CHAPTER XII
RETURN AND FACE MITERS
Problem 41
SQUARE RETURN MITER
78. Square Return Miter.—Figure 245 shows the profile of a moulding. Mouldings are seldom of standard design, although the architect builds up a given design from standardized parts or members. In the profile shown, the compound curve is known as an ogee. This shape is encountered more frequently in mouldings than any of the others. Line 9–10 of Fig. 245 is often referred to as a "fascia," which is a plain band or surface below a moulding. Line 10–11 of Fig. 245 forms the drip of the moulding since it compels the water, flowing down the surface of the moulding, to drop off. The lines 11–12 and 12–13 are called fillets. Fillets are narrow plain surfaces used to separate curved members of a moulding, or to finish a moulding. On a moulding of this design the fillet 12–13 is intended to enter a reglet (slot) in the side wall of the building.
In drawing the ogee curve, a square, 3–A–9–B, Fig. 245, is drawn whose sides are equal in length to the desired height of the member. A horizontal center line CD is then drawn and from points C and D the curves forming the ogee are drawn. This gives an ogee whose height equals its projection. Architects often modify this curve in order to gain height without attaining too great projection.
After the profile is drawn it should have all of its curved lines divided into equal spaces. Numbers should be placed at each angular bend (vertex) and at each division of the curved fines. A line dropped from points 2 and 13 will show the entire width or projection of the moulding, Fig. 246. If this width is carried around the corner at an angle of 90°, a plan of a square return miter will result. The miter line, as shown in Fig. 246, must always bisect the angle formed by the sides of the moulding.
Lines should be dropped from every point in the profile, downward through the plan, an indefinite distance. A line of stretchout should now be drawn at right angles to the side of the plan as shown in Fig. 247. Every space in the profile is now transferred to the line of stretchout, care being taken to get them in the proper sequence, and to have the numbers correspond. Measuring lines are drawn through each division at right angles to the line of stretchout.
Starting at point 1 of the profile, the extension line should be followed downward until it intersects line 1 of the stretchout. In like manner all of the intersections should be located and marked with small circles. The miter cut may now be drawn in by connecting the intersections of the stretchout by straight and curved lines. It should be observed that curved lines in a profile will always produce curved lines in the pattern, and straight lines in the profile will produce straight lines in the pattern.
Figure 248 represents the moulding carried around another corner. Extension lines are carried upwards from this view and are intersected by correspondingly numbered extension lines from the profile. In this manner an elevation, Fig. 249, of any miter may be projected.
It should be observed that the plan, Fig. 246, plays no part in the development of the pattern, the extension lines from the profile remaining unchanged in passing through this view. This is true of all square (90°) return miters. However, if the miter was at any other angle, say 87°, the extension lines would be deflected by the changed position of the miter line, and a plan view would be absolutely necessary for the development of the pattern.
Problem 42
CONDUCTOR HEAD
79. Conductor Head.—Conductor heads are used to ornament the conductor pipes of a building and are usually placed at the point where the "goose neck" from the gutter enters the conductor. As shown by the dotted lines in Fig. 250, a short piece of rectangular or round pipe is carried through the head in order to give a more direct travel to the water.
Conductor heads are made in a great variety of shapes and sizes. On the better class of buildings, they are designed to harmonize with the particular style of architecture adopted.
Figure 250 shows a front elevation of a conductor head. Since, as was explained in the preceding problem, the pattern may be taken directly from the profile as it appears in the elevation, the curved lines may be divided into small parts. It will be noticed that the space between points 20 and 21 is less than that between the other points. This is perfectly permissible, as long as the same distance appears between points 20 and 21 on the line of stretchout, and saves much time that would otherwise have to be spent in making all spaces exactly equal. The dividers are set at any radius not too large and the curve is spaced off, allowing the last space to come wherever it may.
A center line is drawn in Fig. 250 and extended downward to serve as a line of stretchout for Fig. 252. The spacing of the profile is now transferred to this line and numbered to correspond. Measuring lines are drawn at right angles to the line of stretchout and intersected by extension lines dropped from correspondingly numbered points in Fig. 250. The miter cut of one side of the pattern is now drawn in.
