The Study of the Kinematic Parameters of a Vehicle Using the Accelerometer of a Smartphone

Transcription

1 The Study of the Kinematic Parameter of a Vehicle Uing the Accelerometer of a Smartphone Marin Oprea Faculty of Phyic, Univerity of Bucharet, Bucharet-Magurele, Romania opreamarin007@yahoo.com Abtract The modern approach to the teaching and learning of Phyic involve the extenive and creative ue of martphone. Due to the enor embedded in thee mobile device one can develop a wide range of Phyic experiment. One of the enor that i mot extenively ued for experimental purpoe i the accelerometer. In thi tudy, I aim to highlight and illutrate the didactic importance of thi enor for recording and analying the movement of a vehicle, in order to etablih it motion parameter: acceleration, average peed, ditance. The experimental data flow regitered by the enor wa recorded with a free mobile application and exported to an Excel preadheet for a detailed analyi. Keyword: Accelerometer, Smartphone, Uniformly accelerated motion, Velocity, Slope, Ditance 1 Introduction The importance of the mart phone in the field of education, particularly in the teaching of Phyic, ha become acknowledged in the recent year (Countryman, 014; Kiner, 015; Monteiro et al, 015; Monteiro et al, 015; Kuhn and Vogt, 013). A erie of tudie have pointed out that, due to it multiple integrated enor, the martphone i an eential tool for a wide variety of Phyic experiment, particularly in the field of Mechanic, where the ue of the accelerometer play an important role (Kuhn et al, 014; Vogt and Kuhn, 013; Catro-Palacio et al, 013; Tuet-Sanchi et al, 015; Chevrier et al, 013). In thi tudy we focued on the ue of the martphone integrated accelerometer to tudy the motion of a vehicle (a car) on a horizontal rectilinear road and alo while acending and decending, with a contant acceleration, from the lope of a bridge. Vehicle motion on a horizontal rectilinear road The firt part of the meaurement wa performed on a horizontal road with an approximate rectilinear length of 500m..1 Uniformly accelerated motion On the elected rectilinear part of the road the vehicle accelerated uniformly from 0 to 60 km h (Fig.1). Figure 1. Uniformly accelerated motion

2 The 11 th International Conference on Virtual Learning ICVL Uing the application Linear Accelerometer, intalled on the martphone, we recorded the data from the acceleration enor, aved it in.cv file format and exported it to Excel in order to be proceed. The diagram below (Fig.). illutrate the graphic of variation in time of the value of the acceleration vector component on the three Carteian axe Ox, Oy and Oz. Figure. Graph of recorded acceleration (uniformly accelerated motion) The time interval for the recording wa t 4. The medium value of the component of the m m m acceleration vector were: ax 0,046, a 0,075 y and a z 0, 40. Given thee condition, the total value of the meaured acceleration wa: m [1] a ax ay az 0, 407 The pecific ditribution of the medium value of the acceleration component i a conequence of the phyical tructure of the road travelled by the vehicle. The unevenne of the road caue udden fluctuation of thee component. The ditance involved in thi experiment wa determined with the law of pace, with the initial velocity v0 0 : t m 4 [] d a 0, m. The velocity reached by the vehicle calculated uing the meaured value for acceleration and time wa: m m km [3] v v0 a t 0, , 09 61,53 ( v 0 0). h

3 360 Univerity of Bucharet and Univerity of Craiova The relative meaurement error between the calculated value of velocity and the value 61,53 60 diplayed by the peedometer of the vehicle wa,55%. Thi i a good 60 reult which demontrate the quality of the recording performed with the accelerometer.. Uniformly decelerated motion We alo determined the acceleration of a vehicle for an uniformly decelerated motion on a rectilinear road (Fig.3). Figure 3. Uniformly decelerated motion The vehicle in which the mobile phone wa placed, having the Linear Accelerometer application on, gradually reduced it peed from 60 km h to zero. The graphic below (Fig.4) illutrate the variation in time of the value of the acceleration component on the three Carteian axe. Figure 4. Meaurement graphic (uniformly decelerated motion) The time interval for the recording wa t 38. The ign minu preent in the medium value dv of ax and a y indicate the exitence of a decelerated motion ( a 0). The abolute value dt of the total acceleration wa a 0, 448 m. The preence of fluctuation in the value of the acceleration component in the lat ten econd of the motion (the interval 7 38 ) wa triggered by the tructural defect in the urface of the road.

