Sit on your jacket, and it will get wrinkled. Even if you tuck the tails under your butt (which you should always do), stuffing yourself into a coach seat on a plane will leave you looking like a crumpled newspaper. You should take your jacket off while traveling. If you can’t hang it up, then fold it and put it away.
Here’s the right way to do it: First, empty the pockets of all pens, keys and change. Turn the jacket around so that the buttons are facing away from you (Fig. A). Hold the jacket in your left hand just above the left shoulder lapel; reach around and slide your right hand into the right shoulder opening (Fig. B). Pull the right shoulder around toward you, and slip it into the left shoulder, forcing the left shoulder inside out (Fig. C). (This is the same process by which you may have been taught to fold a fitted sheet.)
The jacket’s lining is now on the outside, and the jacket is half its usual width. Make sure the lapels, pocket flaps and sleeves are flat, and fold the jacket in half, top to bottom (Fig. D).
You can now stow your jacket, confident that when you unfurl it and put it on, you will look presentable, if not pristine.