Fast Fourier transform analysis as a new tool for Olympic rifle coaches

Original Article Fast Fourier transform analysis as a new tool for Olympic rifle coaches Proc IMechE Part P: J Sports Engineering and Technology 2017, Vol. 231(1) 63 67 Ó IMechE 2016 Reprints and permissions: sagepub.co.uk/journalspermissions.nav DOI: 10.1177/1754337116639482 journals.sagepub.com/home/pip Grzegorz Gladyszewski 1 and Bozena Gladyszewska 2 Abstract The aim of this study was to examine the possibility of using data collected with an electronic training system to determine the influence of a shooter s heartbeat on shooting precision. Shooting sessions of a rifle in prone position were studied with the use of an electronic training system. As a case study, results of an experienced shooter were analyzed. Fast Fourier transform was applied to raw data extracted from the system and then results were interpreted. The spectrum obtained revealed a wide peak at the frequency f = 2.6 Hz that was considered as the second harmonics of the average frequency corresponding to the heartbeat decreasing down to 69 beats/min when releasing a shot. The session finished with a very modest score of 611.3 points. When a small intentional change in the shooter s equipment (a sling position) was introduced, the spectrum obtained did not reveal any peaks and the shooter reached a much better score of 621.8 points. The use of fast Fourier transform analysis is proposed as a new tool for Olympic rifle shooters and coaches. This new tool does not require any complicated procedures and provides quantitative information on the influence of a heartbeat on the stability of a shooter s aim. Keywords Olympic shooting, shooter s performance, heartbeat, coaching, rifle Date received: 18 December 2015; accepted: 23 February 2016 Introduction Shooting sport events have been present in the program of the Olympic Games from the very first modern Olympic Games in Athens, 1896. 1 All shooting targets used in the Olympic precision shooting competitions, both for the rifle and the pistol, are composed of black circles and rings, in the middle of which the smallest one signifies 10 points (or the so-called inner 10). In all these competitions, weapon precision is a key to success. For example, in rifle competitions, a small caliber rifle (cal. 5.6 mm) is used. The shooting distance measures 50 m while the bull s-eye ring diameter is only 10.4 mm. To be in the forefront and to count on entry to the finals, the player has to hit the bull s-eye practically every time. This requires not only immense concentration of the athlete but also great rifle precision. When using selected ammunition, modern rifles provide the perfect score, of course assuming a totally motionless rifle (standard deviation of the impact point on a target is only about a few millimeters), providing 10 shots edge-to-edge grouping below 13 14 mm. The real score is, therefore, determined by two predominant factors: (1) rifle-ammunition precision and (2) a shooter s aiming and action precision. In fact, there are many other factors like wind and light conditions that influence the final effect, but the influence of these parameters on a shooting score is beyond the scope of this article. It is relatively simple to select the best ammunition for a chosen rifle, as the main producers provide such a possibility at their factory ranges, usually fixing a rifle in a vice and allowing for the testing of different lots of ammunition. In such conditions, the influence of different technical parameters on the shooting precision can be studied. 2 The second factor, a shooter s aiming and action precision, is much more difficult for a coach to judge. It becomes particularly difficult for the prone shooting position (60 shots in men s prone position, and 20 and 40 shots in three position events played by women and men, respectively). Relationships between 1 Department of Applied Physics, Lublin University of Technology, Lublin, Poland 2 Department of Physics, University of Life Sciences in Lublin, Lublin, Poland Corresponding author: Grzegorz Gladyszewski, Department of Applied Physics, Lublin University of Technology, Nadbystrzycka 38, 20-618 Lublin, Poland. Email: g.gladyszewski@pollub.pl

