How does changing rims affect tyre width ?

[Rider5]

Hi I'm just after some advice I enjoy looking at the pics on these forums and thought it would be a good place to ask. I used to ride around on my MTB and recently bought a Electra Townie I really wanted a particular Electra but the Autralian importer doesn't bring the whole range So I chose the Townie. I put on some white Fat Franks, but now I want to change the rims to wider ones but I'm not sure how this is going to affect the tyre width.
I have measured the outside width of the rims and they are 15/16th of an inch(23mm) and the current width of my tyres are now 2''3/16 (55mm)
If I were to put on say 40mm wide rims, an increase of 17mm would that mean that the tyres would widen proportionally say from 55mm (plus17) to 78mm ?
I just dont want to have the tyres rubbing on the chain I've probably got about 2/8" ha ha you can see I don't use imperial I just realized that's 1/4" (6mm) clearance between the chain and the tyre at the moment.
From the above info any ideas on what would be the widest rims I could put on and any recommendations on what brand and where I can get some white alloy rims?
Here's a link to a pic of my bike and the space I'm talking about.
http://www.seabreeze.com.au/Media/View/ ... =1&p=Other

 

[JLarkin]

The tire will only widen a minimal amount at it's maximum width. Basically the inner half of the tire's girth will spread with the rim width. The outer half will remain relatively unchanged. For your situation you really don't have alot of clearance to work with from the start. You should consider shimming your sprocket and chain ring outward from the tire.

 

[Rider5]

OK thanks for that JLarkin, that makes sense and I understand what happens to the tyre width now. Thanks also for the shimming idea.