Pattern development in boilermaker work

In November, after Tank 15 is handed over, Kiera goes back into Ironbridge's fabrication shop for the winter. Her first morning, Joanne Pellerin hands her a roll of drawings and a cardboard tube full of old sheet metal templates, some of them stamped with job numbers from twenty years ago. "Last winter you learned to lay out flat plate and straight cylinders," Joanne says. "This winter it's the shapes that don't lie flat on the drawing: cones, transitions, elbows, tees, nozzles cut into curved shells. Every one of them has to be cut from a flat plate and then bent into a shape that matches a drawing. Getting from the drawing to the flat shape is called pattern development, and it's the oldest skill in the trade." This lesson introduces the ideas behind every pattern in the course: what a development is, which surfaces can be developed, the three methods for developing them, true lengths, and the thickness allowance that decides which line of the plate the pattern describes.

What a pattern is

A pattern, or development, is the flat shape that, when it is rolled, bent or formed, becomes the part on the drawing. A cylinder's pattern is a rectangle whose length is the circumference. A cone's pattern is a sector of a circle. A square-to-round transition's pattern is a fan of triangles and flat faces. Boilermakers, sheet metal workers and pipefitters all develop patterns, and the methods are the same in each trade; what changes is the thickness of the material and the allowances that come with it.

In a boilermaker shop, patterns end up in three forms. Small parts are laid out directly on the plate with a soapstone, a scriber, a steel rule, a trammel and a set of dividers. Repeated parts are laid out once on thin sheet metal or heavy cardboard as a template, then traced onto each plate. Large or complex parts are drawn on a computer and sent to the CNC cutting table as a file of points. Kiera will learn all three, but Joanne insists that she learn the hand method first. "When the CNC file is wrong, and one day it will be, the person who can lay it out by hand is the one who catches it."

Surfaces that can and cannot be developed

Not every shape can be cut from flat plate and bent without stretching. A surface that can be unrolled flat without stretching or tearing is called developable. Cylinders, cones and the flat faces of prisms and pyramids are developable, because each is made of straight lines that lie in the surface, and the surface can be rolled along those lines like a sheet of paper. A transition built from flat triangles and parts of cones is developable for the same reason.

Spheres, ellipsoidal heads, torispherical heads and the knuckles of flanged heads are not developable. They curve in two directions at once, so a flat plate must stretch or shrink to take their shape. Those parts are pressed, spun or formed in segments by specialist head manufacturers, and the boilermaker buys them finished. Lesson 9 covers how heads are ordered, checked and fitted, and how a shop estimates the size of the flat blank that a head maker starts from, but the head itself is not laid out by pattern development in the way a cone is.

Three methods of development

Every developable surface can be laid out by one of three methods, and the method depends on how the straight lines in the surface are arranged. Parallel-line development is used when the lines in the surface are all parallel, as they are on a cylinder or a prism. The surface is divided by lines parallel to its axis, the lengths of those lines are measured, and they are set up at their spacing along a straight stretchout line. Pipe cuts, elbows and tees are developed this way, and lessons 2 and 6 use it.

Radial-line development is used when the lines in the surface all meet at one point, as they do on a right cone or a pyramid. The pattern is drawn around that point, the apex, with a radius equal to the true length of the lines from the apex. Right cones and truncated right cones are developed this way, in lessons 3 and 4. Triangulation is used when neither of those patterns holds: the lines in the surface are not parallel and do not meet at one point. The surface is divided into triangles, the true length of every side is found, and the triangles are laid out side by side to build the pattern. Eccentric cones and transitions are developed by triangulation, in lessons 4 and 5, and the method works on any developable surface if the others do not fit.

True length

The pattern of a surface must be built from the true lengths of the lines in it. A line drawn on a plan or an elevation shows its true length only when it lies parallel to the plane of that view. A line that slopes toward or away from the viewer appears shorter than it is. The corner line of a hopper, running from the top corner of the square to a point on the round outlet below, appears shortened in both the plan and the elevation, because it slopes in both directions.

There are two ways to find a true length. The drafting way is a true length diagram: the plan length of the line is laid off along a horizontal base line, the rise of the line is set up at one end at right angles, and the hypotenuse is the true length. The shop way is the same thing done with arithmetic: the true length is the square root of the sum of the squares of the three distances the line covers, across, along and up. Joanne still draws true length diagrams for a new shape, because the diagram shows when a number looks wrong, but she checks every line with a calculator.

The plan length, the square root of the first two terms, is what a ruler would measure on the plan view. Adding the rise turns it into the true length. For a line that lies in a vertical plane, only one of the plan distances is non-zero and the formula reduces to the familiar right triangle that Kiera used last winter for knee braces.

The thickness allowance: which line does the pattern describe?

