los efectos y potencia en el deporte rey

5/24/2018 Los Efectos y Potencia en El Deporte Rey

1/9

Los efectos y potencia en el deporte rey Descargar PDF

John Eric Goff

julio 2010

ARTCULO ANTERIOR

EST UDIO R PID A

SIGUIENT E ARTCULO

Despus de una pelota deja el pie de un jugador de ftbol la rugosidad superficial y las fuer!as areas asi"tricas

contribuyen a algunas trayectorias aso"brosos#

IR A LA SECCIN ...

Es tiempo e !a Copa e! "#$o y la gente de todo el planeta tienen sus ojos en $ud%frica# &ara un gran e'entoEE#((# co"o el $uper )o*l anual la audiencia es tal 'e! 100 "illones# Esa cifra se ele'a en un orden de "agnitud

cuando la +opa del ,undo llega cada cuatro a-os# Los .ue sintoni!ar a 'er no s/lo el ftbol e"ocionante lla"ado ftbol

en la "ayora de los pases sino ta"bin la fsica fascinantes en acci/n#

+apa l"ite y arrastreIR A LA SECCIN ...&orteros de ftbol profesionales per"iten a la "ayora de los pocos goles en un partido# Los tiros libres y tiros de es.uina

sin e"bargo representan relati'a"ente buenas oportunidades de gol y as son particular"ente e"ocionante# 3lgunos fans

pueden ad"irar sobre todo la potencia su"inistrada por los &ases )ajos 45obin 'an &ersie6 otros pueden ad"irar las

cur'as i"partidas por el ingls $te'en Gerrard# De cual.uier "anera la fsica re'ela por .u la bola se "ue'e co"o lo

hace#

+o"o un bal/n de ftbol se "ue'e a tra's del aire se siente una fuer!a debido a las diferencias de presi/n y de las

interacciones entre el aire 'iscoso y la superficie de la pelota# Las fuer!as 'iscosas son i"portantes en la capa l"ite un

concepto introducido por Lud*ig &randtl en el u"bral del siglo 20# En esa regi/n cerca de la superficie de la bola la

'elocidad del aire en relaci/n con la superficie de la bola se ele'a desde cero en la superficie hasta casi su 'alor sin

corriente 'ase el artculo de John D# 3nderson Jr enPhysics Today dicie"bre de 2007 p%gina 82# La capa l"ite es

"%s delgado en la parte frontal de la pelota .ue se enfrenta al aire en direcci/n contraria y "%s grueso "%s atr%s# +on el

tie"po se separa de la pelota por co"pleto y deja un patr/n de flujo co"plejo con re"olinos re"olinos a su paso# Gran

parte de la "ara'illa de las trayectorias de ftbol depende de d/nde la capa l"ite se separa#

9ui!%s el par%"etro "%s i"portante en la din%"ica de fluidos es el n"ero de 5eynoldsRe: VD / con Vde la bola de

centro de "asa de 'elocidad respecto al aire yDel di%"etro de la bola6 la 'iscosidad cine"%tica es la relaci/n de la

'iscosidad del aire a su densidad ;# ,ediante la aplicaci/n de la segunda ley de


2/9

"o'i"iento alrededor de un objeto se obtiene la ecuaci/n de


3/9

'elocidad de la bola# En las dos inserciones pol'o siste"a de ilu"inaci/n re'ela la separaci/n de la capa l"ite de un

bal/n de ftbol en "o'i"iento a tra's del aire# La i"agen de la i!.uierda corresponde a un n"ero de 5eynolds de 11

10 7y flujo la"inar#&ara la i"agen de la derechaRe: 2 10 7y el flujo es turbulento6 tenga en cuenta .ue la

separaci/n de la capa l"ite es "%s atr%s en esa i"agen# La trayectoria de un lan!a"iento de falta directo golpeado=est%

sie"pre en el rgi"en turbulento#&ara balones de ftbol los juegos de crisis arrastre en cuando la 'elocidad es de unos 12 " ? seg co"parable a la de un

pase de "edio alcance# (n tiro libre de 'an &ersie sale de su !apato conReF 7 10 7y entra en la "eta conReF I

