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width="6000" height="6" align-x="12" align-y="186" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="2770" left="6" top="210.75" width="135" height="14.25" align-x="6" align-y="222" 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"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> Tail Design Parameters</inlineAttr> </b> </f> </p> </text> </region> <region region-id="2771" left="180" top="225" width="81" height="16.5" align-x="194.25" align-y="234" 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/math20"> <ml:id xml:space="preserve" subscript="t">L</ml:id> <ml:id xml:space="preserve" subscript="horizontal.tail">L</ml:id> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="2772" left="6" top="230.25" width="55.5" height="12" align-x="20.25" align-y="240" 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">Length of tail</p> </text> </region> <region region-id="2759" left="12" top="273.75" width="98.25" height="18" align-x="32.25" align-y="288" 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"> <f size="16">Horizontal Tail</f> </p> </text> </region> <region region-id="2747" left="0" top="294" width="6008.25" align-x="0" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="590.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="2739" bottom-lock-id="2746"> <region region-id="83" left="36" top="12.75" width="207" height="14.25" align-x="36" align-y="24" 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"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> <sp count="3"/>Horizontal Tail Design parameters:</inlineAttr> </b> </f> </p> </text> </region> <region region-id="903" left="36" top="32.25" width="76.5" height="12" align-x="36" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" line-through="false">Tail Volume Ratio</inlineAttr> </f> </p> </text> </region> <region region-id="908" left="330" top="39" width="40.5" height="16.5" align-x="346.5" align-y="48" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">V</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> </region> <region region-id="904" left="36" top="50.25" width="117" height="12" align-x="36" align-y="60" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" line-through="false">Horizontal Tail Aspect ratio</inlineAttr> </f> </p> </text> </region> <region region-id="909" left="330" top="57" width="42" height="16.5" align-x="354.75" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">AR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>6</ml:real> </result> </ml:eval> </math> </region> <region region-id="910" left="330" top="75" width="47.25" height="16.5" align-x="353.25" align-y="84" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">TR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> </region> <region region-id="905" left="36" top="104.25" width="87" height="12" align-x="36" align-y="114" 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">Horizontal Tail Twist</p> </text> </region> <region region-id="911" left="330" top="105" width="50.25" height="16.5" align-x="363" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">Twist</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> </region> <region region-id="906" left="36" top="134.25" width="273.75" height="15" align-x="36" align-y="144" 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">assumed dynamic pressure at the tail / dynamic pressure, q<sub>h</sub>/q</p> </text> </region> <region region-id="912" left="330" top="134.25" width="41.25" height="17.25" align-x="347.25" align-y="144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">η</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.9</ml:real> </result> </ml:eval> </math> </region> <region region-id="907" left="36" top="158.25" width="155.25" height="12" align-x="36" align-y="168" 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">incidence angle of the horizontal tail</p> </text> </region> <region region-id="913" left="330" top="159" width="51" height="16.5" align-x="342.75" align-y="168" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">i</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.016228944049669271</ml:real> </result> </ml:eval> </math> </region> <region region-id="95" left="36" top="188.25" width="120.75" height="12" align-x="36" align-y="198" 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"> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false">Elevator design parameters:</inlineAttr> </f> </p> </text> </region> <region region-id="679" left="36" top="207" width="48" height="16.5" align-x="60" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="C.E">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.4</ml:real> </result> </ml:eval> </math> </region> <region region-id="97" left="150" top="212.25" width="184.5" height="12" align-x="150" align-y="222" 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">Elevator, fraction of chord,<sp count="2"/>typically .30-40</p> </text> </region> <region region-id="691" left="36" top="231" width="40.5" height="16.5" align-x="59.25" align-y="240" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="b.E">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> </region> <region region-id="99" left="150" top="230.25" width="180" height="12" align-x="150" align-y="240" 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">Elevator, fraction of span,<sp count="3"/>typically .9 - 1</p> </text> </region> <region region-id="137" left="12" top="276.75" width="216" height="14.25" align-x="12" align-y="288" 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"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> Horizontal Tail, calculated properties:</inlineAttr> </b> </f> </p> </text> </region> <region region-id="914" left="18" top="302.25" width="174" height="12" align-x="18" align-y="312" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false">area of the Horizontal Tail</inlineAttr> </f> </p> </text> </region> <region region-id="795" left="234" top="297" width="54.75" height="22.5" align-x="249.75" align-y="312" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">S</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ft</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>2.7831999999999972</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="foot" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="915" left="18" top="320.25" width="24" height="12" align-x="18" align-y="330" 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">span </p> </text> </region> <region region-id="796" left="234" top="321" width="56.25" height="16.5" align-x="249.75" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">b</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>49.037585584936764</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="797" left="234" top="339" width="62.25" height="16.5" align-x="255.75" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r.h">C</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>10.216163663528494</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="916" left="18" top="344.25" width="43.5" height="12" align-x="18" align-y="354" 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">root chord</p> </text> </region> <region region-id="148" left="18" top="362.25" width="37.5" height="12" align-x="18" align-y="372" 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">tip chord</p> </text> </region> <region region-id="798" left="234" top="363" width="53.25" height="16.5" align-x="255.75" align-y="372" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="t.h">C</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>6.1296981981170964</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="151" left="18" top="380.25" width="51" height="12" align-x="18" align-y="390" 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">mean chord</p> </text> </region> <region region-id="799" left="234" top="381" width="62.25" height="16.5" align-x="260.25" align-y="390" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">mac</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>8.3432003252149354</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="154" left="18" top="398.25" width="124.5" height="12" align-x="18" align-y="408" 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">root