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Effect of Local Conditions on the Flight Trajectory of an Indoor

Badminton Shuttlecock

Raghavan Subramaniyan, Bangalore, Indiaragsubra@gmail.com

30-Mar-2008 Draft Version

Table of Contents

1 Abstract.............................................................................................................................................2

2 Introduction......................................................................................................................................2

3 Theoretical Analysis.........................................................................................................................3

3.1 alculation of Air Density........................................................................................................!

3.2 "u##ary of analysis.................................................................................................................$% &esults..............................................................................................................................................$

%.1 autionary note on shuttlecoc' s(eeds.....................................................................................$

%.2 Variation in Air density............................................................................................................$

%.3 Variation in tra)ectory of the shuttlecoc'.................................................................................*

%.3.1 +on, sere.........................................................................................................................*

%.3.2 erhand clear................................................................................................................../

%.3.3 nderhand clear..............................................................................................................12

%.3.% "hort sere.......................................................................................................................1%

! onclusion......................................................................................................................................1!

$ &eferences......................................................................................................................................1!

ra,subra,#ail.co# 1

mailto:ragsubra@gmail.commailto:ragsubra@gmail.commailto:ragsubra@gmail.commailto:ragsubra@gmail.com

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1 Abstract

+ocal conditions such as te#(erature hu#idity and ,eo,ra(hical altitude of a (lace directly affect the

density of air thus affectin, air resistance and hence the fli,ht of an indoor bad#inton shuttlecoc'. The

effect of local conditions on the #ost co##on ty(es of shots are analyed. 4en thou,h the fli,ht of the

shuttlecoc' is 5uite a co#(le6 (heno#enon a fe7 si#(lifyin, assu#(tions are #ade notably the non-

consideration of (hysical defor#ation of the shuttlecoc' es(ecially )ust after rac'et i#(act. &esults for t7o

different conditions are (resented the first bein, an air-conditioned bad#inton court at sea leel and the

second bein, a non-air conditioned court in an,alore 7hich has an altitude of about 3000 feet. 9or the

sa#e shot (layed it is sho7n that there is oer 10: ariation in the distance traeled by the shuttlecoc'

across the conditions. It also re5uires about %0: #ore ener,y to be i#(arted to the shuttlecoc' in the first

case ;sea leel< for it to follo7 a tra)ectory si#ilar to that in the second case ;hi,h altitude

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the total acceleration due to all forces is deco#(osed into a horiontal and ertical co#(onent denoted by a6and ay. "i#ilarly the elocity is deco#(osed into v6and vy. The (osition of the shuttlecoc' in the ertical

(lane is denoted byxandy. =ith this 7e hae

ax= q v6s5rt;v62G vy

2