10 76 para toda la trayectoria de la pelotaRees superior al 'alor de crisis# nicial"ente la fuer!a de arrastre sobre la bola

es de aproCi"ada"ente 17K "ayor .ue el peso de la pelota# &ara una recta de Grandes LigasReF 2 10 7y la fuer!a de

arrastre es co"parable con el peso de la bola# (na pelota de golf en "archa a 0 " ? s tieneReF 2 10 7y eCperi"enta

una fuer!a de arrastre de "%s de dos 'eces su peso# La si"plificaci/n de la fsica introductoria co"n de ignorar la

resistencia del aire sin duda no es aplicable al estudio de los proyectiles de los deportes#

(n sa.ue de pl%tano con aire batidaIR A LA SECCIN ...&ara el tiro libre de efecti'os un jugador de ftbol co"o Gerrard .uiere dar a la bola una 'elocidad inicial grande para

.ue el portero tiene poco tie"po para reaccionar# Ba"bin .uiere hacer girar la bola de "odo .ue las cur'as "%s all% del

portero# Esas son las necesidades .ue co"piten La gran 'elocidad de traslaci/n re.uiere una patada por el centro de la

bola pero una 'elocidad de giro grande re.uiere un tiro fuera del centro# (na buena patada Gerrard tiene un efecto lateral

inicial de alrededor de H00 rp"# En co"paraci/n una cur'a de Grandes Ligas hace girar a una 'elocidad de alrededor de

2#000 rp" y una pelota de golf de salir de la te podra tener un efecto de retroceso de 2#700 rp" o "%s en parte gracias al

estriado e inclinado el rostro del club de golf#

(na bola .ue gira con 'elocidad angular M a!ota el aire detr%s de l# +o"o la inserci/n a la figura2 "uestra una

caracterstica i"portante de este proceso es .ue la capa l"ite se separa "%s atr%s en el lado de la bola .ue gira en la

direcci/n opuesta a la 'elocidad A# centro=de="asa Debido a .ue la asi"etra la aire ejerce una fuer!a sobre la bola=

lla"ada la fuer!a de ,agnus en honor a einrich Gusta' ,agnus=en la direcci/n de M A# (n fen/"eno si"ilar ocurre

en el "ar cuando el ti"/n de un barco se des'a el agua de for"a asi"trica detr%s de un barco de ejecutar un giro# La

fuer!a de ,agnus acta ade"%s de la fuer!a de arrastre# &or supuesto el aire ejerce s/lo una nica fuer!a en la

pelota6 c/"o se reparte la fuer!a en sus co"ponentes es de hasta el cientfico#
http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2


4/9

aga clic para 'er

%%%Gooooo!&+uando un jugador de ftbol se consigui/ un tiro libre los defensores se renen en una pared segn lo

indicado por el rect%ngulo 'erde# Este gr%fico "uestra dos trayectorias de tiro libre .ue restable!can la pared la cur'a

roja .ue corresponde a una pelota sin giro y la cur'a a!ul="%s dura=para interceptar lo .ue representa una bola con

efecto lateral# Las distancias se eCpresan en "etros# La inserci/n cortesa de Nenneth Oright "uestra una 'ista area de

la pelota .ue des'a el aire hacia la derecha# &or lo tanto de acuerdo con la tercera ley de


5/9

7# )G +oo> JE Goff PEl espacio de par%"etros para el Cito de los retrocesos de ftbolP $ur. %.. Phys. *)

SH7 200H#

)iografasIR A LA SECCIN ...+o,$ Eric Go--goffTlynchburg#edu es profesor asociado de fsica en la uni'ersidad de Lynchburg en Lynchburg

Airginia#

U 2010 nstituto 3"ericano de Vsica

DOI http??dC#doi#org?10#10HI?1#I8HIHIH

COMENTARIOSINICIAR LA CONVERSACIN

Noticias T/rmi$os 0 co$icio$es Pri1acia P#2!icia A0#a Co$tactos

Siga AIPP:

3e2site 4 *5(6 AIP P#2!is,i$g LLC. Art7c#!o cop0rig,t sig#e sie$o como se especi-ica e$ e! art7c#!o.

