Designing ribbons

Before we discuss the design possibilities of these ribbons we should understand the steps involved in making one.
These are:-

If you want anything other than a circular ring you will specify one or more rings which will be assembled to get the shape you want. You will need to work out the details of how the part rings interconnect. This application will give you the details for the individual rings.

This page will deal only with the first item on the above list. The others will be dealt with on the 'Specify','Making'and 'Assembly' pages.

Design parameters

What do we have on a ring to play with? First off we have the usual outside and inside ring radii and the number of segments. Couple these with the shape factors of the outside and inside surfaces of the ring (not limited to be the same), whether we want both the top and/or bottom surfaces of the ribbon to be horizontal and finally whether we want the assembled ring to be dished.

Let us see what the effect each of these choices has upon the shape of the ribbon. First we'll assume that the inside and outside radii of the ring are fixed by the size of the project.

These choices are interrelated and specifying some will cause others to be fixed. The sofware in the 'Specify' page will guide you through these interrelationships.

Number of segments

For a fixed ring radius and shape factors, increasing the number of segments reduces the cone radius and hence the final depth or thickness of the ring and increases the number of ripples.

Shape Factor

For a fixed ring radius and number of segments increasing the shape factors particularly that of the ring outer surface increases the ring depth or thickness. However the appearance of the ring is greatly affected by the shape factors chosen and the difference between them. Note that the shape factors are independent so either can be the larger.

it is useful to be able to quantify these shapes independently of the cone diameter sizes and to do this we will use a dimensionless number which I have derived and called the shape factor. Figure 1 shows the range of shapes and their corresponding shape factors. Theoretically the shape factor has a range between 0 an 2 but practical considerations limit its value to be between 0.30 and 1.80. (If you want to see how this shape factor is defined and the practical limits determined have a look at the theory page.)

Figure 1 Shallow and Deep Shapes.
drawings of shallow and deep shapes

The exact value you use does not have to be precise just choose a shape from figure 1 and use the shape factor associated with it. You can modify this shape factor to give a shape deeper or shallower than the one shown in figure 1.

Ring Dish.

A concave dish (+ve. value) accentuates the ripple on the outer surface of the ring. Flipping the ring over gives a convex dish and accentuates the inner surface of the ring.

Dish refers to the attitude of the cone pieces when they are assembled. Normally the joints between the cone pieces around the ring lie in a plane and this plane is horizontal (ie. normal to the axis of the ring). See figure 2.

Figure 2 Half ring showing extended joints .
drawing of a half ring
This is not a necessary condition these joints can point downwards or upwards. Then the joints lie on a conical surface whose centre is the axis of the ring and its circumference is the same as the ring you have specified.
The amount of dish is the distance from the normal to this centre (positive for down, negative for up).

For small amounts of dish the original surfaces of the split cone will serve well. When the dish exceeds the outer radius of your ring these surfaces will need to be modified to to make acceptable joints, see the assembly page for details.

Ring Surfaces

In figure 2 each of the ripples has a line across the top of it. Imagine a line connecting the inner ends of these lines, then this connecting line will form a circle. We can also do this for the outer ends of the lines. This collection of connected lines defines a surface and we will call this the top surface of the ring. This surface will generally be conical (and the point of the cone will be on the ring axis) but it can be designed to be flat. Similarly we can define a bottom surface for the ring.
Both surfaces need to be horizontal (flat) if you want to incorporate the ring into the wall of a bowl or vase and only one needs to be horizontal if you are going to fix the ring to a flat surface. None if the ring is free standing or joined on its inner or outer surfaces.

Varying these four parameters; number of segments,shape factors,dish and surface orientation allows us to design ribbons that look very different. Couple these with the ability to assemble part rings into various shapes give a great deal of design flexibilty.