m distance from the horse and rider, and perpendicular to their movement. The riders, while riding on a horse, were asked to take three body postures by feeling. One was the correct rider position and two were incorrect positions, specifically, ahead of and behind the movement. “Ahead of” (or “behind”) the movement indicates the rider leans his trunk more forward (or backward) than the
2.1. Model of the Horse and Rider Body Systems and Their Simulation
Fig. 1. Theoretical model of movement of the rider's trunk, represented by a rod pivoting around the center of rotation. Abbreviations: L0, length of rod; r, position vector; rD, vector pointing to the CoG of the rod; 0, center of rotation (origin of the perpendicular Cartesian axes); u, angular velocity; 4, angle between position vector r and axis x; q, angle between the rod and axis x.
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position were defined empirically, not scientifically. The model is exhibited in Fig. 1. A simulation was constructed to confirm this position, and graphs were created. Fig. 1 describes the model with a pivoting rod. The rod describes the simulation of rider's trunk movement during a jump with respect to the angle of imaginary takeoff. If the rod is in the takeoff axis, the reaction to centripetal force is not exerted on the rod. The more the rod deviates (greater angle) from the axis, the larger reaction centripetal force is exerted on the pivoting rod. The calculations were used to build a numerical model that allowed simulation of the jump action of a horse with its rider. Through this simulation, different rider positions can be modeled with respect to horse positions and this information can be used to improve rider positions. Using video data from the real jumps, the following mathematical model was constructed to illustrate possible relationships between the rider's and horse's positions during the flight phase of the jump. In this model, the horse and rider were treated as two different rigid bodies, subject to the equations of motion [12e15]. All equations are in the Appendix. The forward dynamics simulation is based on a numeric solution of these equations by the Euler method, which replaces differentiation. In the case of known linear velocity (vn) and coordinate (rn) in time (t), these values were calculated (with index n þ 1) in duration t þ h from relations (with known force Fa), which depends on rn (Equations 19e22). The value of integration (h) is calculated in the simulation program, using velocity data from several simulation views, that is, selected as small as possible based on computer calculation. If the variables (r, 4) are given, then the above formulas are employed to derive the following values in arbitrary time (t ¼ nh), quantity of motion (p), velocity (v ¼ p/m), angular momentum (J), and angular velocity (u ¼ J/I in duration t ¼ 0 [initial value]). Force resultant (Fn), moment of forces (Mn), and moment of inertia (In) must be calculated for every stride. There are two active forces in this model: 1. Gravitational force, which affects the horse's CoG, was measured by the methods of Buchner et al. [16] and Springings and Leach [17]. The rider has zero angular momentum, and the rider's force moment is calculated with respect to the horse's CoG. The force direction is along the y-axis, and the value Fg ¼ mg. 2. Interaction force (between horse and rider) has its point of action where the rider's knee meets the horse, and the force moment is generally nonzero. Because the calculation of this force is complex, a simulation model is beneficial. In this case, a spring model with a damping was used (Taylor's potential expansion), in which the rider's knees are connected to the saddle. The net (resultant) force is the sum of two vectors: one is proportional to the difference between position vectors and the other is proportional to the difference between the instantaneous velocities. During the first approach, a force acts as a spring and is followed by a simple harmonic motion (Taylor's potential expansion). Before this simulation process, it is necessary to know and input the initial conditions into the modeling program. These include the dimensions of the horse's and rider's body segments and their associated masses, the angles between the body segments, and the coordinates of the CoG of every segment. The net CoG of the horse [16] and the rider [18] is calculated by the formula in Equation 23. The initial input values, determined by the positions of the individual body segments, were (1) the initial angle of lean of the horse's neck and rider's trunk and (2) the initial velocity of the horse's and rider's CoG, and the initial angular velocities of all segments [19].
