{"id":2097,"date":"2012-04-25T03:04:17","date_gmt":"2012-04-25T07:04:17","guid":{"rendered":"http:\/\/blogs.vassar.edu\/magnes\/?p=2097"},"modified":"2013-07-11T10:30:53","modified_gmt":"2013-07-11T14:30:53","slug":"conclusionoverview","status":"publish","type":"post","link":"https:\/\/pages.vassar.edu\/magnes\/2012\/04\/25\/conclusionoverview\/","title":{"rendered":"Conclusion\/Overview"},"content":{"rendered":"

Mistakes were made throughout this process. Some were as simple as a dropped variable and others were intensely more complicated. In the end I was still able to produce what I set out to do: An interactive animation that allows you to see how a single coil in a stator of magnetic induction based wind turbine creates current.<\/p>\n

Much of the work I did was simply writing the code to get the interactive animation to function properly. Below is a screenshot, but the important code is linked to at the end of this post.<\/p>\n

\"\"<\/a><\/p>\n

Just to recap some of the derivation I did in earlier posts, I will present a short breakdown here. I started with the basic equation for B, but in order to have the magnetic field change over time based on my magnet array, I had to use a triangle wave. In my previous post I inserted values for the period, but in my Mathematica code, I made it dependent on the velocity so that all the graphs would match up.<\/p>\n

Triangle Wave Function:<\/p>\n

(1) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

Magnetic Field Equation<\/p>\n

(2) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

Once I had my B(t) I quickly found the flux, but to get to the voltage I had to find the derivative of my triangle wave based B(t) function. I made a square wave approximation to solve for the derivative. In my last post I again plugged in constants in order to show the look of the graph, but in my code I made it dependent on all of the variables.<\/p>\n

(3) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

Using this square wave approximation I was able to find the voltage in the coil.\u00a0Once I had a formula for the voltage, the induced current was simple to find.<\/p>\n

At this point I noticed a grave mistake with my approach to this problem. By approximating the magnetic field with a triangle wave, I made it so the voltage simply flipped back and forth from negative to positive with no gradation. In hindsight it would have been better to use a version of a sin wave as an approximation. That would present its own issues, as the magnetic field would have a fairly linear change. With more time I would have attempted to find a better approximation for the magnetic field that was easier to use.<\/p>\n

It should also be noted that my last post had a few typos in it that could be very confusing. I wrote the equation:<\/p>\n

(4) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

but it should read:<\/p>\n

(5) <\/span>   <\/span>\"\begin{equation*}<\/p>\n

The mu was confused for most of the post, but I was able to correct the issues I had with it for all of the formulas in this post and the code.<\/p>\n

Code: https:\/\/vspace.vassar.edu\/thvandermeer\/Trying%20to%20get%20graphs%20in%20it.nb<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Mistakes were made throughout this process. Some were as simple as a dropped variable and others were intensely more complicated. In the end I was still able to produce what I set out to do: An interactive animation that allows you to see how a single coil in a stator of magnetic induction based wind […]<\/p>\n","protected":false},"author":1760,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4101,29905,29903],"tags":[],"class_list":["post-2097","post","type-post","status-publish","format-standard","hentry","category-advanced-em","category-spring-2012","category-theo"],"_links":{"self":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2097","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/users\/1760"}],"replies":[{"embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/comments?post=2097"}],"version-history":[{"count":7,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2097\/revisions"}],"predecessor-version":[{"id":2116,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/posts\/2097\/revisions\/2116"}],"wp:attachment":[{"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/media?parent=2097"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/categories?post=2097"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/pages.vassar.edu\/magnes\/wp-json\/wp\/v2\/tags?post=2097"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}