The recommended tire size for my Santa Fe limited (2016) is 235/55 R19. I have a set still as new 235/45 R19 tires.
Am I safe changing to the smaller size?
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It's probably "safe" since the tire width (235) has not been changed. But your speedometer and odometer will be off by quite a bit.
The 10% change in aspect ratio (55 minus 45) will amount in almost a 2" difference in diameter, and 46 more revolutions/mile - the increase is roughly a 6-7% error. If the VSS "Vehicle speed sensor" is not separate from the transmission output speed sensor, this may also interfere with transmission shift points - in your case causing early "short" shifts. If you are concerned about resale of the vehicle, know that you will be putting about 107 odometer miles on the vehicle for every 100 actual miles driven.
Sometimes there are ways to reprogram the sensors/instrument cluster/ECU to eliminate the error, but I'm not certain how to do it on a Santa Fe or if it's even possible. It's certainly a "dealer" task. I would inquire with the service department if it's even possible. They may likely avoid the question and just tell you "not approved".
There are "in-between" boxes such as the "Yellow Box" which intercept the speed sensor signal and remodulate it so that it reads correctly. Quite the hassle and expense for regular folk.
Depending on road conditions, you are also putting your [expensive] 19 inch rims at risk. Potholes will have a lot more bite with the reduced sidewall height "cushion".
You will have to operate the engine at a 7% higher RPM in top gear cruise to achieve the same speed, resulting in increased engine wear. Your fuel mileage will suffer as a result as well.
You will, however, have better torque and acceleration, if that's your thing...
Best of luck!