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Release:<tab/>September 11, 2001 Reference:<tab/>Snap loading of Marine cable systems <tab/> <tab/>John M. 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style="default"/> <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:real>4</ml:real> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>3</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ρ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="d">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="anchor">Area</ml:id> </ml:apply> <ml:id xml:space="preserve">Amplitude</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="308" left="408" top="314.5" width="62.5" height="26" align-x="420.5" 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"> 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by: <tab/>Gene Massion Initial Release:<tab/>September 11, 2001 Reference:<tab/>Snap loading of Marine cable systems <tab/> <tab/>John M. Niedzwecki, Sreekumar K. Thampi <tab/> <tab/>Applied Ocean Research, 1991, Vol. 12, No. 1 </text> </region> <region region-id="7" left="12" top="79.5" width="80.5" height="13.5" align-x="22" 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"> <f family="Arial" charset="0" size="12"> <inlineAttr font-weight="normal" line-through="false">Line Properties</inlineAttr> </f> </text> </region> <region region-id="321" left="366" top="85.5" width="88" height="13.5" align-x="376" align-y="96" 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"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Wave Properties</inlineAttr> </f> </text> </region> <region region-id="320" left="30" top="99.5" width="93" height="15.5" align-x="86.5" align-y="108" 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="line">diameter</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>.375</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="2"/> </region> <region region-id="16" left="138" top="92.5" width="71" height="30.5" align-x="151" align-y="108" 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">E</ml:id> <ml:apply> <ml:mult style="default"/> <ml:apply> <ml:mult style="default"/> <ml:real>4.7</ml:real> <ml:apply> <ml:pow/> <ml:real>10</ml:real> <ml:real>6</ml:real> </ml:apply> </ml:apply> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="3"/> </region> <region region-id="17" left="234" top="95" width="83" height="20" align-x="275.5" align-y="108" 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="line">Area</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>.151</ml:real> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real font="0">2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="4"/> </region> <region region-id="278" left="366" top="105.5" width="63" height="12" align-x="399.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Period</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="5"/> </region> <region region-id="279" left="450" top="105.5" width="72" height="12" align-x="498.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">Amplitude</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>1</ml:real> <ml:id xml:space="preserve">m</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="6"/> </region> <region region-id="280" left="540" top="98.5" width="61.5" height="30.5" align-x="553.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">ρ</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>1.99</ml:real> <ml:apply> <ml:div/> <ml:id xml:space="preserve">slug</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">ft</ml:id> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="7"/> </region> <region region-id="324" left="678" top="86.5" width="143.5" height="38" align-x="754.5" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="7H375">Elongation</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>1.4</ml:real> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">ft</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:real font="0">1000</ml:real> <ml:id xml:space="preserve">ft</ml:id> </ml:apply> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>1000</ml:real> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="8"/> </region> <region region-id="328" left="858" top="98.5" width="155" height="26" align-x="933.5" 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="7H375">Elongation</ml:id> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>3.1473252033959472E-07</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="newton" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="9"/> </region> <region region-id="281" left="366" top="121" width="56.5" height="27.5" align-x="381" align-y="138" 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">ω</ml:id> <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">π</ml:id> </ml:apply> <ml:id xml:space="preserve">rad</ml:id> </ml:apply> <ml:id xml:space="preserve">Period</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="10"/> </region> <region region-id="282" left="450" top="122.5" width="61" height="26" align-x="464" align-y="138" 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">ω</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">rad</ml:id> <ml:id xml:space="preserve">sec</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>1.5707963267948966</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="radian"/> <unitReference unit="second" power-numerator="-1"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="11"/> </region> <region region-id="199" left="48" top="135.5" width="87" height="15.5" align-x="83" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="line">EA</ml:id> <ml:apply> <ml:mult style="default"/> <ml:id xml:space="preserve">E</ml:id> <ml:id xml:space="preserve" subscript="line">Area</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="12"/> </region> <region region-id="200" left="156" top="131" width="102.5" height="20" align-x="190" 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="line">EA</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">lbf</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>709700</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="13"/> </region> <region region-id="331" left="684" top="137.5" width="119.5" height="44.5" align-x="724" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve" subscript="7H375">E</ml:id> <ml:apply> <ml:div/> <ml:apply> <ml:div/> <ml:real>1</ml:real> <ml:id xml:space="preserve" subscript="7H375">Elongation</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="line">Area</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="14"/> </region> <region region-id="332" left="840" top="152.5" width="105.5" height="30.5" align-x="879" 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="7H375">E</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">lbf</ml:id> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">in</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>4730368.9687795648</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="-2"/> <unitReference unit="pound_force"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="15"/> </region> <region region-id="283" left="18" top="175.5" width="96" height="13.5" align-x="31" 