Correo Electrónico
DNINFOA - SIA
Bibliotecas
Convocatorias
Identidad U.N.
Published
PROJECTILE MOTION IN A MEDIUM WITH QUADRATIC DRAG AT CONSTANT HORIZONTAL WIND
MOVIMIENTO DE PROYECTIL EN UN MEDIO CON RESISTENCIA CUADRÁTICA CON VIENTO HORIZONTAL CONSTANTE
DOI:
https://doi.org/10.15446/mo.n67.107561Keywords:
projectile motion, horizontal wind, quadratic resistance law (en)movimiento de proyectil, ley de resistencia cuadrática, viento horizontal (es)
Downloads
A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The action of the wind is also taken into account, which is considered constant and horizontal (tailwind or headwind). The projectile velocity hodograph equation is used to take into account the effect of wind. Comparatively simple analytical approximations are proposed for the main variables of motion (cartesian projectile coordinates and time). All obtained formulas contain only elementary functions. The proposed formulas are universal, that is, they can be used for any initial conditions of throwing. In addition, they have acceptable accuracy over a wide range of the change of parameters. The motion of a golf ball, a tennis ball and shuttlecock of badminton are presented as examples. The calculation results show good agreement between the proposed analytical solutions and numerical solutions. The proposed analytical formulas can be useful for all researchers of this classical problem.
Se estudia un problema clásico del movimiento de un proyectil lanzado con un ángulo respecto al horizonte. Se tiene en cuenta la fuerza de resistencia del aire mediante la ley de resistencia cuadrática. También, se tiene en cuenta la acción del viento, que se considera constante y horizontal (viento de cola o viento en contra). Para tener en cuenta el efecto del viento se utiliza la ecuación hodográfica de la velocidad del proyectil. Se proponen aproximaciones analíticas comparativamente sencillas para las principales variables del movimiento (coordenadas cartesianas del proyectil y tiempo). Todas las fórmulas obtenidas contienen solo funciones elementales. Las fórmulas propuestas son universales, es decir, pueden utilizarse para cualquier condición inicial de lanzamiento. Además, tienen una precisión aceptable en un amplio rango de cambio de parámetros. Se presentan como ejemplos el movimiento de una pelota de golf, una pelota de tenis y un volante de bádminton. Los resultados de los cálculos muestran una buena concordancia entre las soluciones analíticas propuestas y las soluciones numéricas. Las fórmulas analíticas propuestas pueden ser útiles para todos los investigadores de este problema clásico.
References
M. Lubarda and V. Lubarda, Archive of App. Mech. 92, 1997 (2022). https://link.springer.com/article/10.1007/s00419-022-02173-7 DOI: https://doi.org/10.1007/s00419-022-02173-7
P. W. Andersen, Eur. J. Phys. 36, 068003 (2015). https://iopscience.iop.org/article/10.1088/0143-0807/36/6/068003 DOI: https://doi.org/10.1088/0143-0807/36/6/068003
R. Bernardo, J. Esguerra, J. Vallejos, and J. Canda, Eur. J. Phys. 36, 025016 (2015). https://iopscience.iop.org/article/10.1088/0143-0807/36/2/025016 DOI: https://doi.org/10.1088/0143-0807/36/2/025016
J. McPhee and G. Andrews, Am. J. Phys. 56, 933 (1988). https://pubs.aip.org/aapt/ajp/article-abstract/56/10/933/1045348/Effect-of-sidespin-and-wind-on-projectile?redirectedFrom=fulltext DOI: https://doi.org/10.1119/1.15363
N. de Mestre, The Anziam 33, 65 (1991). https://www.cambridge.org/core/journals/anziam-journal/article/mathematical-analysis-of-wind-effects-on-a-longjumper/832F203D6E7C071FBD583E5D2204C850
R. Ozarslan, E. Bas, D. Baleanu, and B. Acay, AIMS Mathematics 5, 467 (2020). http://www.aimspress.com/article/10.3934/math.2020031 DOI: https://doi.org/10.3934/math.2020031
S. Ray and J. Fröhlich, Arch. Appl. Mech 85, 395 (2015). https://link.springer.com/article/10.1007/s00419-014-0919-x DOI: https://doi.org/10.1007/s00419-014-0919-x
P. Veeresha, E. Ilhan, and H. Mehmet, Phys. Scripta 96, 075209 (2021). 122 Peter Chudinov, et al. https://iopscience.iop.org/article/10.1088/1402-4896/abf868 DOI: https://doi.org/10.1088/1402-4896/abf868
S. Timoshenko and D. Young, Advanced dynamics (McGrow-Hill, 1948). https://books.google.com.co/books?id=bxjatAEACAAJ
P. Chudinov, V. Eltyshev, and Y. Barykin, Momento 62, 79 (2021). https://revistas.unal.edu.co/index.php/momento/article/view/90752 DOI: https://doi.org/10.15446/mo.n62.90752
C. Cohen, B. Darbois, G. Dupeux, E. Brunel, D. Quéré, and C. Clanet, Proc. Math. Phys. Eng. Sci. 470, 20130497 (2014). https://royalsocietypublishing.org/doi/full/10.1098/rspa.2013.0497 DOI: https://doi.org/10.1098/rspa.2013.0497
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.
Those authors who have publications with this journal, accept the following terms:
a. The authors will retain their copyright and will guarantee the publication of the first publication of their work, which will be subject to the Attribution-SinDerivar 4.0 International Creative Commons Attribution License that permits redistribution, commercial or non-commercial, As long as the Work circulates intact and unchanged, where it indicates its author and its first publication in this magazine.
b. Authors are encouraged to disseminate their work through the Internet (eg in institutional telematic files or on their website) before and during the sending process, which can produce interesting exchanges and increase appointments of the published work.
