When I saw Caryl's design for the Dunrovin Station Star, I decided to make one out of wood instead of paint, as Caryl mentioned yesterday. One-quarter the size of the one on the barn, so it'll fit in the house. I'm afraid I don't have photos of the full step-by-step, but that shouldn't be too much of a problem.
When it comes to projects, I'm a firm believer in being productively lazy where I can, so that I have the mental energy for the challenging parts. This usually pays off double since it can make the challenging parts easier. This is one of those times. I recognized that fitting the ring into the star probably would be the greatest challenge here. Cutting the grooves in the star points to line up with the ring would require a certain degree of precision, so I knew I'd have to put some effort into being as lazy as I could. Fortunately, I saw how I could produce the parts as though on an assembly line.
It should be readily apparent that the Dunrovin Station Star (like most stars) has radial symmetry. Each star point is identical to the other star points except for the rotation about the star's center. Slightly less obvious, if you think of the star as a three-dimensional object then each star point is also rotationally symmetric. This can be demonstrated by thinking about the star's rotational symmetry. Imagine that Caryl had painted the back side of the star onto the back of the plywood panel. Now rotate the plywood around a the diagonal that forms the vertical line in the star as it's hung. Thinking about the top point, what was the back of the right side of that point is now the front of the left side of that point. And you wouldn't be able to tell the difference between either orientation. These two aspects of the star's symmetry means that I can reduce the star to eight half-points.
If each star point occupies a corner of the original plywood panel, then each half-point occupies half of that corner and is fully enclosed by an isosceles right triangle. One angle is 90 degrees, and the other two are 45 degrees. Looking at the black triangle in the picture below, you can convince yourself of this if you think of the angle at the top of the picture as being half of the 90-degree corner of the plywood, or if you think of the angle at the center of the picture as being an eighth of the 360-degree rotation of the star.
So if I had eight identical isosceles right triangles, then I could form each half-point of the foreground star by cutting from one of the corners to halfway along the opposite leg. Then, taking the scrap from that cut, the half-point of the peekaboo star is formed by cutting halfway along the remainder of that leg to some distance up the first cut. If I cut the groove for the ring into the facing surface of the triangle shown above, then it can either be the left half-point (with the ring in the front) or, if I rotate it along the hypotenuse, the right half-point (with the ring in the back).
Taking Caryl's original star and reducing it to one-fourth the size means that each of the triangle's legs should be six inches. I knew I needed eight triangles, but I also wanted one or two extras because I know me -- I'll have to have at least one piece to screw up on. If I had a six inch wide piece of wood then I could make a bunch of these triangles. Well, I didn't have a six inch wide piece. I did have a couple of 1x10s that Caryl got a great deal on. But I also had another piece that I could work with. Do you remember the handles I made for Caryl's antique hand cultivator? I cut those out of one of those 1x10s, and I had left-over a shorter 1x10 and another piece that was 5 1/2" wide. It was sufficiently long that I could make nine triangles out of it -- that gave me my spare.
Before I cut those into half-points, I needed to cut the grooves. Well, I didn't need to, but it was easier for me to visualize the groove on the full triangle. So first I cut out the ring. Actually, I cut out two half-rings and later cut each of those in half to give me the four quarter-rings. Some time ago I made a tabletop for our patio table out of pallet wood (the original tempered glass top had been damaged in a windstorm when it tried to fly and then changed its mind). As part of that project, I made a jig to cut circles (or parts of circles) on the bandsaw.
I put that jig back into service to cut the ring segments out of quarter-inch plywood. I then made a similar jig for the router table to cut the grooves into each triangle.
Did I mention that I knew in advance that I'd need a "sacrificial" triangle to get all of my mistakes out of the way before moving on to the "production" triangles? Yeah... here's where that paid off. On the experimental first groove, I might've made the groove too big. But I corrected and got it right on the second try.
Now I drew the cut lines on the triangles and labelled, labelled, labelled the pieces. I labelled the foreground star's half-point in two locations and I labelled the peekaboo star's half-point in two locations. This is because when using the bandsaw, there are always (hopefully) tiny imperfections, and by making sure I kept the half-point for the peekaboo star paired with the foreground star's half-point that was cut from the same triangle, I know they'll mate properly because adjoining edges were formed with the same cut. Cutting the half-points on the bandsaw was without incident and mostly without error. I could now do the preliminary fitting.
Yes, I intentionally made the ring segments too long. It's easier to remove excess wood than it is to add missing wood. I should note that this was 1/4" plywood cut into 3/8" strips. That makes it fragile. The curvature didn't help matters since you're pretty much guaranteed that there'll be at least one point in the arc where the grain is weak. There was some breakage, but nothing I couldn't recover from.
Then came the stain. For the foreground star, both halves of each star point were stained with the same stain, except the left half had a single application that was quickly wiped dry and the right half had three full applications. For the peekaboo star, the star point halves were stained white and cherry. And the ring was stained black which really brought out the plywood's tiger striping. After everything was dry, I glued half-points together to form the four points. I figured this'd make it easier to get everything lined up if I had only four big pieces to juggle instead of eight.
Then came final assembly. I cut a piece of plywood to form a backing (large enough for the peekaboo points to attach to it but not so large as to be seen); this ended up doubling as a place to attach the hanging hook. I used extra scraps of plywood to support the star points as I fit them back together and marked the edges of the star points on the backing. Add glue to all adjoining edges and place each star point into its place on the backing, using those edge markings as a guide, and then a final tweak when all four are in place. Then I glued the eight half-points from the peekaboo star in place. And waited for the glue to set and mostly cure. The ring segments would torque the star points out of place if they weren't already secure so I exercised patience. Finally I glued the ring segments in place. As I anticipated, the ends of the segments tended to poke up out of the grooves, but eight clamps convinced the eight ends of the ring segments to stay in their eight grooves while the glue set and cured.
And the result now hangs in our kitchen.
Caryl Here- I find it so interesting to see how Doc and I approached problem solving in such a totally different fashion. While both Scientists, the mathematician/engineer just went all Euclidean on this project, using what he KNEW to be accurate and true based on what he was looking at. The Meteorologist/Artist knew what she wanted it to look like, came up with a set of lines that fit the bill, and started playing with the pencil.
I've done so many quilts, that the mariner's compass is no stranger. Docs description of the rotating 1/8th design is completely accurate. It is how a quilter would attack this, and then attach all the pieces together to form a small square, and then three more times to create the largest square, the full pattern.
Had I KNOWN the poor man was out in the barn cranking out math, angles and formulas scratched on the blackboard. I would have gone out and simply given him the drawing with all of the breakdowns on it! LOL.
It is now more complicated than dividing a square on all 4 corners, on the diagonal. Dividing those lines in half. Marking the sides at the half and then at the thirds on those lines. The circles inner radius is also at the 1/3 point, and outer radius in just aesthetically pleasing. Easy peasy!