Determination of the Speed of Sound to Calculate Distances Through Firing a Ri e at 22 C at the Sea Level

Abstract

The purpose of this research is to analyze the speed of sound variations based on ring a ri e at a distance of 1240 meters at 22 ° C at the sea level in the province of Santa Elena, Ecuador. This is a nonexperimental cross-sectional study based on the data collected from 45 students, in addition, it has a descriptive design, and the measurements were taken using a chronometer during the 8 attempts each participant had. The main focus was the variation of time from the sparks ignition until the sound produced by the gunpowder explosion during each attempt. Instruments to establish meteorological conditions were used in order to measure wind time, distance, temperature, speed, and direction. The data analysis was aimed at determining the individual and general median time of shooting ight, having as a result 351,27 m/s. This value is close to the 350 m/s presented by Galileo Galilei and it remarkably di ers from the 372 m/s claimed by Donoso (2013) or the 330 m/s stated by the Military Education and Doctrine Command (2018). This research also aims at contributing to the military eld to calculate distances which allow the determination of the enemy´s position or the location of a missing combatant through ring a ri e. Since precision is a key factor in military operations, this investigation may be considered to design a battling eld simulator in which distances and direction are calculated through a gunshot.

Keywords

• Speed of sound
• Ri e
• Distance Calculation
• Simulator

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The military training process requires not only academic or physical preparation but also a solid commitment to serve the country which includes an adequate aptitude as a combatant. For these reasons, future o cers must know how to apply practical methods that involve simple calculations to determine distances and directions using all the instruments available. One example of military tools are ri es, these are part of shooting practices as well as real situation drilling against an adversary.

The FAL ri e is a Belgian battle weapon, it is chambered for the 7.62×51mm NATO cartridge. The word FAL comes from the French acronym \Fusil Automatique Leger" which is translated in English as Light Automatic Ri e [ 9 ]. It is illustrated in Fig. 1, and it is used during the military training at the Air Force Academy.

According to the Military Education and Doctrine Command of Ecuador [ 11 ], to appreciate a distance means to be able to calculate it, with the lowest possibility of a mistake from the observer to the target or between two points on the ground, which means that weapons could be used to measure indirectly the distance between two points on the ground. A military o cer must be able to know how to optimize resources, especially because of transportation issues, that is why distances can be determined through devices or by plain sight [ 11 ].

Taking into consideration the wide range of natural phenomena that may occur, Aristotle stated that the propagation of sound in the air is generated by a source, a vibrating body, whose movement disturbs the air causing its spread [ 2 ]. The trajectory of this movement can only be considered through the geometric distance commonly known as slope, which is the distance between two points measured as a straight line [ 1 ]. It is considered as a reference for sound spread, Aristotle produced sounds that under some conditions generated scattered sounds, creating an echo, this is considered as the re ection of sound, and for this reason, horizontal and vertical distances are discarded, as it is illustrated in Fig. 2 [ 2 ].

The interval measure of geometric distance is calculated based on the ight system, taking into consideration the time between the transmission and the reception of the echo [ 7 ]. This means that time continues during the emission of short pulses train of ultrasonic waves and their reception after been re ected by some object which is around [ 8 ]. According to the Military Education and Doctrine Command of Ecuador (2018), distances are classi ed as: proximate (100 mts), short (400 mts), median (800 mts) and long (more than 800 mts) and their calculation is a fundamental fact to optimize weapon transportation during combat.

There have been several attempts to calculate distances, Galileo Galilei measured the speed of sound in the air through a simple and precise form with the help of a colleague, who was an Artillery Captain. They red a cannon (loaded with gunpowder) and placed themselves at a distance of 3500 meters away on a nearby mount, they used a \pulsilogium", an invent of Galileo to measure time by counting the oscillations of a small pendulum [ 2 ].

