Force is the ability to overcome resistance—or in cycling terms, the ability of the muscles to turn the cranks and move the bicycle forward. Since power equals force times velocity, it stands to reason that if we can improve velocity (with cadence and speed drills) and also improve our ability to apply more force per pedal stroke. We should be able to improve our power output and speed as a result.
Work Your Core
First things first: No matter how much you develop your hip extensors, quads, hamstrings or calves, you will not be able to utilize their full potential to get force into the pedals unless you have a strong core.
Your "core" consists of all the muscles in and surrounding the lower back and abdomen. Core strength should be worked on almost year-round with any number of specific exercises. Core-strengthening routines might include crunches, back extensions, work with a fit ball or other appropriate exercises.
One on-bike core strength workout is as follows: Begin on a trainer and ride in an aero position with your hands in the drops or on the hoods (forearms parallel to the ground). While keeping your torso in this position, take your hands off the bars and clasp them loosely behind your back while continuing to pedal. Be careful to keep your upper body very still.
While doing this you will be able to feel just how important your core is to the power transfer from the body to the bicycle. You can do this exercise in a variety of gears at different cadences for increasing amounts of time. Start with just five minutes and work up to 15 or more minutes per session. You might find that elevating the front wheel to simulate a climb is helpful as well.
Increase Your Resistance
To improve the force ability, you will need to increase resistance on the bike. This can be accomplished in a variety of ways. The most obvious is using gravity. Increasing the grade of the surface you are riding on is one way to increase resistance; another is riding into a headwind. In the absence of either of these options, you can increase resistance by using very large gears, or using a trainer inside.
Do force work on the bike two to three times per week, using a variety of workouts. If you are still doing weight work at this time, one to two times per week of on-bike force will be sufficient to transfer the gains.