6th topic
6.1. Surface and its projections
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The image carousel shows objects whose drawings and modelling require sections along horizontal and vertical planes.
For each object, simple or complex, when creating an image in a drawing, it is convenient to imagaine cuts along horizontal or vertical planes. This makes it possible to show the outer surface of the object in the drawing, regardless of its shape.
Let's start with the simplest examples.
Picture 6.1. Inclined plane horizontals
Horizontals
Horizontals
The lines of intersection of an inclined surface with a horizontal plane are called horizontals. They are in shown in red, and their projections are in black (Pic. 6.1).
If the vertical distance between the horizontal planes is the same, then the distance between the horizontals on the projection plane will be the same. This distance is the interval with which the angle of inclination of the plane can be estimated.
The interval size or distance between the horizontals depends on the angle of the plane: the smaller the angle, the larger the interval.
Picture 6.2. Inclined plane horizontals and sloped line
Sloped line
Sloped line
When using a vertical cutting plane, we get a section of an inclined plane in the front view.
A sloped line is the steepest straight line in a plane. It is a line in the direction in which water will flow or an object will roll. This line is shown in green (Pic. 6.2).
The projection of the sloped line is perpendicular to all horizontals.
Picture 6.3. The inclined plane projection and scales
Interval scale
Interval scale
By replacing the projection of the sloped line with two lines (wide and narrow) in the top view, you can create an interval scale. Spacing is the horizontal distance between points or lines whose height difference is one unit.
Points located on the same horizontal have the same height, which is the height of this horizontal, and this height should be indicated (Pic. 6.3).
Picture 6.4. Solids surface crossections
Solid surface horizontals and verticals
Solid surface horizontals and verticals
To obtain projections and sections for the surfaces of different bodies, horizontal and vertical cutting planes are also used (Pic. 6.4).
Picture 6.5. Conic surface horizontals images
Picture 6.5 shows how to create horizontal and vertical cross sections for a conical surface.
Dividing a vertical cone using horizontal planes gives a set of concentric circles representing the conical surface on the plane.
The slope scale indicating the heights of the horizontals shows very clearly the rise or fall of a surface. In this case, there is no need for a front view!
Picture 6.6. A topographic surface horizontals getting
Topographic surface horizontals and verticals
Topographic surface horizontals and verticals
Picture 6.6 shows a surface with horizontal cutting planes.
The surface of the earth does not generally consist of the surfaces of regular geometric shapes. The horizontals of the earth's surface are obtained the same way, with horizontal auxiliary planes.
A horizontal obtained by using a horizontal plane of a certain height consists of points at the same height. This is the height of the secant plane.
Picture 6.7. Topographic surface photo, sketch, plan
Rules to follow when drawing the horizontal (Pic. 6.7, plan):
All elevations on the same horizontal plane have the same height.
Horizontals do not intersect or form loops.
Neighbouring horizontals have a similar shape and their spacing changes smoothly.
Horizontals cut perpendicular to the structural lines of the relief.
The distance between the horizontals characterizes the slope. On steeper slopes, the horizontal spacing is smaller than on flatter slopes.
Picture 6.8. Topographic surface verticals
Vertical cutting planes are used to obtain the relief of a topographic surface. Lines perpendicular to the projection of the cutting plane, on which the cut points of the topographic surface are located, are called vertical sections and are necessary for constructing the relief of the topographic surface (Pic. 6.8).
In this case, the section of the topographic surface can be represented by a stepped profile. To obtain a landscape relief, the highest points of the verticals are connected into a smooth line.
Picture 6.9. Resurfacing of topographic surface for a house foundation
To place objects on a horizontal area, an existing topographic surface can be leveled relative to the selected horizontal plane, with a recess in the higher part of the topographic surface and backfill, the addition of the resulting material to the lower part of the surface.
Resurfacing is usually done to make the ground flatter. This is sometimes referred to as leveling.
Leveling can be carried out in the preparation of an adjoining site, a platform for the foundation of a house, an artificial reservoir, paths in the yard, recreation areas, such as a playground, and an access road (Pic. 6.9).
Terracing
Terracing
You will have already noticed the stepped profiles of inclined surfaces.
An inclined object can be replaced with a stepped one. Look at the parts of the fence of the courtyard of the house (Fig. 6.10, a). This replacement is called terracing.
In landscaping, terracing allows water to be retained on horizontal surfaces for plants and keeps soil from being washed away by rapid water runoff.
Ramps are used to allow movement along inclined surfaces with small angles (Fig. 6.10, b), and stairs, movement from one level to another (Fig. 6.10, b, c).
Picture 6.10. Stepped objects: a) yard fence, b) garage ramp and exterior stairs, c) terraces and steps in the yard.
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