thickness, for structures</p> </text> </region> <region region-id="800" left="234" top="399" width="61.5" height="16.5" align-x="259.5" align-y="408" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r.h">Ht</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>0.91945472971756437</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="157" left="18" top="416.25" width="55.5" height="12" align-x="18" align-y="426" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">tip thickness</p> </text> </region> <region region-id="919" left="234" top="417" width="61.5" height="16.5" align-x="259.5" align-y="426" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="t.h">Ht</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>0.55167283783053866</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="160" left="18" top="434.25" width="78" height="12" align-x="18" align-y="444" 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">average thickness</p> </text> </region> <region region-id="920" left="240" top="435" width="49.5" height="16.5" align-x="253.5" align-y="444" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">t</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>0.73556378377405152</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="803" left="210" top="465" width="79.5" height="22.5" align-x="240" align-y="480" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="weth">S</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>837.63187199999936</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="163" left="18" top="476.25" width="50.25" height="12" align-x="18" align-y="486" 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">wetted area</p> </text> </region> <region region-id="963" left="480" top="477" width="78.75" height="15" align-x="490.5" align-y="486" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="true"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="t">l</ml:id> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="t">L</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>.75</ml:real> <ml:id xml:space="preserve" subscript="h">mac</ml:id> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="962" left="240" top="501" width="40.5" height="16.5" align-x="256.5" align-y="510" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">V</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> </region> <region region-id="166" left="18" top="518.25" width="51.75" height="12" align-x="18" align-y="528" 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">volume ratio</p> </text> </region> <region region-id="171" left="18" top="554.25" width="75.75" height="12" align-x="36" 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">Reynolds number</p> </text> </region> <region region-id="172" left="234" top="555" width="147" height="22.5" align-x="327.75" 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 xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:apply> <ml:id xml:space="preserve" subscript="flt">Re</ml:id> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:id xml:space="preserve">fps</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">mac</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>294017.5086449681</ml:real> </result> </ml:eval> </math> </region> </area> <rendering item-idref="6"/> </region> <region region-id="174" left="6" top="294" width="6000" height="6" align-x="6" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <pageBreak/> </region> <region region-id="2758" left="12" top="333.75" width="81.75" height="18" align-x="32.25" align-y="348" 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"> <f size="16">Vertical Tail</f> </p> </text> </region> <region region-id="2781" left="0" top="354" width="6008.25" align-x="0" align-y="354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="566.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="2752" bottom-lock-id="2755"> <region region-id="189" left="6" top="18.75" width="210.75" height="14.25" align-x="6" align-y="30" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false">1.2.3 Vertical Tail Design parameters:</inlineAttr> </b> </f> </p> </text> </region> <region region-id="683" left="6" top="33" width="45" height="16.5" align-x="22.5" align-y="42" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">V</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.03</ml:real> </result> </ml:eval> </math> </region> <region region-id="191" left="84" top="38.25" width="50.25" height="12" align-x="84" align-y="48" 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">tail vol coeff</p> </text> </region> <region region-id="192" left="162" top="38.25" width="327" height="96" align-x="162" align-y="48" 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">This value (C.v) is the y input on Fig. 9-24 in Torenbeek.<sp count="2"/>It must be</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">0.038 or greater for a single engine propeller A/C with little normal</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">force on the vertical tail.<sp count="2"/>Raymer (pg. 125) says that 0.02 is the typical value for a sailplane.<sp count="2"/>0.04 is for a single engle plane and 0.08 is for a military cargo/bomber.</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">Look at the "Checking the Vertical Tail Size" section.<sp count="2"/>As of 2/12/01</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">the analysis shows that a C.vt of 0.04 is required.</p> </text> </region> <region region-id="684" left="6" top="57" width="42" height="16.5" align-x="30.75" align-y="66" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">AR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>2</ml:real> </result> </ml:eval> </math> </region> <region region-id="685" left="6" top="81" width="47.25" height="16.5" align-x="29.25" align-y="90" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">TR</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.6</ml:real> </result> </ml:eval> </math> </region> <region region-id="686" left="6" top="105" width="50.25" height="16.5" align-x="39" align-y="114" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">Twist</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0</ml:real> </result> </ml:eval> </math> </region> <region region-id="687" left="6" top="146.25" width="41.25" height="17.25" align-x="23.25" align-y="156" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">η</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.9</ml:real> </result> </ml:eval> </math> </region> <region region-id="197" left="102" top="152.25" width="273.75" height="15" align-x="102" align-y="162" 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">assumed dynamic pressure at the tail / dynamic pressure, q<sub>h</sub>/q</p> </text> </region> <region region-id="198" left="6" top="176.25" width="129" height="12" align-x="6" align-y="186" 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"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false">Rudder design parameters:</inlineAttr> </b> </f> </p> </text> </region> <region region-id="688" left="6" top="189" width="49.5" height="16.5" align-x="31.5" align-y="198" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="C.R">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.4</ml:real> </result> </ml:eval> </math> </region> <region region-id="200" left="120" top="194.25" width="189.75" height="12" align-x="120" align-y="204" 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">Rudder, fraction of chord,<sp count="2"/>typically .30 - .40</p> </text> </region> <region region-id="689" left="6" top="207" width="42" height="16.5" align-x="30.75" align-y="216" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="b.R">F</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>1</ml:real> </result> </ml:eval> </math> </region> <region region-id="202" left="120" top="212.25" width="176.25" height="12" align-x="120" align-y="222" 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">Rudder, fraction of span,<sp count="3"/>typically .7 - 1</p> </text> </region> <region region-id="239" left="24" top="246.75" width="225.75" height="14.25" align-x="24" align-y="258" 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"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false">1.2.3 Vertical Tail, calculated properties:</inlineAttr> </b> </f> </p> </text> </region> <region region-id="921" left="360" top="278.25" width="265.5" height="24" align-x="360" align-y="288" 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">Note that Ltail is not entirely correct as the term should really</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">be L.v, the length to the quarter chord of the vertical tail.