Since both sides of the front (as divided by the center line) are symmetrical, the distances from the center line of Fig. 252 to each point in the miter cut should be transferred to the other side, thereby obtaining the necessary points for drawing in the other miter cut of the pattern for the front.
The side elevation, Fig. 251, is now drawn and the pattern developed by the method already described for obtaining the pattern of the front. Laps are added and notched as shown in Fig. 253. Two of these patterns must be cut from the metal and while they are both alike, it is evident that they must be formed in pairs; that is, one right-hand and one left-hand, in order to attach them to the front of the head.
The pattern of the back, Fig. 254, is obtained by reproducing
the outline of the front elevation, Fig. 250, and adding laps, which are notched as shown.
80. Related Mathematics on Conductor Head.—Since all conductor heads are composites of the surfaces of many different solids, it is unpracticable to attempt to compute their exact surface area. The most accurate method of obtaining the cost of material entering into their manufacture is to lay out a full size pattern, arrange the several pieces so as to produce a minimum of waste, and compute the area of the rectangle thus obtained.
Problem 42A.—Show how you would arrange the blanks for the conductor head in order to produce as little waste as possible.
Problem 42B.—What is the area in square feet of the metal required as shown by Problem 42A?
Problem 42C.—What would be the weight of the metal if it were 16 oz. copper?
Problem 42D.—Allowing three hours' labor at $1.35, and 30 cents for solder, what would be the selling price of the head if 30 per cent of the cost price were added for profit?
Problem 43
FACE MITERS
81. Face Miters.—A face miter may always be distinguished from a return miter by the fact that the miter line can be seen in the elevation; whereas, the miter line of a return miter always appears in the plan.
Figure 255 gives the same profile as was used in Fig. 245. This profile is used again in order to afford the student an opportunity to compare the two types of miters and note wherein the difference lies.
The ogee is divided into small spaces and numbers placed at each point of the entire profile.
Extension lines are carried over to the right from points 1 and 11 to form the outline of one leg of the miter. These lines are then intersected by a miter line drawn at an angle of 45° since the miter itself is a square, or 90° face miter. The other leg of the miter is now drawn and lines added to complete the elevation as shown by Fig. 256.
A line of stretchout, Fig. 257, is next drawn and the distances between points of the profile transferred in their proper sequence, with numbers to correspond. Measuring lines are drawn through each of these points at right angles to the line of stretchout. Starting from point 1 of the profile an extension line is carried to measuring line 1 of the stretchout. In like manner all other points of intersection are located in the stretchout. Any tendency to "short-circuit" this operation should be guarded against by referring back each time to the starting point in the profile. By neglecting to do this, mistakes are apt to occur, which can be detected only after the parts are formed up and the assembling process has begun. The miter cut of the pattern should now be drawn in, and dots placed on the lines that are to be bent in the cornice brake.
As was the case with the square return miter, the pattern can be taken directly from the profile. The main consideration is the proper placing of the profile with reference to the direction in which the extension lines from the profile are to be drawn. A mistake of this nature will result in a face miter when a return miter was intended; or, a return miter when a face miter was desired. Also, as was the case of the return miter, the extension lines can be taken from the profile, only in case the miter is at an angle of 90°. Otherwise an elevation must be drawn, as the miter line will deflect the
extension lines as they pass through the elevation in a miter other than one of 90°.
Problem 44
WINDOW CAP
84. Window Cap.—Figures 258 and 259 show the elevation and profile of a window cap in the form of an angular pediment. It is a combination of two horizontal mouldings having square return miters on their outer ends and two inclined or rake mouldings that miter upon each other at the center line, and with the horizontal mouldings at their lower ends. The triangular space beneath the rake mouldings contains a sunken panel.
