Sec. 11. Plans, Maps and Their Scales
Plans, maps and charts are reduced generalized representation of horizontal projections of separate parts of the terrain on paper. A plan is a reduced congruent representation of the horizontal projections of the contours and relief features of areas on a plane that are small enough for the Earth's curvature to be ignored.
Maps and charts, on the other hand, are reduced representations on a plane, made in accordance with definite mathematical principles, of substantial parts of the earth's surface that are so large that the effect of the Earth's curvature need be accounted for.
A scale is the amount of the reduction of the representation of the horizontal projections of the terrain lines on plans or maps. There are numerical scales or representative fractions (R.F.), linear scales and graphic scales.
A numerical scale is
an aliquot fraction (the numerator is equal to unity), for example:
.
A linear scale is given by a scale line. Each major division on such a scale line is adopted as the scale's base. This corresponds to a definite number of metres of the horizontal projection of a line segment on the ground (Fig. 11a). One of the major divisions of the scale line is subdivided into a number (5 or 10) of smaller divisions whose fractions are read off by eye alone when making measurements on a map or plan.
A graphic (transverse) scale (Fig. 11b) represents a graph that enables one to estimate hundredths or tenths of the scale base. A numerical scale is equal to the ratio of a line's segment shown on the plane (map) to the horizontal projection of the corresponding segment shown on the ground, the larger the fraction, the larger the scale. The larger, scale plans and maps permit more detail to be represented, thus increasing the precision and quality of the solution.
It is considered that 0.1 mm is the smallest distance that can be distinguished by eye. Therefore the horizontal distance shown on the ground that corresponds to 0.1 mm shown on the plan (map) at the given scale is termed the accuracy of the scale.
The importance of the scale for a map's contents and applications is so great that it is usual to classify maps according to their scales, and
Fig.11
the categories large, medium and small are used. This subdivision is arbitrary and usually large scales are 1/100 000 or larger, medium scales are between 1/200 000 and 1/1 000 000 maps, and small scales are less than 1/1 000 000 maps.
Large scale topographic maps are the most detailed maps and show contours and relief features of the terrain. Such maps are used very much like plans.
A plan can be regarded as a kind of topographic map showing practically no distortion due to the Earth's curvature.
To locate points, lines and objects on the Earth's physical surface, one must also know heights of such points above the datum surface as well as their horizontal distances. The relief features on topographic maps and plans are given by curved lines linking points with the same height; each height is separated from another by a definite interval. These curves are generated by a number of level surfaces cutting the terrain. These level surfaces are separated by the specified vertical intervals and the lines they generate are called contour lines.
The shapes land positions of the contour lines enable one to make judgements about the relief features and detail as delineated on plans and maps. In representing the relief of the bottoms of bodies of water (lakes, ponds, reservoirs, and rivers) sometimes maps and plans contain curved lines connecting equal depths; these are referred to as isobaths.