INGLES

&o*er and spin in the beautiful ga"e Do8$!oa PDF

John Eric Goff

julio 2010

PRE 9IOUS ART ICLE

:UIC; STUD e the

annual $uper )o*l 'ie*ership is perhaps 100 "illion# Bhat nu"ber ju"ps by an order of "agnitude *hen the Oorld +up

arri'es e'ery four years# Bhose *ho tune in *ill see not only eCciting soccer called football in "ost countries but also

fascinating physics in action#

)oundary layer and dragGO TO SECTION...
mailto:[email protected]:[email protected]://dx.doi.org/10.1063/1.3463636http://dx.doi.org/10.1063/1.3463636http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/news;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/termsconditions;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/privacy;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/advertisers;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/help;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/contact;jsessionid=9cfcpqajfr260.x-aip-live-02http://twitter.com/aip_publishinghttp://scitation.aip.org/deliver/fulltext/aip/magazine/physicstoday/63/7/1.3463636.pdf?itemId=/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636&mimeType=pdf&containerItemId=content/aip/magazine/physicstoday/issueshttp://scitation.aip.org/content/contributor/AU0025662http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463635http://scitation.aip.org/content/aip/magazine/physicstoday/63/7/ptolsection?heading=Quick+Studyhttp://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463637http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636http://www.flickr.com/photos/39565660@N03/sets/http://www.facebook.com/AIPPublishinghttp://twitter.com/aip_publishingmailto:[email protected]://dx.doi.org/10.1063/1.3463636http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/news;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/termsconditions;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/privacy;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/advertisers;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/help;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/contact;jsessionid=9cfcpqajfr260.x-aip-live-02http://scitation.aip.org/deliver/fulltext/aip/magazine/physicstoday/63/7/1.3463636.pdf?itemId=/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636&mimeType=pdf&containerItemId=content/aip/magazine/physicstoday/issueshttp://scitation.aip.org/content/contributor/AU0025662http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463635http://scitation.aip.org/content/aip/magazine/physicstoday/63/7/ptolsection?heading=Quick+Studyhttp://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463637http://www.facebook.com/sharer.php?u=http%3A%2F%2Fscitation.aip.org%2Fcontent%2Faip%2Fmagazine%2Fphysicstoday%2Farticle%2F63%2F7%2F10.1063%2F1.3463636&t=fPower+and+spin+in+the+beautiful+gamehttp://twitter.com/home?status=fPower+and+spin+in+the+beautiful+game+http%3A%2F%2Fscitation.aip.org%2Fcontent%2Faip%2Fmagazine%2Fphysicstoday%2Farticle%2F63%2F7%2F10.1063%2F1.3463636http://www.mendeley.com/import/?doi=10.1063/1.3463636http://scitation.aip.org/email?currentTarget=%2Fcontent%2Faip%2Fmagazine%2Fphysicstoday%2Farticle%2F63%2F7%2F10.1063%2F1.3463636&itemId=%2Fcontent%2Faip%2Fmagazine%2Fphysicstoday%2Farticle%2F63%2F7%2F10.1063%2F1.3463636


6/9

&rofessional soccer goalies allo* at "ost only a fe* goals in a ga"e# Vree >ic>s and corner >ic>s though represent

relati'ely good scoring opportunities and so are particularly eCciting# $o"e fans "ay especially ad"ire the po*er

deli'ered by the er farther bac># E'entually it separates fro" the ball altogether and lea'es a co"pleC flo* pattern *ith s*irling

eddies in its *a>e# ,uch of the *onder"ent of soccer trajectories depends on *here the boundary layer separates#