The resultant (net) force (F), the linear momentum (M), and the moment of inertia (I) were calculated. The coordinates (r, 4), together with the dimensions of body segments and the relative angles between them, are used for the calculation of the CoG for each segment. The relative angles between body segments were not influenced by the external forces. To imitate the rider and horse actions, under the three conditions of the rider being in front, behind, or on the horse's CoG, it is necessary to define the rider's trunk position accordingly before calculating the net force, linear momentum, and moment of inertia. Specifically, change in the angle (q) between the horse's trunk and rider's trunk affects the moment of inertia of the horse and its angular velocity. In addition, the angle of the horse landing is calculated at every step of the landing and is compared with the predicted angle of horse landing during the constant angular velocity. The moment of inertia and angular velocity of a horse change with each stride. Finally, in response to the rider's movements, the horse constantly changes its moment of inertia and angular velocity to land the jump at the correct angle, that is, the angle at takeoff with rider's body equals zero angular momentum. His body's CoG is in line with the horse's takeoff force vector. 3. Results The simulation program was written such that the values of mass of each segment and its length were variably set, which increased the scope of the program. Another factor, shown in the software, was the shift of overall CoG of the rider versus the overall CoG of the horse either in the forward or backward direction (Fig. 2), so the rider's trunk does not lie parallel with the vector of horse's takeoff. The figures show a different initial body position than the position at the beginning of the flight phase to which the horse must respond. In the simulation program, the horse's position was set and the body position of the rider was changed to the correct position, to the position ahead of the movement, and to the position behind the movement. The results are shown in Fig. 3 which illustrate how the angles between horse's neck and trunk change. This simulation program allows the researchers to see errors a trainer cannot see, and those that are undetectable based on the trainer's observation or the rider's perception. This further gives trainers the opportunity to work with the horses in a way that allows them to take advantage of their full potential. It is possible to differentiate between the effects of rider postures on jumping horses using a model created from data gathered from single jumps and rider irregularities. Inherent in the validity of this tool is prior analysis of the horse's jump without a rider because of the different modes and natural styles of the riderless jump in each single case. This model shows that, for all horses, only one segment, the horse's neck, can correct the rider's position errors relative to the horse's CoG. The errors of rider position and effects of resulting irregularities are illustrated in Fig. 3, where the displacement of the rider's CoG forward and backward against the horse's CoG (when the rider's body is not positioned parallel to the vector of the horse's takeoff) is depicted. The following figures are taken from the simulation program and length ratios corresponding to the simulation model. Fig. 2 depicts the rider and horse starting positions at the initial “takeoff phase” of the jump, to which a horse must react. It shows the same position for the horse but different positions for the rider. Fig. 2 does not show any substantial changes in the horse's neck with respect to rider's trunk while the individual rider's trunk positions start to project into the horse's neck positions during the flight phase. Fig. 2 shows different body positions of the rider influencing the horse, which instinctively balances “errors” of the
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Fig. 2. Model of the horse with the rider in three different positions. Abbreviations: R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front of the horse's CoG.
Jumping is a popular equestrian activity that requires significant communication between horse and rider. Riders can communicate and interact with their horses in a number of ways, mainly via changes in the rider's body position and use of the rider's limbs [12].
The relationships between horses and riders are interactive and complex [13]. There are different approaches to analyze the interaction between the horse and rider that are based on biomechanical simulation [14]. Powers and Harrison [6] presented a theoretical model that demonstrated the interaction between the horse and rider. In this model, both horse and rider are represented as separate information-processing units. De Cocq et al. [8] used three models of force-driven spring (-damper)-mass systems for modeling horse-riding technique at trot. In their system, horses may be required to carry an inanimate load (dead weight) or an animate load (rider). The determination of the close relationship between the three interacting systemsdhorse, saddle, and riderdis difficult to characterize using a limited number of biomechanical parameters. All three components have their own geometry, inertia, elasticity, degrees of freedom, etc. [15]. Therefore, this study has been simplified by using a model that specifically focuses on CoG to determine the interaction between horse and rider, and the horse's compensation for rider errors as evidenced through changes in both the horse's and rider's CoG. The individual length ratios were taken into consideration and influenced the creation of simulation. The authors are aware that each horse is different and has a different style of jumping. A variety of jumping horses were sought for this study and an average jump
Fig. 3. The angle between horse's neck and trunk from takeoff (time 0 seconds) to landing of the jump. Abbreviations: H, horse without a rider; P1, angle begins to differ between the three rider's positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front of the horse's CoG.
Fig. 4. The trajectory of the COG of the rider during the jump. Abbreviations: P1, angle between the horse's neck and trunk begins to differ between the three rider's positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front the horse's CoG. Origin of the perpendicular Cartesian axes is the horse's takeoff.
