We are making the attic into a loft and the ceiling we need to add drywall to has a slight curve. How do we install the drywall without breaking it? The distance from the floor to the top is about 4 feet.
1/4" drywall will readily bend into a radius and is available at the big box stores. 2 layers of that with glue between the framing and the 2nd layer. A 2X4, as long as the sheet with a few short 2X to hold it while you screw it in place. It must be tight to the framing before you run screws into it to hold it.
Around here (PNW), two layers of 3/8 inch drywall applied one at a time and overlapping so no seams coincide is the easy way to do it. Two layers are needed for fire code in the modern world to give a full 60 minute burn-through time.
I have seen 1/2 inch installed in curves of maybe 24 inch diameter by experienced professionals who prepared by leaving it in hot sun (or maybe it was high humidity) to make it easy to bend without breaking or straining. But 3/8 inch is a lot easier.
This video has a great section on installing board on a curve. It will most likely depend on the board size. The link includes the start time of 34m40s.
You could install strips of drywall to approximate the curve as facets, then fill in the corners to create a smooth curve during the taping/plastering process.
Or use something more flexible than drywall to create that curved surface (make sure it meets code!), and count on the difference being invisible after it's been painted. I think that's the approach more commonly used for arched doorway surrounds.
Or you could give up on maintaining the curve...