1, Assuming the curve would be part of a normal circle if you drew all of it, make a dot at the two end points of the curve.
2. Make another dot at the mid point of the curve at the highest point.
3. Pencil a line directly between the end points and make a perpendicular line from the center point crossing that line. That's the initial setup.
4. Now draw a line from one endpoint to the center dot, measure the length of that line and put a dot in the center.
5. Use a square to draw a line from that dot to the center line perpendicular to the endpoint to center point line. The intersection will be the pivot point for your compass, string, or whatever. Make it's length the distance from that pivot point to either of the endpoints (or the middle dot) and it should let you trace out the curve/arc perfectly.
That's confusing as heck without some diagrams, but play with it using a protractor, ruler, and some paper and you'll see how it works. This may not be suitable for your current task, but it's a good way to get smooth, duplicatable arcs.