If you are looking to build a larger model with a 46-60 engine, figure on using a 3/4 in. fuselage. That fits the rulebook definition.
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Overall, Phil's post has some usefull information. However, the comment about what "fits the rulebook definition" needs some clarification.
There is no specified "rulebook definition" for a profile fuselage or a specification for a profile stunt fuselage minimum or maximum thickness. There are no AMA official rules for any CL Profile Stunt event nor is there any unified unofficial rules for CL Profile Stunt. Different contests might have their own defined fuselage width allowances for such contests, but my experience is that many do not.
The rulebook does contain paragraph 10, CL General, that gives a profile definition that outlines certain aspects of how the fuselage of a profile model should appear. The CL General section also gives a table for the maximum fuselabe width for the several official CL Profile events - 1/2A Proto, Scale Racing, Slow Combat, Navy Carrier, Slow Rat Racing and Rat racing. That table table also gives the maximum width "with additional reinforcements" for each of these events as provided for in this section of the rulebook.
Then, in the CL Profile Scale rules, a maximum fuselage and engine nacelle(s) width of 1 inch is specified with an allowance of a total width 1 1/2 inches for a cowl or cowls.
Otherwise, most of the the information provided in this thread is useful with the exception of the wrong specification in another post about Profile Scale.
Keith