</p> </text> </region> <region region-id="805" left="252" top="279" width="65.25" height="22.5" align-x="267.75" align-y="294" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">S</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>217.7712</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="240" left="30" top="290.25" width="99.75" height="12" align-x="30" align-y="300" 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"> <f family="Arial" charset="0"> <inlineAttr font-weight="normal" line-through="false">area of the Vertical Tail</inlineAttr> </f> </p> </text> </region> <region region-id="922" left="366" top="309" width="45" height="16.5" align-x="379.5" 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:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="t">L</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>62.5</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="925" left="30" top="320.25" width="24" height="12" align-x="30" align-y="330" 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">span </p> </text> </region> <region region-id="806" left="246" top="321" width="51.75" height="16.5" align-x="261.75" align-y="330" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">h</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>20.869652608512677</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="926" left="30" top="338.25" width="43.5" height="12" align-x="30" align-y="348" 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">root chord</p> </text> </region> <region region-id="807" left="246" top="339" width="62.25" height="16.5" align-x="267.75" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r.v">C</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>13.043532880320424</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="927" left="30" top="356.25" width="37.5" height="12" align-x="30" align-y="366" 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">tip chord</p> </text> </region> <region region-id="808" left="246" top="357" width="57.75" height="16.5" align-x="267.75" align-y="366" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="t.v">C</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>7.8261197281922534</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="928" left="30" top="374.25" width="51" height="12" align-x="30" align-y="384" 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">mean chord</p> </text> </region> <region region-id="809" left="240" top="375" width="66.75" height="16.5" align-x="266.25" align-y="384" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">mac</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>10.434826304256339</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="929" left="30" top="392.25" width="124.5" height="12" align-x="30" align-y="402" 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">root thickness, for structures</p> </text> </region> <region region-id="810" left="252" top="393" width="61.5" height="16.5" align-x="277.5" align-y="402" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r.v">Ht</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result 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xml:space="preserve" subscript="flt">Re</ml:id> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:id xml:space="preserve">fps</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="v">mac</ml:id> </ml:sequence> </ml:apply> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>367727.19262753543</ml:real> </result> </ml:eval> </math> </region> </area> <rendering item-idref="7"/> </region> <region region-id="1154" left="60" top="378.75" width="111.75" height="14.25" align-x="60" align-y="390" 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"> <f family="Arial" 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item-idref="12"/> </region> <region region-id="1583" left="60" top="483" width="58.5" height="16.5" align-x="78" align-y="492" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">Q</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="h">eff</ml:id> <ml:id xml:space="preserve" subscript="w">Q</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="13"/> </region> <region region-id="2417" left="258" top="483" width="70.5" height="16.5" align-x="275.25" align-y="492" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="h">Q</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>264.33617986575484</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pascal"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="14"/> </region> <region region-id="1264" left="78" top="564.75" width="188.25" height="14.25" align-x="78" align-y="576" 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="0" text-align="inherit" list-style-type="none" tabs="inherit"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr line-through="false"> flap effectiveness parameter,Tau</inlineAttr> </b> </f> </p> </text> </region> <region region-id="1265" left="150" top="596.25" width="317.25" height="24" align-x="150" align-y="606" 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">Tau is the flap effectiveness parameter and is</p> <p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">found in Fig. 2.21 on pg. 64 in Flight Stability and Control.modeled here<sp count="3"/> </p> </text> </region> <region region-id="1289" left="114" top="632.25" width="3" height="24" align-x="121.5" align-y="642" 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="0" margin-right="0" text-indent="inherit" text-align="left" 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"> <sp/> </p> </text> </region> <region region-id="1292" left="174" top="680.25" width="112.5" height="24" align-x="182.25" align-y="690" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">Flap Fraction defined here</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Needs to be in Layout</p> </text> </region> <region region-id="1293" left="84" top="687" width="56.25" height="16.5" align-x="121.5" align-y="696" show-border="false" show-highlight="true" 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<ml:id xml:space="preserve">in</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>94.499999999999986</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="2054" left="48" top="56.25" width="82.5" height="12" align-x="62.25" align-y="66" 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">Length of Fuselage</p> </text> </region> <region region-id="2728" left="270" top="75" width="45" height="16.5" align-x="286.5" align-y="84" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#ffff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">V</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.03</ml:real> </result> </ml:eval> </math> </region> <region region-id="2055" left="48" top="80.25" width="135" height="12" align-x="48" align-y="90" 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">Vertical Tail Volume Coefficient</p> </text> </region> <region region-id="1069" left="270" top="99" width="36" height="16.5" align-x="286.5" align-y="108" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="w">z</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>5</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2056" left="48" top="104.25" width="162.75" height="12" align-x="48" align-y="114" 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">Vertical Distance from Wing cc to cg </p> </text> </region> <region region-id="1072" left="348" top="128.25" width="181.5" height="24" align-x="357" align-y="138" 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">NOT used in calculations, used to look up k.n factor (Nelson, 74-75)</p> </text> </region> <region region-id="1074" left="270" top="135" width="39.75" height="16.5" align-x="290.25" align-y="144" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="25">h</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2058" left="48" top="140.25" width="126" height="12" align-x="69" align-y="150" 