I don’t know what to do in this situation with my road bike. My aero wheel say max 103 psi on it but my tyre range say 115-145 psi. I weigh 180 lbs. Do I inflate them to 100 psi or 115?
First, in this situation, it’s better to default to the lower of the stated maximum pressures. If someone put a max pressure on something, that means they are concerned (hopefully with good reason) that it can’t withstand higher pressure. You do not want the rim or the tire blowing out or blowing off in motion.
Second, I’m not sure what tire this is. Presumably, 115-145 PSI is meant as a recommended pressure range. That is very likely based on old data and practice, unless these are track tires where high pressure is actually justified. It is true that higher pressure means lower rolling resistance on a very smooth surface like a track. On actual roads, the roughness of the surface causes energy losses due to what Silca and others call impedance - that’s the tire deforming under the roughness and losing energy through hysteresis. Some reading is here, but that is only one post and this is a fairly complex topic. The short version is that there’s an optimum pressure for each tire to minimize rolling resistance, and it’s lower than what you may think.
Silca has a tire pressure calculator here. I believe that Zipp and perhaps a few other companies maintain pressure calculators as well. I think that Silca’s calculator may often put out slightly higher values than Zipp, but not immensely higher. For example, at 135-140 lbs rider weight on 25mm nominal tires (real measured width 26-27mm), Silca recommends that I use about 80 PSI. Silca’s calculator aims to minimize rolling resistance. The owner has stated on his podcast (Marginal Gains) that if you want to maximize comfort instead, you can often set a few psi lower than the pressure on the calculator. Above the optimum pressure, total rolling resistance increases rapidly, whereas below that optimum pressure, total rolling resistance decreases more slowly.