Knowledge You Can Build On — Est. 1998
More on Simple Sphere Turning Aid
Dennis in Southern Oregon
The previous thread is getting a bit long, so I will start afresh. There was interest expressed in the possibility of carrying the polygon approximations to a sphere to an additional stage. The previous post considered 8-sided and 16-sided approximations. This post shows new design graphs that extend the results to 32-sided approximations. For convenience, I am including the original pictures that illustrate the process.
Re: More on Simple Sphere Turning Aid
don stephan
Thanks for offering so much of your time on this.
If the horizontal distance (along the X-axis) RD is 1 unit, the original drawing suggests the vertical distance from R to the vertex is 2.25 units ( 16 squares to 38 squares).
So that I can make my own drawing, if distance RD is 1.0 unit, can you provide the distances RA, RB, and RC? Thanks again.
Re: More on Simple Sphere Turning Aid
Dennis in Southern Oregon
Don, the vertical distance from the bottom of the graph to the vertex has no direct effect on the measurements except that if it is too short, small vertical errors in determining where the diameter that you have set in your calipers matches the distance from R to D translates into large errors in the measurements of A, B and C. I arbitrarily selected 4 inches as the largest diameter for Page 1 of the graph and stretched things out to fill up an 8.5 x 11 sheet of paper.
The important quantities are the relative points along the baseline at which curves R, A, B, C and D cross. If D is 1.0 at the baseline, then the other curves cross the baseline at the following points
R: 0, A: 0.2929, B: 0.1077, C: 0.0502
Printed the Graph
Doug Wolf
Thanks Dennis for the graph and your explanation of the ratios involved in constructing the graph. I understand math but should have paid a little more attention in school. But hindsight is 20/20, I know that ratio well!
Thanks again, now I need to turn some spheres.
