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The image on the right shows the roof of a mini-circuit for testing cars at the Volkswagen factory in Germany - Leaving Cert DCG - Question C-2 - 2021
Question C-2
The image on the right shows the roof of a mini-circuit for testing cars at the Volkswagen factory in Germany. The shape of the roof is based on a hyperbolic parabol... show full transcript
Worked Solution & Example Answer:The image on the right shows the roof of a mini-circuit for testing cars at the Volkswagen factory in Germany - Leaving Cert DCG - Question C-2 - 2021
Step 1
Draw the given plan including the elements as shown.
Answer
To draw the required plan, we need to establish the ellipse formed by the major and minor axes, where the major axis is 42m and the minor axis is 22m. This can be achieved using the following steps:
- Draw the axes: Begin by drawing a horizontal line segment measuring 42m for the major axis, labeling the endpoints as A and C.
- Locate the minor axis: At the midpoint of the major axis (point O), draw a vertical line segment measuring 22m for the minor axis, labeling the endpoints as B and D.
- Construct the ellipse: Using an ellipse drawing method (such as the string and pins method), create the ellipse based on points A, B, C, and D.
- Add elements: Extend the outline elements of the hyperbolic paraboloid by sketching in the curve that connects points B and D.
- Label points: Ensure all relevant points and elements are clearly labeled as per the instructions and the provided figure.
Step 2
Project the given elevation from the plan. Show clearly how to locate the point P.
Answer
To project the elevation from the plan and locate point P:
- Draw projections: From each point in the plan (A, B, C, D), draw vertical lines upwards to represent the elevation. Keep the line perpendicular to the plane.
- Indicate heights: Use the given heights to mark points A', B', C', and D' in the elevation view. For instance, if the height of P at point C is given, this should reflect in the elevation.
- Locate point P: Since point P is at the top of the hyperbolic surface, it should be aligned above point C in the projection. Add a helper line to connect from C to the corresponding elevation point of P, drawing it higher to represent the paraboloid shape.
- Finalize elevation: Complete the elevation view by sketching in the curve that follows the paraboloid shape between points B' and C'.
Step 3
Show the curvature of the surface when intersected by a vertical cutting plane containing B and D.
Answer
To show the curvature along the vertical cutting plane containing points B and D:
- Draw line BD: Start by drawing a vertical line joining points B and D in the plan view.
- Intersections: Identify and mark intersections between the elements from the elevation and projections back to the auxiliary or end view.
- Establish heights: From the created intersection points, project their heights down into auxiliary views. Measure these heights from the elevation to ensure correctness.
- Draw curvature: Lastly, sketch the curvature of the hyperbolic surface as it transitions through the points where the vertical plane intersects. This will create an accurate depiction of the surface along B and D, reflecting the desired curvature.