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">Fuselage height at 1/4 length</p> </text> </region> <region region-id="1076" left="270" top="153" width="46.5" height="16.5" align-x="290.25" align-y="162" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="75">h</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>2.5</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="1077" left="378" top="153" width="45" height="16.5" align-x="398.25" align-y="162" 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/math20"> <ml:id xml:space="preserve" subscript="m">X</ml:id> <ml:id xml:space="preserve" subscript="cg">X</ml:id> </ml:define> </math> </region> <region region-id="2059" left="48" top="158.25" width="126" height="12" align-x="69" align-y="168" 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">Fuselage height at 3/4 length</p> </text> </region> <region region-id="1695" left="270" top="171" width="51.75" height="22.5" align-x="288" align-y="186" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="fs">S</ml:id> <ml:unitOverride> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real font="0">2</ml:real> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>562</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="2060" left="48" top="182.25" width="87" height="12" align-x="69" align-y="192" 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">Fuselage side angle</p> </text> </region> <region region-id="2061" left="48" top="206.25" width="93" height="12" align-x="48" align-y="216" 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">k.n factor (Nelson 74)</p> </text> </region> <region region-id="1697" left="270" top="201" width="71.25" height="22.5" align-x="285" align-y="216" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n">k</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.0075</ml:real> </result> </ml:eval> </math> </region> <region region-id="2062" left="48" top="260.25" width="200.25" height="24" align-x="48" align-y="270" 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"> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">h</inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">.factor - accounts for sidewash and efficiency</inlineAttr> </f> </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">Page 76, Nelson</inlineAttr> </f> </p> </text> </region> <region region-id="2037" left="270" top="255.75" width="263.25" height="54.75" align-x="297.75" align-y="294" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="fact">η</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:real>.724</ml:real> <ml:apply> <ml:mult style="default"/> <ml:real>3.06</ml:real> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="v">S</ml:id> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> <ml:apply> <ml:plus/> <ml:real>1</ml:real> <ml:apply> <ml:id xml:space="preserve">cos</ml:id> <ml:id xml:space="preserve" subscript="c.4w">Λ</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:real>.4</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">z</ml:id> <ml:id xml:space="preserve">d</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>.009</ml:real> <ml:id xml:space="preserve" subscript="w">AR</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="2063" left="48" top="314.25" width="141.75" height="12" align-x="69" align-y="324" 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">Reynolds number of the fuselage</p> </text> </region> <region region-id="2036" left="270" top="315" width="117.75" height="16.5" align-x="290.25" align-y="324" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="l.f">R</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="flt">Re</ml:id> <ml:sequence> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> <ml:apply> <ml:mult style="auto-select"/> <ml:real>50</ml:real> <ml:id xml:space="preserve">fps</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="fuse">L</ml:id> </ml:sequence> </ml:apply> </ml:define> </math> </region> <region region-id="2064" left="48" top="332.25" width="191.25" height="12" align-x="48" align-y="342" 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">k.rl factor, correction for Re.fuse (Nelson 74)</p> </text> </region> <region region-id="2035" left="270" top="333" width="39" height="16.5" align-x="285.75" align-y="342" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="rl">k</ml:id> <ml:real>1.08</ml:real> </ml:define> </math> </region> <region region-id="2065" left="48" top="386.25" width="172.5" height="24" align-x="69" align-y="396" 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">Coeficient of yaw moment from fuselage</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">PER DEGREE</p> </text> </region> <region region-id="2667" left="348" top="376.5" width="143.25" height="35.25" align-x="385.5" align-y="396" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.β.wf">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="n">k</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rl">k</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="fs">S</ml:id> <ml:id xml:space="preserve" subscript="fuse.whole">L</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="w">S</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2666" left="348" top="416.25" width="103.5" height="17.25" align-x="380.25" align-y="426" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.β.v">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="v">V</ml:id> <ml:id xml:space="preserve" subscript="fact">η</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.v">C</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2066" left="48" top="422.25" width="192.75" height="12" align-x="69" align-y="432" 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">Coeficient of yaw from vertical tail, per radian</p> </text> </region> <region region-id="2665" left="348" top="447" width="102" height="16.5" align-x="372.75" align-y="456" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.β">C</ml:id> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="n.β.v">C</ml:id> <ml:id xml:space="preserve" subscript="n.β.wf">C</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2669" left="354" top="470.25" width="68.25" height="27.75" align-x="378" align-y="486" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.β">C</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve">rad</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>0.17354181491319878</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="radian" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> </region> <region region-id="2671" left="450" top="476.25" width="173.25" height="12" align-x="458.25" align-y="486" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">This value should be between .05 and .1</p> </text> </region> </area> <rendering item-idref="36"/> </region> <region region-id="2726" left="0" top="1626" width="6008.25" align-x="0" align-y="1626" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="818.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1917" bottom-lock-id="1921"> <region region-id="1044" left="282" top="21" width="54.75" height="16.5" align-x="312.75" align-y="30" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L0.w">C</ml:id> <ml:real>-0.1</ml:real> </ml:define> </math> </region> <region region-id="1045" left="354" top="20.25" width="135" height="12" align-x="354" align-y="30" 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">From the wing lift vs. alpha plot</p> </text> </region> <region region-id="2113" left="66" top="40.5" width="107.25" height="35.25" align-x="93.75" align-y="60" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.δe">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="h">S</ml:id> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">η</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="el">τ</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2112" left="66" top="80.25" width="112.5" height="17.25" align-x="97.5" align-y="90" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.