Saturday, February 27, 2010

Day 14 "Revenge of the Arc Phasors"

.... Or, "Return of the 3rd Plane."

In a previous post I explained how to turn a two dimensional conical shape into a three dimensional cone, however, we have to build on that information and remember that we are no longer dealing with just a 2d object. when we are taking a 2d object and transferring it into a 3d object we have to consider the z axis and how that effects our shape. Since we are using the diameters of the different sections of the profile of the engineering section we have to think about how we are going to compensate for the additional dimension. In advanced mathematics, especially math that deal with expressing electrical sine waves we work with phasors. This discussion is not going to get into the depth of phasor math, but we can learn a simple lesson involving phasors and use them along with trig and a simple compass to modify our previous discussion, expand on it and create the entire engineering section. Don't get to bogged down with the terminology and don't let it intimidate you. I'll explain graphically what I mean here.

I've some up with a final engineering profile, see below. We are going to use this for the rest of this blog. I'm confident that it's accurate.

In the second photo below I've divided the engineering hull into additional sections so the we can recreate the entire hull. We'll be splitting the hull up into sections, building each section with card stock and assembling them into a whole. Before we move on to that part we need to follow along the top and bottom of the hull and take those lines back to the point of convergence. From the point of convergence we could use a really big compass to cut an arc between certain points after we do the math for each diameter from the previous post.

In the next post I'll show show what I mean graphically.

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