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The image on the right shows a sun canopy over an umpire's chair at a tennis tournament - Leaving Cert DCG - Question C-2 - 2017
Question C-2
The image on the right shows a sun canopy over an umpire's chair at a tennis tournament. The canopy is based on a hyperbolic parabola. The projections of the canopy... show full transcript
Worked Solution & Example Answer:The image on the right shows a sun canopy over an umpire's chair at a tennis tournament - Leaving Cert DCG - Question C-2 - 2017
Step 1
Draw the given plan of the canopy, showing all points of tangency.
Answer
Begin by establishing the four required areas in your plan. You should locate the points of contact, namely points A, B, C, and D, and draw the required tangential edges. These edges ensure that all lines touch the points without crossing.
Step 2
Draw the end view of the generating parabola ABC as shown.
Answer
Construct the required rectangular outline for the curve ABC. Make sure to correctly identify the axes and use the correct measurements to locate points on the required parabola. Finally, draw the parabolic curve, ensuring accuracy in depicting the curve's shape.
Step 3
Project the front elevation of the canopy.
Answer
Establish the necessary rectangular outline for curve DBE. You will then need to construct lines that locate the relevant points on the required parabola. Draw the complete parabolic curve from the information gathered, ensuring that it reflects the canopy's structure accurately. Use appropriately spaced vertical sections and transfer widths from the plan to the end view to maintain proportionality.
Step 4
On a separate diagram, draw a new end view of the extended parabola.
Answer
First, redraw the required construction for parabola ABC to ensure all dimensions are correct. Next, extend the construction horizontally and vertically as indicated in the figure, marking the necessary dimensions. Finally, draw the required extended curve, taking care to keep the aesthetic proportions of the original design.