This problem presents two new features; namely, a face miter at other than right angles, and a sunken panel. A profile is "drawn in" one of the rake mouldings in order to show the amount of "sink," and the method of joining the panel to the mouldings.
The details for a job of this nature are always furnished by the architect. The exact measurements must be taken at the building, where it is often found that a given set of windows will vary from ⅛ in. to ¼ in. in width. This variation is taken care of by lengthening or shortening the horizontal mouldings. This can be done by the cutter since it does not affect the miter cuts.
The elevation, Fig. 258, must be carefully drawn, care being taken to draw the rake mouldings at their proper angles. The miter lines must also exactly bisect the angle of the miter.
The profile, Fig. 259, is next drawn and the curved line divided into small spaces. Each point and vertex are then numbered. An extension line is now carried from the point of intersection of the miter line and the sunken panel, point A of Fig. 258, over into the profile as shown by point A of Fig. 259.
From each point in the profile, extension lines are carried over into the elevation, Fig. 258, until they intersect the first miter line. These extension lines are now carried parallel to the outline of the rake moulding until they intersect the second miter line, which is also the vertical center line of the entire elevation.
A line of stretchout, Fig. 260, is now drawn at right angles to the side of the rake moulding. Upon this line the exact spacing of the profile from points 1 to A inclusive should be laid down. Then by referring to the profile that is drawn in the right-hand rake moulding, it will be seen that distances 18–A, AB, and BC must be added to the line of stretchout beyond point 18. Extension lines should now be drawn at right angles to the sides of the rake moulding from each intersection of both miter lines of the rake moulding. Points of intersection in the stretchout may be determined by following each extension line from its source in the profile to a correspondingly numbered line in the stretchout. The miter cuts of the pattern are drawn by connecting the points of intersection. As in the case of the side patterns for the conductor head,
one pattern will suffice for both rake moulds, but they must be formed in pairs for assembling.
Another line of stretchout is now drawn at right angles to the base line of the horizontal moulding as shown in Fig. 261. Upon this line should be laid down the spacing of the entire profile including the point A. Measuring lines are drawn through each point at right angles to the line of stretchout.
The measuring lines should now be intersected by extension lines dropped from the miter line between the horizontal and rake mouldings, and from each intersection of the profile which appears on the left-hand end of the horizontal moulding (the return miter). Intersections of the stretchout may now be definitely determined by tracing each extension line from its source in the profile to a correspondingly numbered line in the stretchout, Fig. 261. The miter cuts are now drawn. Two blanks from this pattern are needed and they must be formed in pairs.
Using the same set of measuring lines, extension lines are now dropped from each point in the profile, Fig. 259, until they intersect correspondingly numbered lines. Lines connecting these points will give the outline of the pattern for the ends, Fig. 262. A lap is added to the top of the pattern for joining to the "wash" (top surface) of the horizontal moulding. From this pattern two blanks, formed in pairs, must be cut.
The pattern for the panel is obtained by reproducing the surface A, E, F, G, H of Fig. 258. The edge (line BC of profile in Fig. 258) for joining the panel to the rake moulding must be added to four sides of this surface. The spaces between points 19, 20, and 21 of the profile in Fig. 258 must be added to the base of this surface as in Fig. 263. It should be noticed that the space 19–20 of this profile is less than space 19–20 of Fig. 259, because of the sunken panel. From this pattern but one blank is cut, which is formed according to the profile in Fig. 258. The sunken panel leaves small openings along the lines AE and FG of Fig. 258, which may be closed by allowing a "tab" at line A–19 of Fig. 261. However, as this wastes material a small piece of metal may be cut to shape, and inserted after the window cap has been assembled.
The distinction between a rake moulding and a raked or raking moulding should be noted:
A rake moulding is simply a moulding that is inclined to the horizontal. It has the same profile as the horizontal moulding to which it is joined.
A raked or raking moulding is an inclined moulding that joins a horizontal or other moulding that does not lie in the same plane. It does not have the same profile as does the moulding to which it is joined. It takes its name from the fact that its profile must be altered or raked in order to join with the other moulding.