I finally used my HS Trig!!

[joe_m]

Better late than never I guess but 30 years after the fact I finally got a chance to use my high school trigonometry. Just when I was beginning to think it was only good for impressing the girls at Hooters.

I was working on the layout for cutting out the dovetails for an infill plane. I took two scraps of roughly the same length. The thickness was off but that's not a dimension I was worried about for now. I used a carbide dovetail router bit to cut the tails in the side - easy as pie (it's the black piece in the picture). Then I had to cut the pins in what would be the bottom piece of the plane. That involves clamping the piece upright in the vise, turning it 14 degrees (to match the router bit) and routing out one edge of the slots with a regular end mill, and then turning the entire contraption 14 degrees in the other direction to get the other edge. Since each tail was 1.25" apart I thought it would be easy with the DRO to just crank one out, shift 1.25 and do another, shift 1.25 and so on. Well I did that and when I was done nothing fit - a drunken monkey might as well have milled out the slots using a wooden ruler for measuring.

I burned a few brain cells before I figured out that with the piece held 14 degrees off the X-axis, moving the X-axis 1.25" wasn't moving the cutting point on the workpiece 1.25".

I went in and drew a picture and the triangle jumped out at me. I looked up the cosine for 14 degrees (.9703) and figured for the question mark. Turns out I should have been moving it just 1.2128. I tried it with another piece of metal and perfect fit. For the real deal the sides will be peened (peaned? Piened? ) to the bottom so I'll move a skosh more to give it room.

 

[xalky]

Better late than never I guess but 30 years after the fact I finally got a chance to use my high school trigonometry. Just when I was beginning to think it was only good for impressing the girls at Hooters.

I was working on the layout for cutting out the dovetails for an infill plane. I took two scraps of roughly the same length. The thickness was off but that's not a dimension I was worried about for now. I used a carbide dovetail router bit to cut the tails in the side - easy as pie (it's the black piece in the picture). Then I had to cut the pins in what would be the bottom piece of the plane. That involves clamping the piece upright in the vise, turning it 14 degrees (to match the router bit) and routing out one edge of the slots with a regular end mill, and then turning the entire contraption 14 degrees in the other direction to get the other edge. Since each tail was 1.25" apart I thought it would be easy with the DRO to just crank one out, shift 1.25 and do another, shift 1.25 and so on. Well I did that and when I was done nothing fit - a drunken monkey might as well have milled out the slots using a wooden ruler for measuring.

I burned a few brain cells before I figured out that with the piece held 14 degrees off the X-axis, moving the X-axis 1.25" wasn't moving the cutting point on the workpiece 1.25".

I went in and drew a picture and the triangle jumped out at me. I looked up the cosine for 14 degrees (.9703) and figured for the question mark. Turns out I should have been moving it just 1.2128. I tried it with another piece of metal and perfect fit. For the real deal the sides will be peened (peaned? Piened? ) to the bottom so I'll move a skosh more to give it room.
View attachment 45840View attachment 45841

I'm a carpenter, for my paying work, I use trig to figure out rafter runs and stair stringer lengths quite often. It comes in real handy to figure out the missing side of a right angle triangle leg. Good stuff.

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[llarson]

xalky:
Are you aware that by using trig to solve carpentry problems, you can call yourself a "carpentry scientist" ? Read that in a book, thought it was kinda neat.

 

[David Kirtley]

Just being nosey... Why such steep dovetails? Most I have seen for infills have been down to 30 deg and 45. Just prefer the look of the steeper angle? Also, the ones I am familiar with have the tails with angled sides as well to increase the interlock.

What will the materials be? Going all steel or brass and steel? What will the infill be? Going to have adjusters? Adjustable mouth or fixed? Inquiring minds want to know....

 

[joe_m]

14 is the angle of the woodworking dovetail bit I used to cut the tails.
The plane will be all steel because I can buy that a lot cheaper than brass or bronze.
Fixed mouth because I believe in set it and forget it.
Infill wood Bubinga or Mesquite because those are the two biggest chunks I have sitting in my discard bins.

The second angle is created later - after these dovetails are cut out a little bit of the edge of the pins is removed and then the excess from the sides is peened into that gap, creating the interlocking angle. A better description can be found here: http://user.xmission.com/~jry/ww/tools/a13/a13.html

 

[12bolts]

Joe,
What are the 2 pieces that you ran your practice on made of?
Bit more about using the dovetail cutter process please. Chatter problems? depth of cut?

Cheers Phil

 

[David Kirtley]

14 is the angle of the woodworking dovetail bit I used to cut the tails.

That is usually the way I make choices for some things as well.

The Mesquite is usually dead stable so that would be a great choice. Besides, it turns your hands purple when working it. What more could you want?

I like fixed mouths as well. I have a small infill on my to-do list as well but other projects get in the way. I have mostly Krenov style wooden planes and a stash of irons to make some more but have been doing more metalwork than woodwork lately.

 

[joe_m]

Joe,
What are the 2 pieces that you ran your practice on made of?
Bit more about using the dovetail cutter process please. Chatter problems? depth of cut?

Cheers Phil

The metal is your standard CRS bar from Lowes - the trash they sell right next to the angle-iron and the overpriced strips of aluminum.
The dovetail bit I used was a standard 3/4", 14-degree, carbide, 2-flute woodworking router bit that was sitting around.
I used it for the top piece in the picture - one pass for each of those dovetail shaped openings. The openings are 3/4" wide at the bottom, just over 1/4" high and that piece of metal is 3/8" thick.
I just lined up the bit in front of the metal, cranked steadily through it just like I was cutting a groove with an end-mill. I don't have power feed so I can't tell you how fast I went but it wasn't super-slow. I cranked as fast as it felt right, little chips dropping off easily. No chatter, not even a little bit. RPM was mid-range too - I didn't bother to adjust the pulley any.
Most of the chips were shiny silver - but when I slowed down real slow (hand got tired) there were a few purplish ones where it might have gotten hot. In the end the router bit survived - no chips or discoloration. I used the same technique when I had a mill-drill and it worked but there was some hammering if the speeds weren't right. That wasn't a problem with the mill and its extra 500 pounds or so. I like being able to use the woodworking bits on the metal and just wish there was a way I could disassemble a few so I could use the profiled cutters on the lathe. As far as the infill plane goes - based on past and current rate of work it might be done by Christmas if I really push it.

Joe