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Does it have to be 4*2 in section across the whole arch?

When I've been making circular window frames/sashes (the only curved work I've done really), it started with a polygon (often an octagon, sometimes more sides still on big ones) which is oversize relative to the required section, and removed material down to form the curved shape (lots of techniques are possible; bandsaw, spindle moulder, router and jig, handsaw and compass plane)...
 
Rip some of the 4*2 down and laminate onto another piece to make a wider section, then use the trick above would be my solution... there may well be a better one though.

What radius of curviture you want and how many pieces you want to join up to make the blank, depends on exactly how much bigger a section you'd need to make it, if you wanted a semi-circle (28" radius) then you'd need more material and/or pieces in your blank than if you wanted say an 8" rise in the center of the arch relative to the points where it meets the uprights (i.e. a segment with chord length 60" from a circle of 259" radius*)...

*Calculated using the formula R=h/2+c²/8h where R is the radius, h is the height of the segment and c is the chord length of the segment

R = (8/2)+([60²]/[8*2]) = 4+(3600/16) = 4+255 = 259
 
If you have some cardboard or any other sheet material, make a template and you'll see exactly how much timber you need to make a smooth 4x2 arch

Using Jelly's idea, I reckon you could make some 6x2 and that would be enough for your arch - tighter radius means wider stock to start with
 
Years ago I did something similar, I placed the two uprights on the drive spaced as they would be, I then chalked out the arch, when I finished I simply washed the chalk marks off.

BH
 

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