Engineering dudes, awake!

[Dave Bagwill]

Here's the problem:

I want to project a 2 1/4" circle onto a 45 degree slanted surface. IOW I want to cut a hole into a board that is tilted 45 degrees, that will accept a 2 1/4" shop-vac hose. Like this (below)

Tried various things, hoping for a formula that will allow me to print to scale, the resultant hole shape.
Or maybe there's something my level - i.e., caveman simple - that you can share?
Thanks

[John Parchem]

Well I only gave it a little thought. As you are tilting in one direction With 45 degrees I think you end up with an oval that the long axis is the square root of 2(diameter^2) and the short axis is the diameter. you can wiki ovals do find how to draw on with those parameters.

I am a bit confused. I would try to drill the hole with a large bit or hole saw. I would have the bit at a 45 degree angle from the board.

Also as a nutty idea is shine a light through a tube that is the right diameter on a board tilted 45 degrees to the tube and draw the shape.

[Dave Bagwill]

I'd already tried the nutty idea and some other ones. :-)

Thanks John - I don't have a hole cutter that large but perhaps I can get hold of one.

[dave d]

How about starting with a "cube" of wood, otherwise known as a square block. (glued up from a few pieces if you like) Use any size of forstner bit to drill holes around the perimeter of the circle you've drawn on it, using your vacuum hose as the trusty tracing pattern. Then use your Ridgid spindle sander to get right up to the 2 1/2" line. Now you have a 2.5" diameter "well" in your block of wood.
Now take that block to your bandsaw and cut a slice out of it at the 45 degree angle.
Maybe this won't work if your drill bits aren't too long.

I'm sure there's a better way. Why do you need it to be at 45 deg?

[Dave Bagwill]

That would work. DD, and I have the bits. Maybe that's my best option.
I'm making a special kind of fence for a new-ish tool that is now in my possession, and the dust-collecting portion of the fence as I've designed it just necessitates that 45 degree-er. Perhaps I'm going too fancy-pants with the design, but I'll try another day on it before I curse like a drunken sailor, throw tools around the shop in disgust, and drown my sorrows in sarsparilla....

edit - this was the nutty idea I tried earlier. Not actually that nutty, but I was unable to trace the projected dark oblong shape with any accuracy. I still think this is a good approach.

[John Parchem]

get short bit of pipe the right diameter. Cut it at a 45 degree angle. Use it to trace the outline on the board. Or even ink the cut side of the pipe and use it as a stamp.

[Dave Bagwill]

Very good, after 10 or so cuppa Joe's to wake up, I will commute out to the barn and get 'er done.
Thanks John.
And dd.