Dave Mount
05-21-2021, 3:59 PM
Overview of the roughing process: The process from square blank to the initially roughed out sphere is shown in the figure below. The profiles are in plan view, as though you were looking down on the turning from above. The steps are to go from square blank to cylinder, from cylinder to octagonal, then from octagonal to (mostly) spherical. Panel A shows how the sphere is sitting within both the cylinder and the octagon. Panels B through D show the steps to get there, which I explain in more detail below.
458075
Rough round and mark for length: Finally, some actual turning. First step is simple -- mount the blank between centers and rough it round. Your layout will be a little more accurate if the diameter is consistent after roughing round, but it’s not something to fuss over. I visually align the tool rest with the ways of lathe to help make my roughing cut even and then just judge it by eye. If your blank is irregular in shape, it doesn’t have to be completely round except at the center (end to end). Take your calipers and measure the diameter in the middle; this is the (maximum) diameter of your sphere. Lock the calipers on that measurement and hold them lengthways on your cylinder and decide where the ends of your sphere should fall. Mark one end with pencil line, then part in a short distance to mark that end, then using that parting cut as one end, mark the other end and part in a short distance there. Your sphere lies between those parting cuts.
Next mark a center line between these two parting cuts. I usually do this with the calipers by setting them to half the diameter. Extreme accuracy is not really necessary, in fact guessing by eye would probably be OK. Extend the center line clear around the cylindrical blank. This will become the equator of the sphere.
458076
From cylinder to octagon: At this point, some videos have you just part both ends in to close to the center and round over the corners to make the blank spherical. I find this hard to do without some guides. If you can get to roughly spherical just by eye, then just do that and skip this whole octagon business. For the rest of us mortals, I find a great crutch is to turn the cylinder into an octagon first, and then into a sphere. The octagon method does two important things. For one, it gives you the rough proportions of the sphere and a couple landmarks to go by, instead of having to picture spherical in your head and then work toward it. The second is that it allows you to rip off 80% of the waste in a big hurry without any concern that you’re going too far and cutting away something you shouldn’t. I’d guess switching to the octagon method cut the time for this initial shaping step by two thirds for me, maybe more, and saved even more time in the long run because I was closer to spherical when I did the first axis rotation, and the closer you are to spherical at the start, the fewer iterations it’s likely to take to finish. Laying out the octagon requires math. . .but it’s easy math on a calculator. You need to remember only one number: 0.293.
It turns out through some miracle of geometry that 0.293 times the diameter of your cylinder is the distance in from the “corner” of your cylinder where your 45 degree cut should start in order to turn your “square” cylinder (as viewed from above) into an octagon with eight equal sides (see panel B in the figure). So, get your smartphone out and multiply the diameter of your sphere by 0.293 and set (and lock) your calipers for the resulting number (this is why a decimal caliper is easier. . .what’s 0.693” inches in a fraction?). Then make a pencil line on the face of your cylinder that distance in from each of the parting cuts you made to define the ends of the sphere. That’s one side of the 45 degree facet. The other is on the end grain. So, the next step is to extend your parting cut down the end grain until the surface of it is the same distance from the face of the cylinder as the distance locked on your caliper. If you go too far, don’t sweat it, just make a pencil line where you should have stopped.
458077
Now, all you have to do is to connect your two marks (the one on the face of the cylinder and the bottom of your parting cut on the end) with a straight cut. I use a spindle gouge. Even though this is a straight cut, you’ll still have to do some combination of rolling the flute and raising the handle to get a straight cut. Do the best you can, but it doesn’t have to be perfect. Mistakes at any part of this process can be corrected by the later parts of the process, the only penalty might be a slightly smaller sphere.
With that done, you should have an octagon in plan view. If you’ve done it right, each of the facets (and the parted down tenon too) should have the same measurement. If they don’t, it’s not the end of the world, but the closer they are the less finishing work you’ll have to do.
Octagonal to sphere(ish): The next step is to turn the octagon into a sphere(ish) shape. There are folks on the web that advocate going from an octagon to a hexadecagon, a sixteen-sided shape, using another round of a similar marking and straight faceting cuts. For me, I’ve found that just getting to an octagon gives me enough sense of proportion that I can get where I need to get without a bunch more layout and faceting. But it’s something to try if you want to experiment with it. The sides of a hexadecagon are 0.1989 times the diameter.
