Hamilton's Math To Build On - copyright 1993

Concentric Arcs

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About Math To Build On || Contents || Back to Arcs || On to Cutting Elbows || Glossary
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* Concentric Arcs

In this section, we're going to look at elbows and the calculations needed when elbows are joined to straight pieces of material.

Let's first look at the 90 elbow.

First: Draw a four inch radius circle and divide it into quadrants.

Second: Set your compass for a two inch radius and draw another circle, concentric (using the same center point) to the first circle.

Third: set your compass for a three inch radius and make another concentric circle exactly halfway between the other two circles. You now have three concentric circles. Their radii are 2", 3", and 4".

Fourth: Cut the circle out using the outside line as a guide. First, cut out the outside circle. Then cut the inside circle out. The circle should look like this:

Cut the quadrant lines to create four 90° elbows.


The length of the take out for a 90° elbow is the same distance as the center radius measurement of the elbow. To check that statement: Place the bottom of the elbow on a flat surface and measure from the bottom face of the elbow to the center line on the upper face of the elbow.

Remember: Take out = tan /2 x radius of turn. With 90° arcs, the radius of the arc and the take out of the arc are the same, since the tangent of 45° is 1.


Let's use these elbows in an offset.

First: Cut three straight pieces
of cardboard or foam board 2"
wide and 1' long. Be precise.

Second: Use the three straight
pieces and two elbows to make
an offset like the one shown on
the left.

Third: Measure the offset
from center line to center line.
The horizontal runs are 1'3"
(1'+3") in length and the vertical
run is 1'6" (1'+3"+ 3").


Notice that these lengths are 1' from each straight piece, plus the take outs of the elbows. The horizontal runs have one straight piece plus one take out and the vertical run has one straight piece plus two take outs.

On to Cutting Elbows

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