Tale of the Taper: Keeping your fittings symmetrical
With many fittings, there is usually one area that requires more attention to figure out the correct points needed to develop the pattern. That’s why you should keep your fittings symmetrical if possible.
It helps if you can visualize fittings as well.
Shown in Figure 1 are two views - the top and elevation view. The top view shows the top of the fitting (round) and the oblong base of the fitting, as they appear perpendicular to the plane. Because the two sides are straight, since this fitting only tapers on one side, the radius will be the same for the top and the base. From the top view, one can see the overall length and width of the fitting and the radius ends. The elevation view, Figure 1, shows the height of the fitting (true length) and shows the true length of the taper side.
In Figure 2, some of the area that you do not need to draw as you develop the pattern is shaded. All the information you really need is in the one-quarter of the drawing and is for helping you determine the true-length lines for the tapered side.
As for the shaded area, from Point A to Point A1, and to the left of this line, is the length of half of the circumference of the top round. If this fitting is being created in two pieces, then you’ll only use the length from Point 1 to Point 4b - and add this length to the end of the pattern.
Because the radius is the same for the top and the oblong base, you only need to establish the points on the one section, Point 1 to 4a, as shown. Divide the circle into equal sections, as shown from 1 to 4a and reference them. Note that this line or part of the radius you are dividing is in its true shape. Each division or section of the circle is in its true length and it must be true length in the pattern.
Develop the elevation view as shown in Figure 2, by projecting lines down as shown from points A to A1, B to B1 and 4c. Drawing a line perpendicular to the projected lines establishes the base of the elevation view. Measure up from the baseline to establish the height of the fitting and draw an extended perpendicular line from Point 1 to Point 4.
On the elevation view, Figure 2, draw a line from Point 4 to intersect the projected line drawn from Point 4c on the baseline of the fitting. This is a true-length line for 4a to 4c. Draw an angular line from Point 1 to B1, which is also a true length line. This establishes the side, the triangle of points 1, A1 and B1, shown in its true shape. You’ll be using this shape to develop the pattern.
To establish points 2 and 3 on the top plane of the elevation view in Figure 2, drop lines down from the top view that are perpendicular to Line 1-4 on the elevation view.
Now perpendicular to Line 1-B1, draw a line intersecting points 2, 3 and 4, establishing reference points 2a, 3a and 4a. This is easily done by taking a steel square and placing one side on the Line 1-B1, and sliding it up and down this line until the other side of the square intersects the reference points 2, 3, and 4. This is similar to rolling the slope of the fitting and referencing where each point would fall on the line.
To make the pattern shown in Figure 3, you may transfer the triangle from Figure 2 to a new working area or continue to work from the one that you’ve already established. Either way, you will be developing the pattern from the triangle.
The reference marks 2a, 3a and 4a on Line 1-B1 were established in Figure 2 to allow a fixed reference point as you lay out or unfold the pattern. Using a square, as done in Figure 2, keeping one side of the square on Line 1-B1, extend lines from points 4a to 4, 3a to 3’, and 2a to 2’.
These lines extended will be random at this time because you don’t really know where points 2’, 3’ and 4’ are or where they may intersect at this time. To determine where these points intersect each line, you need to set your dividers to the distance or length of Point 1 to Point 2 in Figure 2, which is the length that each section of your circle was divided.
Now by placing one end of the dividers on Point 1 in Figure 3 and using this point as the center, make an arc that intersects with the perpendicular line drawn from Point 2a. This now establishes 2’. Repeat this by setting one end of the dividers on Point 2’ and using it as center, strike an arc that intersects the perpendicular line drawn from Point 3a, establishing 3’. Repeat this again, using 3’ as center to establish Point 4’.
Connect these points or intersections, trying to maintain the proper curve throughout them. This can often be done by placing your steel rule on one end and flexing it to the other end. Tighten or loosen up your steel rule until all points are in check.
There is now a bottom to create. Extend Line 1-B1 as shown and transfer points 2a, 3a and 4a, shown by 2c, 3c and 4c. Extend these lines as you did in the first step and again using your dividers, strike each intersection and mark.
Finally, connect Point 4’ and Point 4” to complete this end of the pattern. The gray shaded area in Figure 3 is basic parallel-line development and using again the lengths of each section, 1 to 2b, 2b to 3b, and so forth.
Why can you use parallel lines for the gray-shaded area in Figure 4, but not for the slope? This is often an area that isn’t understood well. Figure 4 shows you two different methods to compare why parallel lines were used on one side of the pattern (shaded gray) but not for the development of the slope.
The reason parallel lines weren’t used for the slope is back in Figure 2. Remember you divided the circumference of the top (round) section in to equal parts. Because you are looking at the fitting in Figure 2 perpendicular to its plane, you’re seeing these equal sections in their true length.
So you need to keep them “true length” in the pattern as well. This was done by extending lines 2a, 3a and 4a perpendicular to Line 1-B1. Then using the dividers set at their true length from the top view, connecting 1 to 2, 2 to 3 and 3 to 4a as described earlier for Figure 3.
Now when the pattern is rolled, you’ll know that the distance from point to point is the top view. Had you laid out this slope using parallel-line development as shown in Figure 4, (shaded blue), the pattern of the slope would be a bit wider. More importantly, the points from 1 to 2”’, 2”’ to 3”’ and 3”’ to 4 would not be consistent in length with the top view in Figure 2.
Patterns are created finding the true length of lines and connecting the points. If it’s in true-length form on any part of your plane view or elevation view, it’s going to be true length on your pattern. If it’s not, step back and see where or what went wrong. There were no allowances for seaming the halves together or for adding collars to the top or base.
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