Ironing it may give you the best results without having to work too hard. I would just be careful not to burn it.

yes, try ironing it. i've done that to posters before, and it works well. just make sure you don't use an iron that drips water - you don't want to inadvertently destroy it with water spots!

Definitely don't iron it. Take it down and lay it on a flat surface and put some weight on it. Leave it for a few weeks if you can. It should flatten out eventually, and then you'll be able to roll it tightly again. Curling is somewhat inevitable if you keep it unrolled all the time.

You can iron it. I've done it before with great success. Cover it with a towel or something similar to protect it, and then iron it through the towel. You can also take it down and spread it out on a table, and then place some heavy (dictionaries work well) books on the edges you're tyring to flatted back out. Let the edges sit under the heavy books for several days, and that can straighted in out a bit.

I'm with the ironing camp. I believe the light heat will help the paper contract back into shape. It's a risk I'd take, having done as others have mentioned, ironing posters, for instance. On low heat, of course.

You could bulldog clip something like a yardstick to the back. It is, after all, a school supply, so clips on it wouldn't be that weird. Just make sure they don't leave marks (cardboard "shoes" under the clips perhaps?).

I'm wondering if there's any problem with leaving it unrolled, in whatever mechanism rolls it back up again. Are you stretching any springs?

I DO NOT know if this will work..just a thought. So please chime in anyone who thinks it may be a BAD idea.
Applying it to a roller shade?

I have a cheap black plastic poster frame that comes apart at all four sides. It slides onto the edges to hold the backing, poster, and clear plastic. Maybe if you could find one of those you could use the two sides, if it's thick enough, to hold it straight? We have Michael's and AC Moore in this area so it was from either of those places.

Other than that I would try the laying flat and weighing down for a few days idea. Good luck!

I was going to suggest the same thing as tarainsevenvalleys - try the bars from a cheap poster frame that slide on. I think you'll probably want to flatten it with weights for a few days first, but then the plastic slides should help it resist further warping.

Laying it flat and weighting it will do absolutely nothing. The fibers of the paper have been permanently altered by humidity - paper is not a two dimensional object no matter how much we like to think it is.

Think of an area rug with a bump in it - step on that bump and it just pops up somewhere else. The only way to flatten this is by applying some type of substrate to it, but that would mean a permanent change.

Waiting for the husband I got to thinking...if you could roll it back on itself and leave it for a few days. The opposite direction of it's normal way. I buy thick Italian wrapping paper to back shelves and it's always super tight and won't go flat from being in the shipping tube. I take it and roll it up the other way and run my hand up and down it to loosen it. Then the poster frame pieces may help when you get it back up!

I've been a framer for 13 years, and I say it's okay to iron it. It's actually safer to iron it than to try to put it under a weight or roll it backwards. And DO NOT use plastic rails to try to hold the sides straight, those will damage the paper edge. Ironing might help, but the only way to completely flatten it would be to mount it to foamcore, (and if you do that, you might as well just frame it and ditch the roller because it won't roll again.)

These things aren't designed to hang constantly, so they almost always curl over time. Like some others said, use an iron on low/med heat, making sure to test an edge to make sure nothing melts before you slap the whole iron on the map. I would also use a piece of plain printer paper as a buffer between the iron and the map to guard against scorching (which is unlikely, but better safe than sorry).

For a more permanent solution, you might want to talk to a restorer about getting it backed with linen so you could still roll it, but it would be thicker and hold its shape better.

Hope this helps. :)

*or backed with canvas. I think that's probably more common.

We have a 19th century map and it is backed with linen.

More delicate things that are being conserved are backed with linen, but I always see oversize vintage prints that are backed with a thick paper or canvas to make them more durable. That's what I meant to suggest.

I would be very careful about ironing it. I once tried to iron something that I thought was just paper, and it melted. So if it has any kind of lamination or coating, be careful.

So here are my suggestions:
Add more weight to the bottom and maybe it will straighten out on its own
Cut a piece of cardboard, stiff poster board, or foam board to the right size and glue it to the back of the map
Frame it
Gallery-wrap it

Listen to GrimboCrimby. Especially if it's worth some money, take it to a professional restorer. I have learned the hard way that it makes a difference with vintage posters and I'm guessing a map has the same issues. Good luck!

I worked under a paper conservator in a book and paper conservation lab and both weighting it or ironing at a very low heat have proved to be successful. I would try leaving it under weight for a week at least, then carefully iron if weighting it doesn't flatten the map enough. Good luck!

Can I ask why you have to roll it back up when you move? I've never not framed something just because moving it would be an inconvenience later. The most permanent solutions are ones where you would permanently mount it or frame it. Otherwise you might be spending just as much to apply a linen backing and still end up with some curl.

Looks like a fun map but not one where you would need to worry about passing it down to your grand kids. If I had the map, I'd find some kind of heavier, acid free tape and apply it to the back of the sides after lightly ironing it. Or may iron on fusible tape that is only sticky on one side, and is heavy enough to gently make the edges lie flat.

I have a map that is VERY simliar to yours, the only diffence is that mine has two maps on it, one being Europe during the crusades and one being a more detailed look at England at the same period. I had not noticed it before, but mine is also starting to curl up. Now when I look at it, I focus on the curling (gee, thanks :)). Anyway, the Ballard Designs catalog has some lovely (very simliar) maps that are mounted on boards or stretched...not sure which. And I think that they look really lovely. I am now considering mounting mine to a board. Maybe modge-podging it or something. Possibly even having that done professionally. Depends on the expense. I love the maps and I am not that into making sure they 'stay on the roller', not at the expense of losing them to the degradation of time anyway. I would love them either way. So my suggestion is that you go to the Ballard Designs website and look at their maps. And if you don't detest them :) then perhaps consider having them mounted.

Pi took my answer: Rethink the requirement to roll it back up. Moving it to a new home does not require rolling it. Permanently mounting it to foamcore will also let you put it behind UV-resistant glass, further protecting it from fading and other damage. It's time to decide how much you care about it.

I second the framing/mounting it. As paper does NOT age well unless you take precautions like framing it behind UV-filtering glass, it will turn brittle and fade. Also as for moving issues, perhaps having it roll up would be easier to move but moving it framed (assuming you don't get a frame/glass that's ridiculously heavy) should not be that much more of an inconvenience, providing you pack it properly.