PROBLEM 204. Patterns for a Ship Ventilator Having: a Round Base and an Elliptical Mouth.
In Fig. 664 are presented the front and side elevations of a ship ventilator of a style in common use. A1 B1 shows the section or plan of its lower piece A F F B, as well as of the pipe to which it is joined, while R O S P is the shape of its mouth, or a section upon the line C D. The curves E C and F D connecting the two ends of the ventilator and forming the general outlines of the same may be drawn at the discretion of the designer. As the ventilator is constructed after the manner of an elbow, it may be divided into as many sections or pieces as desired. Therefore divide the curved lines E C and F D into the same number of spaces, and connect opposite points by straight lines, as shown by G H, K L and M N. These lines should be so drawn as to produce a general equality in the appearance of the different pieces without reference to equality in the spaces in either outline.
The next step is to establish a profile or section upon each one of these lines. These profiles can be drawn arbitrarily, but each should be so proportioned that the series will form a gradual transition from the circle A1 B1 to the ellipse R O S P. All the profiles will, therefore, be elliptical, those nearer the mouth being more elongated than those nearer the base or neck. Since the lower piece is cylindrical and is cut obliquely by E F, the section at E F must necessarily be a true ellipse and can be developed by a method frequently explained in connection with various problems in the first section of this chapter, and as also explained in Geometrical Problem 68 on page 61. Of the remaining sections, their major axes are, of course, equal to the lengths of the lines G H, K L and M N, and their minor axes may be determined by any method most convenient, or in the following manner: Draw R U and S V, representing a front view of the curved lines passing through the points n, m, k, g and e of the side view. From the points g, k and m project lines horizontally across to the front view, cutting the lines R U and S V and the center line 0 T. Then f l, d o and b c will be respectively one-half the minor axes of the sections above referred to. With the major and minor axes of the several sections given, they may be drawn by any method producing a true ellipse, or in case the mouth has been drawn by means of arcs of circles the other sections may be drawn in the same manner.
Each of the several pieces of which the ventilator is composed (except the lower piece) becomes, as will be seen, a transition piece between two elliptical curves not lying in the same plane, and in that respect is the same as the form shown in Problem 191. The pattern for each piece must, therefore, be obtained at a separate operation, that for the piece MNDC only being given. To avoid confusion of lines a duplicate of it is transferred to the opposite side of the front elevation, as shown by W Y Z X. Drop points from Y and Z perpendicular to the center line O T of the elevation, thus locating the points M2 and N2. Make the distance b2 c equal to b c. Then draw the ellipse M2 b2 N2 which will be a front view of the section M N of the side elevation. On a line parallel with Y Z construct the section M1 b1 N1, as follows: Let M1 N1 be equal to and opposite Y Z. Let the distance c1 b1 be equal to the distance c b of the seetion. With these points determined, draw through them the semi-ellipse M1 b1 N1. Divide the sections M1 b1 N1 and O S P into the same number of equal parts, as indicated by the small figures in the engraving. Drop the points 1, 2, 3, 4, etc., on to and perpendicular to the line YZ; thence carry them perpendicular to the center line O P of the front elevation, cutting the section M2 b2 N2 in the points 12, 22, 32, etc., thus dividing it into the same number of spaces as were given to the original section M1 b1 N1. Next connect the points of like numbers in the two sections of the front elevation by solid lines, thus: Connect 21 with 22, 31 with 32, 41 with 42, etc.; also connect the points 21 with 12, 31 with 22, 41 with 32, etc., by dotted lines, all as shown in the engraving. These lines represent the bases of right angled triangles, whose altitudes may be measured on the horizontal lines cutting the lines W X and Y Z.
Fig. 664. - Elevations and Sections of a Ship Ventilator.
The next step, therefore, is to construct diagrams of these triangles, as shown at A and B of Fig. 665. Draw any two horizontal lines as bases of the triangles, and erect the perpendiculars E C and F D. On both E C and F D set off the various nights of the triangles, measured as above stated and as indicated by the points 1, 2, 3, 4, etc. Next set off the length of the liases of the triangles as follows: In diagram A, let C 1 equal the distance 11 12 of Fig. 664; make C 2 equal to 21 22 and C 3 equal to 31 32, etc. Connect the points in the vertical line with the points in the horizontal line of the same number, thus obtaining by pothenuses of the triangles, or the true distance between the points 11 12, 21 22, etc., of the elevation. In diagram B, let the distances D 2, D 3, D 4, etc., represent the distances l2 21, 22 31, etc., of the elevation. Having located these points, connect 1 in the vertical line with 2 in the base; also 2 in the vertical line with 3 in the base, and proceed in this manner for the other points. This will give the hypothenuses of the triangles, whose bases are 12 21, 22 31, etc., in the elevation.
Fig. 663. - Diagrams of Triangles.
Having thus obtained the dimensions of the various triangles composing the envelope of the first section of the ventilator, proceed to develop the pattern for it, as shown in Fig. 666. On any straight line, as C M, set off a distance equal to 1 1 in diagram A. From C as center, with radius equal to l1 21 of the elevation,
Fig. 664, draw an arc, which cut by another arc drawn from M as center, with radius equal to 1 2 of diagram B, thus establishing the point 2. From 2 as center, with radius equal to 2 2, diagram A, draw an arc, which cut with another arc drawn from 11 as center, with radius equal to 1 2 of the elevation, thus establishing the point 21. Proceed in this manner, next locating the point 3, then the point 31; next the point 4, and then 41, etc. It will be noticed that, after passing points 6 and 61, 71 is obtained before 7. This is for the sake of accuracy, as it will be seen by inspection of the elevation that the distance 72 61 is less, and therefore more accurately measured in the elevation, than the distance from 62 to 71. Having thus located the points 1, 2, 3, etc., 11, 21, 31, etc., trace the lines C D and N M, and connect D with N, as indicated in Fig. 666. Then D N M C will be the pattern for one-half the section M N D C of the elevation.
Fig. 666. - Pattern of First Section of Ship Ventilator.
The pattern of the section E A B F will be the same as that for the corresponding piece in an ordinary elbow, and, therefore, need not be specially explained here.