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New rims for an old bike
I found what appears to be a 1981 Schwinn Varsity in the garbage a few years back. It's getting to the point where I'll need new tires before spring, but I would rather just go ahead and upgrade to lighter rims. The trouble is that I don't believe the rims that are on it now are original (seeing as how the two tires don't match) so I don't have much to go off of. I'm new to bike overhauling, so where do I start?

Any help as to appropriate sizes, where to look, brands, or materials would be much appreciated.

Thank you!
try contacting Schwinn customer services for info.
Well, if you need new tires, you need new tires. Whether you change the rims doesn't affect that. So first question is why you want to change the rims/wheels. (Note that the "rim" is the outer metal hoop only, the "wheel" is the rim, hub, and spokes. You probably would change the whole wheel rather than just a rim because swapping just rims is more expensive due to labor costs.)

If your bike has steel rims now (test with a magnet or look for rust) then switching to aluminum rims will make it a bit lighter and give you better braking. But you have to question if it's worth spending the money on it on this bike. It may be, but it's not a given.

Size wise, I would guess that your bike needs wheels with 27" rims and the rear wheel needs to accept a threaded "freewheel" rather than a "cassette". But you should confirm this before purchase. You also need to decide between quick release or bolt-on wheels with axle nuts. Wheels like this are readily available at most larger bike shops and online.
Just to throw my tidbit in the Schwinn Super LeTour (KC-Steve's) has 27 x 1-1/8 tires. The Schwinn I have Traveler has 27 x 1 1/4 tires. My wheels specifically showes that in these pictures ... http://forums.bikeride.com/thread-1812.html
and I think Steve's may?!? His is pictured here http://forums.bikeride.com/thread-1239.html . But for best advice above is the best.
Good maintenance to your Bike, can make it like the wheels are, true and smooth!
save yourself a headache. get new tires and true the rims(wheels). replace any spokes on the wheel. Overhaul hubs if you want to? Make everything run smoothly. guessing 27 inch rims??
Thanks for all the info!

After learning some terminology, I would certainly like to replace both wheels. Rims, spokes, hubs, tires and all. I'm still just searching for the original wheel size for what came on the bike. Is there a simple way to measure the frame to determine this?

While I'm not prepared to drop a lot of money (less than $250) into the bike, I am quite attached to it, and would rather make it ride nice instead of buying a new one.

Thanks again for all the help! I will look into the 27" rims!.
Tire size indicates wheel size. So if it has 27" tires, you need 27" wheels. It is very rare to put the wrong size on a bike even if the wheels were changed. But an indicator would be a very large gap between the top of the wheel and the frame/fork. 95% sure that bike would have had 27" unless it was something unusual.

You can definitely do a whole new wheel set for under $250.

Here's some very standard wheels: http://www.google.com/products/catalog?hl=en&rlz=1C1SKPC_enUS340US340&biw=1206&bih=652&q=27+wheels+bicycle&um=1&ie=UTF-8&cid=11874188464199908910&ei=nAz4TKmrIpC6sAPn5sXmAQ&sa=X&oi=product_catalog_result&ct=result&resnum=1&ved=0CFgQ8wIwAA#
But there should be a variety available.

You want alloy rims and stainless steel spokes. Unless you're going for pure authentic restoration in which case the bike may have had steel rims. Again, you have to decide quick release or bolt-on. Either should work fine although occasionally you have a little trouble with QR wheels on frames that have very thin dropouts (where the wheel clamps on).

There should be lots of tires to choose from. I say spend a few extra bucks and get ones with kevlar belts to avoid flats.

Finally, maybe check over the whole bike or ask a shop to make sure there is no serious issues (bearings, frame cracking, etc.) before you spend money.

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