δe">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">η</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="el">τ</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2111" left="66" top="118.5" width="75" height="35.25" align-x="100.5" align-y="138" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.trim">C</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="dsgn">W</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="w">Q</ml:id> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2110" left="66" top="190.5" width="80.25" height="36" align-x="81" align-y="210" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="L.w">C</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve" subscript="w">AR</ml:id> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2096" left="258" top="190.5" width="75.75" height="36" align-x="289.5" align-y="210" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">dε_dα</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">π</ml:id> <ml:id xml:space="preserve" subscript="w">AR</ml:id> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2078" left="276" top="254.25" width="86.25" height="24" align-x="286.5" align-y="264" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">Need to check what input to C.M.w</p> </text> </region> <region region-id="2109" left="66" top="250.5" width="197.25" height="35.25" align-x="102.75" align-y="270" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.0.w">C</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:id xml:space="preserve" subscript="M.w">C</ml:id> <ml:real>0</ml:real> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="L0.w">C</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="cg">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ac.w">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2077" left="384" top="260.25" width="154.5" height="12" align-x="400.5" align-y="270" 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">Moment of wing at 0 angle of attack</p> </text> </region> <region region-id="2108" left="66" top="298.5" width="150" height="35.25" align-x="102" align-y="318" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="Mα.w">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="cg">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ac.w">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="2107" left="66" top="350.25" width="155.25" height="17.25" align-x="101.25" align-y="360" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.0.h">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="h">η</ml:id> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="0">ε</ml:id> <ml:id xml:space="preserve" subscript="w">i</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">i</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="2106" left="66" top="380.25" width="174" height="17.25" align-x="121.5" align-y="390" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve" subscript="M.α.h">C</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="h">η</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">dε_dα</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="1526" left="186" top="423" width="39" height="12.75" align-x="204.75" 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:id xml:space="preserve" xmlns:ml="http://schemas.mathsoft.com/math20">Assumed</ml:id> </math> </region> <region region-id="2105" left="66" top="429" width="45.75" height="16.5" align-x="99.75" align-y="438" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.0.f">C</ml:id> <ml:real>0</ml:real> </ml:define> </math> </region> <region region-id="1528" left="186" top="470.25" width="62.25" height="12" align-x="186" align-y="480" 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">Also assumed</p> </text> </region> <region region-id="2104" left="66" top="470.25" width="62.25" height="27.75" align-x="99" align-y="486" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="Mα.f">C</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:apply> <ml:div/> <ml:real font="0">1</ml:real> <ml:id xml:space="preserve">rad</ml:id> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2103" left="66" top="513" width="171" height="16.5" align-x="117.75" align-y="522" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.0.plane">C</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="M.0.w">C</ml:id> <ml:id xml:space="preserve" subscript="M.0.h">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="M.0.f">C</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2102" left="66" top="537" width="191.25" height="16.5" align-x="119.25" align-y="546" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.α.plane">C</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="Mα.w">C</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="M.α.h">C</ml:id> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="Mα.f">C</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2348" left="306" top="555" width="90.75" height="16.5" align-x="358.5" 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:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="M.α.plane">C</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.53788624118126338</ml:real> </result> </ml:eval> </math> </region> <region region-id="2101" left="66" top="578.25" width="217.5" height="17.25" align-x="129.75" align-y="588" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve" subscript="M.plane">C</ml:id> <ml:boundVars> <ml:id xml:space="preserve" subscript="a">α</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:id xml:space="preserve" subscript="M.0.plane">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="M.α.plane">C</ml:id> <ml:apply> <ml:id xml:space="preserve" subscript="fus">α</ml:id> <ml:id xml:space="preserve" subscript="a">α</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> </region> <region region-id="2100" left="66" top="610.5" width="258" height="35.25" align-x="91.5" align-y="630" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="NP">X</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="w">mac</ml:id> <ml:parens> <ml:apply> <ml:plus/> <ml:apply> <ml:minus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="ac.w">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="Mα.f">C</ml:id> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="h">η</ml:id> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:real>1</ml:real> <ml:id xml:space="preserve">dε_dα</ml:id> </ml:apply> </ml:parens> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="2099" left="66" top="664.5" width="93.75" height="35.25" align-x="126.75" align-y="684" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="NP_nondim">X</ml:id> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="NP">X</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2098" left="66" top="712.5" width="209.25" height="35.25" align-x="91.5" align-y="732" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDFunction" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="trim">δ</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>-1</ml:real> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="M.0.plane">C</ml:id> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="Mα.w">C</ml:id> <ml:id xml:space="preserve" subscript="L.trim">C</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:minus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="M.δe">C</ml:id> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="Mα.w">C</ml:id> <ml:id xml:space="preserve" subscript="L.δe">C</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> </region> <region region-id="2097" left="66" top="765.75" width="122.25" height="36" align-x="93.75" align-y="786" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="trim">α</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="L.trim">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="L.δe">C</ml:id> <ml:id xml:space="preserve" subscript="trim">δ</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> </ml:define> </math> </region> </area> <rendering item-idref="37"/> </region> <region region-id="2616" left="30" top="1610.25" width="458.25" height="20.25" align-x="30" align-y="1626" 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"> <f family="Arial" charset="0" size="18"> <inlineAttr font-weight="normal" line-through="false">Stick-Fixed Neutral Point</inlineAttr> </f> </p> </text> </region> <region region-id="2277" left="30" top="1658.25" width="228" height="20.25" align-x="42" align-y="1674" 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"> <f family="Arial" charset="0" size="18"> <inlineAttr font-weight="normal" font-style="normal" line-through="false">Static Margin</inlineAttr> </f> </p> </text> </region> <region region-id="2777" left="0" top="1680" width="6008.25" align-x="0" align-y="1680" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="86.