Topic: Woodworking

Finding the Radius of an Arc.

The Calculator Approach:

This question comes up many times and you can use this formula: R = ((((L/2)2)/H) + H) / 2 if you have a scientific calculator

1. Where L is the length of any chord that touches the arc.
2. Where H is the length of a line from the center of the chord L to the arc.
3. Divide L by 2 then square it.
4. Then divide the answer by the value H.
5. Then add the value of H to the answer.
6. Then divide the answer by 2 and that's the radius.

If you have a Construction Master

If the height is 24 and length is 96 then:

Enter 24{Height} [Inch] [Rise]
Enter 48{1/2 Length}[Inch] [Run] half of chord length
Press [Diag] Returns 53-21/32”
Enter [=] [Rise]
Press [Run] Returns 107-11/32"
Press [Diag] Returns 120”
Enter [÷] [2] Return 60”

Field Method:

I use this method in the field if I don't feel like using a calculator.

1. Cut a straight piece of wood that will fit "inside" the arc and mark its center with a line.
2. Place it inside the arc and measure from the marked center to the arc square with the wood.
3. Place the piece of wood on a plywood floor or sheet of plywood and use it to draw a line.
4. From the center draw a line square to the distance you measured to the arc.
5. Draw a line connecting the all end points. This forms a triangle.
6. Extend the line for the height as far down as possible.
7. Mark the center of one of the line that from a side of the triangle.
8. Using a square line it up with the mark and square to the side and draw a line until it intersect the height line.
9. The length of the line is equal to the radius.

Convex Arcs:

If you find that you need to find the radius of a convex arc you can follow the steps below.

1. Nail a small piece of 2x4 (about 6 inches) onto a larger piece of 2x4 (24-30 inches depending on how big the arc is) at its end. Cut an angle on the end of the small block.
2. Place the long 2x4 on the convex side of the arc and roll it until the small 2x4 touched the arc.
3. Measure the distance from the end of the outside of the 2x4 block to where the large 2x4 touches the arc.

Now you have H (6") and L (whatever the measurement is) to use in either the formula above or by the construction method.
You will have to miter the edge of the small 2x4 to get a good location on the arc.

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