For our project, we wanted to use contour maps and gradient vectors to determine the steepest route out of Park Science Building. To make our contour plot, our first step was to extract the elevation of various points in and around campus. In order to do so, we found an interactive online elevation map where we were able to click on certain points to know the elevation at that given point. To figure out which points to use, we projected a grid onto the map of the campus. Each unit of the gridline was approximately 100 meters. Then, we used the gridlines to make a coordinate system and were able to treat the map as an XY plane. We then input these data into Excel. From this, we created a table, contour map, and model using Excel functions.
To find the gradient we located the Park Science building on our coordinate system(4,7). We then sought out the gradient vector (βπ = (ππ₯, ππ¦) = ππ₯π β ππ¦π). This slope was determined by finding the change in elevation (Ξf) and dividing by the change in the x value (Ξx) between the two adjacent data values (3,7) and (5,7) and (4,7), then taking the average of the two. We then repeated the same process to find the slope of y at (4,7), with x held constant, using the points (4,6) and (4,8). This gave us the gradient vector at (3.5, -6), which gives us the direction of the steepest route from the Park Science Building toward the Main Campus.
