Accumulating Error

<BODY LANG="EN"> <HR><center> <table border=1> <td><A NAME="tex2html152" HREF="node13.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A NAME="tex2html158" HREF="node13.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html160" HREF="node15.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node14.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR><H3><A NAME="SECTION00091100000000000000">Accumulating Error</A></H3> <P> The Outer Banks is a sand bar extending for hundreds of miles along the east coast of the United States, mostly along the coast of North Carolina. The sand bar is broken by shallow channels that connect the Atlantic Ocean on the east to the shallow salt water sounds on the west. The result is a chain of long, thin islands only a few feet above sea level. <P> The Outer Banks were the site of Sir Walter Raleigh's lost colony and the Wright Brothers' first powered flight. It is also known for surf fishing, hazardous navigation, and impressive riptides. <P> The Wright Brothers' first powered flight was made from the highest natural point along the Outer Banks at Kitty Hawk. Kitty Hawk is a broad sand dune that peaks at 38 feet above sea level. The essence of this problem is to determine how far out in Albemarle Sound one can see from the summit of Kitty Hawk. <P> For a figure of the problem please refer to the main menue of the tutor. <P> You are sitting on the top of Kitty Hawk on a calm day with no waves. You are watching a friend swimming across the sound toward the mainland. Because of the curvature of the earth, your friend will eventually disappear across the horizon. How far away (in feet) can your friend get before he disappears from view? We're interested in finding the maximum possible straight line distance from your eye to your friend. <P> See the figure for a sketch of what computations are required to solve this problem. Notice that the solution involves using the Pythagorean Theorem to solve for the unknown side of a triangle. The sketch is not to scale, so be careful to notice that the unknown side is extremely small compared to the two known sides, which are almost identical in length. <P> Now you should experiment with calculating the straight line distance using floating point computations. Begin by setting the floating point precision to 6digits. Compute the value of the formula that you derived. Be sure that all of the numbers that you include in the formula are floating point constants--not integers. (The correct answer is approximately 39,857 feet.) <P> Repeat this process using successively fewer digits of accuracy. Is what happens what you expected? Can you explain what's going on? Think about these questions before continuing. <UL><LI> Prepare a table showing the distance that you calculate for each level of precision. </UL><HR><center> <table border=1> <td><A NAME="tex2html152" HREF="node13.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A NAME="tex2html158" HREF="node13.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html160" HREF="node15.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node14.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I>Joseph Zachary and Thomas L. Marchioro</I> </ADDRESS> </BODY>