<description/> <author/> <company/> <keywords/> <revisedBy>Office of College Computing</revisedBy> </userData> <identityInfo> <revision>2</revision> <documentID>ecce2178-f546-4e54-b17c-67ab6a28a840</documentID> <versionID>a703e94c-4b06-45ac-af67-4b81c1bdfe2e</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="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="inherit"/> </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" color="inherit"/> </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" color="inherit"/> </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" color="inherit"/> </textStyle> <textStyle name="Paragraph"> <blockAttr margin-left="0" margin-right="0" text-indent="21" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="inherit"/> </textStyle> <textStyle name="List"> <blockAttr margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="inherit"/> </textStyle> <textStyle name="Indent"> <blockAttr margin-left="108" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"/> <inlineAttr font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="inherit"/> </textStyle> <textStyle name="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="24" font-weight="bold" font-style="normal" underline="false" line-through="false" vertical-align="baseline" color="inherit"/> </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" color="inherit"/> </textStyle> </textStyles> </textRendering> <mathRendering equation-color="#000"> <operators multiplication="narrow-dot" derivative="derivative" literal-subscript="small" definition="colon-equal" global-definition="triple-equal" local-definition="left-arrow" equality="bold-equal"/> <mathStyles> <mathStyle name="Variables" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="Constants" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 1" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 2" font-family="Courier New" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 3" font-family="Arial" font-charset="0" font-size="10" font-weight="bold" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 4" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="italic" underline="false" color="inherit"/> <mathStyle name="User 5" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 6" font-family="Arial" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="User 7" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> <mathStyle name="Math Text Font" font-family="Times New Roman" font-charset="0" font-size="10" font-weight="normal" font-style="normal" underline="false" color="inherit"/> </mathStyles> <dimensionNames mass="mass" length="length" time="time" current="charge" temperature="temperature" luminosity="luminosity" substance="substance"/> <symbolics derivation-steps-style="vertical-insert" show-comments="false" evaluate-in-place="false"/> <results> <general radix="dec" complex-threshold="10" imaginary-value="i" zero-threshold="15" precision="3" show-trailing-zeros="false" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> </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="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false"/> <units unit-system="us"/> </calculation> <editor protection-level="none" 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="false" save-text-images="false"/> <miscellaneous> <handbook handbook-region-tag-ub="711" 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="196" left="18" top="14.25" width="72" height="12" align-x="18" align-y="24" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NACA 4 Series: </text> </region> <region region-id="139" left="66" top="33" width="18.75" height="12.75" align-x="74.25" align-y="42" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:real>2412</ml:real> </math> <rendering item-idref="2"/> </region> <region region-id="133" left="66" top="57" width="31.5" height="12.75" align-x="78.75" align-y="66" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit"> <ml:id>m</ml:id> <ml:real>.02</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="134" left="132" top="56.25" width="44.25" height="12" align-x="132" align-y="66" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> % camber </text> </region> <region region-id="135" left="66" top="75" width="25.5" height="12.75" align-x="77.25" align-y="84" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>p</ml:id> <ml:real>.4</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="136" left="132" top="74.25" width="141.75" height="12" align-x="132" align-y="84" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> location of max camber (fraction) </text> </region> <region region-id="137" left="66" top="93" width="33" height="12.75" align-x="80.25" align-y="102" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>th</ml:id> <ml:real>.12</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="138" left="132" top="92.25" width="48" height="12" align-x="132" align-y="102" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> t/c (%age) </text> </region> <region region-id="199" left="66" top="135" width="45.75" height="12.75" align-x="95.25" align-y="144" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>chord</ml:id> <ml:real>80</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="200" left="66" top="153" width="57.75" height="12.75" align-x="91.5" align-y="162" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>twist</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-5</ml:real> <ml:id>deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="103" left="18" top="194.25" width="165" height="12" align-x="18" align-y="204" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NACA thickness distribution equation: </text> </region> <region