Sheet metal workers often ignore the thickness of their material, because it is too thin to matter. A boilermaker cannot. When a plate is rolled into a cylinder or a cone, the outside surface stretches and the inside surface compresses. Somewhere in between is a surface that neither stretches nor compresses, called the neutral surface, and for the plate thicknesses and bend radii in boilermaker work it lies very close to the middle of the plate. The pattern's length must equal the length of the neutral surface, so the pattern is developed on the mean diameter, the inside diameter plus one thickness, or the outside diameter minus one thickness.

The difference is not small. Between the inside and outside surfaces of a cylinder, the circumference differs by two times pi times the thickness, about six times the plate thickness. For 10 mm (3/8 in) plate that is more than 60 mm (2 3/8 in), enough to make a shell that will not fit its head or a cone that will not meet its flange. Every development in this course is laid out on the mean line unless the part is thin enough for the difference not to matter, or the drawing dimension is already a mean dimension.

Mean lines also apply to the height and slant of a cone and to the corners of a transition. A transition drawn with outside dimensions is developed with every dimension taken to the middle of the plate. For brake-formed corners, where the plate is bent sharply rather than rolled, the bend allowance is calculated from the inside radius and a factor for where the neutral line falls, which Joanne keeps in a chart for the brake. For rolled parts, the middle of the plate is close enough.

There is one exception that Kiera meets in lesson 2. When a template is wrapped around the outside of a finished pipe to mark a cut, the template lies on the outside surface, so it is developed on the outside diameter. The plate has already been formed; the template is only marking it.

A first worked check

Joanne gives Kiera a sheet of numbers to work through with the shop's code before she draws anything: the true lengths of three lines from this winter's jobs, and the stretchout of a 10 mm (3/8 in) hopper section with an inside diameter of 900 mm (36 in), developed three ways so she can see the difference.

# True lengths and the neutral line: two checks before any pattern is drawn (metric)
import math
from math import gcd
MODE = "mm"

def frac(x, den=16):
    sign = "-" if x < 0 else ""
    n = round(abs(x) * den); whole, rem = divmod(n, den)
    if rem == 0:
        return f"{sign}{whole} in"
    g = gcd(rem, den)
    return f"{sign}{whole} {rem // g}/{den // g} in" if whole else f"{sign}{rem // g}/{den // g} in"

def show(x):
    x = 0.0 if abs(x) < 1e-6 else x
    return f"{x:,.0f} mm" if MODE == "mm" else frac(x)
# 1. true length of a line from its plan run (dx, dy) and its rise (dz)
lines = [("hopper corner line", 400, 300, 900), ("duct hip line", 600, 0, 450), ("transition seam", 250, 0, 900)]
for name, dx, dy, dz in lines:
    plan = math.hypot(dx, dy)
    tl = math.hypot(plan, dz)
    print(f"{name:22} plan length {show(plan):>12}  rise {show(dz):>10}  true length {show(tl):>12}")

# 2. which diameter to develop: inside, outside or mean (neutral line)
ID, t = 900, 10
for label, d in (("inside", ID), ("mean", ID + t), ("outside", ID + 2 * t)):
    print(f"stretchout on the {label:7} diameter: {show(math.pi * d)}")
print("difference between outside and inside stretchout:", show(2 * math.pi * t), "(= 2 pi t)")

hopper corner line     plan length       500 mm  rise     900 mm  true length     1,030 mm
duct hip line          plan length       600 mm  rise     450 mm  true length       750 mm
transition seam        plan length       250 mm  rise     900 mm  true length       934 mm
stretchout on the inside  diameter: 2,827 mm
stretchout on the mean    diameter: 2,859 mm
stretchout on the outside diameter: 2,890 mm
difference between outside and inside stretchout: 63 mm (= 2 pi t)

The duct hip line and the transition seam each lie in a vertical plane, so one of their plan distances is zero. The hopper corner line slopes in both directions, and its true length is twice its plan length. The stretchout figures show the thickness allowance clearly: the three diameters give three different plate lengths, and only the mean one will roll to a cylinder whose inside diameter is right and whose seam closes.

The winter's work

Joanne runs through the jobs on the shop schedule. For Riverbend Unit 2, the ductwork for the induced draft fan inlet is being replaced: a round duct, a segmented elbow, an eccentric reducer and a weather hood for the new silencer vent. For Tamarack Pulp, a dust collector needs a new hopper: a truncated cone with a round side inlet and a square-to-round outlet. For Northgate, the shop is building V-414, a second knockout drum to the V-412 design, with its nozzles and heads, along with a set of fabricated tees and laterals. The last job of the winter is the one Joanne saves for Kiera's capstone: a section of a new column, C-305, with a cone joining a large lower shell to a smaller upper one.