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1913" bottom-lock-id="1915"> <region region-id="1008" left="72" top="10.5" width="78.75" height="35.25" align-x="92.25" align-y="30" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff00" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SM</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="NP">X</ml:id> <ml:id xml:space="preserve" subscript="cg">X</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> </ml:define> </math> </region> <region region-id="2651" left="192" top="27" width="52.5" height="12.75" align-x="211.5" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">SM</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.088062752178129686</ml:real> </result> </ml:eval> </math> </region> <region region-id="2654" left="252" top="26.25" width="80.25" height="12" align-x="265.5" align-y="36" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">Should be 5 - 10%</p> </text> </region> </area> <rendering item-idref="38"/> </region> <region region-id="2640" left="42" top="1694.25" width="130.5" height="20.25" align-x="42" align-y="1710" 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"> <f size="18">Cm Plots</f> </p> </text> </region> <region region-id="2778" left="0" top="1716" width="6008.25" align-x="0" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="1514.25"> <area is-collapsed="true" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="2132" bottom-lock-id="2139"> <region region-id="1819" left="42" top="30" width="324" height="291" align-x="42" align-y="30" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="39"/> </region> <region region-id="2614" left="474" top="36" width="324" height="306" align-x="474" align-y="36" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="40"/> </region> <region region-id="1822" left="54" top="348" width="328.5" height="315" align-x="54" align-y="348" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="41"/> </region> <region region-id="1818" left="18" top="702" width="515.25" height="228.75" align-x="18" align-y="702" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="42"/> </region> <region region-id="1505" left="30" top="960" width="489" height="246.75" align-x="30" align-y="960" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="43"/> </region> <region region-id="1672" left="666" top="1185" width="201.75" height="16.5" align-x="690" align-y="1194" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.h">C</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">f(Unitless, Unitless, Unitless) => Unitless</ml:id> </result> </ml:eval> </math> </region> <region region-id="1506" left="90" top="1212" width="388.5" height="285" align-x="90" align-y="1212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="44"/> </region> </area> <rendering item-idref="45"/> </region> <region region-id="1952" left="30" top="1748.25" width="309.75" height="20.25" align-x="30" align-y="1764" 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"> <f family="Arial" charset="0" size="18"> <inlineAttr font-weight="normal" line-through="false">Control Force for the Rudder</inlineAttr> </f> </p> </text> </region> <region region-id="1905" left="0" top="1767" width="6008.25" align-x="8.25" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="380.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1905" bottom-lock-id="1907" bottom-tag=""> <region region-id="573" left="558" top="1806" width="231" height="180" align-x="558" align-y="1806" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="46"/> <rendering item-idref="47"/> </region> <region region-id="574" left="414" top="1802.25" width="94.5" height="24" align-x="414" align-y="1812" 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">Scaled from a general aviation plane</p> </text> </region> <region region-id="2321" left="36" top="1797.75" width="111" height="36" align-x="59.25" align-y="1818" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="l.δr">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="v">S</ml:id> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="v">z</ml:id> <ml:id xml:space="preserve" subscript="rud">τ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="48"/> </region> <region region-id="576" left="36" top="1850.25" width="114" height="17.25" align-x="62.25" align-y="1860" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.δr">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="v">η</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="v">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="Lα.v">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="rud">τ</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="49"/> </region> <region region-id="578" left="36" top="1882.5" width="93" height="35.25" align-x="56.25" align-y="1902" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="δr">N</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="v">Q</ml:id> <ml:id xml:space="preserve" subscript="v">S</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="v">h</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="n.δr">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="zz">I</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="50"/> </region> <region region-id="580" left="300" top="1898.25" width="163.5" height="12" align-x="300" align-y="1908" 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">Units on this should be s^-2 if correct.</p> </text> </region> <region region-id="581" left="300" top="1916.25" width="213" height="12" align-x="300" align-y="1926" 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">This is in Table 3.6 of Flight Stability and Control.</p> </text> </region> <region region-id="582" left="300" top="1934.25" width="152.25" height="12" align-x="300" align-y="1944" 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">This parameter is a stability check.</p> </text> </region> <region region-id="583" left="36" top="2018.25" width="489.75" height="12" align-x="36" align-y="2028" 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">The side force corresponding to a change in yawing moment created by rudder deflection is calculated as follows:</p> </text> </region> <region region-id="584" left="42" top="2043" width="112.5" height="16.5" align-x="58.5" align-y="2052" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:id xml:space="preserve" subscript="l.0012">C</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>10</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="v">Q</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="v">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="51"/> </region> <region region-id="2737" left="240" top="2049" width="55.5" height="16.5" align-x="255.75" align-y="2058" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="v">F</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">lbf</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>7.5141624542516086</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="52"/> </region> <region region-id="586" left="312" top="2048.25" width="165" height="12" align-x="312" align-y="2058" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#008080" 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"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"><--This is the control force needed!