Mathcad Professional 14.0 <description/> <author>Charles</author> <company>Parametric Technology Corporation</company> <keywords/> <revisedBy>CK</revisedBy> </userData> <identityInfo> <revision>9</revision> <documentID>A60A27BC-01B2-479E-B3BC-B28738418FFC</documentID> <versionID>5C50604E-78D1-4D1B-94F0-2050CC2BE89C</versionID> <parentVersionID>00000000-0000-0000-0000-000000000000</parentVersionID> <branchID>00000000-0000-0000-0000-000000000000</branchID> </identityInfo> </metadata> <settings> <presentation> <textRendering> <textStyles> <textStyle name="Normal"> <blockAttr margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit"/> <inlineAttr font-family="Courier New" font-charset="0" font-size="11" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="#00f"/> </textStyle> <textStyle name="Heading 1"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="14" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 2"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="bold" font-style="italic" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Heading 3"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="12" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="21" 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text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> <textStyle name="Subtitle" base-style="Title"> <blockAttr margin-left="0" margin-right="0" text-indent="inherit" text-align="center" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Times New Roman" font-charset="0" font-size="18" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="x" derivative="derivative" literal-subscript="large" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal" symbolic-evaluation="right-arrow"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="14" font-weight="normal" font-style="normal" underline="false"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="current" thermodynamic-temperature="temperature" luminous-intensity="luminosity" amount-of-substance="substance" display="false"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results numeric-only="true"> <general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true" fractional-unit-exponent="false"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="landscape" print-single-page-width="false" page-width="792" page-height="612"> <margins left="36" right="36" top="36" bottom="36"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> <language math="en" UI="en"/> </presentation> <calculation> <builtInVariables array-origin="0" convergence-tolerance="0.001" constraint-tolerance="0.001" random-seed="1" prn-precision="4" prn-col-width="8"/> <calculationBehavior automatic-recalculation="true" matrix-strict-singularity-check="false" optimize-expressions="false" exact-boolean="true" strings-use-origin="false" zero-over-zero="error"> <compatibility multiple-assignment="MC12" local-assignment="MC11"/> </calculationBehavior> <units> <currentUnitSystem name="si" customized="false"/> </units> </calculation> <editor view-annotations="false" view-regions="false"> <ruler is-visible="false" ruler-unit="in"/> <plotTemplate> <xy item-idref="1"/> </plotTemplate> <grid granularity-x="6" granularity-y="6"/> </editor> <fileFormat image-type="image/png" image-quality="75" save-numeric-results="true" exclude-large-results="true" save-text-images="false" screen-dpi="96"/> <miscellaneous> <handbook handbook-region-tag-ub="808" can-delete-original-handbook-regions="true" can-delete-user-regions="true" can-print="true" can-copy="true" can-save="true" file-permission-mask="4294967295"/> </miscellaneous> </settings> <regions> <region region-id="804" left="36" top="9" width="336.75" height="12" align-x="53.25" align-y="18" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">B45 kWh per year.xmcd<sp count="3"/>Charles Kim 2013</p> </text> </region> <region region-id="801" left="42" top="33" width="556.5" height="252" align-x="57.75" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Micon 750/48 (750-kW, 48 meter rotor)</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">mounted on 50 meter tower</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Average wind speed at 10 meter height = 5 m/s</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"/> <p style="Normal" margin-left="0" margin-right="0" text-indent="0" text-align="left" list-style-type="none" tabs="inherit">Air desnsity = 1.225</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Wind pdf = Rayleigh</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Friction Coefficient=0.1524</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Power Conversion efficiency = 30%<sp count="2"/>---> Estimate the annual energy delivered [kWh/year]</p> </text> </region> <region region-id="790" left="48" top="84" width="177" height="132.75" align-x="48" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="2" display-width="175.5" display-height="131.25"/> </picture> <rendering item-idref="3"/> </region> <region region-id="805" left="300" top="84" width="378.75" height="84.75" align-x="300" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="4" display-width="377.25" display-height="83.25"/> </picture> <rendering item-idref="5"/> </region> <region region-id="808" left="258" top="180" width="174.75" height="42" align-x="258" align-y="180" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <picture> <png item-idref="6" display-width="173.25" display-height="40.5"/> </picture> <rendering item-idref="7"/> </region> <region region-id="742" left="54" top="297" width="156" height="12" align-x="70.5" align-y="306" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Average Speed at 50 meter:</p> </text> </region> <region