After ring the cannon, Galileo saw the gunpowder blaze and counted the oscillations up to ten, until he heard the shot sound and stated that 350 m/s was the speed of sound in the air [ 10 ], nevertheless, further research in the same eld have determined that the speed of sound is 372 m/s [ 6 ]. It can also be con rmed that the sound travels through the air at a speed of 330 m/s, this enables the distance calculation if you can see and hear the action [ 11 ].

Another practical method to calculate the speed of sound is to determine the time from the moment the sparks caused by the shot ignite until the hearing the sound produced by the explosive expansion of gas. The number of seconds which are counted could be considered as the distance in hundreds of meters. For instance, if it stops at the count of three, the possible distance is 300 meters [ 11 ]. It is important to mention that the acoustic waves that come from a whisper or from scream travel at the same speed and it is called the \a" (acoustic) speed of sound. It depends on the air temperature, yet its propagation is from about 340 m/s under ordinary circumstances [ 12 ].

Navarro, Rios & Parra [ 7 ], stated that the speed of sound in the air at 0° centigrade is 331 m/s, therefore, the approximate speed in an environment which is at 20° centigrade is 343 m/s. This value is similar to the reference value which is 343 m/s in dry air at 20° centigrade. The state of art of this research takes into consideration the existence of shooting range simulators, yet there was none related to the calculation and determination of sound speed through ring a ri e. 2

Methodology and procedures This is a non-experimental cross-sectional research, the data were collected once, and the participants were 45 students and an expert ri e shooter. The objective of the experiment was to measure the time from the sparks ignition until the sound produced by the gunpowder explosion during each shot to calculate distances. This study took place in the province of Santa Elena, in the city of Salinas, at the Military Aviation School which is located in the parish of Chipipe. It was used a FAL ri e, which was chambered for the 7.62×51mm NATO cartridge, each student had 8 attempts at a temperature of 22° C at 7:30 in the evening, as it is illustrated in Fig. 3.

The speed of light (c) is faster in a vacuum which is equivalent to: c = 2:998x108m=s

The sparks ignition is immediate and it can be seen by the human eye, it represents the reference to start timing using the chronometer, it stops once the gunpowder explosion is heard. The distance is determined in exact coordinates using a topographic map and a GPS which measured 1240 mts; there were collected eight samples per student and; as a result, it was gathered 357 measurements and only 3 shots were dismissed. It is important to mention that the speed of sound is independent of the pressure, the frequency and the length of the waves [ 4 ], that is why these factors did not interfere with this research.

The measuring instruments used for this study were: topographical map, chronometers (CASIO), GPS (GARMIN Etrex), meteorological measuring equipment (VAISALA), which are illustrated in Fig. 4, Fig. 5, Fig. 6 and Fig. 7. The objective of the experiment was to measure the time from the sparks ignition until the sound produced by the gunpowder explosion during each shot to calculate distances. The results gathered after measuring all the shots are listed in Table 1.

Student 18 Student 19 Student 20 Student 21 Student 22 Student 23 Student 24 Student 25 Student 26 Student 27 Student 28 Student 29 Student 30 Student 31 Student 32 Student 33 Student 34 Student 35 Student 36 Student 37 Student 38 Student 39 Student 40 Student 41 Student 42 Student 43 Student 44 Student 45 3,57 3,79 3,53 3,63 3,53 3,32 3,42 3,6 3,4 3,55 3,6 3,5 3,6 3,38 3,44 3,5 3,76 3,65 3,71 3,53 3,82 3,47 3,42 3,51 3,65 3,65 3,65 3,65 3,6 3,66 3,7 3,72 3,63 3,55 3,71 3,52 3,64 3,58 3,52 3,49

