Often the problem is wrinkles.
If you are going to roll it up, you'll need Rosco paint and you might as well go for Rosco canvas. No crackle, no wrinkle.
Tight budget? The double bed-sheet thing stapled to a DIY 2x4 stretcher is cheap, wrinkle-less and lasts forever.
My way, after a few years of screw-ups.
Lay a room-size plastic sheet on the floor (to keep it clean). Lay down the frame and staple the bed-sheet. Prepare two buckets of diluted white wall paint. Mix a tube of aniline black into one bucket.
Using a roller on a long handle, start with the white on the right hand bottom corner and work fast up to the centre diagonal. Dip the dirty brush into the black and work down to the middle from the top left corner. Add a few drops of aniline blue to the black bucket and a few red drops to the white bucket. Switch to a big brush on a long handle and blend with broad strokes. Somewhere in the middle you should have a medium grey.
BEFORE IT DRIES, mix some white with plenty of water in a garden plant sprayer. Spry up into the air above the sheet so that the a gentle mist falls from above and deposits onto the wet surface. This gives you a vague aerial perspective. Let it dry flat overnight.
Your light source is always from the left (that's tradition). So the illuminated side of the subject separates from the dark side of the background and the shadow side of the subject separates from the light side of the background (that's also tradition, think of how a statue in a niche works).
If you keep the right side white enough you will only ever need one light source for everything - no hair-light, no accents, no backlight, ever.
Examples here.
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