I think I remember this, but someone correct me if I'm wrong. The first number is the max tire width (mm) - call it W. The second number is the sidewall height as a % of the width - call it H. The third number is the ID of the tire in inches - call it D.
OD can thus be calculated (in mm) as
OD = 25.4*D + 2*H*W
For your 195/65/15 :
OD = 25.4*(15)+2*0.65*195 = 634.5 mm
For a 215/xx/18, the profile you need (to be the same OD as the 15s) would be :
H = (OD-25.4*D) / (2W) = 0.412 => so a 215/40 would be close
For a 225/xx/18, the profile you need would be :
H = (634.5-25.4*18) / (2*225) = 0.394 => a 225/40 is still the closest you can get
Of course, you can put it all in 1 equation, but I thought subscripts might be confusing.
