A few weeks ago, I wanted to spend some time in my workshop making small stools with some of the wood I had available. For a moment, I wish I had a lathe so I could turn scrap 2x4 into something more visually pleasing. If you have been playing games in the past, you probably realized how frequently the hexagon shape is being used which got me interested in the geometry of this shape. What I realized is that this shape is ideal for leftover 2x4. Let's look into the geometry of the hexagon first.
Step 1: Geometry of the Hexagon
So the interesting thing about the haxagon is the relationship of the large radius (R),the small radius (r) and the side length (t). It is not everyday that you read the wikipedia entry for specific shape but it turned out very insightful for the next phase of my work.
Here is my main question : What are the dimensions of the hexagon that fits in the height of a 2x3 or 2x4 ?
For those of you following at home, what are the R and t parameters if r =0.75"
Well basically, R and t are equals in an hexagon which I initially thought was an interesting fun fact. If you remember your trigonometry courses, you can then see that r=R x cos(30).
So I made a few test runs with some 2x3 and kind of fine tuned my table saw but it was a bit onerous. I then ran out of scrap 2x3 and turned to my 2x4. My Eureka! moment was when I checked if two hexagon legs would fit. In other words, 4R = 3.5". OMG this is exactly the width of a 2x4. I am going to have EXACTLY two legs per stock and this means I will be able to optimize my cuts quite nicely. So I RUSHED (I wish I was kidding) to a 2x4 and scribbled the outline of two hexagons on the end of the stock and then went to calculate the setting I would need to make my cuts on the table saw.
Step 2: First Cuts : Removing the 4 Corners (ingot Phase)
For the first cut, I know that I can fit EXACTLY two hexagons side by side (4R=3.5") but I need to remove the extra. In other words :
4R = 2t + 4C
C = 7/16"
Where C is the leght of the cut I need to take out of each corner.
Since all the angles of an hexagon are 120deg, you want to angle your table saw at a 30 degree angle cut on the right side of the blade. I initially ran with my calculation (3.5 - 7/16) but that did not take into account the width of the blade. I finally removed half of the blade which gave my a first cut at 3-1/32".
At first I did one side and then to the next but as I progressed, I found out the final result was better if I alternated the corners (Bottom left, Top right, Top left, bottom right).
When you are done with this step, you should have your 2x4 with all 4 corners striped at a 30deg angle. It kind of looked like an ingot so I called this step the ingot phase.
Step 3: Second Cut : Splitting It in Two (teardrop Phase)
That second cut is the most critical part of the project. Now that you have removed the corners, you want to cut the part at exactly the right place. Since they fit quite nicely in a 2x4, you will make 2 cuts in one here. Probably time to take out your best blade with that high tooth count (I used 60 for this project).
You need to take out again that same 7/16" out of the newly splitted parts. Basically you want to end up with t+C or 7/8" + 7/16". Once again, I removed half of the width of the blade and set my table saw to 1-9/32".
When you are satisfied with your cut, you should be left with two parts that kind of look like a teardrop.
Step 4: Final Cut : Making the Hexagon
This is the best part, you only need to take that final extra length and your table saw is already set at the right mark. Flip the teardrop part over and cut that last section to make your final hexagon.
Voilà ! With only 7 cuts and two marks, you have 2 hexagon shaped legs and also something extra...
Step 5: Final Comments
After I was satisfied with my settings, I started making a bunch of them for my future projects. When I was doing that last cut, I realized that the offcut from the last step is a perfect equilateral triangle. I have no idea what I am going to do with them but I do know that it would be a pain to make them so perfect even if I wanted to !
You will see as well that some of your legs might be a bit off compared with the others. On the last picture, I show the run of 16 I made. You can see that some aren't as nice as the others. I think this is mostly because my table saw isn't that precise but also that the width of the scraps I used probably differed a bit. Nontheless, that is good enough to use for a later project.
Happy making !