region-id="125" left="102" top="218.25" width="267.75" height="27.75" align-x="131.25" align-y="234" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="th">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>th</ml:id> <ml:real>.2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>.29690</ml:real> <ml:apply> <ml:sqrt/> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.12600</ml:real> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.35160</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.28430</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.10150</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="123" left="18" top="266.25" width="126" height="12" align-x="18" align-y="276" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Mean line (camber) equation: </text> </region> <region region-id="124" left="156" top="278.25" width="221.25" height="71.25" align-x="181.5" align-y="294" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="c">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>f</ml:id> <ml:id>p</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>m</ml:id> <ml:apply> <ml:pow/> <ml:id>p</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id>p</ml:id> </ml:apply> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>m</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id>p</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">2</ml:real> <ml:id>p</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id>p</ml:id> </ml:apply> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="505" left="600" top="320.25" width="41.25" height="27.75" align-x="619.5" align-y="336" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:eval> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>.05</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="158" left="24" top="375" width="113.25" height="15" align-x="67.5" align-y="384" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="w.top">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="159" left="24" top="405" width="126" height="15" align-x="81" align-y="414" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="w.bottom">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="162" left="24" top="435" width="30.75" height="12.75" align-x="44.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>x</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:id>f</ml:id> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="178" left="18" top="464.25" width="414.75" height="36" align-x="18" align-y="474" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> NACA 4 series airfoil reformulated as a single curve which starts at the upper trailing edge and ends at the lower trailing edge. It also uses a cosine distribution to consentrate the points at the nose and trailing edge. </text> </region> <region region-id="191" left="600" top="477" width="52.5" height="15" align-x="612.75" align-y="486" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="a">f</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>.01</ml:real> </ml:sequence> <ml:real>1</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="183" left="456" top="513" width="113.25" height="29.25" align-x="480.75" align-y="522" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>ff</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id>s</ml:id> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:minus/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="179" left="24" top="512.25" width="106.5" height="27.75" align-x="57" align-y="528" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="cos">f</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id>cos</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:id>π</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="186" left="606" top="519" width="54" height="15" align-x="620.25" align-y="528" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="a">s</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>.05</ml:real> </ml:sequence> <ml:real>2</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="180" left="24" top="549" width="198.75" height="33.75" align-x="52.5" align-y="558" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>yy</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:minus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="184" left="456" top="564" width="223.5" height="175.5" align-x="456" align-y="564" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="19"/> <rendering item-idref="20"/> </region> <region region-id="206" left="30" top="597" width="60" height="15" align-x="55.5" align-y="606" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>xx</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="185" left="18" top="684" width="393" height="205.5" align-x="18" align-y="684" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="22"/> <rendering item-idref="23"/> </region> <region region-id="207" left="528" top="813" width="159" height="57" align-x="569.25" align-y="846" show-border="false" show-highlight="false" is-protected="true" 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show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="root">chord</ml:id> <ml:apply> <ml:div/> <ml:real font="0">83.24</ml:real> <ml:real>12</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="204" left="18" top="947.25" width="98.25" height="15.75" align-x="18" align-y="960" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="14"> Wing definition </f> </text> </region> <region region-id="265" left="204" top="969" width="39" height="12.75" align-x="215.25" align-y="978" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>b</ml:id> <ml:real>116.2</ml:real> 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<text use-page-width="false" push-down="false" lock-width="true"> <f family="Arial" charset="0" size="16"> <inlineAttr line-through="false">move step sizes up here </inlineAttr> </f> </text> </region> <region region-id="649" left="486" top="1455" width="58.5" height="12.75" align-x="528" align-y="1464" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>chordpts</ml:id> <ml:real>15</ml:real> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="565" left="42" top="1485" width="168.75" height="15" align-x="77.25" align-y="1494" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>X</ml:id> <ml:boundVars> <ml:id>s</ml:id> <ml:id>y</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:minus/> <ml:apply> 