If you are correlating the tachometer reading with the speedometer, this will not be affected, because the speedometer only knows the wheel RPM and that's a fixed relationship in top gear with the engine RPM. But it will affect your real road speed, i.e. the speedometer will now have a different amount of error (it's already wrong).
Stock 175/55-15 rear wheels have a theoretical rolling diameter of
175 mm x 0.55 (aspect ratio) x 2 (there are two profile heights included in each diameter) / 25.4 (conversion to inch) + 15 = 22.58 inches
And that results in 5280 x 12 / (22.58 x 3.14159...) = 893.2 wheel revolutions per mile. Multiply that by the final drive ratio and the 5th gear ratio (and these seem not easy to come by!) to get actual engine RPM at actual 60 mph.
Same calc with 185/55 gives 23.01 inches OD and 876.4 wheel revolutions per mile ... a couple percent different.
The common 195/50-15 has 22.68 inches rolling diameter (very close to stock) and 889.4 wheel revolutions per mile.
I have 205/50-15 on the rear. 23.07 inch rolling diameter and 874.2 wheel revs per mile.
~ My Tire Story ~
I had these Tires on my Smart for 5 years: 195/50-15 KUMHO ECSTA AST 50R R15... Then one got a egg size bump on the tread...??? I change it, putting my matching NEW spare on... One month later on a 140 mile round trip from Orlando, I started getting that Old familiar vibration on the way home... When I got home I checked the Tires, and found another one with tread separating...!!!...??? This time it was a section 1 foot long...!!!...YIKES... Well that was it, time for NEW Tires because that left me with two out of 5 that still looked OK...hmmmmmmmmm... I had a Patch on one of the other ones too... Half the tread was left on these tires...!!! SO...I said NO MORE KUMHO's...!!!
The 5 NEW TIRES I had to order into the Discount Tire Store, because they didn't carry them was: Hankook VENTUS V2 CONCEPT2 195/50-15 (directional pattern design)
NOTE: They Track Nice ~ Ride Nice ~ Look Nice ~ I'm Happy With Them On A Smart Car
NOTE: They are the same Diameter as OEM Rears, So my acceleration performance is the same as OEM with NO RUBBING... (38PSI Rear)(34PSI Front)
NOTE: I would recommend these tires for a Smart Car using the Correct Width Rims...YES, the Rims I use are 7" Wide...<) Hankook Ventus V2 Concept2 H457 195/50R15 82H BSW
I find this to be a most outstanding Wheel for the Smart Car... I'm running the 15" X 7" wide, and using 195/50 x 15 Tires... The combo makes for a Great handling Smart Car... Mine are finished in 'Luminescent Silver"... When the Sun hits, they Spark just like chrome...<)
15x6 ET29 for the fronts were the original, but Tire Rack ran out of those before they ran out of the rears, which were ET 30. I tried getting a quote for 4 from the Alibaba seller and they never responded. I think I tried three fronts and one rear though. I guess they may not have been interested in doing that in particular.
Going up one size, as in from 185's to 195's fixes the built in speedometer error, as in with stock tires your speedo reads 70 and actually you are at 67. Your GPS will confirm this. Other than that, manufacturer comes down to your preference. My only advice would be to buy tires like you buy oil, for the climate you live in.
I now have the 2015 ED springs on my 2011, this then allowed me to put on the Continental 185/65/15 tires. I went through the speed camera board on the highway and now the speedo is dead on.
Interesting that car was spec'd with 175/55/15 which is 22.6" in dia. and the new 185/65/15 are 24.5" in dia. being a difference in 8.4% between the two.
So I guess that smart is overcharging you in mileage and est. mpg figures.
I had a custom ordered 2010 AMG e-350 coupe which when the speedo was reading 100, actual speed was 92 as calculated by both lira and radar. When I took this into Mercedes to complain, the answer was "yep" it is doing 92 even though the reading is 100.