Today I took one of my old tires off and cleaned and painted the rim. I just noticed it looks slightly out of round when I sat it down after painting it- is this normal?
The tire is a rubber band, when on the rim it takes a round shape from the air in the tube.
To me this reads to say he found the RIM to appear out of round - ". . . looks . . . out of round when I sat it down after painting it . . ." A rim visibly out of round isn't a good thing, have you recently got new glasses ? Not being a smart guy, that can mess with your perception sometimes. If it's the rim that concerns you, measure it. If the tire, as Dan said, no worries.
Your profile has a 1926 Tudor listed as your car. From the factory it would have come with the 21 inch balloon tires and wood spoke wheels as standard equipment. If it has the 21 inch balloon tires with the wood spoke wheels, it is not uncommon for the split rim to look a little out of round when it is off the wheel, not latched and without a tire on it. With the tire mounted and inflated and mounted onto the wheel it should not be out of round very much -- if things are right. Note it is also fairly easy to bend the rim out of round if you use excessive force or others before you used excessive force on the split rim.
If you have a 21 wire spoke wheel which was optional starting around Jan 1926 the wheel rim should not look out of round.
And you might have the 30 x 3 1/2 inch clincher wheels and rims, but they would not normally have come from the factory on a 1926 USA assembled closed car. But they will fit onto the car -- (needs the 11 inch rear brake drums).
For any of them, you can mount them on the hub, jack the car/wheel up a little, place a piece of wood just touching the rim and/or tire if it is installed to check if it is running true or is out of round or has wobble side to side. If you touch the block of wood to the rim, rotate the rim by hand -- it will move the bock if it is out of round. And then the high spot will just touch the wood and the low spots will have a gap between the rim and the block of wood. A little gap ok. Note the Aug 1923 Kelsey demountable felloe drawing states the felloe must not be out of round or out of true more than 1/8 inch. That was for a new part. And it was the felloe and not the rim. But it shows that some tolerance was / is allowed.
You may also want to check your wheel and rim combinations. You may find that you have one rim that is worse than the others and you can make that your spare as long as it is not too out of round or out of true.
If you have not dealt with mounting the split rims -- recommend you review some posting on that to reduce the chances of hurting your rims. [Note the late 1925-1927 Model T Ford 21 inch balloon tire split rims are NOT like the later rims that have a ring that can come flying off and kill you. Those are often called split rims today but they are not the same thing as the factory rims on the cars and the front of the Ton Trucks.]
Hap 1915 cut off
Yes, Hap, I wasn't specific enough, but you nailed it - 21" wood spoke with split rims. I figured the tire would bring it back into shape, but wasn't sure. I knew if I got it back on the wheel, it would be round again - or close to it!