p.s. I think TeethGrinder uses "strength" to mean something completely different to me, and I suspect to most sports-science-pundits!
[Strength = force a muscle can generate i.e. for biceps, how much can you curl, or how large a weight can you squat, etc ... ]
By strength, I mean being able to keep going without my muscles giving way. If I only rode a 70" fixed all the time, then did a very long ride, my legs would feel it at the end. If I push a big gear for a few long rides, my legs really do feel it at the end. But when I go back to my normal gear my legs are strong to the finish.
But as MSeries says, my big gear work allthough improves my power output, isn't really great for power.
Power is what you need to go fast. Chris Hoy is extremely powerfull, but could he ride for days on end without his legs getting tired?
I can (or I could, I'm out of shape now) but if I try and sprint I might manage 35mph at my best. Chris Hoy could do that without trying.
I'm planning to dabble in time trials this year to improve my power output. But I know that unless I get the miles in, do some hilly rides and big gear work, then my legs will be left wanting at the end of long rides, even if I can ride much faster at the start without much effort.
Not sure riding up hills will improve power, strength yes, but it doesn't really train your muscles to fire quicker.
It would definitely improve strength, which will compliment power. I think it would help your power output if you ride up hills fast. I think that climbing hills fast at your normal flat cadence is really good training. It'll improve the pedalling technique because any dead spots will show up much more when climbing and it will also show if you ease off. Or you could use a turbo with a big resistance and a lowish gear for the same effect.
pp.s. I think riding fixed makes controlled training very difficult. Unless you have a vast selection of different gradient hills of various lengths! Gears are your friend to allow training at the right intensities consistently.
With a great big gear on fixed, it's all just a constant slow grind.
I also feel it on the inside too and not just in the legs.
I'd use a turbo for controlled stuff, especially intervals. But on a fixed it's only the cadence that changes. You can put in a constant effort.