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complex-threshold="10" imaginary-value="i" zero-threshold="15" precision="3" show-trailing-zeros="false" exponential-threshold="3"/> <matrix display-style="auto" expand-nested-arrays="false"/> <unit format-units="true" simplify-units="true"/> </results> </mathRendering> <pageModel show-page-frame="false" show-header-frame="false" show-footer-frame="false" header-footer-start-page="1" paper-code="1" orientation="portrait" page-width="612" page-height="792"> <margins left="86.4" right="86.4" top="86.4" bottom="86.4"/> <header use-full-page-width="false"/> <footer use-full-page-width="false"/> </pageModel> <colorModel background-color="#fff" default-highlight-color="#ffff80"/> </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="true" optimize-expressions="false" exact-boolean="false" strings-use-origin="false"/> <units unit-system="us"/> </calculation> <editor protection-level="none" 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="false" save-text-images="false"/> <miscellaneous> <handbook handbook-region-tag-ub="711" 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="196" left="18" top="14.25" width="72" height="12" align-x="18" align-y="24" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NACA 4 Series: </text> </region> <region region-id="139" left="66" top="33" width="18.75" height="12.75" align-x="74.25" align-y="42" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:real>2412</ml:real> </math> <rendering item-idref="2"/> </region> <region region-id="133" left="66" top="57" width="31.5" height="12.75" align-x="78.75" align-y="66" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit"> <ml:id>m</ml:id> <ml:real>.02</ml:real> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="134" left="132" top="56.25" width="44.25" height="12" align-x="132" align-y="66" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> % camber </text> </region> <region region-id="135" left="66" top="75" width="25.5" height="12.75" align-x="77.25" align-y="84" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>p</ml:id> <ml:real>.4</ml:real> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="136" left="132" top="74.25" width="141.75" height="12" align-x="132" align-y="84" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> location of max camber (fraction) </text> </region> <region region-id="137" left="66" top="93" width="33" height="12.75" align-x="80.25" align-y="102" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>th</ml:id> <ml:real>.12</ml:real> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="138" left="132" top="92.25" width="48" height="12" align-x="132" align-y="102" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> t/c (%age) </text> </region> <region region-id="199" left="66" top="135" width="45.75" height="12.75" align-x="95.25" align-y="144" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>chord</ml:id> <ml:real>80</ml:real> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="200" left="66" top="153" width="57.75" height="12.75" align-x="91.5" align-y="162" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>twist</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>-5</ml:real> <ml:id>deg</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="103" left="18" top="194.25" width="165" height="12" align-x="18" align-y="204" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> NACA thickness distribution equation: </text> </region> <region region-id="125" left="102" top="218.25" width="267.75" height="27.75" align-x="131.25" align-y="234" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="th">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>th</ml:id> <ml:real>.2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:real>.29690</ml:real> <ml:apply> <ml:sqrt/> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.12600</ml:real> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.35160</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.28430</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>.10150</ml:real> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>4</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="123" left="18" top="266.25" width="126" height="12" align-x="18" align-y="276" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="true"> Mean line (camber) equation: </text> </region> <region region-id="124" left="156" top="278.25" width="221.25" height="71.25" align-x="181.5" align-y="294" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="c">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>f</ml:id> <ml:id>p</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>m</ml:id> <ml:apply> <ml:pow/> <ml:id>p</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id>p</ml:id> </ml:apply> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id>m</ml:id> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id>p</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">2</ml:real> <ml:id>p</ml:id> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id>p</ml:id> </ml:apply> <ml:id>f</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:pow/> <ml:id>f</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="9"/> </region> <region region-id="505" left="600" top="320.25" width="41.25" height="27.75" align-x="619.5" align-y="336" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:eval> <ml:apply> <ml:div/> <ml:real>2</ml:real> <ml:real>.05</ml:real> </ml:apply> </ml:eval> </math> <rendering item-idref="10"/> </region> <region region-id="158" left="24" top="375" width="113.25" height="15" align-x="67.5" align-y="384" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="w.top">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="11"/> </region> <region region-id="159" left="24" top="405" width="126" height="15" align-x="81" align-y="414" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="w.bottom">y</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:id>f</ml:id> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="162" left="24" top="435" width="30.75" height="12.75" align-x="44.25" align-y="444" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>x</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:id>f</ml:id> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="178" left="18" top="464.25" width="414.75" height="36" align-x="18" align-y="474" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> NACA 