&erhaps the "ost i"portant para"eter in fluid dyna"ics is the 5eynolds nu"berRe: VD/ *ith Vthe ballWs center=of=

"ass speed relati'e to the air andDthe ballWs dia"eter6 the >ine"atic 'iscosity is the ratio of airWs 'iscosity to its

density ;# )y applying


7/9

+lic> to 'ie*

T,e rag crisis.n this plot of drag coefficient CD as a function of 5eynolds nu"ber Re the rapid drop in CD the

drag crisis indicates the transition fro" la"inar to turbulent air flo*# Bhe crisis is precipitated *hen the surface of the ball

is rough# Vor a soccer ballRe?10 7FV? "?s F V?1H "ph *here Vis the speed of the ball# n the t*o insets illu"inated

dust re'eals the separation of the boundary layer fro" a soccer ball "o'ing through air# Bhe left i"age corresponds to a

5eynolds nu"ber of 1#1 10 7and la"inar flo*# Vor the right i"ageRe: 2# 10 7and flo* is turbulent6 note that the

boundary=layer separation is farther bac> in that i"age# Bhe trajectory of a *ell=struc> free >ic> is al*ays in the turbulent

regi"e#

Vor soccer balls the drag crisis sets in *hen the speed is about 12 "?s co"parable to that of a "ediu"=range pass# 3 'an

&ersie free >ic> lea'es his shoe *ithReF 7 10 7and enters the goal *ithReF I 10 76 for the entire trajectory of the

ballReis abo'e the crisis 'alue# nitially the drag force on the ball is about 17K greater than the ballWs *eight# Vor a

"ajor=league fastballReF 2 10 7and the drag force is co"parable to the *eight of the ball# 3 golf ball launched at 0

"?s hasReF 2 10 7and eCperiences a drag force "ore than t*ice its *eight# Bhe co""on introductory physics

si"plification of ignoring air resistance is certainly not applicable to the study of sports projectiles#

3 banana >ic> *ith *hipped airGO TO SECTION...Vor an effecti'e free >ic> a soccer player li>e Gerrard *ants to gi'e the ball a large initial speed so that the goalie has

little ti"e to react# e also *ants to spin the ball so that it cur'es past the goalie# Bhose are co"peting needs Bhe large

translational speed re.uires a >ic> through the ballWs center but a large rotational speed necessitates an off=center >ic># 3

good Gerrard >ic> has an initial sidespin of so"e H00 rp"# )y co"parison a "ajor=league cur'eball spins at a rate of

about 2000 rp" and a golf ball lea'ing the tee "ight ha'e a bac>spin of 2700 rp" or "ore in part than>s to the golf

clubWs groo'ed and tilted face#

3 rotating ball *ith angular 'elocity M *hips air behind it# 3s the inset to figure2sho*s an i"portant feature of that

process is that the boundary layer separates farther bac> on the side of the ball that rotates in the direction opposite to the

center=of="ass 'elocity A# )ecause of that asy""etry the air eCerts a force on the ballYcalled the ,agnus force in

honor of einrich Gusta' ,agnusYin the direction of M A# 3 si"ilar pheno"enon occurs at sea *hen a boatWs rudder
http://scitation.aip.org/content/figure/aip/magazine/physicstoday/63/7/10.1063/1.3463636.f1http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2http://scitation.aip.org/content/figure/aip/magazine/physicstoday/63/7/10.1063/1.3463636.f1http://scitation.aip.org/content/figure/aip/magazine/physicstoday/63/7/10.1063/1.3463636.f1http://scitation.aip.org/content/figure/aip/magazine/physicstoday/63/7/10.1063/1.3463636.f1http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636#f2