The sphere inside the octagon touches the surface of the octagon in the middle of each facet (see panel A in the diagram), and these are important landmarks for the next step. The middle of the front facet is already marked from the initial layout, so we just need to add marks at the center of the two 45 degree facets (panel C in the diagram). If you want accuracy, you can use your calipers to measure the distance from the arris between the face of the cylinder and the 45 degree face to the centerline you marked earlier, and transfer that distance from the arris down onto the 45 degree face. To be honest, I just mark it by eye with a pencil and the lathe running; I’ve found this to be “good enough”. Quality is conformance to requirements. . .
458078
These midpoint lines are places where the surface of your sphere touch the surface of the octagon, so the next step is to connect the lines in the middle of adjacent faces by removing the “point” and replacing it with a smooth arc that dies into each of the midpoints (to get to panel D in the diagram). Start at the arris and make progressively broader arcs. Do this on both sides of the centerline, without removing any of the pencil lines. While getting as close as you can to spherical is nice, what’s actually more important is that the two sides be symmetrical, as this symmetry is what will help center the workpiece in the compression chucking step that follows. If your shape is lumpy, the NRS is a good tool to smooth things up. I have a heck of a time carving a smooth arc with a spindle gouge.
After this you’re roughly circular from the middle of the 45 degree face on one side to the same place on the other, but you’re shaped (loosely) like a (American) football. . .or rugby ball. . .even though we’re after a soccer ball. How much farther you take the shaping before going to the next step is personal preference. It’s fine to do nothing more and take off all the remaining excess in the next step.
458079
Or, you can take off some of the waste on the ends of the piece by cutting an arc from the middle of the 45 degree faces in toward the centerline of the piece. If you left your blank long, you may have enough room to part farther down and do a fair amount more rounding. If you’re using steb centers on a short blank like I am in the pictures, the steb centers interfere and I just leave most of it go and take it off in the next step.
458080
If you have used a longer blank, after you’re done rounding as much as you care to, part (and/or cut) the waste off both ends of the workpiece. Only caution here is that if you part it all the way in two on the lathe, you might tear some fibers going down into the sphere and that's not good. I turn the tenons down to 1/4" or so and then saw the rest with a handsaw. Before you part off or remove the workpiece, make sure your original centerline is still visible all the way around the piece; we need that landmark at the next step; the lines that were in the middle of the 45 degree facets are not needed further.
Next installment is the first rotation to a new turning axis. Might be a couple days before I can get that posted (busy weekend).
Thanks for all the kind words, I'm glad some folks are finding it interesting and/or useful.
Dave
458075
Rough round and mark for length: Finally, some actual turning. First step is simple -- mount the blank between centers and rough it round. Your layout will be a little more accurate if the diameter is consistent after roughing round, but it’s not something to fuss over. I visually align the tool rest with the ways of lathe to help make my roughing cut even and then just judge it by eye. If your blank is irregular in shape, it doesn’t have to be completely round except at the center (end to end). Take your calipers and measure the diameter in the middle; this is the (maximum) diameter of your sphere. Lock the calipers on that measurement and hold them lengthways on your cylinder and decide where the ends of your sphere should fall. Mark one end with pencil line, then part in a short distance to mark that end, then using that parting cut as one end, mark the other end and part in a short distance there. Your sphere lies between those parting cuts.
Next mark a center line between these two parting cuts. I usually do this with the calipers by setting them to half the diameter. Extreme accuracy is not really necessary, in fact guessing by eye would probably be OK. Extend the center line clear around the cylindrical blank. This will become the equator of the sphere.
458076
From cylinder to octagon: At this point, some videos have you just part both ends in to close to the center and round over the corners to make the blank spherical. I find this hard to do without some guides. If you can get to roughly spherical just by eye, then just do that and skip this whole octagon business. For the rest of us mortals, I find a great crutch is to turn the cylinder into an octagon first, and then into a sphere. The octagon method does two important things. For one, it gives you the rough proportions of the sphere and a couple landmarks to go by, instead of having to picture spherical in your head and then work toward it. The second is that it allows you to rip off 80% of the waste in a big hurry without any concern that you’re going too far and cutting away something you shouldn’t. I’d guess switching to the octagon method cut the time for this initial shaping step by two thirds for me, maybe more, and saved even more time in the long run because I was closer to spherical when I did the first axis rotation, and the closer you are to spherical at the start, the fewer iterations it’s likely to take to finish. Laying out the octagon requires math. . .but it’s easy math on a calculator. You need to remember only one number: 0.293.