64 Proc IMechE Part P: J Sports Engineering and Technology 231(1) postural balance and shooting accuracy were investigated for both novice 3,4 and experienced shooters. 5 7 Considering a top shooter performance, the center of a momentary aiming point scatters on the target inside a circle of a diameter below 10 mm. This means that movement of a rifle s front sights or a barrel end, often controlled by coaches, is inside a circle of a diameter below 0.2 mm and obviously is hardly observable. Therefore, many shooters and coaches use electronic training systems that allow precise observation (and data collection) of the movement of an aiming point as a result of the shooter s aiming procedure. In this work, the SCATT 8 system has been used to collect data of training sessions. The system (like other systems) provides many useful parameters characterizing the aiming procedure. However, we show that extracting raw data from the system allows more advanced analysis of the aiming process by the use of the fast Fourier transform (FFT). 9 Figure 1. Screenshot of one aiming procedure performed by the shooter with the use of the SCATT electronic training system. Materials and methods Training sessions of a 60-shot rifle prone position were conducted with the use of the SCATT system. 8,10,11 The system operates in the following way: an infrared optical sensor fixed to the rifle barrel detects signals from infrared emitters placed closely to the target and measures the barrel alignment during aiming and actuation of the trigger system. Data of a trace of the point of the aim is not only followed in a real-time mode (as displayed on a monitor screen) but also stored in computer memory. Information on horizontal and vertical coordinates gathered in intervals of 0.005 s is, therefore, available for further treatment. The system allows the analysis of many parameters characterizing the accuracy of aiming that are useful for pistol and rifle shooters as well as for their coaches. However, apart from the standard data, by the use of a simple visual basic application provided by the system, one can extract data in the following format: time, x coordinate, y coordinate. Data in this format have been used for the analysis described in this work. As a case study, training sessions of a Polish National Team shooter (with the personal best of 624.4 points scored during regular International Shooting Sport Federation (ISSF) competitions) were examined. To perform FFT analysis, the software Origin 8.1 12 was applied. In spite of the fact that the SCATT system provides numerous parameters of a training session that are built-in to the system, there is still information hidden in the raw data. Figure 1 presents a screenshot of one aiming procedure performed by the shooter. The trace of the point of aim forms a complex curve and therefore it is not at all easy to perform a detailed analysis of the aiming procedure just by eye. However, by extracting raw data, one can draw dependences x(t) and y(t), where x and y are the horizontal and vertical coordinates, respectively, and t refers to the time. Figure 2 Figure 2. x(t) and y(t) dependences of the exemplary aiming procedure shown in Figure 1. The dependences have been shifted for clarity by 10 and 20 mm, respectively. shows the dependences of the exemplary aiming procedure from Figure 1. One can state that from the coach s point of view, indeed information on the aiming point movement is detailed and visible now, but extracting any useful conclusions is still hardly possible. We apply FFT, a tool that is frequently used for a signal treatment and analysis. 9 It is beyond the scope of this article to present the theoretical background of the FFT analysis. Therefore, we recall only that FFT analysis allows one to get information about the magnitude of harmonics of characteristic frequencies hidden in the signal. In very simple words, it works like so-called spectrum analyzers present in most of our domestic audio devices. The SCATT optoelectronic system provides data that are not free from errors. Zanevskyy et al. 13 found three types of errors in defining the coordinates of the aiming point on a SCATT target. All of these errors concern absolute values of coordinates (asymmetry of the left-to-right and up-to-down results, absolute errors in each direction, and the dependence of the error upon the distance to the center of the target). Fortunately,

Gladyszewski and Gladyszewska 65 Figure 3. FFT spectra obtained for changes of horizontal coordinates of the aiming point (a) for the first training session with a score of 611.3 points and (b) for the second session with a score of 621.8 points. FFT analysis is particularly sensitive to periodic changes present in the analyzed data, whereas amplitudes of these changes influence the results insignificantly. Therefore, the reported SCATT system errors are not an issue for the method proposed in this work. The good news for coaches is that they need not bother about the theory of FFT, as there exists easily accessible software that allows one to import SCATT raw data and, after clicking on the FFT option in the menu, instantaneously produces the desired spectrum. The above procedure has been applied to compare two training sessions of the same shooter: the first session when a quite unsatisfactory SCATT optoelectronic score was achieved (611.3 points) and the second session when changes in the shooter s sling position were ordered by a coach (changes based on the applied FFT analysis) and a clear improvement of the SCATT optoelectronic score was observed (621.8 points). All the experiments reported in this article were performed in accordance with the ethical standards of the Helsinki Declaration. Informed consent was obtained from the participant. Results and discussion Figure 3 presents spectra obtained for changes of horizontal coordinates of the aiming point for the first training session (score 611.3 points, Figure 3(a)) and for the second session (score 621.8 points, Figure 3(b)). For the vertical coordinates, the spectra were very similar to each other and no clear peaks are present. This may suggest that the heartbeat has significant influence mainly on horizontal aiming coordinates. In rifle shooting, a sling is attached to the rifle, providing greater stability of the hold. However, the rifle still has higher freedom of movement in the horizontal rather than vertical direction. This often results in so-called wobbling and is particularly inconvenient for shooters in kneeling and is also not negligible in prone position. The spectrum obtained during the first training session reveals a wide peak at the frequency f = 2.6 Hz. The very first interpretation of the appearance of this peak, which immediately comes to mind, concerns eventual correlation with frequency of the shooter s heartbeat. As the frequency f = 2.6 Hz corresponds to the pulse at 156 beats/min, which is obviously too high a value, the peak should be considered as the second or eventually the third harmonics of the basic frequency equal to 1.3 Hz (78 beats/min) or 0.87 Hz (52 beats/ min), respectively. Surprisingly, when we take a look at changes in the speed of the aiming point movement, directly accessible from the SCATT system (see Figure 4 where a screenshot of the corresponding window of the program is shown), one finds the heartbeat equal to about 69 beats/min which corresponds to the frequency 1.14 Hz. This value differs considerably from those calculated from the FFT analysis. However, it is necessary to note that the frequency calculated from the dependence shown in Figure 4 is obtained for the last two heartbeats before releasing a shot, whereas the FFT analysis gives the average frequency over the last 5 s of aiming. Therefore, it seems reasonable to consider the peak at 2.6 Hz as the second harmonics of the average frequency corresponding to the heartbeat