8/9

deflects *ater asy""etrically behind a boat eCecuting a turn# Bhe ,agnus force acts in addition to the drag force# Qf

course the air eCerts only a single force on the ball6 ho* that force is split into co"ponents is up to the scientist#

+lic> to 'ie*

Gooooa!&Ohen a soccer player is a*arded a free >ic> the defenders asse"ble in a *all as indicated by the green

rectangle# Bhis plot sho*s t*o free=>ic> trajectories that clear the *all the red cur'e *hich corresponds to a ball *ithout

spin and the tougher=to=intercept blue cur'e representing a ball *ith sidespin# 3ll distances are in "eters# Bhe inset

courtesy of Nenneth Oright sho*s an o'erhead 'ie* of the ball *hich deflects the air to the right# Bhus in accord *ith

e free >ic># Bhe right=footed Gerrard stri>es the ball fro" a spot about 20 " fro" the goal# 3

*all of defenders shifted to*ard GerrardWs left hopes to be Zluc>y[ enough to be hit by the ball6 the goalie guards

GerrardWs right half of the goal# Gerrard ai"s to put the ball in the upper=left portion of the goal# 3n agile goalie can often

stop a ball >ic>ed *ith no spin but *ill ha'e a "uch tougher ti"e *ith GerrardWs spinning ball *hose banana=shaped

trajectory not only cur'es as sho*n in the figure but actually dips a bit# Bhe initial "agnitude of the ,agnus force on a

free >ic> is co"parable to the ballWs *eight# Li>e*ise a golf ball just dri'en fro" the tee eCperiences a ,agnus force

co"parable to its *eight# Vor a cur'eball the initial ,agnus force is relati'ely s"aller about a .uarter of the baseballWs

*eight#

Bo study the aerodyna"ics of sports balls researchers use *ind tunnels sophisticated co"putational fluid dyna"ics

progra"s and co"putation=based trajectory analysis# ,y colleagues and ha'e studied the I2=panel soccer ball *ith its

*ell=>no*n pentagons=and=heCagons pattern and the 3didas Bea"geist ball *ith its 18 ther"ally bonded panels that *as

used for the 200H Oorld +up# Qur tests failed to discern significant differences in CDo'er a *ide range ofRe but they do

suggest that the ,agnus force on the Bea"geist ball is slightly larger than on the I2=panel ball# Bhis yearWs Oorld +up is

using the 3didas Jabulani ball *hich has eight ther"ally bonded panels and groo'es on its surface# 3 great deal of rich

physics lies behind those spinning sports balls *hose trajectories *ill cause elation in one country and anguish in so

"any others#

3DDBQ


9/9

2# J# Oesson The (cience o) (occer Q& )ristol (N 2002#

I# J# E# Goff ,# J# +arr Z$occer )all Lift +oefficients 'ia Brajectory 3nalysis[$ur. %. Phys.'( 7

2010#

8# J# E# Goff ,# J# +arr ZBrajectory 3nalysis of a $occer )all[A&. %. Phys.)) 1020 200R#

7# )# G# +oo> J# E# Goff Z&ara"eter $pace for $uccessful $occer Nic>s[$ur. %. Phys.*) SH7 200H#

)iographiesGO TO SECTION...+o,$ Eric Go--goffTlynchburg#edu is an associate professor of physics at Lynchburg +ollege in Lynchburg Airginia#U 2010 3"erican nstitute of &hysics

DOIhttp??dC#doi#org?10#10HI?1#I8HIHIH

COMMENTS

http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.363636
mailto:[email protected]:[email protected]://dx.doi.org/10.1063/1.3463636http://dx.doi.org/10.1063/1.3463636http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636mailto:[email protected]://dx.doi.org/10.1063/1.3463636http://scitation.aip.org/content/aip/magazine/physicstoday/article/63/7/10.1063/1.3463636

los efectos y potencia en el deporte rey

Documents