A fictional contour transect and map scale
A school class receives a fictional topographic map with a representative fraction of 1:25,000. The legend gives a contour interval of 20 meters. Along a specified straight transect from point A to point B, the measured horizontal map distance is 4 centimeters and the endpoint elevations are 100 and 180 meters. The exercise explicitly neglects map-projection distortion over this small area. One student uses the 80-meter rise as the actual path length; another says a cross-section must always follow the steepest slope. A third wants to compare line-of-sight visibility without checking intervening ridges. The class must use the stated transect and distinguish average gradient from detailed terrain shape before reporting what the map supports.
1. Calculate the horizontal distance and average percentage gradient.
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Four centimeters at 1:25,000 corresponds to 100,000 centimeters, or 1,000 meters. The rise is 80 meters, giving average gradient 80/1,000 times 100 =8 percent. This is not the actual sloping walking distance.
2. Can endpoints alone establish visibility or the steepest route?
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No. A cross-section may follow any specified transect and requires intermediate contours to show ridges or depressions. Intervisibility depends on the terrain and the sightline between observer heights. Endpoint gradient alone does not establish either visibility or the steepest route.