4 series airfoil reformulated as a single curve which starts at the upper trailing edge and ends at the lower trailing edge. It also uses a cosine distribution to consentrate the points at the nose and trailing edge. </text> </region> <region region-id="191" left="600" top="477" width="52.5" height="15" align-x="612.75" align-y="486" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="a">f</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>.01</ml:real> </ml:sequence> <ml:real>1</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="183" left="456" top="513" width="113.25" height="29.25" align-x="480.75" align-y="522" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>ff</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id>s</ml:id> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:minus/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="15"/> </region> <region region-id="179" left="24" top="512.25" width="106.5" height="27.75" align-x="57" align-y="528" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="cos">f</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id>cos</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:id>π</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="186" left="606" top="519" width="54" height="15" align-x="620.25" align-y="528" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="a">s</ml:id> <ml:range> <ml:sequence> <ml:real>0</ml:real> <ml:real>.05</ml:real> </ml:sequence> <ml:real>2</ml:real> </ml:range> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="180" left="24" top="549" width="198.75" height="33.75" align-x="52.5" align-y="558" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>yy</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:program> <ml:ifThen> <ml:apply> <ml:lessThan/> <ml:id>s</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:plus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:ifThen> <ml:otherwise> <ml:apply> <ml:minus/> <ml:apply> <ml:id subscript="c">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:id subscript="th">y</ml:id> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:otherwise> </ml:program> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="184" left="456" top="564" width="223.5" height="175.5" align-x="456" align-y="564" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="19"/> <rendering item-idref="20"/> </region> <region region-id="206" left="30" top="597" width="60" height="15" align-x="55.5" align-y="606" show-border="false" show-highlight="true" is-protected="true" background-color="#80ff80" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id>xx</ml:id> <ml:boundVars> <ml:id>s</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:id subscript="cos">f</ml:id> <ml:id>s</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="185" left="18" top="684" width="393" height="205.5" align-x="18" align-y="684" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="22"/> <rendering item-idref="23"/> </region> <region region-id="207" left="528" top="813" width="159" height="57" align-x="569.25" align-y="846" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="top">arc</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> <ml:apply> <ml:id subscript="w.top">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id>f</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="24"/> </region> <region region-id="208" left="522" top="885" width="186" height="57" align-x="576.75" align-y="918" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:function> <ml:id subscript="bottom">arc</ml:id> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:integral auto-algorithm="true" algorithm="adaptive"/> <ml:lambda> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> <ml:apply> <ml:sqrt/> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:derivative/> <ml:lambda> <ml:boundVars> <ml:id>f</ml:id> </ml:boundVars> <ml:apply> <ml:id subscript="w.bottom">y</ml:id> <ml:id>f</ml:id> </ml:apply> </ml:lambda> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:lambda> <ml:bounds> <ml:real>0</ml:real> <ml:id>f</ml:id> </ml:bounds> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="540" left="288" top="938.25" width="75" height="27.75" align-x="332.25" align-y="954" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="root">chord</ml:id> <ml:apply> <ml:div/> <ml:real font="0">83.24</ml:real> <ml:real>12</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="26"/> </region> <region region-id="204" left="18" top="947.25" width="98.25" height="15.75" align-x="18" align-y="960" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <text use-page-width="false" push-down="false" lock-width="false"> <f size="14"> Wing definition </f> </text> </region> <region region-id="265" left="204" top="969" width="39" height="12.75" align-x="215.25" align-y="978" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>b</ml:id> <ml:real>116.2</ml:real> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="236" left="564" top="975" width="46.5" height="12.75" align-x="587.25" align-y="984" show-border="false" show-highlight="false" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id>step</ml:id> <ml:real font="0">.001</ml:real> </ml:define> </math> <rendering item-idref="28"/> </region> <region region-id="267" left="288" top="980.25" width="66" height="27.75" align-x="327.75" align-y="996" show-border="false" show-highlight="true" is-protected="true" background-color="inherit" tag=""> <math optimize="false" export="false" disable-calc="false"> <ml:define> <ml:id subscript="tip">chord</ml:id> <ml:apply> <ml:div/> <ml:real>28.3</ml:real> <ml:real>12</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="268" left="198" top="993" width="68.25" height="12.75" align-x="229.5" 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