4 3,8 3,61 3,4 3,37 3,2 3,5 3,4 3,52 3,6 3,45 3,44 3,5 3,54 3,49 3,51 3,61 3,54 3,44 NA 3,59 3,39 3,6 3,4 3,8 3,7 3,76 3,5 3,56 3,46 3,41 3,4 3,74 3,63 3,67 3,5 3,46 3,41 3,45 3,53 3,53 3,53 3,55 3,51 3,57 3,5 3,53 3,58 3,64 3,78 3,58 3,5 3,5 3,48 3,7 3,45 3,47 3,43 3,47 3,53 3,55 3,53 3,47 3,58 3,8 3,6 3,53 3,55 3,55 3,6 3,5 3,54 3,65 3,63 3,59 3,47 3,47 3,54 3,55 3,5 3,57 3,56 3,64 3,65 3,49 3,4 3,45 3,4 NA 3,79 3,52 3,51 3,58 3,53 3,51 3,69 3,61 3,66 3,6 3,47 3,51 3,5 3,52 3,62 3,75 3,59 3,5 3,46 3,37 3,37 3,35 3,5 3,9 3,81 3,82 3,54 3,42 3,63 3,45 3,42 3,75 3,54 3,58 3,52 3,43 3,42 3,62 3,29 3,73 3,43 3,5 3,56 3,59 3,59 3,53 3,48 3,43 3,44 3,52 3,67 3,6 3,41 3,5 3,5 3,64 3,65 3,64 3,54 3,63 3,64 3,64 3,64 3,44 3,53 3,46 3,54 3,52 3,4 3,41 3,51 3,75 3,67 3,6 3,4 3,56 3,43 3,41 3,48 3,56 3,53 3,44 3,64 3,47 3,5 3,44 3,56 NA 3,79 3,65 3,46 3,39 3,39 3,47 3,58

Final result 3,55 3,5 3,59 3,65 3,57 3,45 3,51 3,54 3,53 3,52 3,53 3,54 3,5 3,55 3,55 3,53 3,53 3,56 3,48 3,59 3,53 3,55 3,5 3,64 3,49 3,52 3,52 3,47 3,53

The time in seconds of the speed of sound in the air at 1240 meters was determined through the calculation of the individual median based on the eight attempts that each student had, afterward, it was established the group average having as a result 3,53 seconds. The formula for the calculation of the average speed was taken from the time and total distance. According to Bueche & Hecht [ 5 ] Vprom is a measure that indicates how fast an object travels in space and it is also a scalar value quantity, for instance, the speed of an object that takes the time t to travel a distance l is obtained by the formula: vprom = l t (1)

Once the formula was completed with the research values, l: 1240 mts and t: 3,53 sec, the result was:

This allowed the researchers to establish that the speed of sound at 22° C was 351,27 m/s.

In the case of the studies of Donoso [ 6 ], Sancho [ 10 ], Settles [ 12 ] and the Military Education and Doctrine Command of Ecuador [ 11 ], the calculation of the speed of sound was: 372 m/s, 350 m/s, 340 m/s and 330 m/s respectively. Nevertheless, it is important to mention that these investigations do not specify the temperature in which the shots took place. On the other hand, it was determined by R os, & Parra [ 7 ] and Cros & Ferrer-Roca [ 3 ] that the speed of sound in the air at 0° C is 331 m/s, therefore, within an environment which is at 20° C, it is 343 m/s. Bueche & Hecht [ 4 ], also described that the speed of sound a 0° C is 331 m/s, and that it increases along with the temperature in approximately 0.61 m/s per centigrade. Based on the data of the last two studies and according to the meteorological conditions of this research (22°C), it is added 1,22 m/s, having as a result 344,22 m/s. All the information related to these studies is explained in Fig. 8. During this research, the speed of sound was determined by ring a ri e at 22° C at the sea level, from a distance of 1240 meters and taking into consideration the 3,52 seconds from the sparks ignition to the sound caused by the gunpowder explosion, the result was 351 m/s. The studies conducted by Sancho (2014) and

Galileo Galilei did not include the temperature when determining the speed of sound, however, it could be said that both experiments took place approximately at a temperature of 20° C based on the results of the current research.

