Laying out "BIG" Arcs.
As faith would sometimes have it, you just can't stretch the string long enough to draw the damn arc. . . What is a carpenter to do. . . Well luckily there is help. What follows is a simple method to layout a big arc. You will need a $10.00 scientific calculator to do it, but that's a small price to pay when you're in this fix.
Let's just say you need to draw a really big arc, 420" to be precise. This arc is very large, but with just the radius, a few angles, cosine and sine functions you can "plot" the arc to fabricate it. The light blue rectangle is the end of a platform. The red arc is the arc to create.
- Starting with a line drawn down the center of the platform and using this as one "edge" to measure off of you can find the first point either to the left or right of the line by the following equation.
- r * sin(angle) in this case the first angle will be 10°. This is an arbitrary angle. Calculating the length gives 72.93" from the center line either left or right. The drawing shows it to the left. You can calculate the distance from the center line for any given angle. You now only need the corresponding point measured down from the edge of the platform (the green line). You can get it by using the equation r - (r * cos(angle)).
- You use the same angle to find the length of this line. In this case it would be 6.38". Calculating the "points" using difference angles will "plot" the arc across the board. Using a flexible batten you can easily trace the path of the arc to cut it . The example plots the points for angles from 10° to 40°. You can click on the image to enlarge it for a better view.
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