tag:blogger.com,1999:blog-1564958057737541664.post8686903226731170389..comments2015-03-31T11:08:03.076-07:00Comments on On Bicycles, and.... what else is there?: Calculating Net Climbing and Descendingdjconnelhttp://www.blogger.com/profile/01484858820878605035noreply@blogger.comBlogger1125tag:blogger.com,1999:blog-1564958057737541664.post-8522471860256115152010-11-14T00:02:54.234-08:002010-11-14T00:02:54.234-08:00I'm not sure that sum of delta z approximation...I'm not sure that sum of delta z approximation is any more challenging or different that sum of delta x and or y. The whole thing is indeed muddled since the path our body travels through space is not the same as the bike's, the path is not the straight line we idealize because bike motion is more like a series of jiggly little balance corrections, and the overall function from x1,y1,z1 to xn, yn, zn is not continuous but usually punctuated with a series of stops and/or dismounts. When you add those to the notion that is amplified by your post, that people conceive of our distance as travel across an x-y plane on this bumpy planet, saying how far you went with what sum of delta z is almost never exactly what we're thinking anyway.John Romeo Alphahttp://www.blogger.com/profile/01289456379789026152noreply@blogger.com