prepared for Irving Pollack by

CBA/Coto Sports Research Center

September 1980

In physical science, an essential step in the direction of understanding is to find principles of numerical reckoning and methods for practical measurement. In 1889, Thomson expressed the important relationship of numerical quantification to understanding:

"When you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meager and un¬satisfactory kind; it may be the beginning of know¬ledge, but you have scarcely, in your thoughts, advanced to the stage of science, whatever the matter may be..."

INTRODUCTION

Locomotion of any biological system is a complex mechanism, which depends on the coordinated interaction of many different subsystems. The basic unit for locomotion is the skeletal musculature, which receives neuronal input through the spinal system. It has been demonstrated,  that the spinal system contains a central steeping generator which can operate autonomously to produce locomotor patterns. However, under normal conditions, this generator interacts both with the periphery and with systems located in higher brain centers to transmit locomotor information to the musculature. The outcome of muscle activation is the production of mechanical forces and moments. If certain magnitudes of forces are applied to the limb segments in an appropriate temporal sequence, the body as a whole is translated and the individual segments undergo rotations and relative translations. The ultimate expression of this integrated activity of the system is one of the several characteristic movement patterns termed a gait. A simple diagram of this is given in Figure 1.

Figure 1

An analysis of locomotion, then, demands neural, muscular, and mechanical considerations. Furthermore, these considerations must be at both the experimental and theoretical level. The former provides the relevant empirical data for the physical phenomena, while the latter enables formalization of the concepts and in many cases provides new insights into the physical phenomena.

Since the classic work of Sherrington, many valuable studies of the neural and muscular aspects have been done, at both the experimental and theoretical level for several types of mammalian locomotion; a survey of these has been given by Griliner for vertebrates and by Wetzel and Stuart for the cat. For bipeds, a significant number of biomechanical studies have been done. Experimental work has yielded a wealth of information concerning phase durations, joint and angle excursions, as well as, force and moment profiles. Control theorists have been able to construct mechanical models of biped locomotion based on these data, and through these models to uncover certain fundamental principles under which the locomotor system operates.

In the case of quadruped locomotion, biomechanical knowledge is more limited. Several experimental studies have been done to extract the kinematic features of locomotion. Kinetic data, however, are limited to the pioneer work done by Manter in which spring platforms were used to measure the vertical and longitudinal components of the ground reaction force exerted on the cat during walking. Unfortunately, it is not known how these force parameters vary with velocity, nor is it known what they look like for gaits other than walking. The absence of such data severely restricts the level of sophistication possible for quadruped mechanical models.

Fredricson very recently introduced a method to analyze kinematic parameters in equine locomotion. However, the method utilized two-dimensional, high-speed cinematography from which the kinematic parameters were extracted. In the present study, three-dimensional, high-speed cinematography was used to analyze Thoroughbred racing with the data collected on several different classes of Thoroughbred horses:

1. The best horse - Spectacular Bid
2. A grass runner (happened to be injured at the time) - Clayton Delaney
3. Other turf horses of varying ages, sex, and running at different speeds

METHOD

The analytic technique utilized cinematographic data collected simultaneously from multiple high-speed motion picture cameras. This technique of three-dimensional biomechanical analysis involves three distinct phases: cinematographical, digitizing, and computational.

In the cinematographic phase, the subject and a set of known points referred to as test points are filmed simultaneously from several angles. The set of known points are objects in the field of view having accurately determined 3-D coordinates and are used to calibrate the field of view. This system incorporated three Photosonic high-speed cameras stationers at different locations. These cameras incorporate pin registration for advancing the film and a variable shutter, which was set to 90 degrees, to eliminate any blur at 500 frames per second speed. A light emitting diode driven by a fixed crystal frequency was utilized to calculate exact film speed. The stability of the film speed was measured as better then 0.1% during the analyzed sequences.

