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The graphic on the right shows a pack of potato crisps - Leaving Cert DCG - Question C-2 - 2015
Question C-2
The graphic on the right shows a pack of potato crisps. These potato crisps have a distinctive surface shape, which is based on a hyperbolic paraboloid. The project... show full transcript
Worked Solution & Example Answer:The graphic on the right shows a pack of potato crisps - Leaving Cert DCG - Question C-2 - 2015
Step 1
Draw the given plan, using the same number of elements in each direction on the surface of the crisp as shown.
Answer
To draw the plan of the potato crisp, start by sketching an ellipse that represents the perimeter ABCD. Divide the ellipse into equal sections to represent the elements of the hyperbolic surface. Use a grid to maintain symmetry and ensure that the elements are evenly distributed both horizontally and vertically.
Step 2
Project the given elevation from the plan.
Answer
From the plan drawing, project vertical lines from each point of the ellipse to create the elevation view. Indicate the projection lines and ensure the proportions of the elements in the elevation respect the curvature defined by the hyperbolic paraboloid.
Step 3
Show the curvature of the surface when intersected by a vertical cutting plane passing through points B and D.
Answer
To show the curvature, identify points B and D on the elevation. Draw a vertical cutting plane that intersects the surface. The intersection line should portray the curvature of the hyperbolic paraboloid, showing elevation points above and below the plane.
Step 4
Draw the plan and elevation of the shortest distance between the two skew lines AB and CD.
Answer
For finding the shortest distance, first draw the auxiliary view with line XY parallel to the plan of AB and CD. Define the true lengths of lines AB and CD in this auxiliary view. Finally, determine and draw the required shortest distance, ensuring it is perpendicular to both skew lines.