Cycling-Related Strength & Conditioning

That makes A LOT of sense to me. I've been reading some of this and it's heavily physio for me (I'm a massage therapist, I wasn't trained about exercises, I just have been able to figure out how to deal with the results of injuries and notice potential patterns in movement that might be causing weakness and/or overshort muscles.

I was thinking about this, too, and this seems strange to me. If by "stomp phase" you mean pressing down, I know you use the quads then a bit, but extension is a hamstring/glute thing, flexion is quads. I get more burn in my quads when I purposefully pull up on the pedals or stand up out of the saddle.

I have really been wanting to work with a physio or sports trainer about how to get more power in cycling, I have a few smaller hills that are still kicking my ass. When I take the train in the morning I'm magically refreshed all day but when I ride in I'm often more tired. There is obviously some combination of amount of calories taken in, riding fixed, gear ratio, how fast I ride, and probably something I don't know about, that is killing my energy levels. I want to get faster, I want to ride more easily, I want to be able to get to the top of Bromley Hill without slowing down as much as I have been, and I want not to collapse on the couch at the end of the day. I've got to go back to geared, especially for winter, but I am still missing a few key components (such as a frickin' 90mm 1" quill stem, that everyone wants and no one has) so can't get it out on the road.

The "stomp" bit you speak of is quad dominant for sure. The last part of a knee extension is often recommended by physiotherapists for developing the vastus medialis which is largely responsible for the last part of extension.

The quads extend the knee. The hamstrings & glutes extend the hip. The latter two do this primarily when the hip is right up in flexion, with the knee parallel or higher compared to the hip joint.

When cycling normally on bike, the knees never get very bent. So the pedalling motion is mostly the quads extending the knee.

If you ride clipped in, you can "Scrape back" on pedals at the bottom of their (orbit?) to utilise the hamstrings more. If you have active glutes you can focus on enaging them for the push down during a short power burst. But its difficult to maintain considerable glute contribution for more than a short time.

When going up hill it raises the height of the knee in comparison the the hip engaging the hamstrings and glutes better. I believe sliding back in the seat has the same effect by moving your feet forwards compared to your hips reducing the dominance of knee bend but increasing the contribution of the hip extension. When getting out of the saddle and heaving the bike about it can go a step further by using both upper body strength and adductors.