rider. These changes are also clearly visible in the last portion of Fig. 3. Each simulation scenario began with the horse's body always in the same initial position, changing only the rider's posture to positions “in front of horse's CoG,” or “on the horse's CoG,” or “behind the horse's CoG” in the simulation program. One advantage of this simulation software is that the human and equine anatomical and biomechanical characteristics can be modified to match the actual segment body mass and length of real-life subjects. The inclination of the rider's trunk is graphically represented in Fig. 4. Each rider's trunk position is depicted with comparisons to the jump of a horse without a rider. When the rider's trunk is “in front of the horse's CoG” position, the horse balances force by raising its head and neck, as seen in Fig. 2. When the rider is positioned “behind the horse's CoG” position, the horse lowers its head and neck. 4. Discussion
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was created because the horse's neck length and its mass may significantly influence the curve of jump. All of these were parts of simulation where individual length and mass parameters could be established. The results of studies dealing with the influence of the rider on the execution of movement are not clear. Peham et al. [20] indicate the motion of the horse-professional rider system is more consistent than that of the horse-hobby rider system. On the other hand, in their study dealing with the influence of rider experience on jump kinematics, Powers and Kavanagh [12] indicate inertial effect of the rider on the jumping horse as minimal. This model is able to capture detailed differences in the horse's reaction to rider errors. Because similar studies have not been widely published, it is a challenge to compare this study with similar research. For example, Patterson et al. [7] claim that an experienced horse jumps the same way with either an expert or novice rider. However, the model in this study suggests the horse instinctively corrects balance for a rider's error, regardless of whether the rider is an expert or novice. A similar study by Powers and Harrison [21] shows the rider's influence is minimal. That minimum can be the deciding factor for the horse‘s overall performance during a jump. The model can be used for specific demonstrations of rider position errors on a horse. Further, the model allows researchers to set initial parameters such as the length of body segments and their masses. The model, however, only analyzes the flight phase, which follows the takeoff phase. In this phase, the rider must assume specific body positions as determined by the parameters of the simulation. This model is initiated from the jump execution and therefore the horse and its body segments must always be set to the same initial positions. After the horse positions are established, the rider and his body segments are set to the various body positions so the model will show exactly how the errors are manifested in the horse's activity, thereby validating the calculated presumptions. This simulation model demonstrates relative angles between the horse's neck and trunk (Fig. 3, Table 1) as the horse balances the rider's movement using these two body segments to avoid faulty jumps or falls. When the rider maintains a correct posture, the horse jumps almost as without a rider, which is its natural movement. Different takeoff conditions and velocities affect horse and rider movements, and it is challenging to identify horses' and riders' errors. Moreover, the mental and physical preparation of the horse and rider, and the trainer's skills affect jump movements [22]. A limitation of this model is that these parameters cannot be included in the software program. The simulation program defines the total numerical error as the following: e ¼ h/t, where h is the integration step of simulation, that is, the velocity of the simulation jump, and t is the total duration of simulation (t z 1 s). The total approximate error is 0.001/1 ¼ 0.1%, and the maximum relative error (Erel) is 1%.
Table 1 Values of the angle between horse's neck and trunk in the key simulation points. P1
R1 R2 R3 H
P2
The accuracy of the simulation of the horse jump depends on two factors. First is the accuracy of the data describing initial conditions (such as the horse and rider's body dimensions and masses, angles between body segments, etc). The condition values, given by the simulation program at takeoff, can be changed to reflect measured errors of the rider and horse. However, these values can influence only the total amount of the calculated phenomena, that is, the initial angle changes occur only along y-axis. This phenomenon can be assumed to represent actual and measurable changes because the simulation is shown under real conditions. The second factor in determining accuracy is more important: it is the inaccuracy inherently resulting from using mathematical calculations to simulate motion. The size of such an error depends on the size of the integration used (Equations 24e27). This can also be set in the software program; in this model, the integration h ¼ 1.024 ms was used to obtain the graphs. 5. Conclusions The Figures and Table were based on data that were the output from program SIMULATION. The calculations in the simulation model supported the study's hypothesis that the horse accommodates incorrect rider movement through its neck movement, that is, the horse moves its neck in a specific direction to maintain balance despite rider error. Because the horse's neck is the only free-moving segment that can balance errors made by the rider, its mass and created internal forces are important. It is the only segment that can balance the error made by the rider. This simulation program allowed the examination of rider errors and asymmetries that cannot be seen clearly by the trainer's eye, or felt by a rider, and is also customizable to specific horses and riders because the human and equine anatomical and biomechanical characteristics can be modified to match actual real-life subjects. The program facilitates improved quality and effectiveness of the horse's training and jumping height ability by affording trainers better teaching methods. It has the potential to reduce trauma to the horse's body, reduce incidence of falls, and improve safety for both the horse and rider. In the future, the study should be further explored and developed and could be used to educate trainers and create new software programs that, after video recording, would show the rider's incorrect body positions. Acknowledgments The authors are grateful to the late Professor Vladimir Komarek from Czech University of Life Sciences Prague, who coordinated the research study and to Jiri Cerny for programming the code in Cþþ used in this project. Supplementary Data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jevs.2018.07.001. References
P3
Time (s)
Angle (deg)
Time (s)
Angle (deg)
Time (s)
Angle (deg)
0.150 0.150 0.150 0.150
57.6 57.6 57.6 57.6
0.381 0.361 0.341 0.341
69.8 71.3 71.2 71.2
0.582 0.590 0.604 0.549
123.3 120.8 114.4 123.3
Abbreviations: H, horse without a rider; P1, angle between the horse’s neck and trunk begins to differ between the three rider’s positions; P2, peak of CoG trajectory; P3, landing; R1, rider behind the horse's CoG; R2, rider on the horse's CoG; R3, rider in front the horse's CoG.
