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The image on the right shows a low-energy building which is to be built in Abu Dhabi - Leaving Cert DCG - Question C-2 - 2016
Question C-2
The image on the right shows a low-energy building which is to be built in Abu Dhabi. Its architectural design includes a series of supporting towers. Each tower is... show full transcript
Worked Solution & Example Answer:The image on the right shows a low-energy building which is to be built in Abu Dhabi - Leaving Cert DCG - Question C-2 - 2016
Step 1
Draw the given plan of the tower and project the elevation as shown.
Answer
To start, sketch the base of the tower based on the given plan. Begin by drawing two circles: one with a diameter of 12m and another with a diameter of 5m, aligning them at the appropriate height.
Next, project the sides of the tower from the plan to the elevation. Draw vertical lines from the relevant points of the plan to translate the base diameter measurements to elevation. Then, create the outline of the hyperboloid, ensuring the curvature follows the design shown in the provided figure.
Step 2
Project an end view of the tower as shown.
Answer
For the end view, it is essential to establish an orthographic projection from the front elevation of the tower. Use the previously drawn curves and diameters to guide the projection. Trace the outline of the tower's profile and include the necessary dimensions for clarity, ensuring that the view accurately depicts the contours of the hyperboloid.
Step 3
Determine the positions of the focal point and the directrix for one branch of the hyperbola in the elevation.
Answer
To find the focal point and directrix, first recall the properties of a hyperbola. The standard equation is given by:
rac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1
In this case, identify the values for 'a' and 'b' based on the dimensions of the hyperboloid. The focal point is located at a distance 'c' from the center, where:
For the directrix, utilize the formula:
With this information, mark the positions of both the focal point and the directrix accurately in the elevation drawing.