Topo Map Elevation Profile - Vertical Exaggeration
An elevation profile or a topographic profile is a two-dimensional cross sectional view of the landscape. It provides a side view of the relief of the terrain along a line drawn between two locations on a topographic map.
In order to draw a topographic profile along a desired line on a topo map, put the straight edge of a piece of paper between the end points of the line. Mark with a tick mark on the edge of the paper wherever the paper crosses a contour line. Label each tick mark with the elevation of the corresponding contour line.
Place the edge of the paper along the x-axis of a graph paper. Note the minimum and maximum elevations along the line you've recorded. Label the graph's y-axis with elevation values ensuring that they encompass the minimum and maximum values recorded previously. Therefore the x-axis corresponds to the horizontal distance of the line on map. The y-axis represents the elevation of points along the line. On the graph paper, plot the corresponding elevation above each tick mark. By connecting the dots, the elevation profile along the line of interest is drawn.
Vertical Exaggeration
In some cases topographic relief of the terrain is modest, such as the case of small hills and other subtle features as opposed to mountainous terrain, or the profile of interest is extended over a large horizontal distance relative to vertical relief. In such situations the elevation profile may only show small variations in elevation without much detail of the topography. For this reason some amount of vertical exaggeration [VE] is used in order to get a clearer picture of the subtle changes in topography and emphasize vertical relief and slope steepness. In order to calculate vertical exaggeration, divide the real world units of horizontal scale by the real world units of vertical scale. Make sure same units are used in numerator and denominator of the division. Also always show vertical exaggeration value on your profile graph.
Vertical exaggeration formula: VE = [real world units of horizontal scale] / [real world units of vertical scale].
As an example for a 1:50000 topo map, we can set the horizontal scale [x axis] of the profile the same as the map. Labeling 1 cm units on x axis: 1cm on map = 50000cm in real world = 500m in real world. If we decide to use the same value for our vertical scale [1cm = 500m for y axis], then there will be a vertical exaggeration [VE] of [500m / 500m] = 1x or no vertical exaggeration.
Changing our y axis scale so that 1cm would represent 250m then we would have 500m/250m = 2x [read 2 times] vertical exaggeration.
In order to draw a profile with greater vertical exaggeration such as 5x, real world units of the vertical scale would be equal to the [real world units of horizontal scale / 5] = 500m / 5 = 100m. So on y axis 1 cm should be equal to 100m. VE of 5x indicates that on the map, topography or relief is exaggerated by 5 times than the original map or real world. In this case vertical scale would be 1:10000 since 1cm = 100m = 10000cm.
Google Earth Elevation Profile
It is possible to plot the elevation profile of a path [line] or a track in the newer version of Google Earth [v. 5.2]. After drawing a path, rigth click on the path name in the Places panel and click "Show Elevation Profile", or go to the Edit menu on the top menu bar and choose "Show Elevation Profile" from the drop-down menu. You can change the measurment units from metric to English and vice versa from Tools -> Options, in the "Show Elevation" category. However, apparently there is no option for setting the value of vertical exaggeration or having an option for changing the scales on horizontal or vertical axis at this time.
You can also draw a desired path in Geokov Map Maker on a topographic map or Google Maps base maps. The drawing can then be exported in the form of a kml file. Save the file with .kml extension, and import it to Google Earth. Proceed as above to draw the path's elevation profile.
Below, two parallel paths are drawn in Google Earth. For each path an elevation profile is created showing the cross-sectional view of the topography along the path. Path 1's profile [purple] with a horizontal distance of 5.18km is shown in the top diagram, and path 2's profile [orange] with a horizontal distance of 1.13km is at the bottom. Path 2 runs parallel to path 1 through more or less the same terrain shape up to the first ridge line [from left]. Path 1 crests on the ridge at an elevation of 2287m and path 2 gets to 2290m elevation. The effect of vertical exaggeration can be clearly seen from the profiles of these two paths. The top profile shows a steep rise to the first ridge line from left while the bottom profile shows a gentle slope ascending the terrain to the same ridge. Without any calculations it can be clearly concluded that the top profile has a larger vertical exaggeration than the bottom. Keep in mind that in Google Earth or other mapping software, unless you can set the VE or change the scale of the axis, you might end up with a different VE for your elevation profiles. The vertical exaggeration values for the two profiles are calculated below [by measurments of graphs' axis using ruler on computer screen].
Top profile:
horizontal scale: 6.95cm = 1.5km; 1cm = 1.5/6.95 = 0.216km = 216m; 1cm = 216m
vertical scale: 1.1cm = 100m; 1cm = 100/1.1 = 90.9m; 1cm = 90.9m
VE = 216/90.9 = 2.4x
Bottom profile:
horizontal scale: 10.7cm = 0.5km; 1cm = 0.5/10.7 = 0.047km = 47m; 1cm = 47m
vertical scale: 1.25cm = 75m; 1cm = 75/1.25 = 60m; 1cm = 60m
VE = 47m / 60m = 0.78x
A value of 1x for VE means that there is no vertical exaggeration and the vertical and horizontal scales are equal. A VE value less than 1 actually denotes a horizontal exaggeration which has the effect of smoothing the profile graph.
[Note that the numbers corresponding to measurements on the image may be different on your computer monitor due to resolution difference or when the image is printed. The end result however should be the same].
Since the area of the screen for fitting the profiles remains constant in this case, the profile graphs need to get stretched or compressed in order to fit this area no matter how much distance their path covers on the map. In above cases both 5.18km and 1.13km paths are fitted on the same length axis. Calculations above show how vertical exaggeration is affected by keeping the length of the axis constant and thus changing the scales on the axis for each case.