It turns out through some miracle of geometry that 0.293 times the diameter of your cylinder is the distance in from the “corner” of your cylinder where your 45 degree cut should start in order to turn your “square” cylinder (as viewed from above) into an octagon with eight equal sides (see panel B in the figure). So, get your smartphone out and multiply the diameter of your sphere by 0.293 and set (and lock) your calipers for the resulting number (this is why a decimal caliper is easier. . .what’s 0.693” inches in a fraction?). Then make a pencil line on the face of your cylinder that distance in from each of the parting cuts you made to define the ends of the sphere. That’s one side of the 45 degree facet. The other is on the end grain. So, the next step is to extend your parting cut down the end grain until the surface of it is the same distance from the face of the cylinder as the distance locked on your caliper. If you go too far, don’t sweat it, just make a pencil line where you should have stopped.
458077
Now, all you have to do is to connect your two marks (the one on the face of the cylinder and the bottom of your parting cut on the end) with a straight cut. I use a spindle gouge. Even though this is a straight cut, you’ll still have to do some combination of rolling the flute and raising the handle to get a straight cut. Do the best you can, but it doesn’t have to be perfect. Mistakes at any part of this process can be corrected by the later parts of the process, the only penalty might be a slightly smaller sphere.
With that done, you should have an octagon in plan view. If you’ve done it right, each of the facets (and the parted down tenon too) should have the same measurement. If they don’t, it’s not the end of the world, but the closer they are the less finishing work you’ll have to do.
Octagonal to sphere(ish): The next step is to turn the octagon into a sphere(ish) shape. There are folks on the web that advocate going from an octagon to a hexadecagon, a sixteen-sided shape, using another round of a similar marking and straight faceting cuts. For me, I’ve found that just getting to an octagon gives me enough sense of proportion that I can get where I need to get without a bunch more layout and faceting. But it’s something to try if you want to experiment with it. The sides of a hexadecagon are 0.1989 times the diameter.
The sphere inside the octagon touches the surface of the octagon in the middle of each facet (see panel A in the diagram), and these are important landmarks for the next step. The middle of the front facet is already marked from the initial layout, so we just need to add marks at the center of the two 45 degree facets (panel C in the diagram). If you want accuracy, you can use your calipers to measure the distance from the arris between the face of the cylinder and the 45 degree face to the centerline you marked earlier, and transfer that distance from the arris down onto the 45 degree face. To be honest, I just mark it by eye with a pencil and the lathe running; I’ve found this to be “good enough”. Quality is conformance to requirements. . .
458078
These midpoint lines are places where the surface of your sphere touch the surface of the octagon, so the next step is to connect the lines in the middle of adjacent faces by removing the “point” and replacing it with a smooth arc that dies into each of the midpoints (to get to panel D in the diagram). Start at the arris and make progressively broader arcs. Do this on both sides of the centerline, without removing any of the pencil lines. While getting as close as you can to spherical is nice, what’s actually more important is that the two sides be symmetrical, as this symmetry is what will help center the workpiece in the compression chucking step that follows. If your shape is lumpy, the NRS is a good tool to smooth things up. I have a heck of a time carving a smooth arc with a spindle gouge.
After this you’re roughly circular from the middle of the 45 degree face on one side to the same place on the other, but you’re shaped (loosely) like a (American) football. . .or rugby ball. . .even though we’re after a soccer ball. How much farther you take the shaping before going to the next step is personal preference. It’s fine to do nothing more and take off all the remaining excess in the next step.
458079
Or, you can take off some of the waste on the ends of the piece by cutting an arc from the middle of the 45 degree faces in toward the centerline of the piece. If you left your blank long, you may have enough room to part farther down and do a fair amount more rounding. If you’re using steb centers on a short blank like I am in the pictures, the steb centers interfere and I just leave most of it go and take it off in the next step.
458080
If you have used a longer blank, after you’re done rounding as much as you care to, part (and/or cut) the waste off both ends of the workpiece. Only caution here is that if you part it all the way in two on the lathe, you might tear some fibers going down into the sphere and that's not good. I turn the tenons down to 1/4" or so and then saw the rest with a handsaw. Before you part off or remove the workpiece, make sure your original centerline is still visible all the way around the piece; we need that landmark at the next step; the lines that were in the middle of the 45 degree facets are not needed further.
Next installment is the first rotation to a new turning axis. Might be a couple days before I can get that posted (busy weekend).
Thanks for all the kind words, I'm glad some folks are finding it interesting and/or useful.
Dave