</inlineAttr> </b> </f> </p> </text> </region> <region region-id="587" left="36" top="2090.25" width="171.75" height="12" align-x="36" align-y="2100" 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">And the corresponding yawing moment:</p> </text> </region> <region region-id="588" left="48" top="2115" width="51" height="16.5" align-x="64.5" align-y="2124" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define warning="WarnRedefinedUDScalar" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r">N</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:neg/> <ml:id xml:space="preserve" subscript="t">L</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="v">F</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="53"/> </region> <region region-id="589" left="240" top="2121" width="63.75" height="16.5" align-x="255.75" align-y="2130" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="r">N</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>-53.061647511209664</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="joule"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="54"/> </region> </area> <rendering item-idref="55"/> </region> <region region-id="2317" left="24" top="2162.25" width="302.25" height="20.25" align-x="24" align-y="2178" 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"> <f family="Arial" charset="0" size="18"> <inlineAttr font-weight="normal" line-through="false">Control Force for the Ailerons</inlineAttr> </f> </p> </text> </region> <region region-id="1898" left="0" top="2181" width="6008.25" align-x="8.25" align-y="2190" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="428.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1898" bottom-lock-id="1901" bottom-tag=""> <region region-id="595" left="30" top="2204.25" width="264" height="24" align-x="30" align-y="2214" 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">The force exerted on the ailerons is due to the rolling rate, p, </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">and the change in moment that roll creates.</p> </text> </region> <region region-id="596" left="30" top="2234.25" width="268.5" height="12" align-x="30" align-y="2244" 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">The control power of the ailerons can be calculated as follows:</p> </text> </region> <region region-id="597" left="30" top="2253.75" width="174" height="36" align-x="57.75" align-y="2274" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="true"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.δa">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">τ</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="w">S</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:real>2</ml:real> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="b.A">F</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:parens> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="56"/> </region> <region region-id="598" left="282" top="2264.25" width="159.75" height="12" align-x="282" align-y="2274" 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">Eqn. 2.96 Flight Stability and Control</p> </text> </region> <region region-id="2017" left="54" top="2307" width="42" height="16.5" align-x="72" align-y="2316" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="a">X</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>36</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="57"/> </region> <region region-id="2027" left="180" top="2312.25" width="544.5" height="24" align-x="186.75" align-y="2322" 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">X.a is equal to the distance from the root chord to the closest edge of the aileron in the spanwise direction this value will come from layout </p> </text> </region> <region region-id="2016" left="54" top="2338.5" width="57" height="31.5" align-x="69.75" align-y="2358" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="2">y</ml:id> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">.9</ml:real> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:parens> </ml:define> </math> <rendering item-idref="58"/> </region> <region region-id="2026" left="180" top="2348.25" width="461.25" height="12" align-x="185.25" align-y="2358" 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">y.2 is equal to the half span of the wing minus 10%</p> </text> </region> <region region-id="2025" left="180" top="2378.25" width="433.5" height="12" align-x="185.25" align-y="2388" 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">y.1 is equal to the distance from the root chord to near edge of the aileron in the spanwise direction</p> </text> </region> <region region-id="2015" left="54" top="2380.5" width="87" height="31.5" align-x="69.75" align-y="2400" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="1">y</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:minus/> <ml:real font="0">.9</ml:real> <ml:id xml:space="preserve" subscript="b.A">F</ml:id> </ml:apply> </ml:parens> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:define> </math> <rendering item-idref="59"/> </region> <region region-id="1135" left="30" top="2434.5" width="371.25" height="56.25" align-x="57.75" align-y="2460" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.δa">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="Lα.w">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="a">τ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="r.w">C</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="w">S</ml:id> <ml:id xml:space="preserve" subscript="w">b</ml:id> </ml:apply> </ml:apply> <ml:parens> <ml:apply> <ml:minus/> <ml:parens> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">y</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="w">TR</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="2">y</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> <ml:parens> <ml:apply> <ml:plus/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="1">y</ml:id> <ml:real>2</ml:real> </ml:apply> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:apply> <ml:mult style="default"/> <ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:minus/> <ml:id xml:space="preserve" subscript="w">TR</ml:id> <ml:real>1</ml:real> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="w">b</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:parens> <ml:apply> <ml:div/> <ml:apply> <ml:pow/> <ml:id xml:space="preserve" subscript="1">y</ml:id> <ml:real>3</ml:real> </ml:apply> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:parens> </ml:apply> </ml:parens> </ml:apply> </ml:define> </math> <rendering item-idref="60"/> </region> <region region-id="1152" left="30" top="2499" width="60" height="16.5" align-x="57" align-y="2508" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="L.δa">C</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>0.38073125740092528</ml:real> </result> </ml:eval> </math> <rendering item-idref="61"/> </region> <region region-id="2021" left="114" top="2498.25" width="177.75" height="27" align-x="114" align-y="2508" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">C<sub>L.</sub> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sub>d</sub> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sub>a</sub> </inlineAttr> </f> <sub> <sp/> </sub>should be positive for static stability</p> </text> </region> <region region-id="601" left="30" top="2535" width="126.75" height="16.5" align-x="57.75" align-y="2544" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.δa">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>-0.2</ml:real> <ml:apply> <ml:id xml:space="preserve" subscript="L.w">C</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real>0</ml:real> <ml:id xml:space="preserve">deg</ml:id> </ml:apply> </ml:apply> </ml:apply> <ml:id xml:space="preserve" subscript="L.δa">C</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="62"/> </region> <region region-id="602" left="192" top="2535" width="65.25" height="16.5" align-x="219" align-y="2544" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="n.δa">C</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <ml:real>-0.044141220520548481</ml:real> </result> </ml:eval> </math> <rendering item-idref="63"/> </region> <region region-id="2020" left="276" top="2534.25" width="182.25" height="15" align-x="292.5" align-y="2544" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#f00" 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">C<sub>n.</sub> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sub>d</sub> </inlineAttr> </f> <f family="Arial" charset="0" size="10"> <inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false"> <sub>a</sub> </inlineAttr> </f> <sub> <sp/> </sub>should be negative for static stability</p> </text> </region> <region region-id="603" left="30" top="2577" width="80.25" height="16.5" align-x="49.5" align-y="2586" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="δa">F</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="n.