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"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Anchor Properties</inlineAttr> </f> </text> </region> <region region-id="284" left="42" top="201.5" width="87.5" height="15.5" align-x="90.5" align-y="210" 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="dry">Weight</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>900</ml:real> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="16"/> </region> <region region-id="285" left="162" top="201.5" width="72.5" height="12" align-x="205.5" align-y="210" 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">Diameter</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>16</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="17"/> </region> <region region-id="291" left="252" top="193.5" width="111" height="27" align-x="305" align-y="210" 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="anchor">Area</ml:id> <ml:apply> <ml:mult style="auto-select"/> <ml:apply> <ml:div/> <ml:id xml:space="preserve">π</ml:id> <ml:real>4</ml:real> </ml:apply> <ml:apply> <ml:pow/> <ml:id xml:space="preserve">Diameter</ml:id> <ml:real font="0">2</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="18"/> </region> <region region-id="322" left="402" top="201.5" width="39" height="15.5" align-x="420.5" align-y="210" 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="d">C</ml:id> <ml:real>1.2</ml:real> </ml:define> </math> <rendering item-idref="19"/> </region> <region region-id="286" left="42" top="225.5" width="88.5" height="15.5" align-x="91.5" 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="wet">Weight</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>250</ml:real> <ml:id xml:space="preserve">lbf</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="20"/> </region> <region region-id="287" left="162" top="225.5" width="62" height="12" align-x="195" 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">Height</ml:id> <ml:apply> <ml:mult style="default"/> <ml:real>24</ml:real> <ml:id xml:space="preserve">in</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="21"/> </region> <region region-id="292" left="252" top="227" width="105.5" height="20" align-x="304" 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="anchor">Area</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>201.06192982974676</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="inch" power-numerator="2"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="22"/> </region> <region region-id="319" left="12" top="262" width="146" height="30.5" align-x="64" align-y="282" 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="added">Mass</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:real>2</ml:real> <ml:real>3</ml:real> </ml:apply> <ml:id xml:space="preserve">ρ</ml:id> </ml:apply> <ml:id xml:space="preserve">π</ml:id> </ml:apply> <ml:apply> <ml:pow/> <ml:parens> <ml:apply> <ml:div/> <ml:id xml:space="preserve">Diameter</ml:id> <ml:real>2</ml:real> </ml:apply> </ml:parens> <ml:real>3</ml:real> </ml:apply> </ml:apply> </ml:define> </math> <rendering item-idref="23"/> </region> <region region-id="295" left="204" top="273.5" width="98" height="15.5" align-x="255" align-y="282" 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="added">Mass</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">slug</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>1.2349174085222099</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="slug"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="24"/> </region> <region region-id="296" left="324" top="263" width="162.5" height="29.5" align-x="378" align-y="282" 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="virtual">Mass</ml:id> <ml:apply> <ml:plus/> <ml:apply> <ml:div/> <ml:id xml:space="preserve" subscript="dry">Weight</ml:id> <ml:id xml:space="preserve">g</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="added">Mass</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="25"/> </region> <region region-id="297" left="510" top="273.5" width="105" height="15.5" align-x="563" align-y="282" 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="virtual">Mass</ml:id> <ml:unitOverride> <ml:id xml:space="preserve">slug</ml:id> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>29.207772562932671</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="slug"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="26"/> </region> <region region-id="68" left="18" top="319.5" width="193" height="13.5" align-x="44" 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"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Hydrodynamic Damping Coeffecient</inlineAttr> </f> </text> </region> <region region-id="307" left="234" top="313" width="160.5" height="29" align-x="247.5" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">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:apply> <ml:div/> <ml:apply> <ml:mult style="default"/> <ml:real>4</ml:real> <ml:id xml:space="preserve">ω</ml:id> </ml:apply> <ml:apply> <ml:mult style="default"/> <ml:real>3</ml:real> <ml:id xml:space="preserve">π</ml:id> </ml:apply> </ml:apply> <ml:id xml:space="preserve">ρ</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="d">C</ml:id> </ml:apply> <ml:id xml:space="preserve" subscript="anchor">Area</ml:id> </ml:apply> <ml:id xml:space="preserve">Amplitude</ml:id> </ml:apply> </ml:define> </math> <rendering item-idref="27"/> </region> <region region-id="308" left="408" top="314.5" width="62.5" height="26" align-x="420.5" 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">C</ml:id> <ml:unitOverride> <ml:apply> <ml:div/> <ml:id xml:space="preserve">slug</ml:id> <ml:id xml:space="preserve">s</ml:id> </ml:apply> </ml:unitOverride> <result xmlns="http://schemas.mathsoft.com/math20"> <unitedValue> <ml:real>7.2928193416665916</ml:real> <unitMonomial xmlns="http://schemas.mathsoft.com/units10"> <unitReference unit="second" power-numerator="-1"/> <unitReference unit="slug"/> </unitMonomial> </unitedValue> </result> </ml:eval> </math> <rendering item-idref="28"/> </region> <region region-id="237" left="18" top="361.5" width="115.5" height="13.5" align-x="39.5" 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"> <f family="Arial" charset="0" size="12"> <inlineAttr line-through="false">Calculations vs depth</inlineAttr> </f> </text> </region> <region region-id="255" left="30" top="381.5" width="32.5" height="12" align-x="44.5" 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:define warning="WarnRedefinedBIUnit" xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">N</ml:id> <ml:real>20</ml:real> </ml:define> </math> <rendering item-idref="29"/> </region> <region region-id="258" left="96" top="381.5" width="39" height="12" align-x="106" 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:define xmlns:ml="http://schemas.mathsoft.com/math20"> <ml:id xml:space="preserve">i</ml:id> <ml:range> <ml:real>0</ml:real> <ml:id xml:space="preserve">N</ml:id> </ml:range> </ml:define> </math> <rendering item-idref="30"/> </region> <region region-id="259" left="180" top="374.5" width="136" height="26" align-x="210.5" align-y="390" 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