Often when building a model you have a need for a centering ring that you don't have on hand, can't get quickly, or just simply isn't available for the tube combination you want. The method described here allows making custom rings that are consistent once the correct radius has been determined for the arc-scribe tool.
The scribing tool is essentially a crude custom beam-compass for each desired inside or outside tube diameter. A piece of spruce 1/4" tall and 1/2" wide is suitable for the beam. The pivot point is a pin such as a map pin or round-headed pin (as used to put notes on a cork board), about 1/32" diameter, protruding about 1/4" from the bottom of the spruce beam.
The scribing pin needs to be located at just the right distance away from the pivot pin to produce the desired tube radius. Whatever the tube's inside or outside diameter is, divide by two and that is the distance you need. However, the exact fit is rarely obtained on the first try, test first by scribing out (explained later) the desired ring or hole in some scrap material then compared to the tube. Relocate the scribing pin hole as needed until the test scribes produce a ring or hole with a good fit. Once the right location for the hole is confirmed, use Cyanoacrylate (CA) to help secure the pins into the spruce so they can't work loose. It can help to use some rough sandpaper or a file on the body portion of the pins to give the CA a good surface to bond to. The scribing pin's point should protrude from the spruce beam bottom by about 1/16".
For each scribing tool you make, mark on it what tube it is for, and whether inside or outside. If you know you'll make a lot of rings of one type, make up tools that will scribe both circles for the ring at the same time. So instead of using one tool to scribe a circle for the inside of a 1.64" diameter tube and then use another tool to scribe the outside of an 18mm tube, you can scribe both at the same time.
Once you get a certain diameter of scribing tool just right, you can use it to help make dual arc-scribing tools to produce a particular centering ring set. Say you want to make a dual scribing tool to make a centering ring to mount a BT-50 inside of a BT-80. Drill a small hole into the new dual arc-scribing tool, to be uses later for the pivot pin. Then take a scribing tool for the outside of a BT-50, insert its pivot pin into the new dual scribing tool you are making, and scribe an arc towards one end for the BT-50 tube hole to be scribed. Then do the same thing using a BT-80 inner Diameter scribing tool., towards the other end. Then, drill a hole into each of those two arcs, and insert and glue the pins into all of the holes. Remember to mark the new dual arc-scribing tool for what tube sizes it is used for.
This method works great on plastic sheet and plywood up to 1/16" thick, in a pinch it can do thicker plywood, but there is an alternative for thicker rings which will be covered later. For most model rockets, 1/32" ply most model rockets, 1/32" plywood is fine for rings. Since this method works best of all with plastic, it is preferable to make rings out of plastic such as .04" sheet for uses where plastic is acceptable. Obviously plastic is NOT acceptable for a top centering ring of an engine mount, as it would be subject to melting from ejection heat, for other uses such as centering rings for a nose sections's paper shroud it's fine.
After deciding which material to use for the ring, make a pinhole into the material that is greater than the large radius of the ring you are making. Put the scribing tool's pivot pin into the hole. Press down onto the scribing tool while rotating it, to scribe circles into the material. Rotate enough times with adequate force to scribe almost halfway through. Then, flip the material over and scribe the other side about halfway through. You can decide whether or not to scribe even more to break through to the other side or to simply flex the material back and forth to cause the plastic or plywood to fatigue enough to pop free.
If you use a scribing tool that cuts both the inner and outer radiuses at the same time, always apply a bit more pressure to the outer radius area so that whenever the ring pops free it will be the outside, and not the inside hole. If the inside hole pops free first, you won't be able to easily use the scribing tool to cut the rest of the outer portion of the ring.
That is essentially all there is to making rings by scribing. Now that you know how to make basic rings, there are some other tricks you can do. As referred to before, this method cannot make thick rings. Not one single thick ring. But, if you want a 1/8" plywood ring, you can make two 1/16" plywood rings and glue them together (cross-grain) to make one strong 1/8" ring.
The multiple ring method also can be used for making stiff rings that are strong but also light. Make up two plywood rings of whatever thickness would be suitable, then make a thick balsa ring - using one of the plywood rings as a guide for cutting out with a model knife. Glue all three together to create one very thick, stiff, strong, yet relatively light ring.
This method also is practical for cutting rings with multiple holes as used for clustered models. You first scribe out just the outer portion of the desired ring. Draw a straight line across the ring, running through the center pinhole, as a reference line for a 2-engine cluster. Using a compass pivoting in the center pin hole, make short arcs to mark the center location for the cluster tube holes to be scribed from, then make pin holes in those arcs to define the pivot points for the tube holes to be scribed out.
Also shown in the 2-engine example is how to mark off two different pairs of pivot point locations so that a bottom centering ring could have the tube holes farther out than the holes in the top ring. Why do this? The result of that would be to cant the engine mount tubes inwards, so their thrust lines come closer to the center of gravity of a clustered model, so it is less affected by uneven ignition of the cluster. The example shown for 2 engines works for any cluster combination, as long as there is room in the model's main body to space the engine tubes that way.
For more than 2-engine clusters, mark off more reference lines from the center of the main ring, spacing all the lines the same angle apart (# of outer holes / 360). For example a 7 engine cluster with 6 outer engine tubes, make the lines 60 degrees apart from the center. Determine the radius location for the center pivot point of the outer tubes, mark off the radial arcs, then put 1/32" pinholes into each location. You may want to do the above with a plastic ring instead of plywood, and save the plastic ring to use as a template - that way you don't have to mark off every complex ring you want to make, just use the plastic ring as a guide to transfer every complex ring like this that you want to make, just use the plastic ring as a pattern guide to transfer the pivot pinholes to the material you plan to cut the real rings from.
If you really like this method you will end up with a number of different arc-scribing tools, so save them in the same place such as a drawer or parts bin box.