Hiya.
I'm running the same 15 inch rims that were on my last trike, shod with 50 profile tyres.
We're collecting parts for Taz's trike at the moment, which will be 14 inch, also with 50 profiles but much wider than mine. As the profile is a percentage of the width of the tyre, (the height of 50 profiles are 50% of the width of the tyre), the wider you go, the taller they get. Does that make sense?
My Reliant axle's standard width, but we'll shorten Taz's, just to keep everything in proportion, cos her tyres will be wider than mine. Anyway, some of our trikes run 14 inch rims & some 15. If they're 14s they're usually wider tyres. If we were to fit narrower 14s we'd have to go up to 60 profiles. We aim to end up with an overall wheel/tyre combined diameter of around 24 inches. That seems to work best with the gearing of the Reliants. We get 3 useable gears, with very quick acceleration & great performance for blatting around town & A roads, with 4th gear as an overdrive for motorway cruising. Taz's tyres are 265/50/14s, (same as Flap's orange trike), which are 24 1/2 inches tall -near enough.
So if you're running 17s & want to be able to actually pull away on the thing, you'd have to run ultra, ultra low profile tyres.
There's a tyre size calculator here in the Motors, 3 wheeled tech bit of the main site:
http://mankymonkeymotors.co.uk/Tech/pcd/tyresize.htm