4 The 11 th International Conference on Virtual Learning ICVL The initial velocity of the vehicle wa determined baed on the law of velocity with a null final velocity. It calculated value wa: m m km [4] v0 a t 0, , 0 61, 8. h 61,8 60 The relative meaurement error wa,13%. The ditance covered by the 60 vehicle until it topped wa calculated uing the Galileo equation, with a null final velocity: m (17, 0 ) v0 [5] d 33m. a m 0, 448 The comparative analyi of the acceleration graphic ax, a y and a z for the two type of tudied motion indicated the preence of local value fluctuation that were more evident in the uniformly accelerated motion compared to the uniformly decelerated motion. 3 Vehicle motion with contant acceleration on the lope of a bridge We determined the acceleration ax, a y and a z for the acending and decending motion of a vehicle on the lope of a bridge (Fig.5). Bridge acending Bridge decending (view from the car) Figure 5. The bridge travelled by the vehicle 3.1 Acending motion During the firt phae of the experiment, we determined the component of acceleration for the upward motion of a vehicle on the lope of a bridge (Fig.6). Figure 6. Car acending on the lope of the bridge When the vehicle travelled up the bridge, the following graphic were obtained (Fig.7):

5 36 Univerity of Bucharet and Univerity of Craiova Figure 7. Meaurement graphic (acceleration recorded on bridge acenion) The initial velocity of the car, indicated by it peedometer when tarting the acenion on the bridge wa v0 80 km. At the top end of the lope, the peed indicated by the peedometer wa h 30 km. The time interval for the recording wa 3 h t. We compared thi value to the one calculated uing the law of velocity for the uniformly decelerated motion: v v0 a t. The acceleration of the car determined from the graphic wa a 0, 46 m. We obtained the reult: km m km [6] v 80 0, , 6. h h 30 7, 6 The value calculated experimentally ha a relative error of 8% compared 30 to the value indicated by the peedometer of the car (30 km h ), which illutrate a good preciion of the data recorded with the application Linear Accelerometer. The ditance travelled by the vehicle during the recording wa: t km m (3 ) [7] d v 0 t a , m h.

6 The 11 th International Conference on Virtual Learning ICVL Decending motion We performed another meaurement when the car decended from the lope of the bridge (Fig.8) and had an uniformly accelerated motion with the initial velocity: v0 30 km. The data h recording interval wa t 19. Figure 8. Car decending on the lope of the bridge The diagram with the meaured acceleration graphic i illutrated below (Fig.9). Figure 9. Meaurement graphic (acceleration recorded on bridge decending) The meaured acceleration had the value a 0,646 m. The velocity reached by the vehicle at the end of the time interval for the recording wa km m km [8] v v0 a t 30 0, , 43. h h We compared thi value with the one indicated by the peedometer of the car v 80 km. The h 74,43 relative error wa 1 6,9%, a value which i within the experimental limit. At 80

7 364 Univerity of Bucharet and Univerity of Craiova the ame time, the ditance travelled by the vehicle in the time interval t 19 wa calculated uing the pace law: t m m (19 ) [9] d v0 t a 8, , m The map of the road travelled by the vehicle wa drawn uing Google Map (Fig.10). Thi way the total length of the road travelled by the car wa determined D 1, km. The meaurement were performed when the car travelled on thi road for a ditance d 481m 83m 764m, acending and decending from the bridge. 4 Concluion Figure 10. Map of road travelled by the car (bridge lope) The ue of the accelerometer for the tudy of the kinematic parameter of a vehicle i an engaging proce for nowaday tudent, who etablih a link between their portable device (martphone) and it potential role in learning about and exploring phyical phenomena. Thi tudy ha hown that the acceleration enor integrated in a martphone i reliable and ha a high degree of accuracy when meauring the acceleration of a vehicle. Therefore, it i expected that in the following year more Phyic teacher will chooe to integrate into their clae experiment baed on the ue of the accelerometer. The potential of a martphone enor for education related purpoe hould be further explored and exploited by the cience teacher. Reference Catro-Palacio, J.C., Luiberi, V.A., Marco, H.G., Monoriu, J.A. (013): Uing The Mobile Phone Acceleration Senor In Phyic Experiment: Free And Damped Harmonic Ocillation, American Journal of Phyic 81, Chevrier, J., Madani, L., Ledenmat, S., Biey, A. (013): Teaching Claical Mechanic Uing Smartphone, The Phyic Teacher 51, Countryman, C.L. (014): Familiarizing Student with the Baic of a Smartphone Internal Senor, The Phyic Teacher 5, Kuhn, J., Vogt, P., Müller, A. (014): Analyzing Elevator Ocillation with the Smartphone Acceleration Senor, The Phyic Teacher 5, Kuhn, J., Vogt, P. (013): Application and Example of Experiment with Mobile Phone and Smartphone in Phyic Leon, Frontier in Senor (FS) 1, 4,

8 The 11 th International Conference on Virtual Learning ICVL Monteiro, M., Stari, C., Cabeza, C., Marti, A.C. (015): The Atwood machine reviited uing martphone, The Phyic Teacher 53, Kiner, J.M. (015), Relating Time-Dependent Acceleration and Height Uing an Elevator, The Phyic Teacher 53, 0-1. Monteiro, M., Cabeza, C., Marti, A.C. (015): Acceleration Meaurement Uing Smartphone Senor: Dealing With The Equivalence Principle, Revita Braileira de Enino de Fiica 37, 1, 1303 (1-6). Tuet-Sanchi, L., Catro-Palacio, J.C., Gómez-Tejedor, J.A., Manjón, F.J., Monoriu, J.A. (015): The Study of Two-dimenional Ocillation Uing a Smartphone Acceleration Senor: Example of Liajou Curve, Phyic Education 50, 5, Vogt, P., Kuhn, J. (013): Analyzing Radial Acceleration with a Smartphone Acceleration Senor, The Phyic Teacher 51,