Earnest T. Childs.

Projection, or descriptive geometry, treats of the delineation of solids, that is objects having length, breadth and thickness are represented or the flat surface of a sheet of paper in such a way that their form becomes evident at a glance. The( subject may be subdivided into three branches known as Orthographic projection, Isometric projection, and Perspective. The first, which treats of the representation of objects placed in any given position by means of parallel lines drawr from given plans, elevations, etc., is the one which requires the greatest attention.

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

The student who has carefully followed the course in Mechanical Drawing, and completed all the plates shown therein, will be well equipped to continue his studies along the lines of Projection.

The first problem which presents itself is the projection of planes.

Assume a plane, A B C D, shown in elevation, and represented in plan by the line E F (Fig. 1). If the plane is turned on its axis A B, point F will travel through the arc of a circie as shown by points F1, F2 and F8 (Fig. 2). When the plane stands at E F8, the elevation becomes a line, AB. When it stands at E F2, the elevation becomes A B C2 D2; when at E F1, the elevation becomes ABC1 D1, and at E F it is the same as Fig. 1. It will be readily seen that the width of the elevation depends upon the distance that point F has moved along the arc F-F8, and is obtained in each instance by drawing construction lines from the points in the arc up to the elevation.

If the plane be turned to E F8, with elevation shown by line A B (Fig. 3), and with E F3 as a center, and the plane be swung through arc A-A3, the elevation will in each instance be shown by a line, B A1, B A2 and B A3. The plan will be obtained by drawing perpendicular lines from points A1, A2 and A3, forming figures E F8, A1, C1 from A1; E F3, A2, C2 from A2, and E F3, A8, C3, which is the same as A B C D from A.

Let it be next assumed that the plan E F8 A8 C8 is turned at an angle, as shown by Fig. 4, and assume that the plan is to be shown as stopping at points A1 and A'2 on arc A A8. Plan E F8 C8 A8 will be shown by line D A8 in elevation. The plane B A2, as shown in plan by figure E F8 C2 A2, will be shown in elevation by figure A2 C2B D, and plane B A1, as shown in plan by the line E F8 C1 A1, will be shown in elevation by figure A1 C1 B D; and plane B A, as shown in plan by E F8, will be shown in elevation by figure A C B D.

Fig. 5.

Fig. 6.

Fig. 7.

This first illustration may be taken as an index to the character of the work which is to be covered under the first heading of "Orthographic Projection." It will be immediately perceived that accuracy in construction and careful forethought are both essential to obtain helpful and satisfactory results.

Having completed the plane projection shown by Figs. 1, 2, 3 and 4, it will be advisable to make a practical application of the principles. This method will be found most helpful in fixing principles in one's memory.

Let it be supposed that we wish to represent a door of common boards, standing partly open.

This wil! be a practical application of the problem shown by Fig. 2. It will be necessary to first draw a plan showing the wall and doorway, and also showing the door swung open at 45°. Having this information, it is simply necessary to know the height of the door to be able to make the necessary drawing. The doorway will, of course, be shown of its full width and height. On account of the door being swung at an angle, it will appear foreshortened, that is it will appear narrower, and parallel lines must be drawn from the plan up to the elevation to determine the appearance of the door. This is very clearly shown in Fig. 5.

A practical illustration of the application of Fig. 4 may be made by the representation of a trap door. Fig. 6 shows the trap door partially open, exactly the same as Fig. 5, except that the observer is directly above, instead of directly in front of the object. If we assume that the trap door is turned at an angle, as shown in Fig. 7, the plan view will be identical with Fig. 6; but the elevation will be materially different, as may be seen by the dotted projected lines drawn from the plan up to the elevation. It will be readily seen that the character of the elevation view is determined entirely by the angle at which the door is turned.

In order to complete the study of planes, it is necessary to present one more series of problems. Assume that we have a square, ABCD, which in elevation will be represented by the line A1 D. Assume that this plane be elevated so that it stands at an angle of 45° to the horizontal plane. The elevation will now be represented by the line

A1 D1, and by projecting downward it is found that the plan will be represented by the outline A B2 C2 D2, which is diamond shaped. (See Fig. 8.)

Fig. 8.

Fig. 9.

Fig. 10.

Let the angle of 45° be maintained, and let the plane be turned through an angle of 45° as shown in the plan view of Fig. 9. By projecting upwards from points A, B, C and D, it is found that the elevation now becomes a parallelogram, A1 B1 C1 D1. - Fig. 9.

If the plane be revolved through 90° and the angle of 45° from the horizontal be maintained as before, the plan view will be represented by Fig. 10 - A BCD, and the elevation will be identical, as shown by Fig. A1 B1 C1 D1. - Fig. 10.

These exercises should be thoroughly mastered by the student before attempting to advance to the representation of solids, as they contain the fundamental principles which may be applied to all line projections.