-MIKE- wrote:

https://photos.app.goo.gl/DqXrs5DI2roJTli22

I need to replace the white board above this garage door. The 2x12 is
rotted out pretty bad. It will just fall out when poked with a
screwdriver or putty knife, so I'm going to replace with a new, treated
2x12. (Client wants cheapest option.)

What I need help with is figuring out how to transfer that arch to the
new 2x12. This isn't an arch that was drawn with a radius or trammels.
If this was a perfectly cut arch, I could just determine the radius by
bisecting the chords and extending perpendicular lines to find the radius.

If you look closely, you will see that it's not even and the arch
"flattens out" near both ends. So I believe I'm left with trying to
transfer the exact line of the bottom of the soldier course of bricks to
the new 2x12.

Remember, the existing 2x12 will not come out in one piece or even
several pieces which could be reassembled to use to trace the "arch"
onto the new board. It's pretty much, mulch, held together with paint.

Any ideas?

You're dealing with a kinda elliptical segmental arch.
http://www.sweethaven02.com/BldgCons...02/fig0748.jpg

Rather than trying to transfer the archline with large dividers, what
about cheap, narrow, double sided tape along the curved bottom face
of the soldiers?
https://www.harborfreight.com/8-1-2-...ape-45882.html

Since dimensions weren't given let's say the arch is 16' wide, and
the top of the soldiers are 20" at the peak (pinnacle?) of the arch.

From a 4X8 sheet of lauan (or cheap thin ply) rip 2 ea. 15" X 8' pieces.
Divide the task in half (left half & right half). Measure/mark the center of the keystone.

Right side - From that mark, lightly apply the double sided tape
directly to the brick all the way to the bottom of the arch.

Since you've got that piece of molding protruding outward, ruining
the length of the span under the arch, rest the factory edge of one
of the 15" X 8' pieces of ply on it and apply just enough pressure to
get the tape to stick to the smooth, CLEAN ply.
Carfully remove said ply ,aking sure the tape stays on and voila!

Using the other piece of ply, do the above for the left side as well.

* Hopefully the tape will not adhere to the dirty rough bricks as
strongly as it will to the CLEAN smooth ply but you'd prolly want to
test it first. If it does stick to brick too much, apply blue
painter's tape to the bricks 1st, then the double sided tape.