{"id":295,"date":"2017-10-17T16:34:20","date_gmt":"2017-10-17T16:34:20","guid":{"rendered":"https:\/\/www.macalester.edu\/160-mscs\/squarewheelbike\/"},"modified":"2024-07-08T15:52:15","modified_gmt":"2024-07-08T15:52:15","slug":"squarewheelbike","status":"publish","type":"page","link":"https:\/\/www.macalester.edu\/mscs\/multimedia\/squarewheeledbike\/squarewheelbike\/","title":{"rendered":"A Square Wheel, or The Ultimate Flat Tire"},"content":{"rendered":"<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/www.macalester.edu\/mscs\/wp-content\/uploads\/sites\/591\/2011\/04\/squarewheelbike646.jpg\" alt=\"Bike demonstration\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">In 1997 mathematics professor Stan Wagon and bicycle mechanic Loren Kellen constructed a square wheel bike that rolls smoothly over a road made out of inverted catenaries.<\/h2>\n\n\n\n<p>The original vehicle wore out and was replaced in April, 2004. More robust materials were used and the ride is now much smoother: so smooth that one cannot tell one is not riding a round-wheel bike. The photo above shows President Rosenberg taking the inaugural ride.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Frequently Asked Questions<\/h3>\n\n\n\n<p><strong>Can I ride this bike?<\/strong> <br>Yes. The device is on the lower-level of the Olin-Rice Science Center and anyone can ride it.<\/p>\n\n\n\n<p><strong>What is a catenary? <\/strong><br>A catenary is the shape one gets when one lets a chain or a string droop between two endpoint. Its equation is y = 1\/2 (e^x &#8211; e^(-x)). This is also known as cosh x. Catenaries, when inverted, form the strongest arch \u2014 the St. Louis Arch has such a shape \u2014 and often appear in bridge construction.<\/p>\n\n\n\n<p><strong><a class=\"download\" href=\"https:\/\/www.macalester.edu\/mscs\/wp-content\/uploads\/sites\/591\/2011\/07\/catenaries.pdf\">Why do catenaries work for the square wheel?<\/a><\/strong><\/p>\n\n\n\n<p><strong>In a normal bike the forward motion is proportional to the pedaling speed. Is that true here?<\/strong><br>No. The relationship is almost linear, but not quite.<\/p>\n\n\n\n<p><strong>Who first realized that a square could roll in catenaries?<\/strong><br>G. B. Robison in 1960.<\/p>\n\n\n\n<p><strong>What is it good for? <\/strong><br>Near some ancient pyramids in Egypt various pieces of wood cut into quarter-circles have been found. One theory is that they were used so that large blocks of marble with square cross-sections could be easily rolled. Indeed, a quarter-circle is close enough to a catenary that this would work. In more modern terms, if you had a multi-ton cube over a catenary road, then you could roll it in much the same way that you can roll a multi-ton car over a flat road.<\/p>\n\n\n\n<p><strong>How far does it go in a year? <\/strong><br>An odometer on the vehicle showed that it travelled just over 15 miles between Sept. 2004 and Sept. 2005.<\/p>","protected":false},"excerpt":{"rendered":"<p>In 1997 mathematics professor Stan Wagon and bicycle mechanic Loren Kellen constructed a square wheel bike that rolls smoothly over a road made out of inverted catenaries. The original vehicle wore out and was replaced in April, 2004. More robust materials were used and the ride is now much smoother: so smooth that one cannot [&hellip;]<\/p>","protected":false},"author":1,"featured_media":0,"parent":294,"menu_order":0,"comment_status":"open","ping_status":"open","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-295","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/pages\/295","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/comments?post=295"}],"version-history":[{"count":2,"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/pages\/295\/revisions"}],"predecessor-version":[{"id":1677,"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/pages\/295\/revisions\/1677"}],"up":[{"embeddable":true,"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/pages\/294"}],"wp:attachment":[{"href":"https:\/\/www.macalester.edu\/mscs\/wp-json\/wp\/v2\/media?parent=295"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}