The film record from a single camera of a given activity is called a view. The three simultaneous views comprise a sequence, which is the basic unit of 3-D analysis. While only six known test points in the field of two different views are necessary to perform a 3-D analysis, additional camera views and test points enhance the accuracy of the technique.

In this study three camera views and twelve test points were used for each sequence. The test points consisted of twelve 2 1/2 inch spheres securely fixed to a 3' x 3- x 4" cube. Eight points were placed at the corners of the cube and four in the interior. The array was constructed from aluminum tubing. Among the advantages of this arrangement was the ease with which the cube could be assembled, disassembled, and transported. Its shape was also highly reproducible between each assembly/disassembly session. 

Additionally, for the analysis of Spectacular Bid, test points were defined by known locations along the rail and on the rail supports.

In order to avoid having the subject obscure the test points, the following procedure was utilized. The test point apparatus was placed on the track in the approximate location where the horses would gallop, and was oriented so that all cameras had an unobstructed view of all the points. The cameras were rigidly fixed and focused and the apparatus was filmed. Next the test point apparatus was removed and the horses were filmed at 200 frames per second, as they ran across this path. After the calibration points were filmed, the cameras were not moved or refocused until the end of the activity.

The digitizingphase involves the conversion of cinematographical data to numerical information, which is stored in the computer for the subsequent computation phase. 

For each view, the film is projected, one frame at a time, onto the back of a ground-glass screen, while the person digitizing is situated on the other side. As each frame is projected, the points of interest on the image (joint locations and test points) are touched with an electronic stylus and the “X-Y” position is determined. For each point, the result is a “U-V” pair (“U” is horizontal and “V” is vertical), which is automatically transmitted to the computer. The digitized image is simultaneously displayed on a CRT for visual feedback and verification of correctness. This same sequence of events is repeated for each frame. For the present study, the digitizing order began with the twelve test points, followed by the 30 data points for each frame of the film. Figure 4 illustrates the points traced on the horse. In addition to “X-Y” coordinate data, a synchronizing event (such as hoof impact) was also included in the stored data. This information was used later during the 3-D calculation phase.

Once all views from a given sequence are digitized, the computational phase begins. In this phase, two or more sets of two-dimensional relative coordinates (U-V) are converted to a single set of absolute three-dimensional coordinates (X-Y-Z) utilizing a direct linear transformation method. Briefly, this transformation involves the solution of a set of simultaneous equations, which relate known quantities (3D locations of test points and relative locations of test points and data points) to the desired unknown quantities, that is, the 3-D coordinates of the data points. If more than two views and/or more than six-test points are used, this set of equations becomes over-determined and a best fit is computed using a least squares method. Additional test points and views enhance the accuracy of the technique. 

The first operation in the computation phase is called time matching. The film speed of each camera is accurately determined from timing marks on the film. Using this information the time of each frame relative to the synchronization event (the same time in all views) is known. Since the film speeds of different views need not be identical, frames for different sequences may not correspond to the same time. A time interval was selected, in this case every 10 milliseconds, and the “U-V” information was interpolated to those times for all views using a linear interpolation. In this manner, all views were synchronized to an identical time base.

With “U-V” information time matched, 3-D coordinates were computed for each point at each time using the direct linear transformation. Following computation of the 3-D coordinates, a smoothing process is performed. The purpose of this smoothing is two fold: (1) to remove random error (which results primarily from digitizing) from the data and (2) to compute the first and second derivatives of position as a function of time (velocity and acceleration). When the computation phase is complete, all quantities are stored in a standard format for subsequent listing, plotting, or display in stick figure format.

