Ground clearance with low profile tires
 

I need help in settling an argument and I figured I could find the unequivocal answer here. I've sufficiently stripped down the details as follows:

Let's say I've got a choice between an 18inch rim with a low profile tire and a 20inch rim with a low profile tire. Let's also say that to compensate for the bigger rim (i.e. to let the bigger rim and wheel combined fit properly into the wheel well), the tire height on the 20inch rim is reduced. Howver, in both cases, let's say there is 1/2 inch tire height under each rim when on the vehicle (i.e. if I were to take a ruler up to both wheels each rim would sit on top of 1/2 inch of tire).

Now, the question is: won't I gain some additional ground clearance with the larger rim? In other words, isn't the wheel center (where you'd find the hub and axle) 1 inch higher on the 20 inch tire (2 inch diameter difference divided by 2 to get the radius)? Therefore, if the center of the wheel is higher, where the wheel attaches to the axle is higher, and thus the vehicle sits higher.

Am I missing something?

You do not have the only factual piece of information that will answer your question. The outside diameter of the tire will determine how much ground clearance you have. A 30" tire will put your axle center at 15" regardless of the rim size.
:fyi:

He's right. It's tire height that determines ground clearance. A 30 inch tall tire on a 16 inch wheel will give the same ground clearance as a 30 inch tall tire on a 20 inch wheel.

Okay, I think I understand. Isn't the 1/2 inch tire height under both rims all the info that's needed though?

I know I'm probably missing something obvious here, but let's get away from tires all together. Let's say I've got two pieces of wood, both are 1/2 inch thick (this represents the tire height under the rim, which I said is both under the 18inch and 20inch tire). I now place an 18 inch rim on one piece of wood, and a 20inch rim on the other. Seems to me if I took a ruler and measured to the center of the 20inch rim, it would sit 10 1/2 inches off the ground, while the center of the 18inch rim would sit exactly 9 1/2 inches off the ground.

In other words, if what sits under the rim is exactly the same height, how can you not have higher ground clearance with a larger wheels? Seems like an impossibility to me.

Yes, if there is 1/2" under each rim, then your tires would have a 18" + 1/2" + 1/2" diameter (19"), and 20" + 1/2" + 1/2" would be 21"

You are correct in your reasoning, the 20" tire package would give you more ground clearance since the amount of rubber under each wheel is constant.

Unless you plan on driving on your wheels its the Overall height of the tire that determines ground clearance. Yes you will have more ground clearance with a 20" wheel with a 1/2" sidewall tire over an 18" wheel with a 1/2" tire, but its still the overall height of the tire that gives you the extra clearance because the tire is still 21" overall on the 20" wheel whereas the tire on the 18" wheel is only 19" overall. So if you plan on putting tires on your vehicle then your clearance is determined by the overall tire height not the wheel diameter. You can look at it like this, a 20" wheel with a tire with a sidewall height of 5" has an overall height of 30"(20+5+5) and a 10" wheel with a tire on it with a sidewall height of 10" also has an overall height of 30" (10+10+10). Same ground clearance with different size wheels.