cp2 singh arjun report
DESCRIPTION
Computer project 2 for ME 2016TRANSCRIPT
ArjunSingh3/29/2016
CP2Report
Summary Thiscomputerprojectinvolvedtheuseofnumericalintegrationforanalyzingarealworldprobleminthefieldofwindenergy.TheTrapezoidalandSimpson’s1/3rdmethodswereusedtocalculatetheintegralvaluesusingfunctions,polynomials,splinesanddatapoints,whilereachingtheconclusionthattheSimpson’s1/3rdmethodismoreefficientatcalculatingintegrals.A. TheoreticalmodelanalysisIntegralusedtocalculatethetotalforce:
𝐼 = 200𝑥
𝑥 + 5
)*+
,𝑒.(
)01)*+)
Comparingthe3methods:Simpson’s1/3rdmethodusedlessnumberofintervals(512comparedtoTrapezoidal’s8192)thanthetrapezoidalmethodandcamemuchclosertotheMATLABintegralfunction’svalueof≈11461.83N
Figure1–FunctionPlotwithpressureCenter
ArjunSingh3/29/2016
B. Experimentaldataanalysis
Figure2–PolynomialFitsItcanbeobservedthatthebestfittingpolynomialisoforder9sinceithastheleastamountofvariationfromtheactualdatapointsascomparedtoorders8and10
Figure3–SplineInterpolation
ArjunSingh3/29/2016
SplinevsPolynomial:TotalForceusingPolynomialOrder9=11131.142450NTotalForceusingSplineInterpolation=11065.215644NWhileusingtheexperimentaldata,thepolynomialfitappearstogiveavaluethatisclosertothetheoreticalvalueof11461.83NascalculatedinpartA.