CALIBRATION OF 3-D TECHNIQUE

In order to determine the accuracy of the technique, a method was used to calculate the coordinates of points for which 3-D coordinates were already known. A comparison of the computed 3-D coordinates and the known coordinates would demonstrate the accuracy of the technique. A specially machined apparatus consisting of posts of varying heights fixed onto a metal base at 2" intervals was used in this test. The 3-D coordinates for the posts were known to 1/1000 of an inch. The array was photographed from two views. Six of these known points were considered as unknown and the technique was used to compute their 3-D coordinates. The largest error was .035 inches with an average of only .017 inches. This degree of agreement indicates that the method demonstrates an acceptable level of accuracy. As the field of view in the horse study is about 30 times larger than in the test just described, the estimated error is about 30 times larger for the horse study. However, the estimated level of accuracy (average error about .5 inch or 1.25 cm) is more than sufficient to perform this study. This method of error estimation was verified during calibration of the test point apparatus, which was determined using this technique in a manner similar to that described above.

DATA COLLECTION

Much of the cinematographical data was collected at Calder, Gulfstream, and Monmouth Park racetracks in April of 1980.

Spectacular Bid was filmed at Monmouth Park on Aug. 16, 1980. Each horse was photographed from three views as it ran at a full gallop. A coordinate system was chosen such that “X” points towards the direction of the forward motion of the horse, “Y” points up, and “Z” points across the track (from the infield toward the stands). Prior to each filming sequence, the test point array was moved onto the track, photographed from each camera view, and then moved out of the way. The cameras were securely positioned so that no camera movement occurred between the filming of the cube and the filming of the horse.

RESULTS

The results of this study are presented in three different formats. The first is a stick figure representation of the motion of each of the horses in an orientation such that the horse is running from left to right across the page. Figure 6 is an example of the motion of one of the horses displayed in this mode.

Figure 6

Notice in this figure how Spectacular Bid does not display his body up and down. He galloped like an arrow. 

Note that the lines connect actual body joints and, thus, represent the bone structure of the horse, rather than an outline of the body of the horse. The head is represented by a single line from nose to ears and is not connected to the body so that the number of lines on the figure of the horse is reduced in an effort to enhance clarity especially when multiple images are presented in the same figure. Another format used to present results is that of the graph or “X-Y” plot of the biomechanical data. Figures 7 through 13 show the various parameters that were discussed in this study, and include the displacement of various body joints and segments during the stride. The third type of format used to represent the results of this study is that of the gait analysis. Four of these analyses are included for horses for which a full stride of data was collected. The footfall pattern and the data measured in the 3-D analysis are utilized in a gait analysis, which determines the following parameters:

1. Various timing and displacement relationships for the forelegs, the hindlegs, and the legs considered in ipsilateral (same side) and diagonal pairs
2. The stance and swing phase for each leg provided information on the stride as a whole (e.g. stride length, duration, and period of suspension). The data is reported by absolute magnitude and by percentage of a full stride, the latter being useful in comparing animals running at different velocities. A gait analysis is a good summary of the locomotion pattern of a horse since it most directly relates to the horse's efficiency in propelling itself along the track. To better understand just what factors make one horse more efficient or faster than another requires an examination of the more complex relationships between the various body joints and limbs especially in the patterns and magnitudes of accelerations produced by muscular action. For this, graphed results of displacement, velocity, and acceleration are most useful.

GAIT ANALYSIS

In the following discussion, information for Spectacular Bid is summarized in Table 2; Midnight Mystique in Table 3; Arkansas Bev in Table 4; and Clayton Delaney in Table 5. It is observed that Spectacular Bid, our model horse, exhibits the longest stride length (899 cm) of any of the horses, which is a full 20% longer than the next best horse. Despite having a longer stride duration, (indications are that Bid was being held back), this long stride length resulted in the highest average velocity of the group (2024 cm/sec). Of the other three horses, Midnight Mystique demonstrated the highest average velocity (1941 cm/sec), followed by Arkansas Bev (1864 cm/sec) and Clayton Delaney (1746 cm/sec). The last horse was running on grass, while the others ran on turf, so a direct comparison of velocity is probably invalid. Midnight Mystique achieved a high velocity, through a significantly, shorter stride duration (.37 sec, vs. .40 sec for the other two horses), despite having a shorter stride length than Arkansas Bev . Since Mystique is a smaller horse than Bev, the shorter stride length is not unexpected. It appears, however, that Bev is not running at full speed (this was indicated by the trainer at the time of filming). If a similar, stride duration could be achieved Bev could have an average velocity significantly greater than Mystique (2016 cm/sec - close to that of Spectacular Bid). Clayton Delaney exhibits the shortest stride length, and a stride, duration similar to that of Bev. Again this may be partially due to the grass track, however it was subsequently learned that Delaney was experiencing shoulder problems, and this may be the prime factor behind the short stride and low velocity.

