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Cutting Irregular Shapes
If you want to build your own climbing wall, get this book. Gives info about measuring and cutting dihedral angles, compound angles, and irregular shapes, and more. It's a small investment compared to the cost of a climbing wall, and hopefully will save you a lot of time and money in your project.
An irregular shape does not have a right angle. These are slightly more difficult to measure and cut, but there's an easy trick I'll explain below.
For a straight inclined wall it is not difficult to mark, cut and fit the pieces together. However if you have features or shapes built into your wall you need to be able to accurately cut a piece to fit.
How to measure, mark and cut irregular shapes.
In a nutshell, from each end of one of the sides draw arcs with a radius of the other two sides. Where the two arcs meet is where the cut lines meet. Below is a more detailed explanation.
You will need to know the lengths of all three sides. Get these lengths from your drawing or model design, or measure them directly from the gap space between panels or features. Knowing three sides, draw arcs on your plywood or your model material at each of these lengths. Draw lines from one intersecting point to the next. This is your cut line.
This example shows an irregular shape formed at a corner where both walls are inclined vertically. The top corners of each wall meets, but the gap at the bottom needs to be cut and fitted.
The three known sides are the height of the wall, which is one and a half plywood panels -- which is 12 feet. The third side is the gap at the base -- the length of gap between the two pieces at the bottom. Just measure the base of the gap with a tape measure. The gap at the bottom is two feet at the base.
Now, knowing the three sides draw an arc from one corner of a piece of plywood 12 feet long, and draw another arc from the other end which has the radius 2 feet, which is the gap at bottom.
Marking Full Size Plywood Sheets. When working with full size sheets of plywood there are two ways to mark an arc this long. 1) Tap a nail into the corner then use a string measured to one of the lengths with a pencil tied to the end. 2) Another method is using a tape measure. Hold the tape measure at the center point of the arc and mark several small arcs, then connect the marks by hand.
The point at the intersection of the two arcs is the third corner. Draw cut lines from each corner to the intersection.
You can make a lot of interesting shapes this way, or make volumes or features that you might add after the basic wall is completed.
Using this method to mark and cut your gap pieces makes it easier and more accurate.
The next step in making a nice flush fitting gap piece is to cut the edge of the plywood, and the supporting back structure at the correct angle. This is called the bevel on the plywood edge.
Dihedral angles. When two planes intersect, the intersecting line is called the dihedral. To make the pieces meet with nice flush edges cut the plywood at the correct angle. A bevel is the tilt on the saw blade. A miter is the angle of the wood relative to the direction of cut. To make the two edges meet flush the angle needs to be cut by adjusting the bevel and miter at the same time.
Take a look at the online Dihedral Angle Calculator