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You don't really use the full range of movement when cycling/running so no, stretching doesn't make you more powerful. There is some evidence stretched muscles are less powerful.
Obviously a bit of mobility means you can comfortably get aero and aero = speed.
This is why you stretch for flexibility after riding, not before. You might do some warm up stretches before though.
I read something recently debunking the long-held view re. power and stretched muscles. @dancing james might have some thoughts on the latest thinking?
miro_o-
Stretching can increase the functional range of muscles. By lengthening the hamstrings the body can adopt a lower position (more aeros etc). Many people do put themselves near the limits of their physiology (slam that stem etc). Spinning pedals does not use the full range of movement of muscles/bones but poor positioning can put someone closer to their actual limits. A lot of people after working on flexibility can raise their saddle a bit.
Flexibility with out strength to support it can lead to instability, whereas strength without flexibility will lead to a very limited range of motion. As with many of these things people should be looking for a comfortable compromise, that is relevant for their discipline.
Ideally your bike fit won't be set up for you at the limit of your functional range. Your flexibility will vary from day to day, and how much exercise you have been doing that day. If your position is near your limit the muscles and tendons are more likely to become sore (the body's signal to stop using them). This is why you may feel stiffer at the end of a long or hard day in the saddle, your body is asking for you to back off a bit.
dancing james
I read recently that flexibility isn't actually that beneficial for going fast on a bike, as long as you can get fairly aero, you don't need to be any more flexible.
In the running thread there was a link to an article about the sub two hour marathon that mentioned one of the ways Paula Radcliffe got faster was by getting less flexible and further reading suggests that applies even more to cycling.
(That's my excuse for not being able to touch my toes,.. It's so I'm faster, not because I'm fat)