Functional training

I have a handful of personal training clients who are interested in improving their cycling performance. Part of the training involves a variety of lunges, squats, single leg exercises, core work, and plyometrics. Everyone of them has told me that they had no idea they had so many muscles they weren't using and how they could feel these muscles engaging when they hit the bike. My goal in training them is to improve their functional fitness or, in other words, to optimize their power on the bike. A Power meter measures force either in the hub or crank arm or soon will be offered in the pedal. The force comes not just from the muscles in our legs but also from our core. If your core isn't strong, and our leg muscles are essentially firing from the hips down and the hips are tied to our core,you can't possibly be applying all of the force possible. Now I know plenty of cyclists who can hit the leg press and do multiple reps of 500, 600, 700 or more pounds. Many of these same riders can't complete even one proper single leg squat. The single leg squat requires strength and balance through the leg and core while the leg press is both legs working against your compressed spine with very little core involvment. Which is better for cycling? Be sure that your off the bike training is designed to optimize your on the bike power.