Pre Calculus II Project Setup: Term Paper

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The semi-minor and semi-major axis are easily determined, and can then be subbed into the standard equation for an ellipse. Taking the square root of y will result in a plus/minus, and discarding the minus erases the lower half of the ellipse. The long axis extends horizontally, and the short axis extends vertically. The x and y axis bisects the ellipse already, so both a and B. are available: 525' and 350'.

The width of the channel is, once again, determined by inputting a known point.

Hence, the semi-elliptic bridge allows 315 ft of clearance from the centerline, or 630 ft in all.

If the river flooded, the tanker would sit 10 ft higher and would, hence, have only the clearance available at 290 ft. For the parabola:

For the semi-ellipse:

Thus, the parabolic bridge with a raised water level would have only a minor decrease in clearance from 470ft to 435ft.

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The semi-ellipse would alter slightly more, from 630ft to 588ft. While the semi-ellipse still offers better clearance, the parabolic architecture shows a greater resilience for changes in water level. This could be an advantage as tanker's would not be required to check clearance distances before passing under the bridge, but the semi-elliptical architecture demonstrates a great overall clearance, and, all other considerations aside, would likely be the choice of architecture for a….....

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