The Military Education and Doctrine Command of Ecuador [ 11 ] stated that the speed of sound travels at 330 m/s, yet Navarro, R os, & Parra [ 7 ], Bueche & Hecht [ 4 ] and Cros & Ferrer-Roca [ 3 ] described in their studies, that this speed may occur at a temperature below 0° C. Likewise, after ring a ri e the distance could be determined by counting the seconds until the gunshot is heard by considering each second as 100 meters, this means that if the count stops after 3 to 8 seconds, the approximate distance is 300 or 800 meters.

Donoso [ 6 ] determined in his eld studies that the median speed of sound in Chile is 372 m/s. After comparing the data presented in his research with the constant of 0.61 m/s per centigrade proposed by Bueche & Hecht [ 4 ], and in relation with the temperature in which this research took place, it could be said that Donoso´s investigation was at 68° C, therefore, this relation is discarded. On the other hand, Settles [ 12 ] claimed that the speed of sound of acoustic waves that come from a whisper or a scream travels at the same speed depending on the air temperature. Accordingly, to the data provided by Bueche & Hecht [ 5 ], it could be de ned that the approximate temperature in this experimentation was 15° C.

The speed of sound determined in this research was 351,27 m/s which di ers from some of the studies previously cited. However, it is convenient to consider the value obtained under this speci c meteorological condition (22° C at the sea level), especially in the military eld, since precision is a determining factor in all operations. By applying this procedure to calculate the distance by using a ri e, it would be easier to intercept enemy forces or locate a missing combatant. Finally, this research could be taken as part of the basis to create simulators for virtual battling elds, in which users may be able to calculate distances by using a rearm.

References

1. Almondi , C. , Ovidio , H.: Control horizontal, observacion, calculo y compensacion por m nimos cuadrados de una poligonal cerrada, m nimo ocho lados con detalle. Zona Cota Cota-predios UMSA departamento de La Paz . Ph.D. thesis ( 2015 )

2. Bermudez Moreno , S.A. : La caracterizacion del sonido como onda mecanica: una propuesta para la ensen~anza en la escuela ( 2016 )

3. Cros , A. , Ferrer-Roca , C.: F sica por un tubo. mide la velocidad del sonido en el aire y diviertete con los tubos sonoros ( 2011 )

4. y E. Hecht , F.B.: F sica General . McGraw-Hill/Interamericana Editores S.A , 1 edn . ( 2007 )

5. y E. Hecht , F.B.: F sica General . McGraw-Hill/Interamericana Editores S.A , 1 edn . ( 2007 )

6. Larra n Donoso, T.: Practica cient ca en america meridional: Experiencias sobre la velocidad del sonido en santiago de chile a nes del siglo xviii . Revista de Geograf a Norte Grande (56) , 189 { 206 ( 2013 )

7. NAVARRO , D. , RIOS , L.H. , PARRA, H.: Sensores de ultrasonido usados en robotica movil para la medicion de distancias . Scientia et technica 10 ( 25 ), 35 { 40 ( 2004 )

8. Parrilla , M. , Anaya , J. , Fritsch , C. : Digital signal processing techniques for high accuracy ultrasonic range measurements . IEEE Transactions on instrumentation and measurement 40(4) , 759 { 763 ( 1991 )

9. Raumer: Historia del fusil de asalto . clubensayos (12) , 2 ( 2013 )

10. Sancho , J.M. : En l nea. urlhttp://museovirtual.csic.es/ ( 2014 )

11. Sangolqui: Comando de educacion y doctrina militar terrestre, manual de instruccion indivudual de combate. urlhttps://www.comil3.edu.ec/assets/instructivo.pdf ( 2018 )

12. Settles , G.S. : Toma ultrarrapida de imagenes de ondas de choque, explosiones y disparos. Investigacion y ciencia p. 75 ( 2006 )