In a comparison of the stance (ground contact) phase and swing (airborne) phase for individual limbs for the various horses, Midnight Mystique exhibited the shortest stance phase (in both time and percentage) of any horse. Grillner (9) indicates that the higher the speed of the animal, the higher the impulse (force times time) and thus the shorter the stance phase for each foot contact. The limiting factor in the animal's ability to produce a high impulse is the individual limb structure and muscular strength. It appears that Mystique is more closely approaching this physiological limit than any of the other horses in the group, as indicated by the short stance durations (.06 to .08 sec). Thus in considering the potential of the various horses, Mystique appears to be running near maximum speed, while the others, assuming that they have the ability to similarly shorten their stance phase through an increase in impulse (i.e. exerting more force) show a potential for an increase in speed of at least 10%. In that case, Bev would be running considerably faster than Mystique, and Delaney only slightly slower than Mystique. Spectacular Bid would still be in a class by himself, a full 10% faster than Bev.  It is useful to compare other aspects of the gait analysis, so as to determine what relationships in the footfall pattern most influence efficiency in running. Although the magnitude of the fore step length varies among the horses, fore step length, as a percentage of stride length is almost constant. Hind step length shows a large variation in both magnitude and as a percentage of stride length. Since a larger proportion, of propulsive force is exerted by the hind legs, this variation should be of concern in selecting for efficiency of motion. Spectacular Bid demonstrates the longest hind step, the largest percentage of stride length in the hind step, and the longest hind step duration. These combined characteristics result in propulsive force being applied over a larger part of the stride than with the other horses. This in turn results in more efficient propulsion. The horse that most closely resembles Spectacular Bid in this respect is Arkansas Bev .

Another factor of concern in stride efficiency is overreach. This is the distance beyond the point of foreleg lift that the same side (ipsilateral) hind leg strikes. Obviously it is directly related to the speed of the horse, but by comparing the percentage of overreach length and duration to total stride length and duration, relative efficiencies in this area can be compared. A long overreach indicates good hind leg extension, which in turn indicates a good use of the large muscle groups in the area of the back and rump. Spectacular Bid again shows his superiority with both the longest overreach and the highest percentage of the overreach to the total stride when compared to the group of horses.

Spectacular Bid also shows the greatest degree of bilateral symmetry, which may be a factor in efficiency of stride. All horses favor one side or the other in normal locomotion and this bias is referred to as footedness. In this study, Bid and Bev are left-footed, while Mysitque and Delaney are right footed. However, if one side is considerably less efficient than the other side, then the horse cannot achieve maximum propulsion through the entire stride. Mystique shows the greatest degree of asymmetry in the area of overreach and may be an area for improvement. Bev again shows the most similarity to Bid in this aspect of gait.

A final concern in comparing the gaits of the various horses is the suspension phase, which is the time the horse has no ground contact. It is probably advantageous to minimize this time since, while the horse is airborne, he cannot be exerting propulsive force. Also, excessive time in suspension may indicate misdirected force (i.e. too much vertical and insufficient horizontal). However, one must realize that certain positive aspects of efficient locomotion tend to lengthen suspension. The first is good hind leg extension, which is the movement of the hind legs forward during suspension in preparation for the next stride. The second is that increased impulse (higher force between the hoof and ground) results in a shorter time on the ground and a longer time in the air. Spectacular Bid demonstrates the longest suspension, both in magnitude and percentage, which is probably due to his excellent hind leg extension.

