Ah, so the black isn't additional in terms of proportions - it would now be a part of the original sized arc.....Got it.
On further thought...when you sew the pieces together to form the arc, the top(red) and bottom (black) of the arc will have a very smooth curve.
However, the curve on the color change might be a little choppy because you're not curving the black where it meets the red.
Draw two lines on a piece of copy paper about an 3/4" apart.
One represents the color change seam between the red and black, and the other is the bottom of the strip set, which would be the bottom of the black strip.
Now cut some pieces out with the bottom of your template lined up to the lower line.
When you put them next to each other (taking into consideration the seam allowances), there will not be a nice smooth line for the color change seam, right?
The lines will match up piece to piece, but it's not a smooth curve.
If that doesn't bother you, then fine, proceed.
If it does, then you'd have to add the black as a whole separate piece, with one long curved seam (not a big deal) joining the two sections.