The graphic on the right shows deck chairs in the form of hyperbolic parabolids - Leaving Cert DCG - Question C-2 - 2016
Question C-2
The graphic on the right shows deck chairs in the form of hyperbolic parabolids.
Fig. C-2 shows the plan and elevation of a typical hyperbolic paraboloid surface AB... show full transcript
Worked Solution & Example Answer:The graphic on the right shows deck chairs in the form of hyperbolic parabolids - Leaving Cert DCG - Question C-2 - 2016
Step 1
Outline of surface ABCD in plan
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Answer
To outline surface ABCD in plan, sketch a rectangle representing the base of the chairs, label points A, B, C, and D, and ensure proportions match the provided dimensions in the graphic. Include necessary divisions to indicate the structure's division of surface.
Step 2
Elements in plan (incl. division)
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Draw the elements emerging from points A, B, C, and D, representing the structure's heights and slopes. Include line segments that indicate the curvature and angles as shown in the plan view.
Step 3
Outline of surface in elevation
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For the elevation, depict the heights of points A, B, C, and D as they correspond to the plan. Create a vertical projection reflecting the sloped surfaces and the overall shape of the hyperbolic paraboloid. Maintain the scale of 1:1 as indicated.
Step 4
Elements in elevation (incl. division or proj.)
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Illustrate elements in elevation by drawing lines connecting the heights of the outline points, clearly showing the slant and curvature of the surface. Ensure divisions that reflect the chair design are included.
Step 5
Curve in elevation
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Draw the curve representing the hyperbolic nature of the surface, focusing on the points of intersection from the elevation view. Present the curve using smooth lines that flow to indicate the design.
Step 6
Determine heights and widths for surface ABCD
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Measure and document the heights and widths at points defined in the plan view. Convert these measurements into proper scale for the end view representation, which reflects the actual dimensions of the hyperbolic paraboloid.
Step 7
Draw the outline of the hyperbolic paraboloid
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Sketch the outermost contours reflective of the hyperbolic paraboloid shape. Utilize smooth curved lines to portray the unique shape, ensuring to align with the points projected from the plan.
Step 8
Draw the elements
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In your drawing of the end view, ensure all elements align with the hyperbolic outline. Draw vertical and angled lines to further illustrate the curvature of the structures.
Step 9
Curve in end view
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Render the curve visible in the end view by illustrating the transformation and intersection of the surfaces, capturing the curvature of the hyperbolic paraboloid.
Step 10
Presentation
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Ensure that all drawings are neatly presented, following standard drawing practices. Clean and clear line work, proper labeling of elements, and adherence to scale will enhance the quality of the submission.
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