Monday, March 17, 2014

Faking a Parabolic Curve

Today someone wanted to waste a roll of aluminium foil to make a solar death ray generator.  Luckily Science! and Geometry! prevailed and I was able to find a quick and dirty way to approximate parabolic curves using just a straight edge and compass.  The advantage to this method is that it doesn't require knowing the equation for a parabola, drawing a graph onto cardboard, or using a 3D printer or paper cutter-plotter.

Finished Parabolic Template
I cheated and used a right-triangle to draw a right angle on cardboard.
Then I put the point of my compass at the vertex of the right angle and drew a circle centered on it.

Satisfied that the distance was neither too large nor small, I used the compass as dividers to measure the same distance along the lines; as a check, once I was done, I opened up the compass and confirmed the ticks I'd put along the lines were on the same ever-increasing circles.

I numbered the ticks along the lines 1 through 8 so I wouldn't get confused.

Then I used a straight edge to connect points 1 to 8, 2, to 7, 3 to 6, etc.  The result is an approximation of a parabolic curve.  If I'd used more points and spaced them closer together, I'd get a more accurate curve.

I cut out the cardboard to use as a template.  I snipped off the origin by cutting a straight line through points 1 to save material.

We'll see if it actually gets used as a template.  The idea was to trace the shape on stiff construction paper, slot eight cutouts together, then fit aluminum foil over resulting paper frame; but the Mad Scientist got bored and went on to other Mad Science, so I may have to make the solar death ray generator myself.
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