Originally Posted by
YWoodman
In exactly the same way as you cannot push a car forward by pushing at the steering wheels, you cannot push a bicycle forward by pushing at the handle-bars. Period. All notions to the contrary are erroneous.
Any forward push that you may believe is occurring is purely an illusion. I don't suppose that you also believe that it's possible to slow a bicycle by pulling on the handlebars? No, of course not. If the one operation is impossible then the other couldn't possible be.
Suppose we are riding side by side, evenly matched, and the winner is the person whose right hand crosses the finish line first. As we approach the finish line, you confidently keep your hands on the bars. I remove my right hand from the bar and extend it forward to one foot forward of the bars. I have beaten you by almost one foot. Not a full foot, because the mass of my hand moving forward (relative to my center of mass) caused the rest of me (body and bike) to move rearward (relative to my COM). But this effect is proportional to the masses, my hand's mass is tiny compared to the mass of the rest, so my hand moves forward (relative to COM) much more than the rest moves rearward (relative). I beat you by 0.995 foot or something like that. If "relative to COM" is confusing, think about it as speed relative to ground. My hand accelerates more than the rest decelerates, resulting in my hand crossing the finish line ahead of your hand.
Now suppose we are riding side by side, equally matched, both carrying softballs, and the winner is the one whose softball crosses the line first. Again, you confidently ride to the finish, holding your softball. I throw my softball forward, when we are twenty feet from the line. I have beaten you by a bit less than 20 feet. Reason is the same as with the hands.
Finally we are riding side by side, evenly matched, and the winner is the one whose bike - specifically, the leading edge of the front tire - crosses the line first. Again, you confidently ride to the finish, not doing anything but pedaling. I wait until we are a couple feet from the line and extend my hands forward, doing what we call a "bike throw". Just like I beat you by extending my hand in the first race, and beat you by throwing the ball in the second race, I beat you now, by "throwing" the bike. Since I have to maintain my hold on the bike (unlike the softball), I can only beat you by the distance that I can extend my arms and torso (maybe a foot), slightly reduced by the rest of me moving rearward (relative to COM). But I only need an inch.
That is the reality. Your analysis is wrong. If the winner in these races was the rider whose got the combined center of mass of himself and his bike across the line first, then you'd be on the right track. That is not, however, the rule of a bike race.