Setup for making conical surface with disk sander tool. Crutches were not needed.
Convex wood surfaces can have a lot of uses in telescope making:
The method of making spherical surfaces in glass is well known: rotate the workpiece with its axis under the edge of a cylindrical cutting tool. This might be extended to wood by using a fly cutter, but sometimes bad things happen with fly cutters. (Things fly across the room, fingers get severed, the blood bank gets depleted, etc.) A sanding disk is a lot safer, but you must approximate the desired surface with conical segments. You do not need to precisely locate the axis of the turntable under the edge of the tool.
It is not at all difficult to make precise curved wooden surfaces. If you have ground, polished, and figured a mirror, you already know part of how to do it.
The idea here is to start with a plywood disk and a wood square of sufficient thickness. The disk may be several layers glued together to form a step function approximation of your desired curve. Plywood "door skin" will allow you to do this with thin layers and save a lot of sanding. I use white glue, sandwich the material between two pieces of plywood, and park my car on them overnight.
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Setup for making conical surface with disk sander tool. Crutches were not needed. |
First, chuck up a disk sander in your drill press. With the drill press table flat, LIGHTLY sand both sides of the disk flat. Then clamp the square onto your drill press table, and pound a nail through the center of the disk into the square. You should be able to turn the disk without moving it. Now the fun starts.
You are going to use sandpaper to remove a lot of wood from the disk. You can save a lot of work, save a lot of sandpaper, and make a lot less dust if you begin with a disk that is a step-function approximation of your desired curve. I do the calculations for several zones, and use a router bit at the maximum speed my drill press can deliver. This is nowhere near the speed of a router, so I take very light cuts. At the same time, I can trim the edge of the disk to be a perfect circle, just in case I did not get the nail through the exact center.
Calculate the edge angle of your desired curve; this is merely arcsin(r/R). If you are so lame that you don't have an arcsin button on your calculator, calculate .0175 * r/R degrees. (this approximation is OK for angles less than 6 degrees.) Set the tilt of your drill press table to this angle. Now all you have to do is rotate the wooden disk against the sander to form a conical surface around the edge. Keep sanding until the width of that cone is equal to the radius of the inside flat area.
The next step is to set the tilt of your drill press to about half its initial tilt. Sand the ridge at the 50% zone until you have created a shallower cone region whose width is equal to the sum of the inside radius plus the remaining width of the outer conical region. When this is done, you have a piecewise linear approximation to your curve that is very close to the desired shape. This should be satisfactory for many applications, continue only if you need more accuracy.
Result of a flat central zone and two conical segments already looks very nearly spherical. |
The flat and two-cone approximation can be made more accurate by sanding. I made a matching dental stone form from my plywood disk by the same methods I would use to make a pitch lap foundation. When the dental stone was hard and dry, I attached small squares of coarse sandpaper to the inside surface with Kodak Photo Spray mount. I then pretended I was grinding a mirror. Pretty soon the plywood was perfectly spherical. Not only that, I found that I could deepen the curve or make it more shallow by the standard methods of mirror making: convex plywood disk on top to reduce the curve, long strokes with dental stone tool on top to deepen the curve, and short strokes to return to an accurate sphere. Once the plywood disk was spherical, I peeled the sandpaper off of the dental stone and pasted it onto the plywood. I then repeated the process to clean up the inside surface of the dental stone and get it perfectly spherical. Because ink penetrates into dental stone and wood, I suggest the PENCIL TEST instead of the Sharpie test to verify contact.
Final convex dome of dental stone. (This failed at high temperature.) |
That's all there is to it. I am convinced that the techniques we learn in optics can be easily used for other purposes and can yield surprizing accuracies. Although the final dental stone dome failed at high temperature, I learned a lot from this quacktivity.
Meanwhile, machinists with lathes continue to use step function approximations instead of piecewise linear approximations that would yield a much smoother workpiece.