PK PAbwwmathcad/worksheet.xml (Free Fall SpeedsI just watched the video and recorded the speeds and fall times shown on the screen. There was a lot of quantization noise because time was reported in 1 second intervals and I could not always grab the data exactly when the time changed.Smoothed, interpolated version of the speed data. Velocity going down is defined to be negative for my ODE below.t21222324252728313537384142474849505960616263svempirical68171376079183587689595910531090111511431158117311731173117311731132102610191005kmhrvempτinterpcsplinetksmoothtsvempiricalkmhr5kmhrtksmoothtsvempiricalkmhr5kmhrτMeasured Speed Versus Timei011000tFinei21si100040s<legend /><traces><trace resultRef="8"><traceStyle color="#FF00008B" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle></trace><trace resultRef="9"><traceStyle color="#FFCB4C23" symbol="none" line-weight="1" line-style="Solid">lines</traceStyle></trace></traces><graph-size width="216.529307713361" height="199.035133880167" /><axes><xAxis rank="1" legend-position="PlotBoundaryBottom" start="21" end="65"><axisLine position="ticknumberlock" positionticmark="0" legendWidth="86.2533333333333" /><axisGrid><gridFrequency>12</gridFrequency><gridLabels display="true" /><gridLines /><tickMarks display="true" /></axisGrid><axisLabel /><markers 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xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run Background="#FFC3D9A5">Fall Time</Run></Paragraph></FlowDocument></text></region><region region-id="10" top="1267.2000000000003" left="19.200000000000003" width="243.80218616833491"><text><FlowDocument PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" FontSize="16" Foreground="#FF1C155E">Air Density Versus Altitude</Run></Paragraph></FlowDocument></text></region><region region-id="11" top="1267.2000000000003" left="480.00000000000006" width="264.24320638022448"><text><FlowDocument PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" FontSize="16" Foreground="#FF1C155E">Gravity Versus 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Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">I captured the data in the reverse order that cspline needed it. I will reverse it.</Run></Paragraph></FlowDocument></text></region><region region-id="15" top="1689.6000000000004" left="499.20000000000005"><math resultRef="24"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">g1</ml:id><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">reverse</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">g1</ml:id></ml:apply></ml:define></math></region><region region-id="16" top="1689.6000000000004" left="633.60000000000014" width="209.49047366980585"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">I captured the data in reverse order from the table.</Run></Paragraph></FlowDocument></text></region><region region-id="17" top="1708.8000000000002" left="76.800000000000011"><math resultRef="26"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">h</ml:id><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">sort</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">h</ml:id></ml:apply></ml:define></math></region><region region-id="18" top="1708.8000000000002" left="172.8"><math resultRef="28"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">r</ml:id><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">reverse</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">r</ml:id></ml:apply></ml:define></math></region><region region-id="19" top="1747.2000000000003" left="57.600000000000009" width="294.17470026191995"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Here are my interpolation functions.</Run></Paragraph></FlowDocument></text></region><region region-id="20" top="1747.2000000000003" left="499.20000000000005"><math resultRef="30"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">g1</ml:id><ml:apply><ml:mult /><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">g1</ml:id><ml:id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">g</ml:id></ml:apply></ml:define></math></region><region region-id="21" top="1747.2000000000003" left="633.60000000000014" width="200"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">The table data is relative to nominal surface g.</Run></Paragraph></FlowDocument></text></region><region region-id="22" top="1785.6000000000004" left="76.800000000000011"><math resultRef="32"><ml:define><ml:function><ml:id labels="VARIABLE" xml:space="preserve">ρ</ml:id><ml:boundVars><ml:id labels="VARIABLE" xml:space="preserve">x</ml:id></ml:boundVars></ml:function><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">interp</ml:id><ml:sequence><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">cspline</ml:id><ml:sequence><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">h</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">r</ml:id></ml:sequence></ml:apply><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">h</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">r</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</ml:id></ml:sequence></ml:apply></ml:define></math></region><region region-id="23" top="1785.6000000000004" left="403.20000000000005" width="217.5208744673339"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Air density versus altitude</Run></Paragraph></FlowDocument></text></region><region region-id="24" top="1824.0000000000002" left="76.800000000000011"><math resultRef="34"><ml:define><ml:function><ml:id labels="VARIABLE" xml:space="preserve">gravity</ml:id><ml:boundVars><ml:id labels="VARIABLE" xml:space="preserve">x</ml:id></ml:boundVars></ml:function><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">interp</ml:id><ml:sequence><ml:apply><ml:id