region-id="747" left="84" top="309" width="35.25" height="12.75" align-x="102" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">H1</ml:id> <ml:real>10</ml:real> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="748" left="144" top="309" width="35.25" height="12.75" align-x="162" align-y="318" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIFunction" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">H2</ml:id> <ml:real>50</ml:real> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="749" left="222" top="315" width="45.75" height="12.75" align-x="234.75" align-y="324" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">α</ml:id> <ml:real>0.1524</ml:real> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="746" left="90" top="333" width="48.75" height="12.75" align-x="126" align-y="342" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v10avg</ml:id> <ml:real>5</ml:real> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="744" left="84" top="356.25" width="116.25" height="33.75" align-x="120" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v50avg</ml:id> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">v10avg</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">H2</ml:id> <ml:id xml:space="preserve">H1</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve">α</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="750" left="246" top="369" width="63.75" height="12.75" align-x="280.5" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">v50avg</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>6.3898848653757891</ml:real> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="763" left="330" top="369" width="42" height="12" align-x="333" align-y="378" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">[m / s]</p> </text> </region> <region region-id="754" left="60" top="405" width="180" height="12" align-x="76.5" align-y="414" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Average Power Density Equation</p> </text> </region> <region region-id="755" left="90" top="423" width="40.5" height="12.75" align-x="102" align-y="432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">ρ</ml:id> <ml:real>1.225</ml:real> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="752" left="78" top="446.25" width="148.5" height="27.75" align-x="114" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P50avg</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:parens> <ml:apply> <ml:div/> <ml:real>6</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:parens> <ml:real>0.5</ml:real> </ml:apply> <ml:id xml:space="preserve">ρ</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">v50avg</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="756" left="288" top="453" width="77.25" height="12.75" align-x="322.5" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">P50avg</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>305.20143391606513</ml:real> </result> </ml:eval> </math> <rendering item-idref="16"/> </region> <region region-id="760" left="384" top="453" width="48" height="12" align-x="388.5" align-y="462" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">[W / m2]</p> </text> </region> <region region-id="765" left="54" top="483" width="324" height="12" align-x="68.25" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Energy Calculation: Energy = Efficiency x Power x time</p> </text> </region> <region region-id="767" left="84" top="507" width="33" height="12.75" align-x="97.5" align-y="516" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">κ</ml:id> <ml:real>0.3</ml:real> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="781" left="90" top="525" width="66" height="12" align-x="100.5" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Blade area:</p> </text> </region> <region region-id="782" left="168" top="512.25" width="67.5" height="33.75" align-x="182.25" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:real>48</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="783" left="282" top="519" width="66.75" height="18.75" align-x="294.75" align-y="534" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">A</ml:id> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>1809.5573684677208</ml:real> </result> </ml:eval> </math> <rendering item-idref="19"/> </region> <region region-id="766" left="84" top="555" width="125.25" height="12.75" align-x="105.75" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E50</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:apply> <ml:mult/> <ml:id xml:space="preserve">κ</ml:id> <ml:id xml:space="preserve">P50avg</ml:id> </ml:apply> <ml:id xml:space="preserve">A</ml:id> </ml:apply> <ml:real>8760</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="772" left="216" top="555" width="72" height="12" align-x="220.5" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">[W h /year ]</p> </text> </region> <region region-id="784" left="312" top="555" width="234" height="12" align-x="313.5" align-y="564" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">1 Year = 365 day x 24 hour = 8760 hours</p> </text> </region> <region region-id="785" left="576" top="555" width="93" height="18.75" align-x="615" align-y="570" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval placeholderMultiplicationStyle="default" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:apply> <ml:mult/> <ml:real>365</ml:real> <ml:real>24</ml:real> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math30"> <ml:real>8760</ml:real> </result> </ml:eval> </math> <rendering item-idref="21"/> </region> <region region-id="773" left="90" top="579" width="77.25" height="18.75" align-x="111.75" align-y="594" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math30"> <ml:id xml:space="preserve">E50</ml:id> <ml:apply> <ml:mult/> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>-6</ml:real> </ml:apply> <ml:id xml:space="preserve">E50</ml:id> </ml:apply> </ml:define> </math> 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