66 Proc IMechE Part P: J Sports Engineering and Technology 231(1) Figure 4. Changes in speed of the aiming point movement in the last 2 s before the shot, directly accessible from the SCATT system. decreasing down to 69 beats/min when releasing a shot. According to Reinkemeier et al., 14 an experienced shooter uses the breathing to slow down the beating of the heart during the aiming phase. Such breathing control results in the decrease in a heart rate even from 120 to 70 beats/min. The shot release automatically occurs between heartbeats during the diastole phase of the cardiac cycle. 15 This is in agreement with the results presented in Figure 4. As mentioned above, this first training session led to the quite unsatisfactory score, 611.3 points. However, the performed FFT analysis showing significant influence of a heartbeat on collected x(t) profiles gave to the coach an indication that the influence of this factor should be reduced by implementing changes in the shooter s position. The shooter s pulse is often transmitted to the rifle via the shooting sling supporting the rifle. The sling is attached to the shooter s arm close to the biceps and risks pulling on the brachial artery. 11 Therefore, before the second training session (which started about 10 min after finishing the first session), a small change in the sling position was introduced. The best solution to avoid the pulse beat being transferred along the sling is to move the upper arm sling loop slightly down toward the elbow. 11 No other changes in the shooter s position were ordered before the second SCATT shooting session. As already mentioned, the second training session provided a much better score of 621.8. After the second training session, the following FFT analysis was performed in the same way as for the first one. In this case, the spectrum obtained did not reveal any peaks (see Figure 3(b)), indicating that the introduced changes in the sling position provided the desirable effect. It is necessary to stress that, in spite of the fact that the SCATT system provides very detailed information on the shooting parameters, the evidence of influence of the heartbeat on the aiming process has become possible only after performing the FFT analysis described in this work. Conclusion This work shows that by applying FFT along with easily accessible software, it is possible to analyze in detail the shooter s training sessions. This new tool does not require any complicated procedures and provides not only qualitative (as it was only possible up to now) but also quantitative information on the influence of a heartbeat on the stability of a shooter s aim. In principle, during training sessions, it is also possible to control a heart rate with additional devices (e.g. attached to the shooter s ear); however, one should note that this could be treated by the shooter as a distracting element and therefore influence a score. The described method offers the possibility to control a shooter s position within a few minutes after finishing the chosen part of a training session and to introduce necessary changes. The method is particularly useful when coaching top rifle prone shooters; however, it can also be applied for other shooter s positions, as well as for pistol shooting. Taking into account that the method allows for the study of the influence of a heartbeat, we suppose it should be very useful for biathlon shooters and coaches. Acknowledgements The authors thank Professor Keshra Sangwal for his encouragement and careful reading of the manuscript. Declaration of conflicting interests The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The author(s) received no external financial support for the research, authorship, and/or publication of this article. References 1. Official statutes, rules and regulations. Mu nchen: International Shooting Sport Federation, 2012. 2. Gladyszewska B, Baranowski P, Mazurek W, et al. External barrel temperature of a small bore Olympic rifle and shooting precision. Biol Sport 2013; 30: 47 50. 3. Mononen K. The effects of augmented feedback on motor skill learning in shooting. Jyvaskyla: Jyvaskyla University Printing House, 2007. 4. Mononen K, Konttinen N, Viitasalo J, et al. Relationships between postural balance, rifle stability and shooting accuracy among novice rifle shooters. Scand J Med Sci Sports 2007; 17: 180 185. 5. Lakie M. The influence of muscle tremor on shooting performance. Exp Physiol 2010; 95: 441 450. 6. Goonetilleke RS, Hoffmann ER and Lau WC. Pistol shooting accuracy as dependent on experience, eyes being opened and available viewing time. Appl Ergon 2009; 40: 500 508.

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