labels="FUNCTION" label-is-contextual="true" xml:space="preserve">cspline</ml:id><ml:sequence><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">h</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">g1</ml:id></ml:sequence></ml:apply><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">h</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">g1</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">x</ml:id></ml:sequence></ml:apply></ml:define></math></region><region region-id="25" top="1824.0000000000002" left="403.20000000000005" width="200"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Gravity versus altitude</Run></Paragraph></FlowDocument></text></region><region region-id="26" top="1862.4000000000003" left="19.200000000000003"><math resultRef="36"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">A</ml:id><ml:apply><ml:scale /><ml:real>1.0</ml:real><ml:apply><ml:pow /><ml:id labels="UNIT" label-is-contextual="true" xml:space="preserve">m</ml:id><ml:real>2</ml:real></ml:apply></ml:apply></ml:define></math></region><region region-id="27" top="1862.4000000000003" left="115.20000000000002" width="240.88204042377925"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Effective area of the skydiver</Run></Paragraph></FlowDocument></text></region><region region-id="28" top="1900.8000000000002" left="19.200000000000003"><math resultRef="38"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">C</ml:id><ml:real>1</ml:real></ml:define></math></region><region region-id="29" top="1900.8000000000002" left="115.20000000000002" width="200"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Drag coefficient</Run></Paragraph></FlowDocument></text></region><region region-id="30" top="1939.2000000000003" left="19.200000000000003"><math resultRef="40"><ml:define><ml:id labels="VARIABLE" xml:space="preserve">m</ml:id><ml:apply><ml:scale /><ml:real>100</ml:real><ml:id labels="UNIT" label-is-contextual="true" xml:space="preserve">kg</ml:id></ml:apply></ml:define></math></region><region region-id="31" top="1939.2000000000003" left="134.40000000000003"><math resultRef="42"><ml:eval><ml:apply><ml:mult /><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">m</ml:id><ml:id labels="CONSTANT" label-is-contextual="true" xml:space="preserve">g</ml:id></ml:apply><ml:unitOverride><ml:id labels="UNIT" xml:space="preserve">lbf</ml:id></ml:unitOverride></ml:eval></math></region><region region-id="32" top="1939.2000000000003" left="288.00000000000006" width="252.56262340200181"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">My guess for the total weight of the suit and skydiver.</Run></Paragraph></FlowDocument></text></region><region region-id="33" top="1977.6000000000004" left="19.200000000000003"><math resultRef="44"><ml:define><ml:id labels="VARIABLE" xml:space="preserve"><Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:pw="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">t<pw:Subscript>end</pw:Subscript></Span></ml:id><ml:apply><ml:scale /><ml:real>80</ml:real><ml:id labels="UNIT" label-is-contextual="true" xml:space="preserve">s</ml:id></ml:apply></ml:define></math></region><region region-id="34" top="1977.6000000000004" left="115.20000000000002" width="189.04945345791629"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Simulation Duration</Run></Paragraph></FlowDocument></text></region><region region-id="35" top="1996.8000000000002" left="76.800000000000011" height="296.40000000000003" width="571.85000000000014"><solveblock><regions><region region-id="36" top="134.40000000000003" left="19.2" solve-block-category="constraint"><math resultRef="46"><ml:apply><ml:equal /><ml:apply><ml:id xml:space="preserve">x</ml:id><ml:real>0</ml:real></ml:apply><ml:apply><ml:scale /><ml:real>39600</ml:real><ml:id labels="UNIT" xml:space="preserve">m</ml:id></ml:apply></ml:apply><resultFormat><matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /></resultFormat></math></region><region region-id="37" top="134.40000000000003" left="172.8" solve-block-category="constraint"><math resultRef="48"><ml:apply><ml:equal /><ml:apply><ml:apply><ml:functionDerivative /><ml:id xml:space="preserve">x</ml:id></ml:apply><ml:real>0</ml:real></ml:apply><ml:apply><ml:scale /><ml:real>0</ml:real><ml:apply><ml:div /><ml:id labels="UNIT" xml:space="preserve">m</ml:id><ml:id labels="UNIT" 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xml:space="preserve">C</ml:id></ml:boundVars></ml:function><ml:apply><ml:id labels="KEYWORD" xml:space="preserve">odesolve</ml:id><ml:sequence><ml:apply><ml:id labels="UNIT" label-is-contextual="true" xml:space="preserve">x</ml:id><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve">t</ml:id></ml:apply><ml:id labels="VARIABLE" label-is-contextual="true" xml:space="preserve"><Span xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation" xmlns:pw="clr-namespace:Ptc.Wpf;assembly=Ptc.Core">t<pw:Subscript>end</pw:Subscript></Span></ml:id></ml:sequence></ml:apply></ml:define><resultFormat><matrix size="12,12" offset="0,0" show-indices="false" expand-nested-arrays="false" /></resultFormat></math></region></regions></solveblock></region><region region-id="40" top="2054.4" left="96.000000000000014" width="243.80218616833474"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">Differential Equation Solution</Run></Paragraph></FlowDocument></text></region><region region-id="41" top="2265.6000000000004" left="96.000000000000014" width="549.68745291054006"><text><FlowDocument FontFamily="Tahoma" FontStyle="Normal" FontWeight="Normal" FontSize="14.6666666666667" Foreground="#FF000000" Background="#00FFFFFF" TextAlignment="Left" PagePadding="5,0,5,0" AllowDrop="True" NumberSubstitution.CultureSource="User" Typography.Variants="Normal" xmlns="http://schemas.microsoft.com/winfx/2006/xaml/presentation"><Paragraph><Run FontStyle="Italic" FontWeight="Bold" Foreground="#FF360151">The drag coefficient is a parameter that I can use to optimize the 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