In a [webpage][1] on Mercator's projection, [Robert Israel][2] offers the following suggestion:

> If you want a physical model of
> Mercator's projection, let the globe
> be a spherical balloon that is blown
> up inside the cylinder, and sticks to
> the cylinder when it comes into
> contact with it.


[1]: http://www.math.ubc.ca/~israel/m103/mercator/mercator.html
[2]: https://mathoverflow.net/users/13650/robert-israel