As per I know, Turbo Phil use a widebody, and maybe the rear wheels are installed more outward. I suppose that 15 rear wheels are really tight with the lower wishbone.
For track car, like mine, it is welcome to use a different design of rear upright like those sold at Eliseparts.com, and custom like mine. I have a bearing offset of 15mm, and bump steer adjustment. I am pretty certain that 15 wheels are too small for those improvement.
About the tire construction, and here I dont really know, but small tire are probably more design oriented for light car, and bigger tire for heavier car. Here I am talking about the sidewall construction. Since the Elige are a lot lighter in the front, tire for ligther car are welcome in the front I guess. Anyway, my car react really well with R7 track and R1R street tire with the 15/17 combo. Still hard to heat the front tire, the pressure needs to be low.
About the 13 wheels on Formula 1, it was mandatory, and maybe not because it was better. And now about the new bigger wheel, with the new areo regulation of last year, it was many issues about the vibration at high speed, and not caused by the wheels size. But I dont know the reality of it.
