Perfect Octagons from Squares with the “Wallace Factor”

 

In geometry, a “Regular Polygon” is defined as a convex polygon (polygon is a closed figure formed by a finite number of coplanar segments) with all sides congruent and all angles congruent.  So, a star is not ‘regular’ because it does have concave and convex alternating at every vertex.  Generally, we deal with squares and equilateral triangles.

My last project was to make an Octagon, and I did want all the sides to be equal.  As I played with the measure of the angles and the length of the sides, I realized that it is much better to start with a square and then cut the corners off such that I am left with the octagon shape as I wanted it.  I thought that if I start with a square, then I will have the project under control.  I went to the table saw and cut a piece of plywood to be a square.  Next, I reset my miter to 45 degrees instead of 90.  Now the only thing was to measure from the fence to the saw blade, so that after I cut two of the corners off, I will have three sides of my octagon.  The problem was to determine just what the measure from the fence to the saw blade had to be.  So, I worked for a couple of days and came up with a constant number that calculates the measure I was needing (“e”) as it relates to the length of the side of the square that I was cutting.  I like to call this constant number the “Wallace Factor”.  Here is the work sheet that I developed with Microsoft Excel.

Since I used Excel, I was able to put the calculations within a cell, and that saves you from having to go through all the work for yourself.  Note that in the rectangle that contains ENTER “x”, all you have to do is enter the length of the side of the square and the measure of “e” will be calculated immediately for you.  At the bottom of the page, it automatically calculates ‘a’, ‘b’, and ‘e’, then it does double check the numbers by adding “a + b + a” which is the measure of the side of the square. 

NOTE OF CAUSION:  The measure from the fence to the blade must be made to the correct side of the blade which is the left side of the blade, since the blade width is also part of what you are removing.

The Wallace Factor equals “.207119737”.  If you multiply this .207119737 times the length of a side of the square, you will have the measure, perpendicular to the cut, to remove from the square’s corner. 

If you would like to have the “file” that I created (the photo worksheet shown above), then just email me (stirlingbay@gmail.com) and I will attach the worksheet in the reply back to you for you to have for future work.

 

BEST GLUE HOLDER EVER …

For a long time, I have been wanting to add this to my blog, but it is so simple that I just kept putting it off until I had nothing else to do.  Finally, I am going to share what has become the ultimate glue holder that I have ever had or used.  Most of my work is on single projects, and not mass production.  Kind of like one-time things that I need around the house, or for a friend.  I have always applied glue to BOTH surfaces when I am joining two pieces of my project together.  Some folks just nail it and let it be.  I know the glue will extend the life of the item, and after many years, I have realized the glue applied before nailing will help.  Then I noticed that spreading the glue on one area, then put the two pieces together, does not spread the glue properly to the second area of the second piece.  It is much better when I apply the glue to both surfaces that will be joined, then nail if that is the plan, or clamp the two pieces together.

Using the glue straight from the container from the store where I purchased it will work.  Pull the round cover on the top of the bottle, if it is not stuck from the last time I used it, hold the container upside down until the glue decides to gravitate down to the nozzle, and squirt through the nozzle as I put it on the surface.  Then I spread that with my finger.  Next, I have to wipe my finger before I pick up my nail gun or hammer, and hope I did get all the glue off my finger.

I have tried glue bottles that claim to be better than the original container, but they get clogged up worse than the original.  Those are also harder to clean out from the residue of dried glue that still coats the side of the container and clogs the point where the glue actually comes out.

I thought a long time as to what might be a much better idea for having the glue ready to apply in just a minute, no mess on my hands that transfers to everything I touch, and the easiest container to clean out when a long time goes past between uses. 

My daughter was cleaning out her room and throwing away everything she did not want to keep.  I noticed a small glass jar in the trash, so I picked it up.  My daughter said it had been a jar of skin lotion or face cream, or something like that and she did not need the empty jar.

I was impressed that it was heaver than I expected and the sides were thicker than I first thought.  The diameter of the jar was perfect, the lid was solid plastic without a liner, and the depth of the jar was also just as I thought I needed.  An extra about this jar is that the interior has a parabolic design which makes the lowest point in a bowl center.  This makes the last amount of glue grouped right in the middle.  The thick heavy bottom and the short height would prevent the chance of knocking it over.

I took it to my woodshop and began to think what I might do with it.  I realized that I would definitely need some sort of applicator to dip into the glue from the jar and spread it on the surface of the wood.  Also, I thought I might increase the usefulness of the jar if I had a place to rest what ever type of applicator I designed.  In my scrap of small pieces cut from other projects, I found two pieces short enough and shaped like a triangle on each end.  So, I glued the two together and then glued that to the top of the jar.

Now I wanted to figure what other type of applicators I might use.  Luckily, I had a package of small metal handle paint brushes with horse hair.  There were 36 brushes when I bought the package, and it was just for touchup jobs, then probably throw away instead of trying to clean out the horse hairs.

This worked perfectly.  The glue was open and ready to stick the brush in, then spread it on the surface.  Next a rest for the brush on the holder on top of the jar lid so my hands were free to work and no glue on my hands anywhere.  Over the next few months as I found this to be more and more useful, and I found different types of jobs that required different types of applicators. 

If the job requires a small area to have glue added, I used about an 8-inch piece of 3/16” wood dowel sanded both sides at one end as my applicator.  Then for glue joints that have, over the ages of time, pulled apart, I made a very thin piece of metal with a hole in the center and joined another wood dowel as a handle.  The hole is so the glue will stay on the applicator as I slide the metal into the very thin slit in the area where the old piece has separated.  This is also good for when a small piece might split under pressure when you are assembling a project.  Finally, there is a thin nail with another wood dowel as the handle that allows me to put glue in holes where I will insert dowels or other types of joining with plugs.

The difference between using the original container and the new open jar is easy to see.

Even if I only want to attach a small piece of cork to the bottom of a leg of something to prevent scratching and noise when sliding it across the floor, my jar is quick to open, the glue is there ready to dip my applicator, and when finished, I just screw the lid back on the jar and wipe the applicator off with a shop rag.

Now if I have the jar open for a long time, I just use a spray bottle like the ones used to mist plants, and put a thin layer of water over the glue surface before putting the top on and the jar back on the shelf. 

I hope some of you will try this idea.  I have found this to be so helpful and easy for most any glue jobs you might encounter.

Thanks for looking and good luck.