Here are three (or four) field-expedient methods for drawing curves that I use frequently when building houses and furniture. Each method produces a different type of curve, so pick whichever suits your application.
These are demonstrated here in small scale, but I usually use them in the field to draw curves from 1' or 2' long up to 20' or 30' long.
Step 1: True Arc
This method produces an arc, a segment of a circle. Mark the width of the arc and the height of the arc at the midpoint. Place a nail or other restraining implement at either end of the arc.
Place two straight strips of material so that they are touching the nails and intersecting at the midpoint. Fasten them securely at the midpoint and place your marking implement in the apex. Slide the contraption to one side and then the other, keeping the marker in the apex, and the "legs" in contact with the nails.