When trying to improve in cycling, it's usually not one major thing that makes an athlete better, but a lot of little things. The athletes that pay attention to detail and look for new training techniques to experiment with are the ones that are successful. One of the classic ways to develop a smooth pedal stroke is by riding a fixed gear in the off-season, but doing so also has a host of additional benefits for your overall cycling fitness.
Improving Your Pedal StrokeThis is the obvious benefit. After a long, hard season in the saddle, our pedal stoke can use some help. It loses its suppleness, especially as we get older. Supple and smooth pedaling is essential to being successful on the bike, and too few athletes address this important issue. Fixed gearing is such a simple way to do it. Even a short ride has purpose in that you are constantly pedaling and learning to pedal through the two dead spots of the pedal rotation. Training the legs to transition thru the different muscle groups with smoothness eliminates wasted energy and will improve your efficiency.
Strength and Aerobic Capacity
Yes, fixed gearing can help your power when riding in the hills and over rolling terrain. Ride them in the hills and you will immediately see the benefit. The gear you choose is essential. You don't want too much gear that it causes problems in terms of climbing (like falling over), or back and knee pain. Choose a gear that is slightly difficult, but not impossible, keeping in mind that the idea of having a fixed gear is improvement of pedaling technique.
I have been using a 39x16 for years in the hills around the Gold Country of Sacramento. However, it is better to start out with something easier and build up, and I recommend 39x18 or 17 for those brand new to fixed-gear riding. Remember, by being in the rolling hills you will naturally get the benefit of spinning high revolutions-per-minute (RPM) on descents and on the flats, thus improving your aerobic capacity. Start by taking the descents slow, by sucking up as much wind as possible (like a parachute) and feathering the brakes. Build up slowly to those super high speeds and cadences.
Think about it for a minute. You consistently pedal for hours with no freewheeling. One major benefit is muscle endurance. In addition, the lack of wasted time spent freewheeling means it's also a very time-efficient mode of training in the off-season, especially with the decreasing hours of available light. I have never seen a direct calculation as to how long a fixed-gear ride translates to a regular road bike in terms of pedaling time. My gut feel is it's about three to five, such that a three hour fixed-gear ride is equal to five hours on the road bike.