I normally wear a cotton t-shirt when I ride. If I get a bike jersey, how much difference will the reduced air resistance make at, for example, 20 mph? I realize it's not possible to be precise, but I am wondering how much difference it makes.
No, you will not ride faster in any meaningful way unless you're doing time trials at an elite level where mere seconds (or less) of improvement are gained through optimizing a long list of equipment (with clothing in the middle of that list). As always, the overwhelming determinant of performance is training.
The real reason for wearing a jersey is the following:
- Sweat management. Wicking fabric has to lie against to the skin to actually wick the sweat and transport it to the exterior where the wind will evaporate it quickly.
- Pockets in rear. Pockets are useful. The only place you can reasonably put them is in back.
- Long rear. It looks better when you're hunched over the bike.
- A zipper. So you can regulate temperature.
- Fitted + Flat seams. Flapping fabric is annoying on a ride and seams tend to painfully rub on long rides.
This page contains a table with improvements that can be made with various aero clothing and equipment. Unfortunately the baseline is already a cycling jersey, not a standard cotton t-shirt. Given the improvements that clothing can provide though I would suggest the bike jersey would make a pretty big difference.
For me, though the big improvement is in comfort. A sweat wicking jersey is so much more comfortable than a wet, heavy cotton t-shirt.
There are several differences between a plain cotton t-shirt and a cycling jersey. @Mac has already highlighted the sweat wicking potential. Some jerserys are tailored, so they'll certainly be more comfortable and possible aero-dynamic.
After all a tight t-shirt won't necessarily be worse aero-dynamically - it might flap around less, aside from the different flow properties of the chosen materials.
Many jerseys have other attributes though: pockets, zips, reflective strips, longer backs - all of these things might help make other aspects of your attire more stream-lined.
In short - the effort required to reach and maintain a given speed is a combination of overcoming the forces of gravity, friction and wind resistance. The key factor in reducing wind resistance is minimizing the frontal area of the bike and the rider. A tight, form fitting t-shirt or cycling jersey will provide some benefit, and will reduce the 'parachute' effect of flapping clothing. But at the rates of speed we are talking about for recreational or utility cycling, the impact will be minimal.