The angle will change.
You can calculate the angle here https://www.scrollmania.com/
This is from Carole at SSW
Now, down to business. If you go to Dave's program (AngleCalc), enter the thickness of your wood as a decimal. Then, enter the ring width, also as a decimal. Go to where it says "angle" and click on "solve". The correct angle should appear. Round the number up, if necessary, and add one degree. That should work. However, to play it safe, send me a PM with your specs and I'll compute it for you. That way you can check your own work, and not risk ruining your wood.