[1] Leach DH, Ormrod K, Clayton HM. Standardized terminology for the description and analysis of equine locomotion. J Equine Vet Sci 1984;16: 522e8. [2] Clayton HM. Time-motion analysis of show jumping competitions. J Equine Vet Sci 1996;16:262e6. [3] Clayton HM. Terminology for description of equine jumping kinematics. J Equine Vet Sci 1989;9:341e8. €llhorn WI, Peham C, Licka T, Scheidl M. A pattern recognition approach [4] Scho for the quantification of horse and rider interactions. J Equine Vet Sci 2006;(36):400e5.
P. Nemecek et al. / Journal of Equine Veterinary Science 70 (2018) 26e31 [5] Galloux P, Barrey E. Components of the total kinetic moment in jumping horses. Equine Vet J 1997;29:41e4. [6] Powers PNR, Harrison AJ. Influences of a rider on the rotation of the horserider system during jumping. Equine Comp Exerc Physiol 2004;1:33e40. [7] Patterson M, Doyle J, Cahill E, Caulfield B, Mccarthy Persson U. Quantifying show jumping horse rider expertise using IMUs. Conf Proc IEEE Eng Med Biol Soc 2010;2010:684e7. [8] De Cocq P, Muller M, Clayton HM, Van Leeuwen JL. Modelling biomechanical requirements of a rider for different horse-riding techniques at trot. J Exp Biol 2013;216:1850e61. [9] Lewczuk D, Słoniewski K, Reklewski Z. Repeatability of the horse’s jumping parameters with and without the rider. Livest Sci 2006;99:125e30. [10] Appendix - USDF Teaching Manual Articles. In: German National Equestrian (GNEF). The principles of riding: the official instruction handbook of the German National Equestrian Federation. London: Kenilworth Press Ltd; 1985. p. 121e5. zda; 1999. [11] Dusek J, et al. Horse breeding (in Czech). Prague: Bra [12] Powers PNR, Kavanagh AM. Effect of rider experience on the jumping kinematics of riding horses. Equine Comp Exerc Physiol 2005;2:263e7. [13] Zetterqvist-Blokhuis M, Aronsson A, Hartmann E, Van Reenen CG, Keeling L. Assessing the rider’s seat and horse’s behavior: difficulties and perspectives. J Appl Anim Welf Sci 2008;11:191e203.
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[14] Powers PNR, Harrison AJ. Models for biomechanical analysis of jumping horses. J Equine Vet Sci 1999;19:799e806. [15] Witte K, Schobesberger H, Peham C. Motion pattern analysis of gait in horseback riding by means of principal component analysis. Hum Mov Sci 2009;28:394e405. [16] Buchner HHF, Savelberg HHCM, Schamhardt HC, Barneveld A. Inertial properties of Dutch warmblood horses. J Biomech 1997;30:653e8. [17] Springings E, Leach D. Standardized technique for determining the center of gravity of body and limb segments of horses. J Equine Vet Sci 1986;18: 43e9. [18] Fredriksson I, Gernandt A, Hendlund G, Sederholm L. Horses and jumping. London: Pelham; 1976. [19] Fuss FK, Fuss AH. Angular acceleration in horse jumping. J Biomech 1998;31(Suppl. 1):180. [20] Peham C, Kapaun M, Licka T, Scheidl M. Motion pattern consistency of the rider-horse system. ISBS 16 Proc. https://ojs.ub.uni-konstanz.de/cpa/article/ view/1641. [Accessed 30 May 2008]. [21] Powers PNR, Harrison AJ. Effects of the rider on the linear kinematics of jumping horses. Sports Biomech 2002;1:135e46. [22] Dobes J. Riding: training a rider and a horse in jump riding, variety and dressage (in Czech). Prague: Olympia; 1986.