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A topographical map contains curved lines called contour lines. Each contour line corresponds to the points on the map that have equal elevation (Figure 1). A level curve of a function of two variables [latex]f\,(x,\ y)[/latex] is completely analogous to a counter line on a topographical map.
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Directions
We are all familiar with the points of the compass (Figure 15.1a), also known as cardinal directions. These allow us to specify general directions, but are insufficient to define specific values. For this we use an azimuth, which is the angle measured clockwise from north (Figure 15.1b). The term bearingis often used synonymously with azimuth, although there are also some other uses of the term, so azimuth will primarily be used here. Therefore, north has an azimuth of 0°, northeast is 45°, e...
Height Datums and Units
When talking about how high a land surface is, we need a reference level, sometimes referred to as the height datum (not to be confused with a geodetic datum, which is an issue that we don’t need to discuss here). Hereafter, we will use the term elevationto define the height above (or, sometimes, below) a height datum. A standard convention in topographic maps is to define elevation relative to the mean sea level (metres above sea level, m a.s.l). In all cases where elevation is involved, be...
Spot Heights and Benchmarks
One of the simplest ways to indicate the elevation of land on a map is to use a spot height, which is simply the elevation of a particular point (e.g. the summit of a hill or mountain). Many spot heights are determined from aerial photographs, rather than being surveyed on the ground. Occasionally, you may also see a benchmark shown on a map. These are points that have been surveyed, perhaps as part of construction projects such as highways or rail lines. Locations that have been surveyed for...
In this lab you will practice 1. Defining direction. 2. Interpreting elevation from contour lines. 3. Calculating slope gradient. 4. Drawing and interpreting topographic profiles. You will need a calculator, plus an internet connection to download a map and access Google Earth. Some of the exercises may be easier if you are able to print the releva...
Figure 15.5 1. Figure 15.5 [PDF] 2. Figure 15.5 [WORD] 3. Figure 15.5 [ODT] Graph paper 1. Lab 15 Graph paper [PDF] Map of Spot Heights at Acme Creek 1. Map of Spot Heights at Acme Creek [PDF] 1. Map of Spot Heights at Acme Creek [WORD] 2. Map of Spot Heights at Acme Creek [ODT]
essence, a \topographical map" of the graph of z = f(x;y). A topographical map is a two-dimensional visualization of three-dimensional terrain through the so-called level curves or contours corresponding to points of equal elevation. Example 1. Here is a map of the region near South Hamilton, NY:
Level curves are the equivalent of contours on a topographical map. In such a map the terrain is shown by drawing curves through all points which have the same height above sea level. The numbers on the curves in the map shown below are the heights above sea level in metres. 🔗. Figure 3.2.1. Sample Topographic Map (Part of the Watagan Mountains)
Solution. We can extend the concept of level curves to functions of three or more variables. Definition 1. Let f: U ⊆ R n → R. Those points x in U for which f (x) has a fixed value, say f (x) = c, form a set denoted by L (c) or by f − 1 (c), which is called a level set of f. L (c) = {x | x ∈ U and f (x) = c} When n = 3, the level set is ...
Both profiles represent the same topographic profile along line A-B on the topographic map in Figure 7.5. If the topographic map in Figure 7.5 has a fractional scale of 1:2667 then 1 cm is equal to 2667 cm or ~27 m; thus, 1 cm = 27 m for the horizontal scale on this map.
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How do you find the level curve of a topographical map?
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What is a topographic map?
How do you find elevation on a map?
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It is a curve where x and y can vary, but z does not change. Imagine standing on a hill, and taking a step such that you neither go uphill nor downhill. If you do this repeatedly, you will (theoretically) walk along a path that is level, and end at the same point from which you started. A level curve projected onto the xy-plane is called a contour.