δa">C</ml:id> <ml:id xml:space="preserve" subscript="w">Q</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="64"/> </region> <region region-id="1184" left="138" top="2577" width="63.75" height="16.5" align-x="156.75" align-y="2586" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <math optimize="false" disable-calc="false"> <ml:eval xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="δa">F</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">lbf</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>-4.3692572822690385</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="65"/> </region> <region region-id="1185" left="228" top="2576.25" width="165" height="12" align-x="228" align-y="2586" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#008080" 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"> <f family="Arial" charset="0"> <b> <inlineAttr line-through="false"><--This is the control force needed!</inlineAttr> </b> </f> </p> </text> </region> </area> <rendering item-idref="66"/> </region> <region region-id="2633" left="24" top="2624.25" width="153.75" height="20.25" align-x="46.5" align-y="2640" 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"> <f size="18">Directional Stabilit</f> <f size="18">y</f> </p> </text> </region> <region region-id="1881" left="0" top="2643" width="6008.25" align-x="8.25" align-y="2652" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="440.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1881" bottom-lock-id="1878" bottom-tag=""> <region region-id="1857" left="78" top="2678.25" width="197.25" height="17.25" align-x="153" align-y="2688" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:function> <ml:id xml:space="preserve" subscript="n.total">C</ml:id> <ml:boundVars> <ml:id xml:space="preserve">δr</ml:id> <ml:id xml:space="preserve">δa</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:boundVars> </ml:function> <ml:apply> <ml:plus/> <ml:apply> <ml:plus/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="n.β">C</ml:id> <ml:id xml:space="preserve">β</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="n.δr">C</ml:id> <ml:id xml:space="preserve">δr</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="n.δa">C</ml:id> <ml:id xml:space="preserve">δa</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="67"/> </region> <region region-id="1862" left="48" top="2724" width="328.5" height="283.5" align-x="48" align-y="2724" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="68"/> <rendering item-idref="69"/> </region> <region region-id="1896" left="408" top="2736" width="328.5" height="283.5" align-x="408" align-y="2736" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag=""> <plot disable-calc="false" item-idref="70"/> <rendering item-idref="71"/> </region> </area> <rendering item-idref="72"/> </region> <region region-id="1955" left="30" top="3098.25" width="123.75" height="20.25" align-x="30" align-y="3114" 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"> <f size="18">Lateral Stabilit</f> <f size="18">y</f> </p> </text> </region> <region region-id="1938" left="0" top="3123" width="6008.25" align-x="8.25" align-y="3132" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="" height="56.25"> <area is-collapsed="false" name="" show-name="false" show-border="true" show-icon="true" show-timestamp="true" allow-expand="false" is-locked="false" timestamp="" top-lock-id="1938" bottom-lock-id="1939" bottom-tag=""> <region region-id="2282" left="24" top="3135" width="63.75" height="16.5" align-x="45.75" align-y="3144" 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/math20"> <ml:id xml:space="preserve" subscript="l.β">C</ml:id> <ml:real>-.017555</ml:real> </ml:define> </math> <rendering item-idref="73"/> </region> </area> <rendering item-idref="74"/> </region> <region region-id="606" left="18" top="3192.75" width="175.5" height="14.25" align-x="18" align-y="3204" 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"> <f family="Arial" charset="0" size="12"> <b> <inlineAttr underline="false" line-through="false">Control Forces for the Elevator</inlineAttr> </b> </f> </p> </text> </region> <region region-id="607" left="24" top="3218.25" width="390.75" height="60" align-x="24" align-y="3228" 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">The servos must be powerful enough to actuate the elevator during all loading conditions.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The most critical flight segments are take-off and climb-out.<sp count="2"/>For these conditions (as well</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">as all others) the force the servos exert is equal to the force felt by the elevator.<sp count="2"/>This can </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">quantified by multiplying the coefficient of the normal force on the elevator by the weight of </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">the aircraft.<sp count="2"/>However, the same result can be produced using the two equations below.</p> </text> </region> <region region-id="608" left="24" top="3290.25" width="392.25" height="48" align-x="24" align-y="3300" 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">The elevator changes the longitudinal orientation of the airplane, i.e. produces a change</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">in lift as a function of the pitching velocity, q.<sp count="2"/>The following equation quantifies this change</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">in lift, neglecting the contribution of the wing because it's quite small in comparison to that </p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">of the horizontal tail.</p> </text> </region> <region region-id="609" left="24" top="3345" width="104.25" height="16.5" align-x="49.5" align-y="3354" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="Z.q">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>-2</ml:real> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">eff</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="75"/> </region> <region region-id="611" left="24" top="3374.25" width="382.5" height="36" align-x="24" align-y="3384" 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">The next equation calculates the corresponding change in pitching moment.</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">(Both of these equations can be found on pgs. 112-113 of "Flight Stability and Automatic</p> <p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Control", 2nd ed., Robert C. Nelson.)</p> </text> </region> <region region-id="1186" left="24" top="3418.5" width="140.25" height="35.25" align-x="50.25" align-y="3438" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="m.q">C</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>-2.2</ml:real> <ml:id xml:space="preserve" subscript="Lα.h">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">eff</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="h">V</ml:id> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="t">L</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="76"/> </region> <region region-id="2626" left="36" top="3502.5" width="131.25" height="35.25" align-x="54" align-y="3522" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="q">m</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="m.q">C</ml:id> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">Q</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>2</ml:real> <ml:id xml:space="preserve" subscript="cruise">V</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="yy">I</ml:id> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="77"/> </region> <region region-id="2627" left="36" top="3550.5" width="134.25" height="35.25" align-x="55.5" align-y="3570" show-border="false" show-highlight="true" is-protected="true" z-order="0" background-color="#80ff80" tag=""> <math optimize="false" disable-calc="false"> <ml:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="α">m</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve" subscript="M.α.plane">C</ml:id> <ml:id xml:space="preserve" subscript="w">Q</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">S</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="w">mac</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="yy">I</ml:id> 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