Now I Know That I Am Capable

Hello again! First, I wanted to share that Ashley and I picked up fresh new Disneyland passes yesterday, and the return after months away was wonderful! Strange how a place can have such an effect on you, almost like an old friend.

Well, life has been rather busy lately. With only two weeks of class left before what will unfortunately be described as my summer vacation (One whole week off! Yay! I suppose it could be worse), the time has come to buckle down and get everything finished. Luckily, one of my projects has been completed and turned in as of Wednesday, which I am very excited to share about.

The goal of our project was to, as a group, write a computer program to calculate the area moment of inertia for a cross section of a bone. In layman’s terms, this simply describes how resistant a beam is to bending, which is then used to calculate potential stress values prior to fracture (Think about an I-beam used in bridges. It is possible to imagine that the shape alone will reduce the amount the beam bends when a heavy load is placed on it; this is due to the beam having a large area moment of inertia). In order to do this, my partner and I obtained several hundred points of data on a graph to resemble the shape of the inner and outer diameters along the bone. Here’s a picture of that initial data:

Blue represents outer, red represents inner (in between is considered constant density)

With this data, our program created interpolation functions in order to approximate points between the known values. With one function for the inner and one for the outer, we selected 360 points, one for each degree around the center, going counter clockwise, starting from the rightmost points. These points were then triangulated, or set into triangles based on adjacent points. This image below should help explain this:

The Xi,Yi terms refer to the coordinates for the inner data points, while the Xo,Yo terms refer to the coordinates for the outer data points. These were connected using a single diagonal for every set of two inner and two outer points, which created two triangles. For all 720 total points, there are 720 total triangles.

These triangles approximate the total cross section of the bone, and are useful in order to calculate the area moment of inertia. A few simple definitions enable us to calculate the moment of inertia for each triangle, which are then added up for all triangles, and referenced to the centroid, or center of mass of the overall shape.

These dimensions are used to calculate the area moment of inertia for each triangle

After a few errors we had to debug, my partner and I successfully calculated the values of the moment of inertia along the X and Y axis using our estimation technique within 5% of the actual results. My advice for anyone attempting a similar project: watch your positive and negative signs. Very closely.

The success of this project was a great sigh of relief because I have never before felt like my programming skills are adequate. Now I know that I am capable, and we even had the satisfaction of being the first group finished! If only every project went as smoothly…

As a final note to share, I have been fortunate enough to spend some time making new friends with some Imagineering legends from the past. George McGinnis and Bill Watkins worked together at Disney Imagineering beginning in the late 1960’s, and collaborated on projects such as Space Mountain, Indiana Jones, and the Monorail. George has been a wonderful friend for a few months now, and has shared a lot of knowledge about his work with transportation design, and Bill shared an excellent past in the motor sport world, where he has enjoyed the company of people such as Carroll Shelby, Phil Hill, and Jim Hall (the man behind Chaparral cars, which was arguably the most interesting Can Am racing team of the 60’s and 70’s). I was fortunate enough to spend a few hours with them last weekend that helped me to believe I can be a part of the magic someday, and I look forward to anyone else that will share their experiences with me.

That’s all that I have to share right now, but there will be plenty more to discuss with the upcoming semester.

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~ by MichaelStaudenmeir on August 2, 2010.

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