cp2 singh arjun report

3
Arjun Singh 3/29/2016 CP2 Report Summary This computer project involved the use of numerical integration for analyzing a real world problem in the field of wind energy. The Trapezoidal and Simpson’s 1/3 rd methods were used to calculate the integral values using functions, polynomials, splines and data points, while reaching the conclusion that the Simpson’s 1/3 rd method is more efficient at calculating integrals. A. Theoretical model analysis Integral used to calculate the total force: = 200 +5 )*+ , .( )01 )*+ ) Comparing the 3 methods: Simpson’s 1/3 rd method used less number of intervals (512 compared to Trapezoidal’s 8192) than the trapezoidal method and came much closer to the MATLAB integral function’s value of 11461.83 N Figure 1 – Function Plot with pressure Center

Upload: ajspsp

Post on 13-Jul-2016

13 views

Category:

Documents


1 download

DESCRIPTION

Computer project 2 for ME 2016

TRANSCRIPT

Page 1: CP2 Singh Arjun Report

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

Page 2: CP2 Singh Arjun Report

ArjunSingh3/29/2016

B. Experimentaldataanalysis

Figure2–PolynomialFitsItcanbeobservedthatthebestfittingpolynomialisoforder9sinceithastheleastamountofvariationfromtheactualdatapointsascomparedtoorders8and10

Figure3–SplineInterpolation

Page 3: CP2 Singh Arjun Report

ArjunSingh3/29/2016

SplinevsPolynomial:TotalForceusingPolynomialOrder9=11131.142450NTotalForceusingSplineInterpolation=11065.215644NWhileusingtheexperimentaldata,thepolynomialfitappearstogiveavaluethatisclosertothetheoreticalvalueof11461.83NascalculatedinpartA.