Clayton Delaney shows the shortest suspension, but has poor hind leg extension (smallest percentage of overreach). Arkansas Bev shows perhaps the most efficient suspension phase combining good overreach with a short time in the air. With greater impulse and at a higher speed, however, this time might well lengthen and, thus, it is difficult to draw any direct conclusion in comparison to Spectacular Bid. Midnight Mystique already demonstrates a high impulse (short stance phase), and thus any efficiency increase would have to come through an increase in hind leg extension and a corresponding increase in suspension.

KINEMATICS

The discussion of gait analyses thus far has considered only the horizontal component of the motion of the feet. Brief consideration should be given to the vertical motion of the feet during the execution of a typical stride since this will yield additional information on how each of the horses uses the various limbs during locomotion. Figures 7 to 10 show, for each of the horses, the vertical displacement of the four hooves as a function of time over a full stride. The general pattern for each hoof is the same: ground contact, followed by a rapid raising of the hoof, followed by a forward motion of the hoof during which the height of the hoof may vary, followed by a rapid lowering of the hoof, and ground contact. Within this general pattern, several distinct variations were noted. Midnight Mystique, for example, shows a high degree of symmetry in the motion of the fore legs and the hind legs. Also, the peak height of each foot is almost identical (Figure 8). Arkansas Bev shows good symmetry between the fore legs, but the left hind hoof demonstrates a slow, steady descending pattern, while the right hind hoof performs a hitch followed by a more rapid descent (Figure 9). Spectacular Bid shows this same hind hoof pattern with an even more exaggerated hitch, while his front hoofs show a higher degree of asymmetry (Figure 7). In fact, his right fore hoof reaches a peak height of 51 cm while his left fore hoof reaches a peak height of only half that value. This may indicate a strong footedness in his gait, or it may perhaps reveal that he is favoring the left foreleg for some unknown reason (perhaps pain or discomfort). Clayton Delaney (Figure 10) shows a lower magnitude of vertical hoof motion, which may be due to the grass track. Symmetry is high for the fore legs, less so for the hind legs.

In addition to the motion of the hooves, it is valuable to consider the motion of other major body points during the stride. Figures 11 through 13 depict the linear displacement (vertical vs. horizontal) of the upper body points for three of the horses (all except Spectacular Bid). The magnitude, of the horizontal and vertical scales, are different for Clayton Delaney than for the other horses because of being filmed with a different origin of the test points. Comparison is still valid as the range of values for the vertical and horizontal axes are the same. Motion of the body points for all the horses follows the same general pattern with the head (nose and ears) showing the most vertical motion through the stride and the withers showing the least. Midnight Mystique and Clayton Delaney demonstrate considerably more vertical motion in the back and rump than does Arkansas Bev . Reducing the up-and-down motion of these heavy body parts minimizes the motion of the center of gravity and, thus, conserves energy and increases efficiency. Another interesting observation is the lack of smoothness in the motion of the shoulders for Clayton Delaney as compared to Bev and Mystique, especially for the right shoulder. It was learned after filming that Delaney was experiencing soreness in the shoulder, and this may well be indicated by the differences observed in the motion curves.

CONCLUSIONS AND RECOMMENDATIONS:

The data collected and analyzed in this study demonstrates that differences in locomotion patterns between horses can be measured in a valid and consistent way using the methods employed. Furthermore, measured differences can be related to the goal of maximizing the speed of the horse and the overall efficiency of motion. In a specific sense, this study showed that several unknown horses (Midnight Mystique, Arkansas Bev , and Clayton Delaney) could be compared to a model horse (Spectacular Bid) in a practical and straight-forward manner. This comparison demonstrated which of the horses (Arkansas Bev ) showed the most potential for being able to approach the performance of the model horse and which other horse Midnight Mystique) was near the limit of its potential development.

These analyses performed many times in many races.  The results gave Mr. Pollack an advantage and information to make his bets. And he made millions using our analyses.