Computer Program #8

<body topmargin=0 leftmargin=0 marginheight=0 marginwidth=0> <table cellpadding=0 cellspacing=0 border=0><tr> <td valign="top" colspan=2 height=50 BGCOLOR="#CC0000" TEXT="#080000"> <div> <B>Computer Program #8</B></div> <div> </div> </td> </tr><tr> <td valign="top" width=165 BGCOLOR="#0066FF" TEXT="#080000"> <div> <B> <TABLE BORDER="0" CELLPADDING="2" CELLSPACING="1" WIDTH="132" BORDERCOLORLIGHT="#C0C0C0" BORDERCOLORDARK="#808080" FRAME="BOX" RULES="ALL" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" > <tR> <tD VALIGN=TOP HEIGHT= 35 ><NOBR><div> <A HREF="id16.htm" TARGET="_top" TITLE="Computer Program 7"><U><B><IMG SRC="007151d0.gif" border=0 width="21" height="29" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG BORDER="0" SRC="1x1.gif" HEIGHT="29" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" WIDTH="21"></div> </NOBR></tD> <tD VALIGN=TOP WIDTH="20"><IMG BORDER="0" SRC="1x1.gif" HEIGHT="35" ALIGN="bottom" WIDTH="20" HSPACE="0" VSPACE="0"></tD> <tD VALIGN=TOP><NOBR><div> <A HREF="id2.htm" TARGET="_top" TITLE="Course Calendar"><U><B><IMG SRC="00d0d1d0.gif" border=0 width="13" height="29" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></B></U></A></div> </NOBR></tD> <tD VALIGN=TOP><NOBR><div> <IMG BORDER="0" SRC="1x1.gif" HEIGHT="29" ALIGN="BOTTOM" HSPACE="0" VSPACE="0" WIDTH="27"></div> </NOBR></tD> </tR> </TABLE></B></div> <div> <A HREF="id10.htm" TARGET="_top" TITLE="Computer Program 1"><U>Computer Program #1</U></A></div> <div> <A HREF="id11.htm" TARGET="_top" TITLE="Computer Program 2"><U>Computer Program #2</U></A></div> <div> <A HREF="id12.htm" TARGET="_top" TITLE="Computer Program 3"><U>Computer Program #3</U></A></div> <div> <A HREF="id13.htm" TARGET="_top" TITLE="Computer Program 4"><U>Computer Program #4</U></A></div> <div> <A HREF="id14.htm" TARGET="_top" TITLE="Computer Program 5"><U>Computer Program #5</U></A></div> <div> <A HREF="id15.htm" TARGET="_top" TITLE="Computer Program 6"><U>Computer Program #6</U></A></div> <div> <A HREF="id16.htm" TARGET="_top" TITLE="Computer Program 7"><U>Computer Program #7</U></A></div> <div> <B>Computer Program #8</B></div> </td> <td valign="top" height=430 BGCOLOR="#FFFFFF" TEXT="#080000"> <div> <FONT SIZE="2" COLOR="#000000" FACE="Arial" >The figure below shows the geometry of an aircraft arresting gear system, which is designed to halt a moving aircraft that would otherwise overrun the end of a runway. It is similar in principle to the gear used on aircraft carriers. A plot of the "water squeezer" damping function, </FONT><I>f(y</I><FONT SIZE="1" COLOR="#000000" FACE="Times New Roman" ><I>3</I></FONT><I>)</I><FONT SIZE="2" COLOR="#000000" FACE="Arial" >, is also shown on the figure. You are to investigate the range of aircraft weights and speeds that can be accomodated without exceeding the working limits of the cables or the allowable piston travel. Two specific cases are assigned, but you are encouraged to try other aircraft masses and speeds.</FONT></div> <div> The differential equations describing the acceleration of the three masses are:</div> <div> <IMG SRC="0328d870.gif" border=0 width="141" height="135" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> where the cable tension is given by:</div> <div> <IMG SRC="033c1330.gif" border=0 width="193" height="51" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> <IMG SRC="034b7330.gif" border=0 width="183" height="51" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Drag force from the water squeezer is given by:</div> <div> <IMG SRC="03579310.gif" border=0 width="121" height="49" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Geometrical constraints lead to:</div> <div> <IMG SRC="036a44b0.gif" border=0 width="164" height="75" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Constants used in the model are as follows:</div> <div> <IMG SRC="03770900.gif" border=0 width="112" height="144" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Initial conditions are given by:</div> <div> <IMG SRC="038f0600.gif" border=0 width="240" height="96" ALT="Microsoft Equation 3.0" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> <div> Write a C++ program that uses RKSUITE to solve the set simultaneous ordinary differential equations for this system. Output your numerical results to an external data file that is compatible with Excel. Import your data into Excel and generate appropriate graphs of results. Results of particular interest would be the acceleration the pilot will experience during the arresting process and the forces in the two arresting cables. Feel free to include other meaningful results.</div> <div> <IMG SRC="03a26a10.gif" border=0 width="550" height="673" ALT="aags diagram" ALIGN="BOTTOM" HSPACE="0" VSPACE="0"></div> </td> </tr></table></body>